%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:25 AM UTC 2026
% Result : Theorem 97.14s 16.48s
% Output : CNFRefutation 16.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 71
% Syntax : Number of formulae : 3427 ( 759 unt; 0 typ; 0 def)
% Number of atoms : 38615 (13969 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 88747 (20444 ~;14706 |; 167 &;53047 @)
% ( 187 <=>; 196 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 170 ( 167 usr; 14 con; 0-5 aty)
% Number of variables : 12652 ( 0 ^;12596 !; 56 ?;12652 :)
% 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_sK100_SY902,type,
sK100_SY902: $i > $i > $i ).
thf(tp_sK101_SY904,type,
sK101_SY904: $i > $i > $i > $i ).
thf(tp_sK102_SY906,type,
sK102_SY906: $i > $i > $i > $i ).
thf(tp_sK103_SY907,type,
sK103_SY907: $i > $i > $i ).
thf(tp_sK104_SY865,type,
sK104_SY865: $i > $i > $i > $i ).
thf(tp_sK105_SY861,type,
sK105_SY861: $i > $i > $i > $i ).
thf(tp_sK106_SY870,type,
sK106_SY870: $i > $i > $i > $i > $i ).
thf(tp_sK107_SY912,type,
sK107_SY912: $i > $i > $i > $i ).
thf(tp_sK108_SY878,type,
sK108_SY878: $i > $i > $i > $i ).
thf(tp_sK109_SY882,type,
sK109_SY882: $i > $i > $i > $i ).
thf(tp_sK10_SY282,type,
sK10_SY282: $i > $i ).
thf(tp_sK110_SY868,type,
sK110_SY868: $i > $i > $i ).
thf(tp_sK111_SY888,type,
sK111_SY888: $i > $i > $i > $i > $i ).
thf(tp_sK112_SY892,type,
sK112_SY892: $i > $i > $i > $i > $i ).
thf(tp_sK113_SY915,type,
sK113_SY915: $i > $i > $i > $i > $i ).
thf(tp_sK114_SY876,type,
sK114_SY876: $i > $i > $i > $i ).
thf(tp_sK115_SY881,type,
sK115_SY881: $i > $i > $i ).
thf(tp_sK116_SY885,type,
sK116_SY885: $i > $i > $i ).
thf(tp_sK117_SY891,type,
sK117_SY891: $i > $i > $i > $i ).
thf(tp_sK118_SY895,type,
sK118_SY895: $i > $i > $i > $i ).
thf(tp_sK119_SY881,type,
sK119_SY881: $i > $i > $i > $i ).
thf(tp_sK11_SY288,type,
sK11_SY288: $i > $i ).
thf(tp_sK120_SY921,type,
sK120_SY921: $i > $i > $i > $i ).
thf(tp_sK121_SY885,type,
sK121_SY885: $i > $i > $i > $i ).
thf(tp_sK122_SY917,type,
sK122_SY917: $i > $i > $i > $i > $i > $i ).
thf(tp_sK123_SY868,type,
sK123_SY868: $i > $i > $i > $i ).
thf(tp_sK124_SY920,type,
sK124_SY920: $i > $i > $i > $i ).
thf(tp_sK125_SY891,type,
sK125_SY891: $i > $i > $i > $i > $i ).
thf(tp_sK126_SY895,type,
sK126_SY895: $i > $i > $i > $i > $i ).
thf(tp_sK127_SY876,type,
sK127_SY876: $i > $i > $i > $i > $i > $i ).
thf(tp_sK128_SY920,type,
sK128_SY920: $i > $i > $i > $i > $i ).
thf(tp_sK129_SY922,type,
sK129_SY922: $i > $i > $i > $i > $i > $i ).
thf(tp_sK12_SY471,type,
sK12_SY471: $i > $i ).
thf(tp_sK13_SY322,type,
sK13_SY322: $i > $i > $i ).
thf(tp_sK14_SY331,type,
sK14_SY331: $i > $i > $i ).
thf(tp_sK15_SY349,type,
sK15_SY349: $i > $i > $i ).
thf(tp_sK16_SY381,type,
sK16_SY381: $i > $i > $i > $i ).
thf(tp_sK17_SY383,type,
sK17_SY383: $i > $i > $i > $i ).
thf(tp_sK18_SY385,type,
sK18_SY385: $i > $i > $i > $i ).
thf(tp_sK19_SY391,type,
sK19_SY391: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY398,type,
sK20_SY398: $i > $i > $i > $i ).
thf(tp_sK21_SY411,type,
sK21_SY411: $i > $i > $i ).
thf(tp_sK22_SY370,type,
sK22_SY370: $i > $i > $i ).
thf(tp_sK23_SY448,type,
sK23_SY448: $i > $i > $i ).
thf(tp_sK24_SY462,type,
sK24_SY462: $i > $i > $i > $i ).
thf(tp_sK25_SY502,type,
sK25_SY502: $i > $i > $i ).
thf(tp_sK26_SY468,type,
sK26_SY468: $i > $i > $i > $i ).
thf(tp_sK27_SY376,type,
sK27_SY376: $i > $i > $i > $i ).
thf(tp_sK28_SY406,type,
sK28_SY406: $i > $i > $i ).
thf(tp_sK29_SY328,type,
sK29_SY328: $i > $i > $i ).
thf(tp_sK2_SY158,type,
sK2_SY158: $i ).
thf(tp_sK30_SY416,type,
sK30_SY416: $i > $i > $i ).
thf(tp_sK31_SY436,type,
sK31_SY436: $i > $i > $i ).
thf(tp_sK32_SY453,type,
sK32_SY453: $i > $i > $i > $i ).
thf(tp_sK33_SY516,type,
sK33_SY516: $i > $i > $i ).
thf(tp_sK34_SY457,type,
sK34_SY457: $i > $i > $i > $i ).
thf(tp_sK35_SY518,type,
sK35_SY518: $i > $i > $i ).
thf(tp_sK36_SY480,type,
sK36_SY480: $i > $i > $i ).
thf(tp_sK37_SY521,type,
sK37_SY521: $i > $i > $i ).
thf(tp_sK38_SY523,type,
sK38_SY523: $i > $i > $i > $i ).
thf(tp_sK39_SY525,type,
sK39_SY525: $i > $i > $i > $i ).
thf(tp_sK3_SY160,type,
sK3_SY160: $i ).
thf(tp_sK40_SY526,type,
sK40_SY526: $i > $i > $i ).
thf(tp_sK41_SY484,type,
sK41_SY484: $i > $i > $i > $i ).
thf(tp_sK42_SY476,type,
sK42_SY476: $i > $i > $i > $i ).
thf(tp_sK43_SY489,type,
sK43_SY489: $i > $i > $i > $i > $i ).
thf(tp_sK44_SY531,type,
sK44_SY531: $i > $i > $i > $i ).
thf(tp_sK45_SY497,type,
sK45_SY497: $i > $i > $i > $i ).
thf(tp_sK46_SY503,type,
sK46_SY503: $i > $i > $i > $i ).
thf(tp_sK47_SY487,type,
sK47_SY487: $i > $i > $i ).
thf(tp_sK48_SY507,type,
sK48_SY507: $i > $i > $i > $i > $i ).
thf(tp_sK49_SY511,type,
sK49_SY511: $i > $i > $i > $i > $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK50_SY534,type,
sK50_SY534: $i > $i > $i > $i > $i ).
thf(tp_sK51_SY495,type,
sK51_SY495: $i > $i > $i > $i ).
thf(tp_sK52_SY500,type,
sK52_SY500: $i > $i > $i ).
thf(tp_sK53_SY506,type,
sK53_SY506: $i > $i > $i ).
thf(tp_sK54_SY510,type,
sK54_SY510: $i > $i > $i > $i ).
thf(tp_sK55_SY514,type,
sK55_SY514: $i > $i > $i > $i ).
thf(tp_sK56_SY500,type,
sK56_SY500: $i > $i > $i > $i ).
thf(tp_sK57_SY540,type,
sK57_SY540: $i > $i > $i > $i ).
thf(tp_sK58_SY506,type,
sK58_SY506: $i > $i > $i > $i ).
thf(tp_sK59_SY536,type,
sK59_SY536: $i > $i > $i > $i > $i > $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK60_SY487,type,
sK60_SY487: $i > $i > $i > $i ).
thf(tp_sK61_SY539,type,
sK61_SY539: $i > $i > $i > $i ).
thf(tp_sK62_SY510,type,
sK62_SY510: $i > $i > $i > $i > $i ).
thf(tp_sK63_SY514,type,
sK63_SY514: $i > $i > $i > $i > $i ).
thf(tp_sK64_SY495,type,
sK64_SY495: $i > $i > $i > $i > $i > $i ).
thf(tp_sK65_SY539,type,
sK65_SY539: $i > $i > $i > $i > $i ).
thf(tp_sK66_SY541,type,
sK66_SY541: $i > $i > $i > $i > $i > $i ).
thf(tp_sK67_SX0,type,
sK67_SX0: $i ).
thf(tp_sK68_SX0,type,
sK68_SX0: $i ).
thf(tp_sK69_SX0,type,
sK69_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK70_SX0,type,
sK70_SX0: $i ).
thf(tp_sK71_SY732,type,
sK71_SY732: $i > $i > $i ).
thf(tp_sK72_SY677,type,
sK72_SY677: $i > $i ).
thf(tp_sK73_SY549,type,
sK73_SY549: $i > $i ).
thf(tp_sK74_SY649,type,
sK74_SY649: $i > $i ).
thf(tp_sK75_SY852,type,
sK75_SY852: $i > $i ).
thf(tp_sK76_SY709,type,
sK76_SY709: $i > $i > $i ).
thf(tp_sK77_SY713,type,
sK77_SY713: $i > $i > $i ).
thf(tp_sK78_SY726,type,
sK78_SY726: $i > $i > $i ).
thf(tp_sK79_SY765,type,
sK79_SY765: $i > $i > $i > $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK80_SY772,type,
sK80_SY772: $i > $i > $i > $i ).
thf(tp_sK81_SY775,type,
sK81_SY775: $i > $i > $i > $i ).
thf(tp_sK82_SY777,type,
sK82_SY777: $i > $i > $i > $i ).
thf(tp_sK83_SY779,type,
sK83_SY779: $i > $i > $i > $i ).
thf(tp_sK84_SY787,type,
sK84_SY787: $i > $i > $i ).
thf(tp_sK85_SY816,type,
sK85_SY816: $i > $i > $i ).
thf(tp_sK86_SY748,type,
sK86_SY748: $i > $i > $i ).
thf(tp_sK87_SY839,type,
sK87_SY839: $i > $i > $i > $i ).
thf(tp_sK88_SY849,type,
sK88_SY849: $i > $i > $i > $i ).
thf(tp_sK89_SY887,type,
sK89_SY887: $i > $i > $i ).
thf(tp_sK8_SY367,type,
sK8_SY367: $i > $i > $i ).
thf(tp_sK90_SY758,type,
sK90_SY758: $i > $i > $i > $i ).
thf(tp_sK91_SY782,type,
sK91_SY782: $i > $i > $i ).
thf(tp_sK92_SY792,type,
sK92_SY792: $i > $i > $i ).
thf(tp_sK93_SY728,type,
sK93_SY728: $i > $i > $i ).
thf(tp_sK94_SY821,type,
sK94_SY821: $i > $i > $i ).
thf(tp_sK95_SY897,type,
sK95_SY897: $i > $i > $i ).
thf(tp_sK96_SY899,type,
sK96_SY899: $i > $i > $i ).
thf(tp_sK97_SY834,type,
sK97_SY834: $i > $i > $i > $i ).
thf(tp_sK98_SY844,type,
sK98_SY844: $i > $i > $i > $i ).
thf(tp_sK99_SY853,type,
sK99_SY853: $i > $i > $i ).
thf(tp_sK9_SY315,type,
sK9_SY315: $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_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(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(20,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(23,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_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(30,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(36,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_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(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,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(49,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(53,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(54,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(55,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(57,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] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(62,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(63,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(64,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(65,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(66,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(67,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(69,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(70,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(71,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(72,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(74,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(75,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(76,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(77,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(78,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(79,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(80,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(81,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(84,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(86,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(90,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(91,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(92,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(94,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(95,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(96,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(97,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(98,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(99,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(100,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(101,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(103,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(105,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(106,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(108,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(109,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(110,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(111,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(112,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(114,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(118,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(119,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(131,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(144,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(161,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(169,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(171,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(177,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(190,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(202,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(204,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(215,conjecture,
! [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(216,negated_conjecture,
( ( ! [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 ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[215]) ).
thf(217,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 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[216]) ).
thf(218,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(219,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(220,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(221,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(222,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(223,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(224,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(225,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(226,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(227,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(231,plain,
$true = $true,
inference(unfold_def,[status(thm)],[53]) ).
thf(232,plain,
$true = $true,
inference(unfold_def,[status(thm)],[54]) ).
thf(233,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(235,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(237,plain,
$true = $true,
inference(unfold_def,[status(thm)],[63]) ).
thf(238,plain,
$true = $true,
inference(unfold_def,[status(thm)],[64]) ).
thf(239,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(240,plain,
$true = $true,
inference(unfold_def,[status(thm)],[66]) ).
thf(241,plain,
$true = $true,
inference(unfold_def,[status(thm)],[67]) ).
thf(242,plain,
$true = $true,
inference(unfold_def,[status(thm)],[69]) ).
thf(243,plain,
$true = $true,
inference(unfold_def,[status(thm)],[70]) ).
thf(244,plain,
$true = $true,
inference(unfold_def,[status(thm)],[71]) ).
thf(245,plain,
$true = $true,
inference(unfold_def,[status(thm)],[72]) ).
thf(246,plain,
$true = $true,
inference(unfold_def,[status(thm)],[74]) ).
thf(247,plain,
$true = $true,
inference(unfold_def,[status(thm)],[75]) ).
thf(248,plain,
$true = $true,
inference(unfold_def,[status(thm)],[76]) ).
thf(249,plain,
$true = $true,
inference(unfold_def,[status(thm)],[77]) ).
thf(250,plain,
$true = $true,
inference(unfold_def,[status(thm)],[78]) ).
thf(251,plain,
$true = $true,
inference(unfold_def,[status(thm)],[79]) ).
thf(252,plain,
$true = $true,
inference(unfold_def,[status(thm)],[80]) ).
thf(253,plain,
$true = $true,
inference(unfold_def,[status(thm)],[81]) ).
thf(254,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)],[84]) ).
thf(255,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)],[86]) ).
thf(256,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)],[90]) ).
thf(257,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)],[91]) ).
thf(258,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)],[92]) ).
thf(259,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)],[94]) ).
thf(260,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)],[95]) ).
thf(261,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)],[96]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(263,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)],[98]) ).
thf(264,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)],[99]) ).
thf(265,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)],[100]) ).
thf(266,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)],[101]) ).
thf(267,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)],[103]) ).
thf(268,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(269,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(270,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)],[108]) ).
thf(271,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)],[109]) ).
thf(272,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)],[110]) ).
thf(273,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)],[111]) ).
thf(274,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)],[112]) ).
thf(275,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)],[114]) ).
thf(276,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(277,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(278,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(279,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)],[131]) ).
thf(280,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(281,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)],[161]) ).
thf(282,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)],[169]) ).
thf(283,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)],[171]) ).
thf(284,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)],[177]) ).
thf(285,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)],[190]) ).
thf(286,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)],[202]) ).
thf(287,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)],[204]) ).
thf(288,plain,
( ( ! [SY158: $i,SY159: $i] :
( ( ( relation @ SY159 )
& ( function @ SY159 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ SY158 ) @ SY159 )
<=> ( ( in @ sK1_A @ ( relation_dom @ SY159 ) )
& ( SY158
= ( apply @ SY159 @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[217]) ).
thf(289,plain,
( ( ! [SY160: $i] :
( ( ( relation @ SY160 )
& ( function @ SY160 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ SY160 )
<=> ( ( in @ sK1_A @ ( relation_dom @ SY160 ) )
& ( sK2_SY158
= ( apply @ SY160 @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[288]) ).
thf(290,plain,
( ( ( ( relation @ sK3_SY160 )
& ( function @ sK3_SY160 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 )
<=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
& ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[289]) ).
thf(291,plain,
( ( relation @ sK3_SY160 )
= $true ),
inference(standard_cnf,[status(thm)],[290]) ).
thf(292,plain,
( ( function @ sK3_SY160 )
= $true ),
inference(standard_cnf,[status(thm)],[290]) ).
thf(293,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 )
<=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
& ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[290]) ).
thf(294,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
& ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[293]) ).
thf(295,plain,
( ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
& ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[293]) ).
thf(296,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
& ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[294]) ).
thf(297,plain,
( ( ~ ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
& ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[295]) ).
thf(298,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(copy,[status(thm)],[287]) ).
thf(299,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(copy,[status(thm)],[286]) ).
thf(300,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(copy,[status(thm)],[285]) ).
thf(301,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(copy,[status(thm)],[284]) ).
thf(302,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(303,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(304,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(copy,[status(thm)],[281]) ).
thf(305,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(306,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(copy,[status(thm)],[279]) ).
thf(307,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(308,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(309,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(310,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(copy,[status(thm)],[275]) ).
thf(311,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(copy,[status(thm)],[274]) ).
thf(312,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(copy,[status(thm)],[273]) ).
thf(313,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(copy,[status(thm)],[272]) ).
thf(314,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(copy,[status(thm)],[271]) ).
thf(315,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(316,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(317,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(318,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(copy,[status(thm)],[267]) ).
thf(319,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(320,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(copy,[status(thm)],[265]) ).
thf(321,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(copy,[status(thm)],[264]) ).
thf(322,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(copy,[status(thm)],[263]) ).
thf(323,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(324,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(copy,[status(thm)],[261]) ).
thf(325,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(copy,[status(thm)],[260]) ).
thf(326,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(copy,[status(thm)],[259]) ).
thf(327,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(328,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(copy,[status(thm)],[257]) ).
thf(329,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(copy,[status(thm)],[256]) ).
thf(330,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(copy,[status(thm)],[255]) ).
thf(331,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(copy,[status(thm)],[254]) ).
thf(332,plain,
$true = $true,
inference(copy,[status(thm)],[253]) ).
thf(333,plain,
$true = $true,
inference(copy,[status(thm)],[252]) ).
thf(334,plain,
$true = $true,
inference(copy,[status(thm)],[251]) ).
thf(335,plain,
$true = $true,
inference(copy,[status(thm)],[250]) ).
thf(336,plain,
$true = $true,
inference(copy,[status(thm)],[249]) ).
thf(337,plain,
$true = $true,
inference(copy,[status(thm)],[248]) ).
thf(338,plain,
$true = $true,
inference(copy,[status(thm)],[247]) ).
thf(339,plain,
$true = $true,
inference(copy,[status(thm)],[246]) ).
thf(340,plain,
$true = $true,
inference(copy,[status(thm)],[245]) ).
thf(341,plain,
$true = $true,
inference(copy,[status(thm)],[244]) ).
thf(342,plain,
$true = $true,
inference(copy,[status(thm)],[243]) ).
thf(343,plain,
$true = $true,
inference(copy,[status(thm)],[242]) ).
thf(344,plain,
$true = $true,
inference(copy,[status(thm)],[241]) ).
thf(345,plain,
$true = $true,
inference(copy,[status(thm)],[240]) ).
thf(346,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(347,plain,
$true = $true,
inference(copy,[status(thm)],[238]) ).
thf(348,plain,
$true = $true,
inference(copy,[status(thm)],[237]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(350,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(352,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(353,plain,
$true = $true,
inference(copy,[status(thm)],[232]) ).
thf(354,plain,
$true = $true,
inference(copy,[status(thm)],[231]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(356,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(357,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(358,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(359,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(360,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(361,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(362,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(363,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(364,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(366,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(367,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(368,plain,
( ( function @ sK3_SY160 )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(369,plain,
( ( relation @ sK3_SY160 )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(370,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
& ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(371,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(372,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_dom_restriction @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( 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 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(373,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX3 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX3 @ SX0 ) @ SX2 ) )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX3 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX3 @ SX0 ) @ SX2 ) )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(374,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( subset @ 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 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(375,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(376,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(377,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_rng_restriction @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( 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 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_rng_restriction @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(378,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(379,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(380,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(381,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(382,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(383,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(384,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(385,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(386,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(387,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(388,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( ~ ( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ( ~ ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( ~ ( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) )
| ~ ( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(389,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(390,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(391,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(392,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(393,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(394,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(395,plain,
( ( ~ ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 )
| ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
| ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(396,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ~ ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(397,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) )
| ( SX0 = SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(398,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(399,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(400,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(401,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(402,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( relation_inverse_image @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( relation_inverse_image @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(403,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(404,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_composition @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [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 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_composition @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(405,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(406,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(407,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(408,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(409,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(410,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(411,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(412,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(413,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ 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 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(414,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(415,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(416,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(417,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(418,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(419,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(420,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ! [SX1: $i,SX2: $i] :
~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(421,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ ( relation_field @ SX2 ) )
| ~ ( in @ SX1 @ ( relation_field @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(422,plain,
! [SV1: $i] :
( ( relation @ ( identity_relation @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(423,plain,
! [SV2: $i] :
( ( ! [SY161: $i] :
~ ( empty @ ( ordered_pair @ SV2 @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(424,plain,
! [SV3: $i] :
( ( ! [SY162: $i] :
~ ( ~ ( ( SY162
!= ( union @ SV3 ) )
| ! [SY163: $i] :
~ ( ~ ( ~ ( in @ SY163 @ SY162 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ( in @ SY163 @ SY164 )
| ~ ( in @ SY164 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( in @ SY163 @ SY165 )
| ~ ( in @ SY165 @ SV3 ) )
| ( in @ SY163 @ SY162 ) ) ) )
| ~ ( ~ ! [SY166: $i] :
~ ( ~ ( ~ ( in @ SY166 @ SY162 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY166 @ SY167 )
| ~ ( in @ SY167 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY166 @ SY168 )
| ~ ( in @ SY168 @ SV3 ) )
| ( in @ SY166 @ SY162 ) ) )
| ( SY162
= ( union @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(425,plain,
! [SV4: $i] :
( ( ~ ( relation @ SV4 )
| ! [SY169: $i,SY170: $i] :
( ~ ( relation @ SY170 )
| ~ ( ~ ( ( SY170
!= ( relation_dom_restriction @ SV4 @ SY169 ) )
| ! [SY171: $i,SY172: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SY170 )
| ~ ( ~ ( in @ SY171 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY171 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SY170 ) ) ) )
| ~ ( ~ ! [SY173: $i,SY174: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SY170 )
| ~ ( ~ ( in @ SY173 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY173 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SY170 ) ) )
| ( SY170
= ( relation_dom_restriction @ SV4 @ SY169 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(426,plain,
! [SV5: $i] :
( ( ! [SY175: $i,SY176: $i] :
( ~ ( relation @ SY176 )
| ~ ( ~ ( ~ ( in @ SV5 @ ( relation_image @ SY176 @ SY175 ) )
| ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY177 @ ( relation_dom @ SY176 ) )
| ~ ( in @ ( ordered_pair @ SY177 @ SV5 ) @ SY176 ) )
| ~ ( in @ SY177 @ SY175 ) ) )
| ~ ( ~ ~ ! [SY178: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY178 @ ( relation_dom @ SY176 ) )
| ~ ( in @ ( ordered_pair @ SY178 @ SV5 ) @ SY176 ) )
| ~ ( in @ SY178 @ SY175 ) )
| ( in @ SV5 @ ( relation_image @ SY176 @ SY175 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(427,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ! [SY179: $i] :
( ~ ( relation @ SY179 )
| ~ ( ~ ( ~ ( subset @ SV6 @ SY179 )
| ! [SY180: $i,SY181: $i] :
( ~ ( in @ ( ordered_pair @ SY180 @ SY181 ) @ SV6 )
| ( in @ ( ordered_pair @ SY180 @ SY181 ) @ SY179 ) ) )
| ~ ( ~ ! [SY182: $i,SY183: $i] :
( ~ ( in @ ( ordered_pair @ SY182 @ SY183 ) @ SV6 )
| ( in @ ( ordered_pair @ SY182 @ SY183 ) @ SY179 ) )
| ( subset @ SV6 @ SY179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(428,plain,
! [SV7: $i] :
( ( ! [SY184: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV7 @ SY184 )
| ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ SY185 @ SV7 )
| ~ ( in @ SY185 @ SY184 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY186: $i] :
~ ~ ( ~ ( in @ SY186 @ SV7 )
| ~ ( in @ SY186 @ SY184 ) )
| ~ ( disjoint @ SV7 @ SY184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(429,plain,
! [SV8: $i] :
( ( ! [SY187: $i] :
~ ( ~ ( ( SY187
!= ( singleton @ SV8 ) )
| ! [SY188: $i] :
~ ( ~ ( ~ ( in @ SY188 @ SY187 )
| ( SY188 = SV8 ) )
| ~ ( ( SY188 != SV8 )
| ( in @ SY188 @ SY187 ) ) ) )
| ~ ( ~ ! [SY189: $i] :
~ ( ~ ( ~ ( in @ SY189 @ SY187 )
| ( SY189 = SV8 ) )
| ~ ( ( SY189 != SV8 )
| ( in @ SY189 @ SY187 ) ) )
| ( SY187
= ( singleton @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(430,plain,
! [SV9: $i] :
( ( ! [SY190: $i] :
( ~ ( relation @ SY190 )
| ! [SY191: $i] :
( ~ ( relation @ SY191 )
| ~ ( ~ ( ( SY191
!= ( relation_rng_restriction @ SV9 @ SY190 ) )
| ! [SY192: $i,SY193: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY192 @ SY193 ) @ SY191 )
| ~ ( ~ ( in @ SY193 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY192 @ SY193 ) @ SY190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY193 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY192 @ SY193 ) @ SY190 ) )
| ( in @ ( ordered_pair @ SY192 @ SY193 ) @ SY191 ) ) ) )
| ~ ( ~ ! [SY194: $i,SY195: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY194 @ SY195 ) @ SY191 )
| ~ ( ~ ( in @ SY195 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY194 @ SY195 ) @ SY190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY195 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY194 @ SY195 ) @ SY190 ) )
| ( in @ ( ordered_pair @ SY194 @ SY195 ) @ SY191 ) ) )
| ( SY191
= ( relation_rng_restriction @ SV9 @ SY190 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(431,plain,
! [SV10: $i] :
( ( ! [SY196: $i,SY197: $i,SY198: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV10 @ SY196 ) @ ( cartesian_product2 @ SY197 @ SY198 ) )
| ~ ( ~ ( in @ SV10 @ SY197 )
| ~ ( in @ SY196 @ SY198 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV10 @ SY197 )
| ~ ( in @ SY196 @ SY198 ) )
| ( in @ ( ordered_pair @ SV10 @ SY196 ) @ ( cartesian_product2 @ SY197 @ SY198 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(432,plain,
! [SV11: $i] :
( ( ~ ( relation @ SV11 )
| ( ( relation_inverse @ ( relation_inverse @ SV11 ) )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(433,plain,
! [SV12: $i] :
( ( ! [SY199: $i] :
( ~ ( relation @ SV12 )
| ( relation @ ( relation_dom_restriction @ SV12 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(434,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ( relation @ ( relation_inverse @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(435,plain,
! [SV14: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV14 )
| ~ ( relation @ SV14 ) )
| ~ ( empty @ ( relation_dom @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(436,plain,
! [SV15: $i] :
( ( ! [SY200: $i] :
( ~ ( relation @ SY200 )
| ( relation @ ( relation_rng_restriction @ SV15 @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(437,plain,
! [SV16: $i] :
( ( ~ ( relation @ SV16 )
| ! [SY201: $i] :
~ ( ~ ( ( SY201
!= ( relation_rng @ SV16 ) )
| ! [SY202: $i] :
~ ( ~ ( ~ ( in @ SY202 @ SY201 )
| ~ ! [SY203: $i] :
~ ( in @ ( ordered_pair @ SY203 @ SY202 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY204: $i] :
~ ( in @ ( ordered_pair @ SY204 @ SY202 ) @ SV16 )
| ( in @ SY202 @ SY201 ) ) ) )
| ~ ( ~ ! [SY205: $i] :
~ ( ~ ( ~ ( in @ SY205 @ SY201 )
| ~ ! [SY206: $i] :
~ ( in @ ( ordered_pair @ SY206 @ SY205 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ ( ordered_pair @ SY207 @ SY205 ) @ SV16 )
| ( in @ SY205 @ SY201 ) ) )
| ( SY201
= ( relation_rng @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(438,plain,
! [SV17: $i] :
( ( ! [SY208: $i] :
~ ~ ( ~ ( in @ SV17 @ SY208 )
| ~ ( empty @ SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(439,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(440,plain,
! [SV18: $i] :
( ( ~ ( empty @ SV18 )
| ( relation @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(441,plain,
! [SV19: $i] :
( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ! [SY209: $i,SY210: $i] :
~ ( ~ ( ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( SY210 = empty_set ) )
| ~ ( ( SY210 != empty_set )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(442,plain,
! [SV20: $i] :
( ( ! [SY211: $i,SY212: $i,SY213: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV20 @ SY211 ) @ ( cartesian_product2 @ SY212 @ SY213 ) )
| ~ ( ~ ( in @ SV20 @ SY212 )
| ~ ( in @ SY211 @ SY213 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV20 @ SY212 )
| ~ ( in @ SY211 @ SY213 ) )
| ( in @ ( ordered_pair @ SV20 @ SY211 ) @ ( cartesian_product2 @ SY212 @ SY213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(443,plain,
! [SV21: $i] :
( ( ! [SY214: $i,SY215: $i] :
~ ( ~ ( ( SY215
!= ( unordered_pair @ SV21 @ SY214 ) )
| ! [SY216: $i] :
~ ( ~ ( ~ ( in @ SY216 @ SY215 )
| ( SY216 = SV21 )
| ( SY216 = SY214 ) )
| ~ ( ~ ( ( SY216 = SV21 )
| ( SY216 = SY214 ) )
| ( in @ SY216 @ SY215 ) ) ) )
| ~ ( ~ ! [SY217: $i] :
~ ( ~ ( ~ ( in @ SY217 @ SY215 )
| ( SY217 = SV21 )
| ( SY217 = SY214 ) )
| ~ ( ~ ( ( SY217 = SV21 )
| ( SY217 = SY214 ) )
| ( in @ SY217 @ SY215 ) ) )
| ( SY215
= ( unordered_pair @ SV21 @ SY214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(444,plain,
! [SV22: $i] :
( ( ! [SY218: $i,SY219: $i] :
~ ( ~ ( ( SY219
!= ( set_union2 @ SV22 @ SY218 ) )
| ! [SY220: $i] :
~ ( ~ ( ~ ( in @ SY220 @ SY219 )
| ( in @ SY220 @ SV22 )
| ( in @ SY220 @ SY218 ) )
| ~ ( ~ ( ( in @ SY220 @ SV22 )
| ( in @ SY220 @ SY218 ) )
| ( in @ SY220 @ SY219 ) ) ) )
| ~ ( ~ ! [SY221: $i] :
~ ( ~ ( ~ ( in @ SY221 @ SY219 )
| ( in @ SY221 @ SV22 )
| ( in @ SY221 @ SY218 ) )
| ~ ( ~ ( ( in @ SY221 @ SV22 )
| ( in @ SY221 @ SY218 ) )
| ( in @ SY221 @ SY219 ) ) )
| ( SY219
= ( set_union2 @ SV22 @ SY218 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(445,plain,
! [SV23: $i] :
( ( ! [SY222: $i] :
( ~ ( in @ SV23 @ SY222 )
| ~ ( in @ SY222 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(446,plain,
! [SV24: $i] :
( ( ! [SY223: $i,SY224: $i] :
( ~ ( relation @ SY224 )
| ~ ( ~ ( ~ ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SY224 @ SY223 ) ) )
| ~ ( ~ ( in @ SV24 @ SY223 )
| ~ ( in @ SV24 @ ( relation_dom @ SY224 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SY223 )
| ~ ( in @ SV24 @ ( relation_dom @ SY224 ) ) )
| ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SY224 @ SY223 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(447,plain,
! [SV25: $i] :
( ( ! [SY225: $i] :
~ ( ~ ( ~ ( subset @ SV25 @ SY225 )
| ! [SY226: $i] :
( ~ ( in @ SY226 @ SV25 )
| ( in @ SY226 @ SY225 ) ) )
| ~ ( ~ ! [SY227: $i] :
( ~ ( in @ SY227 @ SV25 )
| ( in @ SY227 @ SY225 ) )
| ( subset @ SV25 @ SY225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(448,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 )
| ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
| ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(449,plain,
! [SV26: $i] :
( ( ! [SY228: $i,SY229: $i] :
( ~ ( relation @ SY229 )
| ~ ( in @ ( ordered_pair @ SV26 @ SY228 ) @ SY229 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SY229 ) )
| ~ ( in @ SY228 @ ( relation_rng @ SY229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(450,plain,
! [SV27: $i] :
( ( ~ ( relation @ SV27 )
| ! [SY230: $i] :
( ~ ( relation @ SY230 )
| ~ ( ~ ( ( SV27 != SY230 )
| ! [SY231: $i,SY232: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SV27 )
| ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SY230 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SY230 )
| ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY233: $i,SY234: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SV27 )
| ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SY230 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SY230 )
| ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SV27 ) ) )
| ( SV27 = SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(451,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(452,plain,
! [SV28: $i] :
( ( ! [SY235: $i,SY236: $i] :
~ ( ~ ( ( SY236
!= ( set_intersection2 @ SV28 @ SY235 ) )
| ! [SY237: $i] :
~ ( ~ ( ~ ( in @ SY237 @ SY236 )
| ~ ( ~ ( in @ SY237 @ SV28 )
| ~ ( in @ SY237 @ SY235 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY237 @ SV28 )
| ~ ( in @ SY237 @ SY235 ) )
| ( in @ SY237 @ SY236 ) ) ) )
| ~ ( ~ ! [SY238: $i] :
~ ( ~ ( ~ ( in @ SY238 @ SY236 )
| ~ ( ~ ( in @ SY238 @ SV28 )
| ~ ( in @ SY238 @ SY235 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY238 @ SV28 )
| ~ ( in @ SY238 @ SY235 ) )
| ( in @ SY238 @ SY236 ) ) )
| ( SY236
= ( set_intersection2 @ SV28 @ SY235 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(453,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(454,plain,
! [SV29: $i] :
( ( ~ ( empty @ SV29 )
| ( function @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(455,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ! [SY239: $i,SY240: $i] :
~ ( ~ ( ( SY240
!= ( relation_inverse_image @ SV30 @ SY239 ) )
| ! [SY241: $i] :
~ ( ~ ( ~ ( in @ SY241 @ SY240 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY241 @ SY242 ) @ SV30 )
| ~ ( in @ SY242 @ SY239 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY241 @ SY243 ) @ SV30 )
| ~ ( in @ SY243 @ SY239 ) )
| ( in @ SY241 @ SY240 ) ) ) )
| ~ ( ~ ! [SY244: $i] :
~ ( ~ ( ~ ( in @ SY244 @ SY240 )
| ~ ! [SY245: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY244 @ SY245 ) @ SV30 )
| ~ ( in @ SY245 @ SY239 ) ) )
| ~ ( ~ ~ ! [SY246: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY244 @ SY246 ) @ SV30 )
| ~ ( in @ SY246 @ SY239 ) )
| ( in @ SY244 @ SY240 ) ) )
| ( SY240
= ( relation_inverse_image @ SV30 @ SY239 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(456,plain,
! [SV31: $i] :
( ( ! [SY247: $i,SY248: $i] :
~ ( ~ ( ( SY248
!= ( cartesian_product2 @ SV31 @ SY247 ) )
| ! [SY249: $i] :
~ ( ~ ( ~ ( in @ SY249 @ SY248 )
| ~ ! [SY250: $i] :
~ ~ ! [SY251: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY250 @ SV31 )
| ~ ( in @ SY251 @ SY247 ) )
| ( SY249
!= ( ordered_pair @ SY250 @ SY251 ) ) ) )
| ~ ( ~ ~ ! [SY252: $i] :
~ ~ ! [SY253: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY252 @ SV31 )
| ~ ( in @ SY253 @ SY247 ) )
| ( SY249
!= ( ordered_pair @ SY252 @ SY253 ) ) )
| ( in @ SY249 @ SY248 ) ) ) )
| ~ ( ~ ! [SY254: $i] :
~ ( ~ ( ~ ( in @ SY254 @ SY248 )
| ~ ! [SY255: $i] :
~ ~ ! [SY256: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY255 @ SV31 )
| ~ ( in @ SY256 @ SY247 ) )
| ( SY254
!= ( ordered_pair @ SY255 @ SY256 ) ) ) )
| ~ ( ~ ~ ! [SY257: $i] :
~ ~ ! [SY258: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY257 @ SV31 )
| ~ ( in @ SY258 @ SY247 ) )
| ( SY254
!= ( ordered_pair @ SY257 @ SY258 ) ) )
| ( in @ SY254 @ SY248 ) ) )
| ( SY248
= ( cartesian_product2 @ SV31 @ SY247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(457,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ! [SY259: $i] :
( ~ ( relation @ SY259 )
| ! [SY260: $i] :
( ~ ( relation @ SY260 )
| ~ ( ~ ( ( SY260
!= ( relation_composition @ SV32 @ SY259 ) )
| ! [SY261: $i,SY262: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY261 @ SY262 ) @ SY260 )
| ~ ! [SY263: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY261 @ SY263 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY263 @ SY262 ) @ SY259 ) ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY261 @ SY264 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY264 @ SY262 ) @ SY259 ) )
| ( in @ ( ordered_pair @ SY261 @ SY262 ) @ SY260 ) ) ) )
| ~ ( ~ ! [SY265: $i,SY266: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY265 @ SY266 ) @ SY260 )
| ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY265 @ SY267 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY267 @ SY266 ) @ SY259 ) ) )
| ~ ( ~ ~ ! [SY268: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY265 @ SY268 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY268 @ SY266 ) @ SY259 ) )
| ( in @ ( ordered_pair @ SY265 @ SY266 ) @ SY260 ) ) )
| ( SY260
= ( relation_composition @ SV32 @ SY259 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(458,plain,
! [SV33: $i] :
( ( ! [SY269: $i,SY270: $i,SY271: $i] :
( ( ( ordered_pair @ SV33 @ SY269 )
!= ( ordered_pair @ SY270 @ SY271 ) )
| ~ ( ( SV33 != SY270 )
| ( SY269 != SY271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(459,plain,
! [SV34: $i] :
( ( ! [SY272: $i] :
( ~ ! [SY273: $i] :
~ ( ~ ( ~ ( in @ SY273 @ SV34 )
| ( in @ SY273 @ SY272 ) )
| ~ ( ~ ( in @ SY273 @ SY272 )
| ( in @ SY273 @ SV34 ) ) )
| ( SV34 = SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(460,plain,
! [SV35: $i] :
( ( ! [SY274: $i] :
( ~ ( relation @ SY274 )
| ~ ( ~ ( ( SY274
!= ( identity_relation @ SV35 ) )
| ! [SY275: $i,SY276: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY275 @ SY276 ) @ SY274 )
| ~ ( ~ ( in @ SY275 @ SV35 )
| ( SY275 != SY276 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY275 @ SV35 )
| ( SY275 != SY276 ) )
| ( in @ ( ordered_pair @ SY275 @ SY276 ) @ SY274 ) ) ) )
| ~ ( ~ ! [SY277: $i,SY278: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY277 @ SY278 ) @ SY274 )
| ~ ( ~ ( in @ SY277 @ SV35 )
| ( SY277 != SY278 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY277 @ SV35 )
| ( SY277 != SY278 ) )
| ( in @ ( ordered_pair @ SY277 @ SY278 ) @ SY274 ) ) )
| ( SY274
= ( identity_relation @ SV35 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(461,plain,
! [SV36: $i] :
( ( ~ ( ~ ( ~ ( relation @ SV36 )
| ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY279
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY282: $i] :
~ ~ ( ~ ( in @ SY282 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY282
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(462,plain,
! [SV37: $i] :
( ( ! [SY285: $i] :
( ~ ( in @ SV37 @ SY285 )
| ( element @ SV37 @ SY285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(463,plain,
! [SV38: $i] :
( ( ! [SY286: $i] :
( ~ ~ ( ~ ( relation @ SV38 )
| ~ ( relation @ SY286 ) )
| ( relation @ ( set_intersection2 @ SV38 @ SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(464,plain,
! [SV39: $i] :
( ( ~ ( ~ ( ( SV39 != empty_set )
| ! [SY287: $i] :
~ ( in @ SY287 @ SV39 ) )
| ~ ( ~ ! [SY288: $i] :
~ ( in @ SY288 @ SV39 )
| ( SV39 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(465,plain,
! [SV40: $i] :
( ( ~ ( empty @ SV40 )
| ~ ( ~ ( empty @ ( relation_dom @ SV40 ) )
| ~ ( relation @ ( relation_dom @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(466,plain,
! [SV41: $i] :
( ( ~ ( relation @ SV41 )
| ! [SY289: $i] :
( ~ ( relation @ SY289 )
| ~ ( ~ ( ( SY289
!= ( relation_inverse @ SV41 ) )
| ! [SY290: $i,SY291: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SY289 )
| ( in @ ( ordered_pair @ SY291 @ SY290 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY291 @ SY290 ) @ SV41 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SY289 ) ) ) )
| ~ ( ~ ! [SY292: $i,SY293: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY292 @ SY293 ) @ SY289 )
| ( in @ ( ordered_pair @ SY293 @ SY292 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY293 @ SY292 ) @ SV41 )
| ( in @ ( ordered_pair @ SY292 @ SY293 ) @ SY289 ) ) )
| ( SY289
= ( relation_inverse @ SV41 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(467,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(468,plain,
! [SV42: $i] :
( ( ! [SY294: $i,SY295: $i] :
~ ( ~ ( ( SY295
!= ( set_difference @ SV42 @ SY294 ) )
| ! [SY296: $i] :
~ ( ~ ( ~ ( in @ SY296 @ SY295 )
| ~ ( ~ ( in @ SY296 @ SV42 )
| ~ ~ ( in @ SY296 @ SY294 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY296 @ SV42 )
| ~ ~ ( in @ SY296 @ SY294 ) )
| ( in @ SY296 @ SY295 ) ) ) )
| ~ ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SY295 )
| ~ ( ~ ( in @ SY297 @ SV42 )
| ~ ~ ( in @ SY297 @ SY294 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY297 @ SV42 )
| ~ ~ ( in @ SY297 @ SY294 ) )
| ( in @ SY297 @ SY295 ) ) )
| ( SY295
= ( set_difference @ SV42 @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(469,plain,
! [SV43: $i] :
( ( ~ ( relation @ SV43 )
| ! [SY298: $i,SY299: $i] :
~ ( ~ ( ( SY299
!= ( relation_image @ SV43 @ SY298 ) )
| ! [SY300: $i] :
~ ( ~ ( ~ ( in @ SY300 @ SY299 )
| ~ ! [SY301: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY301 @ SY300 ) @ SV43 )
| ~ ( in @ SY301 @ SY298 ) ) )
| ~ ( ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY302 @ SY300 ) @ SV43 )
| ~ ( in @ SY302 @ SY298 ) )
| ( in @ SY300 @ SY299 ) ) ) )
| ~ ( ~ ! [SY303: $i] :
~ ( ~ ( ~ ( in @ SY303 @ SY299 )
| ~ ! [SY304: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY304 @ SY303 ) @ SV43 )
| ~ ( in @ SY304 @ SY298 ) ) )
| ~ ( ~ ~ ! [SY305: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY305 @ SY303 ) @ SV43 )
| ~ ( in @ SY305 @ SY298 ) )
| ( in @ SY303 @ SY299 ) ) )
| ( SY299
= ( relation_image @ SV43 @ SY298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(470,plain,
! [SV44: $i] :
( ( ! [SY306: $i] :
( ~ ~ ( ~ ( relation @ SV44 )
| ~ ( relation @ SY306 ) )
| ( relation @ ( relation_composition @ SV44 @ SY306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(471,plain,
! [SV45: $i] :
( ( ~ ( relation @ SV45 )
| ! [SY307: $i] :
~ ( ~ ( ( SY307
!= ( relation_dom @ SV45 ) )
| ! [SY308: $i] :
~ ( ~ ( ~ ( in @ SY308 @ SY307 )
| ~ ! [SY309: $i] :
~ ( in @ ( ordered_pair @ SY308 @ SY309 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY310: $i] :
~ ( in @ ( ordered_pair @ SY308 @ SY310 ) @ SV45 )
| ( in @ SY308 @ SY307 ) ) ) )
| ~ ( ~ ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SY307 )
| ~ ! [SY312: $i] :
~ ( in @ ( ordered_pair @ SY311 @ SY312 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY313: $i] :
~ ( in @ ( ordered_pair @ SY311 @ SY313 ) @ SV45 )
| ( in @ SY311 @ SY307 ) ) )
| ( SY307
= ( relation_dom @ SV45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(472,plain,
! [SV46: $i] :
( ( ! [SY314: $i] :
( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( relation @ SY314 ) )
| ( relation @ ( set_union2 @ SV46 @ SY314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(473,plain,
! [SV47: $i] :
( ( ~ ( relation @ SV47 )
| ~ ! [SY315: $i,SY316: $i] :
~ ( in @ ( ordered_pair @ SY315 @ SY316 ) @ SV47 )
| ( SV47 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(474,plain,
! [SV48: $i] :
( ( ! [SY317: $i,SY318: $i] :
( ~ ( relation @ SY318 )
| ~ ( in @ ( ordered_pair @ SV48 @ SY317 ) @ SY318 )
| ~ ( ~ ( in @ SV48 @ ( relation_field @ SY318 ) )
| ~ ( in @ SY317 @ ( relation_field @ SY318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(475,plain,
! [SV49: $i,SV2: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV2 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(476,plain,
! [SV3: $i,SV50: $i] :
( ( ~ ( ~ ( ( SV50
!= ( union @ SV3 ) )
| ! [SY319: $i] :
~ ( ~ ( ~ ( in @ SY319 @ SV50 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ( in @ SY319 @ SY164 )
| ~ ( in @ SY164 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( in @ SY319 @ SY165 )
| ~ ( in @ SY165 @ SV3 ) )
| ( in @ SY319 @ SV50 ) ) ) )
| ~ ( ~ ! [SY322: $i] :
~ ( ~ ( ~ ( in @ SY322 @ SV50 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY322 @ SY167 )
| ~ ( in @ SY167 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY322 @ SY168 )
| ~ ( in @ SY168 @ SV3 ) )
| ( in @ SY322 @ SV50 ) ) )
| ( SV50
= ( union @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(477,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ! [SY169: $i,SY170: $i] :
( ~ ( relation @ SY170 )
| ~ ( ~ ( ( SY170
!= ( relation_dom_restriction @ SV4 @ SY169 ) )
| ! [SY171: $i,SY172: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SY170 )
| ~ ( ~ ( in @ SY171 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY171 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SY170 ) ) ) )
| ~ ( ~ ! [SY173: $i,SY174: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SY170 )
| ~ ( ~ ( in @ SY173 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY173 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SY170 ) ) )
| ( SY170
= ( relation_dom_restriction @ SV4 @ SY169 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(478,plain,
! [SV51: $i,SV5: $i] :
( ( ! [SY325: $i] :
( ~ ( relation @ SY325 )
| ~ ( ~ ( ~ ( in @ SV5 @ ( relation_image @ SY325 @ SV51 ) )
| ~ ! [SY326: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ ( relation_dom @ SY325 ) )
| ~ ( in @ ( ordered_pair @ SY326 @ SV5 ) @ SY325 ) )
| ~ ( in @ SY326 @ SV51 ) ) )
| ~ ( ~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY327 @ ( relation_dom @ SY325 ) )
| ~ ( in @ ( ordered_pair @ SY327 @ SV5 ) @ SY325 ) )
| ~ ( in @ SY327 @ SV51 ) )
| ( in @ SV5 @ ( relation_image @ SY325 @ SV51 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(479,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ! [SY179: $i] :
( ~ ( relation @ SY179 )
| ~ ( ~ ( ~ ( subset @ SV6 @ SY179 )
| ! [SY180: $i,SY181: $i] :
( ~ ( in @ ( ordered_pair @ SY180 @ SY181 ) @ SV6 )
| ( in @ ( ordered_pair @ SY180 @ SY181 ) @ SY179 ) ) )
| ~ ( ~ ! [SY182: $i,SY183: $i] :
( ~ ( in @ ( ordered_pair @ SY182 @ SY183 ) @ SV6 )
| ( in @ ( ordered_pair @ SY182 @ SY183 ) @ SY179 ) )
| ( subset @ SV6 @ SY179 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(480,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV7 @ SV52 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( in @ SY329 @ SV7 )
| ~ ( in @ SY329 @ SV52 ) )
| ~ ( disjoint @ SV7 @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(481,plain,
! [SV8: $i,SV53: $i] :
( ( ~ ( ~ ( ( SV53
!= ( singleton @ SV8 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV53 )
| ( SY330 = SV8 ) )
| ~ ( ( SY330 != SV8 )
| ( in @ SY330 @ SV53 ) ) ) )
| ~ ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV53 )
| ( SY331 = SV8 ) )
| ~ ( ( SY331 != SV8 )
| ( in @ SY331 @ SV53 ) ) )
| ( SV53
= ( singleton @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(482,plain,
! [SV9: $i,SV54: $i] :
( ( ~ ( relation @ SV54 )
| ! [SY332: $i] :
( ~ ( relation @ SY332 )
| ~ ( ~ ( ( SY332
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
| ! [SY333: $i,SY334: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SY332 )
| ~ ( ~ ( in @ SY334 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY334 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SY332 ) ) ) )
| ~ ( ~ ! [SY335: $i,SY336: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SY332 )
| ~ ( ~ ( in @ SY336 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY336 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SY332 ) ) )
| ( SY332
= ( relation_rng_restriction @ SV9 @ SV54 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(483,plain,
! [SV55: $i,SV10: $i] :
( ( ! [SY337: $i,SY338: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SY337 @ SY338 ) )
| ~ ( ~ ( in @ SV10 @ SY337 )
| ~ ( in @ SV55 @ SY338 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV10 @ SY337 )
| ~ ( in @ SV55 @ SY338 ) )
| ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SY337 @ SY338 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(484,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV11 ) )
= SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(485,plain,
! [SV56: $i,SV12: $i] :
( ( ~ ( relation @ SV12 )
| ( relation @ ( relation_dom_restriction @ SV12 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(486,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(487,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV14 )
| ~ ( relation @ SV14 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(488,plain,
! [SV15: $i,SV57: $i] :
( ( ~ ( relation @ SV57 )
| ( relation @ ( relation_rng_restriction @ SV15 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(489,plain,
! [SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ! [SY201: $i] :
~ ( ~ ( ( SY201
!= ( relation_rng @ SV16 ) )
| ! [SY202: $i] :
~ ( ~ ( ~ ( in @ SY202 @ SY201 )
| ~ ! [SY203: $i] :
~ ( in @ ( ordered_pair @ SY203 @ SY202 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY204: $i] :
~ ( in @ ( ordered_pair @ SY204 @ SY202 ) @ SV16 )
| ( in @ SY202 @ SY201 ) ) ) )
| ~ ( ~ ! [SY205: $i] :
~ ( ~ ( ~ ( in @ SY205 @ SY201 )
| ~ ! [SY206: $i] :
~ ( in @ ( ordered_pair @ SY206 @ SY205 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ ( ordered_pair @ SY207 @ SY205 ) @ SV16 )
| ( in @ SY205 @ SY201 ) ) )
| ( SY201
= ( relation_rng @ SV16 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(490,plain,
! [SV58: $i,SV17: $i] :
( ( ~ ~ ( ~ ( in @ SV17 @ SV58 )
| ~ ( empty @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(491,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[439]) ).
thf(492,plain,
! [SV18: $i] :
( ( ( ~ ( empty @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(493,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) ) )
= $true )
| ( ( ! [SY209: $i,SY210: $i] :
~ ( ~ ( ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( SY210 = empty_set ) )
| ~ ( ( SY210 != empty_set )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(494,plain,
! [SV59: $i,SV20: $i] :
( ( ! [SY339: $i,SY340: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SY339 @ SY340 ) )
| ~ ( ~ ( in @ SV20 @ SY339 )
| ~ ( in @ SV59 @ SY340 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV20 @ SY339 )
| ~ ( in @ SV59 @ SY340 ) )
| ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SY339 @ SY340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(495,plain,
! [SV60: $i,SV21: $i] :
( ( ! [SY341: $i] :
~ ( ~ ( ( SY341
!= ( unordered_pair @ SV21 @ SV60 ) )
| ! [SY342: $i] :
~ ( ~ ( ~ ( in @ SY342 @ SY341 )
| ( SY342 = SV21 )
| ( SY342 = SV60 ) )
| ~ ( ~ ( ( SY342 = SV21 )
| ( SY342 = SV60 ) )
| ( in @ SY342 @ SY341 ) ) ) )
| ~ ( ~ ! [SY343: $i] :
~ ( ~ ( ~ ( in @ SY343 @ SY341 )
| ( SY343 = SV21 )
| ( SY343 = SV60 ) )
| ~ ( ~ ( ( SY343 = SV21 )
| ( SY343 = SV60 ) )
| ( in @ SY343 @ SY341 ) ) )
| ( SY341
= ( unordered_pair @ SV21 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(496,plain,
! [SV61: $i,SV22: $i] :
( ( ! [SY344: $i] :
~ ( ~ ( ( SY344
!= ( set_union2 @ SV22 @ SV61 ) )
| ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SY344 )
| ( in @ SY345 @ SV22 )
| ( in @ SY345 @ SV61 ) )
| ~ ( ~ ( ( in @ SY345 @ SV22 )
| ( in @ SY345 @ SV61 ) )
| ( in @ SY345 @ SY344 ) ) ) )
| ~ ( ~ ! [SY346: $i] :
~ ( ~ ( ~ ( in @ SY346 @ SY344 )
| ( in @ SY346 @ SV22 )
| ( in @ SY346 @ SV61 ) )
| ~ ( ~ ( ( in @ SY346 @ SV22 )
| ( in @ SY346 @ SV61 ) )
| ( in @ SY346 @ SY344 ) ) )
| ( SY344
= ( set_union2 @ SV22 @ SV61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(497,plain,
! [SV62: $i,SV23: $i] :
( ( ~ ( in @ SV23 @ SV62 )
| ~ ( in @ SV62 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(498,plain,
! [SV63: $i,SV24: $i] :
( ( ! [SY347: $i] :
( ~ ( relation @ SY347 )
| ~ ( ~ ( ~ ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SY347 @ SV63 ) ) )
| ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SY347 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SY347 ) ) )
| ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SY347 @ SV63 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(499,plain,
! [SV64: $i,SV25: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV25 @ SV64 )
| ! [SY348: $i] :
( ~ ( in @ SY348 @ SV25 )
| ( in @ SY348 @ SV64 ) ) )
| ~ ( ~ ! [SY349: $i] :
( ~ ( in @ SY349 @ SV25 )
| ( in @ SY349 @ SV64 ) )
| ( subset @ SV25 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(500,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(501,plain,
( ( ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
| ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(502,plain,
! [SV65: $i,SV26: $i] :
( ( ! [SY350: $i] :
( ~ ( relation @ SY350 )
| ~ ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SY350 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SY350 ) )
| ~ ( in @ SV65 @ ( relation_rng @ SY350 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(503,plain,
! [SV27: $i] :
( ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ! [SY230: $i] :
( ~ ( relation @ SY230 )
| ~ ( ~ ( ( SV27 != SY230 )
| ! [SY231: $i,SY232: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SV27 )
| ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SY230 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SY230 )
| ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY233: $i,SY234: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SV27 )
| ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SY230 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SY230 )
| ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SV27 ) ) )
| ( SV27 = SY230 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(504,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[451]) ).
thf(505,plain,
! [SV66: $i,SV28: $i] :
( ( ! [SY351: $i] :
~ ( ~ ( ( SY351
!= ( set_intersection2 @ SV28 @ SV66 ) )
| ! [SY352: $i] :
~ ( ~ ( ~ ( in @ SY352 @ SY351 )
| ~ ( ~ ( in @ SY352 @ SV28 )
| ~ ( in @ SY352 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY352 @ SV28 )
| ~ ( in @ SY352 @ SV66 ) )
| ( in @ SY352 @ SY351 ) ) ) )
| ~ ( ~ ! [SY353: $i] :
~ ( ~ ( ~ ( in @ SY353 @ SY351 )
| ~ ( ~ ( in @ SY353 @ SV28 )
| ~ ( in @ SY353 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY353 @ SV28 )
| ~ ( in @ SY353 @ SV66 ) )
| ( in @ SY353 @ SY351 ) ) )
| ( SY351
= ( set_intersection2 @ SV28 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(506,plain,
( ( ~ ~ ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[453]) ).
thf(507,plain,
! [SV29: $i] :
( ( ( ~ ( empty @ SV29 ) )
= $true )
| ( ( function @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(508,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ! [SY239: $i,SY240: $i] :
~ ( ~ ( ( SY240
!= ( relation_inverse_image @ SV30 @ SY239 ) )
| ! [SY241: $i] :
~ ( ~ ( ~ ( in @ SY241 @ SY240 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY241 @ SY242 ) @ SV30 )
| ~ ( in @ SY242 @ SY239 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY241 @ SY243 ) @ SV30 )
| ~ ( in @ SY243 @ SY239 ) )
| ( in @ SY241 @ SY240 ) ) ) )
| ~ ( ~ ! [SY244: $i] :
~ ( ~ ( ~ ( in @ SY244 @ SY240 )
| ~ ! [SY245: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY244 @ SY245 ) @ SV30 )
| ~ ( in @ SY245 @ SY239 ) ) )
| ~ ( ~ ~ ! [SY246: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY244 @ SY246 ) @ SV30 )
| ~ ( in @ SY246 @ SY239 ) )
| ( in @ SY244 @ SY240 ) ) )
| ( SY240
= ( relation_inverse_image @ SV30 @ SY239 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(509,plain,
! [SV67: $i,SV31: $i] :
( ( ! [SY354: $i] :
~ ( ~ ( ( SY354
!= ( cartesian_product2 @ SV31 @ SV67 ) )
| ! [SY355: $i] :
~ ( ~ ( ~ ( in @ SY355 @ SY354 )
| ~ ! [SY356: $i] :
~ ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY356 @ SV31 )
| ~ ( in @ SY357 @ SV67 ) )
| ( SY355
!= ( ordered_pair @ SY356 @ SY357 ) ) ) )
| ~ ( ~ ~ ! [SY358: $i] :
~ ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY358 @ SV31 )
| ~ ( in @ SY359 @ SV67 ) )
| ( SY355
!= ( ordered_pair @ SY358 @ SY359 ) ) )
| ( in @ SY355 @ SY354 ) ) ) )
| ~ ( ~ ! [SY360: $i] :
~ ( ~ ( ~ ( in @ SY360 @ SY354 )
| ~ ! [SY361: $i] :
~ ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY361 @ SV31 )
| ~ ( in @ SY362 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY361 @ SY362 ) ) ) )
| ~ ( ~ ~ ! [SY363: $i] :
~ ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV31 )
| ~ ( in @ SY364 @ SV67 ) )
| ( SY360
!= ( ordered_pair @ SY363 @ SY364 ) ) )
| ( in @ SY360 @ SY354 ) ) )
| ( SY354
= ( cartesian_product2 @ SV31 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(510,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ! [SY259: $i] :
( ~ ( relation @ SY259 )
| ! [SY260: $i] :
( ~ ( relation @ SY260 )
| ~ ( ~ ( ( SY260
!= ( relation_composition @ SV32 @ SY259 ) )
| ! [SY261: $i,SY262: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY261 @ SY262 ) @ SY260 )
| ~ ! [SY263: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY261 @ SY263 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY263 @ SY262 ) @ SY259 ) ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY261 @ SY264 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY264 @ SY262 ) @ SY259 ) )
| ( in @ ( ordered_pair @ SY261 @ SY262 ) @ SY260 ) ) ) )
| ~ ( ~ ! [SY265: $i,SY266: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY265 @ SY266 ) @ SY260 )
| ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY265 @ SY267 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY267 @ SY266 ) @ SY259 ) ) )
| ~ ( ~ ~ ! [SY268: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY265 @ SY268 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY268 @ SY266 ) @ SY259 ) )
| ( in @ ( ordered_pair @ SY265 @ SY266 ) @ SY260 ) ) )
| ( SY260
= ( relation_composition @ SV32 @ SY259 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(511,plain,
! [SV68: $i,SV33: $i] :
( ( ! [SY365: $i,SY366: $i] :
( ( ( ordered_pair @ SV33 @ SV68 )
!= ( ordered_pair @ SY365 @ SY366 ) )
| ~ ( ( SV33 != SY365 )
| ( SV68 != SY366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(512,plain,
! [SV69: $i,SV34: $i] :
( ( ~ ! [SY367: $i] :
~ ( ~ ( ~ ( in @ SY367 @ SV34 )
| ( in @ SY367 @ SV69 ) )
| ~ ( ~ ( in @ SY367 @ SV69 )
| ( in @ SY367 @ SV34 ) ) )
| ( SV34 = SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(513,plain,
! [SV35: $i,SV70: $i] :
( ( ~ ( relation @ SV70 )
| ~ ( ~ ( ( SV70
!= ( identity_relation @ SV35 ) )
| ! [SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 )
| ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) )
| ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 ) ) ) )
| ~ ( ~ ! [SY370: $i,SY371: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 )
| ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) )
| ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(514,plain,
! [SV36: $i] :
( ( ~ ( ~ ( relation @ SV36 )
| ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY279
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY282: $i] :
~ ~ ( ~ ( in @ SY282 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY282
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV36 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(515,plain,
! [SV71: $i,SV37: $i] :
( ( ~ ( in @ SV37 @ SV71 )
| ( element @ SV37 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(516,plain,
! [SV72: $i,SV38: $i] :
( ( ~ ~ ( ~ ( relation @ SV38 )
| ~ ( relation @ SV72 ) )
| ( relation @ ( set_intersection2 @ SV38 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(517,plain,
! [SV39: $i] :
( ( ~ ( ( SV39 != empty_set )
| ! [SY287: $i] :
~ ( in @ SY287 @ SV39 ) )
| ~ ( ~ ! [SY288: $i] :
~ ( in @ SY288 @ SV39 )
| ( SV39 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(518,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV40 ) )
| ~ ( relation @ ( relation_dom @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(519,plain,
! [SV41: $i] :
( ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ! [SY289: $i] :
( ~ ( relation @ SY289 )
| ~ ( ~ ( ( SY289
!= ( relation_inverse @ SV41 ) )
| ! [SY290: $i,SY291: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SY289 )
| ( in @ ( ordered_pair @ SY291 @ SY290 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY291 @ SY290 ) @ SV41 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SY289 ) ) ) )
| ~ ( ~ ! [SY292: $i,SY293: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY292 @ SY293 ) @ SY289 )
| ( in @ ( ordered_pair @ SY293 @ SY292 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY293 @ SY292 ) @ SV41 )
| ( in @ ( ordered_pair @ SY292 @ SY293 ) @ SY289 ) ) )
| ( SY289
= ( relation_inverse @ SV41 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(520,plain,
( ( ~ ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( relation_empty_yielding @ sK7_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[467]) ).
thf(521,plain,
! [SV73: $i,SV42: $i] :
( ( ! [SY372: $i] :
~ ( ~ ( ( SY372
!= ( set_difference @ SV42 @ SV73 ) )
| ! [SY373: $i] :
~ ( ~ ( ~ ( in @ SY373 @ SY372 )
| ~ ( ~ ( in @ SY373 @ SV42 )
| ~ ~ ( in @ SY373 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY373 @ SV42 )
| ~ ~ ( in @ SY373 @ SV73 ) )
| ( in @ SY373 @ SY372 ) ) ) )
| ~ ( ~ ! [SY374: $i] :
~ ( ~ ( ~ ( in @ SY374 @ SY372 )
| ~ ( ~ ( in @ SY374 @ SV42 )
| ~ ~ ( in @ SY374 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY374 @ SV42 )
| ~ ~ ( in @ SY374 @ SV73 ) )
| ( in @ SY374 @ SY372 ) ) )
| ( SY372
= ( set_difference @ SV42 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(522,plain,
! [SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( ! [SY298: $i,SY299: $i] :
~ ( ~ ( ( SY299
!= ( relation_image @ SV43 @ SY298 ) )
| ! [SY300: $i] :
~ ( ~ ( ~ ( in @ SY300 @ SY299 )
| ~ ! [SY301: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY301 @ SY300 ) @ SV43 )
| ~ ( in @ SY301 @ SY298 ) ) )
| ~ ( ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY302 @ SY300 ) @ SV43 )
| ~ ( in @ SY302 @ SY298 ) )
| ( in @ SY300 @ SY299 ) ) ) )
| ~ ( ~ ! [SY303: $i] :
~ ( ~ ( ~ ( in @ SY303 @ SY299 )
| ~ ! [SY304: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY304 @ SY303 ) @ SV43 )
| ~ ( in @ SY304 @ SY298 ) ) )
| ~ ( ~ ~ ! [SY305: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY305 @ SY303 ) @ SV43 )
| ~ ( in @ SY305 @ SY298 ) )
| ( in @ SY303 @ SY299 ) ) )
| ( SY299
= ( relation_image @ SV43 @ SY298 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(523,plain,
! [SV74: $i,SV44: $i] :
( ( ~ ~ ( ~ ( relation @ SV44 )
| ~ ( relation @ SV74 ) )
| ( relation @ ( relation_composition @ SV44 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(524,plain,
! [SV45: $i] :
( ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ! [SY307: $i] :
~ ( ~ ( ( SY307
!= ( relation_dom @ SV45 ) )
| ! [SY308: $i] :
~ ( ~ ( ~ ( in @ SY308 @ SY307 )
| ~ ! [SY309: $i] :
~ ( in @ ( ordered_pair @ SY308 @ SY309 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY310: $i] :
~ ( in @ ( ordered_pair @ SY308 @ SY310 ) @ SV45 )
| ( in @ SY308 @ SY307 ) ) ) )
| ~ ( ~ ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SY307 )
| ~ ! [SY312: $i] :
~ ( in @ ( ordered_pair @ SY311 @ SY312 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY313: $i] :
~ ( in @ ( ordered_pair @ SY311 @ SY313 ) @ SV45 )
| ( in @ SY311 @ SY307 ) ) )
| ( SY307
= ( relation_dom @ SV45 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(525,plain,
! [SV75: $i,SV46: $i] :
( ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( relation @ SV75 ) )
| ( relation @ ( set_union2 @ SV46 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(526,plain,
! [SV47: $i] :
( ( ( ~ ( relation @ SV47 ) )
= $true )
| ( ( ~ ! [SY315: $i,SY316: $i] :
~ ( in @ ( ordered_pair @ SY315 @ SY316 ) @ SV47 )
| ( SV47 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(527,plain,
! [SV76: $i,SV48: $i] :
( ( ! [SY375: $i] :
( ~ ( relation @ SY375 )
| ~ ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SY375 )
| ~ ( ~ ( in @ SV48 @ ( relation_field @ SY375 ) )
| ~ ( in @ SV76 @ ( relation_field @ SY375 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(528,plain,
! [SV49: $i,SV2: $i] :
( ( empty @ ( ordered_pair @ SV2 @ SV49 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(529,plain,
! [SV3: $i,SV50: $i] :
( ( ~ ( ( SV50
!= ( union @ SV3 ) )
| ! [SY319: $i] :
~ ( ~ ( ~ ( in @ SY319 @ SV50 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ( in @ SY319 @ SY164 )
| ~ ( in @ SY164 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( in @ SY319 @ SY165 )
| ~ ( in @ SY165 @ SV3 ) )
| ( in @ SY319 @ SV50 ) ) ) )
| ~ ( ~ ! [SY322: $i] :
~ ( ~ ( ~ ( in @ SY322 @ SV50 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY322 @ SY167 )
| ~ ( in @ SY167 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY322 @ SY168 )
| ~ ( in @ SY168 @ SV3 ) )
| ( in @ SY322 @ SV50 ) ) )
| ( SV50
= ( union @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(530,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( ! [SY169: $i,SY170: $i] :
( ~ ( relation @ SY170 )
| ~ ( ~ ( ( SY170
!= ( relation_dom_restriction @ SV4 @ SY169 ) )
| ! [SY171: $i,SY172: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SY170 )
| ~ ( ~ ( in @ SY171 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY171 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY171 @ SY172 ) @ SY170 ) ) ) )
| ~ ( ~ ! [SY173: $i,SY174: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SY170 )
| ~ ( ~ ( in @ SY173 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY173 @ SY169 )
| ~ ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY173 @ SY174 ) @ SY170 ) ) )
| ( SY170
= ( relation_dom_restriction @ SV4 @ SY169 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(531,plain,
! [SV51: $i,SV5: $i,SV77: $i] :
( ( ~ ( relation @ SV77 )
| ~ ( ~ ( ~ ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY376 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY376 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY376 @ SV51 ) ) )
| ~ ( ~ ~ ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY377 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY377 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY377 @ SV51 ) )
| ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(532,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ! [SY179: $i] :
( ~ ( relation @ SY179 )
| ~ ( ~ ( ~ ( subset @ SV6 @ SY179 )
| ! [SY180: $i,SY181: $i] :
( ~ ( in @ ( ordered_pair @ SY180 @ SY181 ) @ SV6 )
| ( in @ ( ordered_pair @ SY180 @ SY181 ) @ SY179 ) ) )
| ~ ( ~ ! [SY182: $i,SY183: $i] :
( ~ ( in @ ( ordered_pair @ SY182 @ SY183 ) @ SV6 )
| ( in @ ( ordered_pair @ SY182 @ SY183 ) @ SY179 ) )
| ( subset @ SV6 @ SY179 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(533,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV7 @ SV52 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( in @ SY329 @ SV7 )
| ~ ( in @ SY329 @ SV52 ) )
| ~ ( disjoint @ SV7 @ SV52 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(534,plain,
! [SV8: $i,SV53: $i] :
( ( ~ ( ( SV53
!= ( singleton @ SV8 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV53 )
| ( SY330 = SV8 ) )
| ~ ( ( SY330 != SV8 )
| ( in @ SY330 @ SV53 ) ) ) )
| ~ ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV53 )
| ( SY331 = SV8 ) )
| ~ ( ( SY331 != SV8 )
| ( in @ SY331 @ SV53 ) ) )
| ( SV53
= ( singleton @ SV8 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(535,plain,
! [SV9: $i,SV54: $i] :
( ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ! [SY332: $i] :
( ~ ( relation @ SY332 )
| ~ ( ~ ( ( SY332
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
| ! [SY333: $i,SY334: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SY332 )
| ~ ( ~ ( in @ SY334 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY334 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SY332 ) ) ) )
| ~ ( ~ ! [SY335: $i,SY336: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SY332 )
| ~ ( ~ ( in @ SY336 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY336 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SY332 ) ) )
| ( SY332
= ( relation_rng_restriction @ SV9 @ SV54 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(536,plain,
! [SV78: $i,SV55: $i,SV10: $i] :
( ( ! [SY378: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SY378 ) )
| ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SY378 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SY378 ) )
| ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SY378 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(537,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV11 ) )
= SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(538,plain,
! [SV56: $i,SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV12 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(539,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( relation @ ( relation_inverse @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(540,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV14 )
| ~ ( relation @ SV14 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(541,plain,
! [SV15: $i,SV57: $i] :
( ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV15 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(542,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ! [SY201: $i] :
~ ( ~ ( ( SY201
!= ( relation_rng @ SV16 ) )
| ! [SY202: $i] :
~ ( ~ ( ~ ( in @ SY202 @ SY201 )
| ~ ! [SY203: $i] :
~ ( in @ ( ordered_pair @ SY203 @ SY202 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY204: $i] :
~ ( in @ ( ordered_pair @ SY204 @ SY202 ) @ SV16 )
| ( in @ SY202 @ SY201 ) ) ) )
| ~ ( ~ ! [SY205: $i] :
~ ( ~ ( ~ ( in @ SY205 @ SY201 )
| ~ ! [SY206: $i] :
~ ( in @ ( ordered_pair @ SY206 @ SY205 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ ( ordered_pair @ SY207 @ SY205 ) @ SV16 )
| ( in @ SY205 @ SY201 ) ) )
| ( SY201
= ( relation_rng @ SV16 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(543,plain,
! [SV58: $i,SV17: $i] :
( ( ~ ( ~ ( in @ SV17 @ SV58 )
| ~ ( empty @ SV58 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(544,plain,
( ( ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(545,plain,
! [SV18: $i] :
( ( ( empty @ SV18 )
= $false )
| ( ( relation @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(546,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) ) )
= $false )
| ( ( ! [SY209: $i,SY210: $i] :
~ ( ~ ( ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( SY210 = empty_set ) )
| ~ ( ( SY210 != empty_set )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(547,plain,
! [SV79: $i,SV59: $i,SV20: $i] :
( ( ! [SY379: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SY379 ) )
| ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SY379 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SY379 ) )
| ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SY379 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(548,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ~ ( ~ ( ( SV80
!= ( unordered_pair @ SV21 @ SV60 ) )
| ! [SY380: $i] :
~ ( ~ ( ~ ( in @ SY380 @ SV80 )
| ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ~ ( ~ ( ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ( in @ SY380 @ SV80 ) ) ) )
| ~ ( ~ ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV80 )
| ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ~ ( ~ ( ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ( in @ SY381 @ SV80 ) ) )
| ( SV80
= ( unordered_pair @ SV21 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(549,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ~ ( ~ ( ( SV81
!= ( set_union2 @ SV22 @ SV61 ) )
| ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV81 )
| ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ~ ( ~ ( ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ( in @ SY382 @ SV81 ) ) ) )
| ~ ( ~ ! [SY383: $i] :
~ ( ~ ( ~ ( in @ SY383 @ SV81 )
| ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ~ ( ~ ( ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ( in @ SY383 @ SV81 ) ) )
| ( SV81
= ( set_union2 @ SV22 @ SV61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(550,plain,
! [SV62: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV62 ) )
= $true )
| ( ( ~ ( in @ SV62 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(551,plain,
! [SV63: $i,SV24: $i,SV82: $i] :
( ( ~ ( relation @ SV82 )
| ~ ( ~ ( ~ ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
| ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
| ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(552,plain,
! [SV64: $i,SV25: $i] :
( ( ~ ( ~ ( subset @ SV25 @ SV64 )
| ! [SY348: $i] :
( ~ ( in @ SY348 @ SV25 )
| ( in @ SY348 @ SV64 ) ) )
| ~ ( ~ ! [SY349: $i] :
( ~ ( in @ SY349 @ SV25 )
| ( in @ SY349 @ SV64 ) )
| ( subset @ SV25 @ SV64 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(553,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(554,plain,
( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
| ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(555,plain,
! [SV65: $i,SV26: $i,SV83: $i] :
( ( ~ ( relation @ SV83 )
| ~ ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV83 ) )
| ~ ( in @ SV65 @ ( relation_rng @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(556,plain,
! [SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( ! [SY230: $i] :
( ~ ( relation @ SY230 )
| ~ ( ~ ( ( SV27 != SY230 )
| ! [SY231: $i,SY232: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SV27 )
| ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SY230 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SY230 )
| ( in @ ( ordered_pair @ SY231 @ SY232 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY233: $i,SY234: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SV27 )
| ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SY230 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SY230 )
| ( in @ ( ordered_pair @ SY233 @ SY234 ) @ SV27 ) ) )
| ( SV27 = SY230 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(557,plain,
( ( ~ ( ~ ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(558,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ~ ( ~ ( ( SV84
!= ( set_intersection2 @ SV28 @ SV66 ) )
| ! [SY384: $i] :
~ ( ~ ( ~ ( in @ SY384 @ SV84 )
| ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) )
| ( in @ SY384 @ SV84 ) ) ) )
| ~ ( ~ ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV84 )
| ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) )
| ( in @ SY385 @ SV84 ) ) )
| ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(559,plain,
( ( ~ ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(560,plain,
! [SV29: $i] :
( ( ( empty @ SV29 )
= $false )
| ( ( function @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(561,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ! [SY239: $i,SY240: $i] :
~ ( ~ ( ( SY240
!= ( relation_inverse_image @ SV30 @ SY239 ) )
| ! [SY241: $i] :
~ ( ~ ( ~ ( in @ SY241 @ SY240 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY241 @ SY242 ) @ SV30 )
| ~ ( in @ SY242 @ SY239 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY241 @ SY243 ) @ SV30 )
| ~ ( in @ SY243 @ SY239 ) )
| ( in @ SY241 @ SY240 ) ) ) )
| ~ ( ~ ! [SY244: $i] :
~ ( ~ ( ~ ( in @ SY244 @ SY240 )
| ~ ! [SY245: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY244 @ SY245 ) @ SV30 )
| ~ ( in @ SY245 @ SY239 ) ) )
| ~ ( ~ ~ ! [SY246: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY244 @ SY246 ) @ SV30 )
| ~ ( in @ SY246 @ SY239 ) )
| ( in @ SY244 @ SY240 ) ) )
| ( SY240
= ( relation_inverse_image @ SV30 @ SY239 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(562,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ~ ( ~ ( ( SV85
!= ( cartesian_product2 @ SV31 @ SV67 ) )
| ! [SY386: $i] :
~ ( ~ ( ~ ( in @ SY386 @ SV85 )
| ~ ! [SY356: $i] :
~ ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY356 @ SV31 )
| ~ ( in @ SY357 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY356 @ SY357 ) ) ) )
| ~ ( ~ ~ ! [SY358: $i] :
~ ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY358 @ SV31 )
| ~ ( in @ SY359 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY358 @ SY359 ) ) )
| ( in @ SY386 @ SV85 ) ) ) )
| ~ ( ~ ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV85 )
| ~ ! [SY361: $i] :
~ ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY361 @ SV31 )
| ~ ( in @ SY362 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY361 @ SY362 ) ) ) )
| ~ ( ~ ~ ! [SY363: $i] :
~ ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV31 )
| ~ ( in @ SY364 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY363 @ SY364 ) ) )
| ( in @ SY391 @ SV85 ) ) )
| ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(563,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ! [SY259: $i] :
( ~ ( relation @ SY259 )
| ! [SY260: $i] :
( ~ ( relation @ SY260 )
| ~ ( ~ ( ( SY260
!= ( relation_composition @ SV32 @ SY259 ) )
| ! [SY261: $i,SY262: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY261 @ SY262 ) @ SY260 )
| ~ ! [SY263: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY261 @ SY263 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY263 @ SY262 ) @ SY259 ) ) )
| ~ ( ~ ~ ! [SY264: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY261 @ SY264 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY264 @ SY262 ) @ SY259 ) )
| ( in @ ( ordered_pair @ SY261 @ SY262 ) @ SY260 ) ) ) )
| ~ ( ~ ! [SY265: $i,SY266: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY265 @ SY266 ) @ SY260 )
| ~ ! [SY267: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY265 @ SY267 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY267 @ SY266 ) @ SY259 ) ) )
| ~ ( ~ ~ ! [SY268: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY265 @ SY268 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY268 @ SY266 ) @ SY259 ) )
| ( in @ ( ordered_pair @ SY265 @ SY266 ) @ SY260 ) ) )
| ( SY260
= ( relation_composition @ SV32 @ SY259 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(564,plain,
! [SV86: $i,SV68: $i,SV33: $i] :
( ( ! [SY396: $i] :
( ( ( ordered_pair @ SV33 @ SV68 )
!= ( ordered_pair @ SV86 @ SY396 ) )
| ~ ( ( SV33 != SV86 )
| ( SV68 != SY396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(565,plain,
! [SV69: $i,SV34: $i] :
( ( ( ~ ! [SY367: $i] :
~ ( ~ ( ~ ( in @ SY367 @ SV34 )
| ( in @ SY367 @ SV69 ) )
| ~ ( ~ ( in @ SY367 @ SV69 )
| ( in @ SY367 @ SV34 ) ) ) )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(566,plain,
! [SV35: $i,SV70: $i] :
( ( ( ~ ( relation @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( ( SV70
!= ( identity_relation @ SV35 ) )
| ! [SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 )
| ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) )
| ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 ) ) ) )
| ~ ( ~ ! [SY370: $i,SY371: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 )
| ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) )
| ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV35 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(567,plain,
! [SV36: $i] :
( ( ~ ( ~ ( relation @ SV36 )
| ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY279
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(568,plain,
! [SV36: $i] :
( ( ~ ( ~ ! [SY282: $i] :
~ ~ ( ~ ( in @ SY282 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY282
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(569,plain,
! [SV71: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ SV71 ) )
= $true )
| ( ( element @ SV37 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(570,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV38 )
| ~ ( relation @ SV72 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(571,plain,
! [SV39: $i] :
( ( ~ ( ( SV39 != empty_set )
| ! [SY287: $i] :
~ ( in @ SY287 @ SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[517]) ).
thf(572,plain,
! [SV39: $i] :
( ( ~ ( ~ ! [SY288: $i] :
~ ( in @ SY288 @ SV39 )
| ( SV39 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[517]) ).
thf(573,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV40 ) )
| ~ ( relation @ ( relation_dom @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(574,plain,
! [SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( ! [SY289: $i] :
( ~ ( relation @ SY289 )
| ~ ( ~ ( ( SY289
!= ( relation_inverse @ SV41 ) )
| ! [SY290: $i,SY291: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SY289 )
| ( in @ ( ordered_pair @ SY291 @ SY290 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY291 @ SY290 ) @ SV41 )
| ( in @ ( ordered_pair @ SY290 @ SY291 ) @ SY289 ) ) ) )
| ~ ( ~ ! [SY292: $i,SY293: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY292 @ SY293 ) @ SY289 )
| ( in @ ( ordered_pair @ SY293 @ SY292 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY293 @ SY292 ) @ SV41 )
| ( in @ ( ordered_pair @ SY292 @ SY293 ) @ SY289 ) ) )
| ( SY289
= ( relation_inverse @ SV41 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(575,plain,
( ( ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( relation_empty_yielding @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(576,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ~ ( ~ ( ( SV87
!= ( set_difference @ SV42 @ SV73 ) )
| ! [SY397: $i] :
~ ( ~ ( ~ ( in @ SY397 @ SV87 )
| ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) )
| ( in @ SY397 @ SV87 ) ) ) )
| ~ ( ~ ! [SY398: $i] :
~ ( ~ ( ~ ( in @ SY398 @ SV87 )
| ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) )
| ( in @ SY398 @ SV87 ) ) )
| ( SV87
= ( set_difference @ SV42 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(577,plain,
! [SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( ! [SY298: $i,SY299: $i] :
~ ( ~ ( ( SY299
!= ( relation_image @ SV43 @ SY298 ) )
| ! [SY300: $i] :
~ ( ~ ( ~ ( in @ SY300 @ SY299 )
| ~ ! [SY301: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY301 @ SY300 ) @ SV43 )
| ~ ( in @ SY301 @ SY298 ) ) )
| ~ ( ~ ~ ! [SY302: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY302 @ SY300 ) @ SV43 )
| ~ ( in @ SY302 @ SY298 ) )
| ( in @ SY300 @ SY299 ) ) ) )
| ~ ( ~ ! [SY303: $i] :
~ ( ~ ( ~ ( in @ SY303 @ SY299 )
| ~ ! [SY304: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY304 @ SY303 ) @ SV43 )
| ~ ( in @ SY304 @ SY298 ) ) )
| ~ ( ~ ~ ! [SY305: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY305 @ SY303 ) @ SV43 )
| ~ ( in @ SY305 @ SY298 ) )
| ( in @ SY303 @ SY299 ) ) )
| ( SY299
= ( relation_image @ SV43 @ SY298 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(578,plain,
! [SV74: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV44 )
| ~ ( relation @ SV74 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV44 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(579,plain,
! [SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( ! [SY307: $i] :
~ ( ~ ( ( SY307
!= ( relation_dom @ SV45 ) )
| ! [SY308: $i] :
~ ( ~ ( ~ ( in @ SY308 @ SY307 )
| ~ ! [SY309: $i] :
~ ( in @ ( ordered_pair @ SY308 @ SY309 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY310: $i] :
~ ( in @ ( ordered_pair @ SY308 @ SY310 ) @ SV45 )
| ( in @ SY308 @ SY307 ) ) ) )
| ~ ( ~ ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SY307 )
| ~ ! [SY312: $i] :
~ ( in @ ( ordered_pair @ SY311 @ SY312 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY313: $i] :
~ ( in @ ( ordered_pair @ SY311 @ SY313 ) @ SV45 )
| ( in @ SY311 @ SY307 ) ) )
| ( SY307
= ( relation_dom @ SV45 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(580,plain,
! [SV75: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( relation @ SV75 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV46 @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(581,plain,
! [SV47: $i] :
( ( ( relation @ SV47 )
= $false )
| ( ( ~ ! [SY315: $i,SY316: $i] :
~ ( in @ ( ordered_pair @ SY315 @ SY316 ) @ SV47 )
| ( SV47 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(582,plain,
! [SV76: $i,SV48: $i,SV88: $i] :
( ( ~ ( relation @ SV88 )
| ~ ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 )
| ~ ( ~ ( in @ SV48 @ ( relation_field @ SV88 ) )
| ~ ( in @ SV76 @ ( relation_field @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(583,plain,
! [SV3: $i,SV50: $i] :
( ( ~ ( ( SV50
!= ( union @ SV3 ) )
| ! [SY319: $i] :
~ ( ~ ( ~ ( in @ SY319 @ SV50 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ( in @ SY319 @ SY164 )
| ~ ( in @ SY164 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( in @ SY319 @ SY165 )
| ~ ( in @ SY165 @ SV3 ) )
| ( in @ SY319 @ SV50 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(584,plain,
! [SV3: $i,SV50: $i] :
( ( ~ ( ~ ! [SY322: $i] :
~ ( ~ ( ~ ( in @ SY322 @ SV50 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY322 @ SY167 )
| ~ ( in @ SY167 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY322 @ SY168 )
| ~ ( in @ SY168 @ SV3 ) )
| ( in @ SY322 @ SV50 ) ) )
| ( SV50
= ( union @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(585,plain,
! [SV89: $i,SV4: $i] :
( ( ( ! [SY399: $i] :
( ~ ( relation @ SY399 )
| ~ ( ~ ( ( SY399
!= ( relation_dom_restriction @ SV4 @ SV89 ) )
| ! [SY400: $i,SY401: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY400 @ SY401 ) @ SY399 )
| ~ ( ~ ( in @ SY400 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY400 @ SY401 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY400 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY400 @ SY401 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY400 @ SY401 ) @ SY399 ) ) ) )
| ~ ( ~ ! [SY402: $i,SY403: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SY399 )
| ~ ( ~ ( in @ SY402 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY402 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY402 @ SY403 ) @ SY399 ) ) )
| ( SY399
= ( relation_dom_restriction @ SV4 @ SV89 ) ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(586,plain,
! [SV51: $i,SV5: $i,SV77: $i] :
( ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY376 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY376 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY376 @ SV51 ) ) )
| ~ ( ~ ~ ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY377 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY377 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY377 @ SV51 ) )
| ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(587,plain,
! [SV6: $i,SV90: $i] :
( ( ( ~ ( relation @ SV90 )
| ~ ( ~ ( ~ ( subset @ SV6 @ SV90 )
| ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV6 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV90 ) ) )
| ~ ( ~ ! [SY406: $i,SY407: $i] :
( ~ ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV6 )
| ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV90 ) )
| ( subset @ SV6 @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(588,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV7 @ SV52 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(589,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( in @ SY329 @ SV7 )
| ~ ( in @ SY329 @ SV52 ) )
| ~ ( disjoint @ SV7 @ SV52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(590,plain,
! [SV8: $i,SV53: $i] :
( ( ~ ( ( SV53
!= ( singleton @ SV8 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV53 )
| ( SY330 = SV8 ) )
| ~ ( ( SY330 != SV8 )
| ( in @ SY330 @ SV53 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(591,plain,
! [SV8: $i,SV53: $i] :
( ( ~ ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV53 )
| ( SY331 = SV8 ) )
| ~ ( ( SY331 != SV8 )
| ( in @ SY331 @ SV53 ) ) )
| ( SV53
= ( singleton @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(592,plain,
! [SV9: $i,SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( ! [SY332: $i] :
( ~ ( relation @ SY332 )
| ~ ( ~ ( ( SY332
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
| ! [SY333: $i,SY334: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SY332 )
| ~ ( ~ ( in @ SY334 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY334 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY333 @ SY334 ) @ SY332 ) ) ) )
| ~ ( ~ ! [SY335: $i,SY336: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SY332 )
| ~ ( ~ ( in @ SY336 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY336 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY335 @ SY336 ) @ SY332 ) ) )
| ( SY332
= ( relation_rng_restriction @ SV9 @ SV54 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(593,plain,
! [SV91: $i,SV78: $i,SV55: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
| ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) )
| ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(594,plain,
! [SV56: $i,SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV12 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(595,plain,
! [SV14: $i] :
( ( ( ~ ~ ( empty @ SV14 )
| ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(596,plain,
! [SV15: $i,SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV15 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(597,plain,
! [SV16: $i,SV92: $i] :
( ( ( ~ ( ~ ( ( SV92
!= ( relation_rng @ SV16 ) )
| ! [SY408: $i] :
~ ( ~ ( ~ ( in @ SY408 @ SV92 )
| ~ ! [SY203: $i] :
~ ( in @ ( ordered_pair @ SY203 @ SY408 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY204: $i] :
~ ( in @ ( ordered_pair @ SY204 @ SY408 ) @ SV16 )
| ( in @ SY408 @ SV92 ) ) ) )
| ~ ( ~ ! [SY411: $i] :
~ ( ~ ( ~ ( in @ SY411 @ SV92 )
| ~ ! [SY206: $i] :
~ ( in @ ( ordered_pair @ SY206 @ SY411 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ ( ordered_pair @ SY207 @ SY411 ) @ SV16 )
| ( in @ SY411 @ SV92 ) ) )
| ( SV92
= ( relation_rng @ SV16 ) ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(598,plain,
! [SV58: $i,SV17: $i] :
( ( ~ ( in @ SV17 @ SV58 )
| ~ ( empty @ SV58 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(599,plain,
( ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(600,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
= $true )
| ( ( ! [SY209: $i,SY210: $i] :
~ ( ~ ( ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( SY210 = empty_set ) )
| ~ ( ( SY210 != empty_set )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(601,plain,
! [SV93: $i,SV79: $i,SV59: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
| ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) )
| ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(602,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ~ ( ( SV80
!= ( unordered_pair @ SV21 @ SV60 ) )
| ! [SY380: $i] :
~ ( ~ ( ~ ( in @ SY380 @ SV80 )
| ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ~ ( ~ ( ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ( in @ SY380 @ SV80 ) ) ) )
| ~ ( ~ ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV80 )
| ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ~ ( ~ ( ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ( in @ SY381 @ SV80 ) ) )
| ( SV80
= ( unordered_pair @ SV21 @ SV60 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(603,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ~ ( ( SV81
!= ( set_union2 @ SV22 @ SV61 ) )
| ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV81 )
| ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ~ ( ~ ( ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ( in @ SY382 @ SV81 ) ) ) )
| ~ ( ~ ! [SY383: $i] :
~ ( ~ ( ~ ( in @ SY383 @ SV81 )
| ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ~ ( ~ ( ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ( in @ SY383 @ SV81 ) ) )
| ( SV81
= ( set_union2 @ SV22 @ SV61 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(604,plain,
! [SV62: $i,SV23: $i] :
( ( ( in @ SV23 @ SV62 )
= $false )
| ( ( ~ ( in @ SV62 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(605,plain,
! [SV63: $i,SV24: $i,SV82: $i] :
( ( ( ~ ( relation @ SV82 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
| ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
| ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(606,plain,
! [SV64: $i,SV25: $i] :
( ( ~ ( ~ ( subset @ SV25 @ SV64 )
| ! [SY348: $i] :
( ~ ( in @ SY348 @ SV25 )
| ( in @ SY348 @ SV64 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(607,plain,
! [SV64: $i,SV25: $i] :
( ( ~ ( ~ ! [SY349: $i] :
( ~ ( in @ SY349 @ SV25 )
| ( in @ SY349 @ SV64 ) )
| ( subset @ SV25 @ SV64 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(608,plain,
( ( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) ) )
= $true )
| ( ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(609,plain,
! [SV65: $i,SV26: $i,SV83: $i] :
( ( ( ~ ( relation @ SV83 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV83 ) )
| ~ ( in @ SV65 @ ( relation_rng @ SV83 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(610,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( relation @ SV94 )
| ~ ( ~ ( ( SV27 != SV94 )
| ! [SY414: $i,SY415: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY416: $i,SY417: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 ) ) )
| ( SV27 = SV94 ) ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(611,plain,
( ( ~ ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(612,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ~ ( ( SV84
!= ( set_intersection2 @ SV28 @ SV66 ) )
| ! [SY384: $i] :
~ ( ~ ( ~ ( in @ SY384 @ SV84 )
| ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) )
| ( in @ SY384 @ SV84 ) ) ) )
| ~ ( ~ ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV84 )
| ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) )
| ( in @ SY385 @ SV84 ) ) )
| ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(613,plain,
( ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(614,plain,
! [SV95: $i,SV30: $i] :
( ( ( ! [SY418: $i] :
~ ( ~ ( ( SY418
!= ( relation_inverse_image @ SV30 @ SV95 ) )
| ! [SY419: $i] :
~ ( ~ ( ~ ( in @ SY419 @ SY418 )
| ~ ! [SY420: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY419 @ SY420 ) @ SV30 )
| ~ ( in @ SY420 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY419 @ SY421 ) @ SV30 )
| ~ ( in @ SY421 @ SV95 ) )
| ( in @ SY419 @ SY418 ) ) ) )
| ~ ( ~ ! [SY422: $i] :
~ ( ~ ( ~ ( in @ SY422 @ SY418 )
| ~ ! [SY423: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY423 ) @ SV30 )
| ~ ( in @ SY423 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY424: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY422 @ SY424 ) @ SV30 )
| ~ ( in @ SY424 @ SV95 ) )
| ( in @ SY422 @ SY418 ) ) )
| ( SY418
= ( relation_inverse_image @ SV30 @ SV95 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(615,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ~ ( ( SV85
!= ( cartesian_product2 @ SV31 @ SV67 ) )
| ! [SY386: $i] :
~ ( ~ ( ~ ( in @ SY386 @ SV85 )
| ~ ! [SY356: $i] :
~ ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY356 @ SV31 )
| ~ ( in @ SY357 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY356 @ SY357 ) ) ) )
| ~ ( ~ ~ ! [SY358: $i] :
~ ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY358 @ SV31 )
| ~ ( in @ SY359 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY358 @ SY359 ) ) )
| ( in @ SY386 @ SV85 ) ) ) )
| ~ ( ~ ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV85 )
| ~ ! [SY361: $i] :
~ ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY361 @ SV31 )
| ~ ( in @ SY362 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY361 @ SY362 ) ) ) )
| ~ ( ~ ~ ! [SY363: $i] :
~ ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV31 )
| ~ ( in @ SY364 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY363 @ SY364 ) ) )
| ( in @ SY391 @ SV85 ) ) )
| ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(616,plain,
! [SV32: $i,SV96: $i] :
( ( ( ~ ( relation @ SV96 )
| ! [SY425: $i] :
( ~ ( relation @ SY425 )
| ~ ( ~ ( ( SY425
!= ( relation_composition @ SV32 @ SV96 ) )
| ! [SY426: $i,SY427: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY426 @ SY427 ) @ SY425 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY426 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY427 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY426 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY427 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY426 @ SY427 ) @ SY425 ) ) ) )
| ~ ( ~ ! [SY430: $i,SY431: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY430 @ SY431 ) @ SY425 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY430 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY431 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY430 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY431 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY430 @ SY431 ) @ SY425 ) ) )
| ( SY425
= ( relation_composition @ SV32 @ SV96 ) ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(617,plain,
! [SV97: $i,SV86: $i,SV68: $i,SV33: $i] :
( ( ( ( ordered_pair @ SV33 @ SV68 )
!= ( ordered_pair @ SV86 @ SV97 ) )
| ~ ( ( SV33 != SV86 )
| ( SV68 != SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(618,plain,
! [SV69: $i,SV34: $i] :
( ( ( ! [SY367: $i] :
~ ( ~ ( ~ ( in @ SY367 @ SV34 )
| ( in @ SY367 @ SV69 ) )
| ~ ( ~ ( in @ SY367 @ SV69 )
| ( in @ SY367 @ SV34 ) ) ) )
= $false )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(619,plain,
! [SV35: $i,SV70: $i] :
( ( ( relation @ SV70 )
= $false )
| ( ( ~ ( ~ ( ( SV70
!= ( identity_relation @ SV35 ) )
| ! [SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 )
| ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) )
| ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 ) ) ) )
| ~ ( ~ ! [SY370: $i,SY371: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 )
| ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) )
| ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV35 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(620,plain,
! [SV36: $i] :
( ( ~ ( relation @ SV36 )
| ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY279
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(621,plain,
! [SV36: $i] :
( ( ~ ! [SY282: $i] :
~ ~ ( ~ ( in @ SY282 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY282
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV36 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(622,plain,
! [SV71: $i,SV37: $i] :
( ( ( in @ SV37 @ SV71 )
= $false )
| ( ( element @ SV37 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(623,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ( ~ ( relation @ SV38 )
| ~ ( relation @ SV72 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(624,plain,
! [SV39: $i] :
( ( ( SV39 != empty_set )
| ! [SY287: $i] :
~ ( in @ SY287 @ SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(625,plain,
! [SV39: $i] :
( ( ~ ! [SY288: $i] :
~ ( in @ SY288 @ SV39 )
| ( SV39 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(626,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV40 ) )
| ~ ( relation @ ( relation_dom @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(627,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 )
| ~ ( ~ ( ( SV98
!= ( relation_inverse @ SV41 ) )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 )
| ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 )
| ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 ) ) ) )
| ~ ( ~ ! [SY436: $i,SY437: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 )
| ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 )
| ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 ) ) )
| ( SV98
= ( relation_inverse @ SV41 ) ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(628,plain,
( ( ~ ( relation @ sK7_SX0 )
| ~ ( relation_empty_yielding @ sK7_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(629,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ~ ( ( SV87
!= ( set_difference @ SV42 @ SV73 ) )
| ! [SY397: $i] :
~ ( ~ ( ~ ( in @ SY397 @ SV87 )
| ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) )
| ( in @ SY397 @ SV87 ) ) ) )
| ~ ( ~ ! [SY398: $i] :
~ ( ~ ( ~ ( in @ SY398 @ SV87 )
| ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) )
| ( in @ SY398 @ SV87 ) ) )
| ( SV87
= ( set_difference @ SV42 @ SV73 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(630,plain,
! [SV99: $i,SV43: $i] :
( ( ( ! [SY438: $i] :
~ ( ~ ( ( SY438
!= ( relation_image @ SV43 @ SV99 ) )
| ! [SY439: $i] :
~ ( ~ ( ~ ( in @ SY439 @ SY438 )
| ~ ! [SY440: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY440 @ SY439 ) @ SV43 )
| ~ ( in @ SY440 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY441: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY441 @ SY439 ) @ SV43 )
| ~ ( in @ SY441 @ SV99 ) )
| ( in @ SY439 @ SY438 ) ) ) )
| ~ ( ~ ! [SY442: $i] :
~ ( ~ ( ~ ( in @ SY442 @ SY438 )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY443 @ SY442 ) @ SV43 )
| ~ ( in @ SY443 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY444 @ SY442 ) @ SV43 )
| ~ ( in @ SY444 @ SV99 ) )
| ( in @ SY442 @ SY438 ) ) )
| ( SY438
= ( relation_image @ SV43 @ SV99 ) ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(631,plain,
! [SV74: $i,SV44: $i] :
( ( ( ~ ( ~ ( relation @ SV44 )
| ~ ( relation @ SV74 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV44 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(632,plain,
! [SV45: $i,SV100: $i] :
( ( ( ~ ( ~ ( ( SV100
!= ( relation_dom @ SV45 ) )
| ! [SY445: $i] :
~ ( ~ ( ~ ( in @ SY445 @ SV100 )
| ~ ! [SY309: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY309 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY310: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY310 ) @ SV45 )
| ( in @ SY445 @ SV100 ) ) ) )
| ~ ( ~ ! [SY448: $i] :
~ ( ~ ( ~ ( in @ SY448 @ SV100 )
| ~ ! [SY312: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY312 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY313: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY313 ) @ SV45 )
| ( in @ SY448 @ SV100 ) ) )
| ( SV100
= ( relation_dom @ SV45 ) ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(633,plain,
! [SV75: $i,SV46: $i] :
( ( ( ~ ( ~ ( relation @ SV46 )
| ~ ( relation @ SV75 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV46 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(634,plain,
! [SV47: $i] :
( ( ( ~ ! [SY315: $i,SY316: $i] :
~ ( in @ ( ordered_pair @ SY315 @ SY316 ) @ SV47 ) )
= $true )
| ( ( SV47 = empty_set )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(635,plain,
! [SV76: $i,SV48: $i,SV88: $i] :
( ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 )
| ~ ( ~ ( in @ SV48 @ ( relation_field @ SV88 ) )
| ~ ( in @ SV76 @ ( relation_field @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(636,plain,
! [SV3: $i,SV50: $i] :
( ( ( SV50
!= ( union @ SV3 ) )
| ! [SY319: $i] :
~ ( ~ ( ~ ( in @ SY319 @ SV50 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ( in @ SY319 @ SY164 )
| ~ ( in @ SY164 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( in @ SY319 @ SY165 )
| ~ ( in @ SY165 @ SV3 ) )
| ( in @ SY319 @ SV50 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(637,plain,
! [SV3: $i,SV50: $i] :
( ( ~ ! [SY322: $i] :
~ ( ~ ( ~ ( in @ SY322 @ SV50 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY322 @ SY167 )
| ~ ( in @ SY167 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY322 @ SY168 )
| ~ ( in @ SY168 @ SV3 ) )
| ( in @ SY322 @ SV50 ) ) )
| ( SV50
= ( union @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(638,plain,
! [SV89: $i,SV4: $i,SV101: $i] :
( ( ( ~ ( relation @ SV101 )
| ~ ( ~ ( ( SV101
!= ( relation_dom_restriction @ SV4 @ SV89 ) )
| ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 )
| ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 ) ) ) )
| ~ ( ~ ! [SY453: $i,SY454: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 )
| ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 ) ) )
| ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(639,plain,
! [SV51: $i,SV5: $i,SV77: $i] :
( ( ( relation @ SV77 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY376 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY376 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY376 @ SV51 ) ) )
| ~ ( ~ ~ ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY377 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY377 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY377 @ SV51 ) )
| ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(640,plain,
! [SV6: $i,SV90: $i] :
( ( ( ~ ( relation @ SV90 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV6 @ SV90 )
| ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV6 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV90 ) ) )
| ~ ( ~ ! [SY406: $i,SY407: $i] :
( ~ ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV6 )
| ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV90 ) )
| ( subset @ SV6 @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(641,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV7 @ SV52 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(642,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( in @ SY329 @ SV7 )
| ~ ( in @ SY329 @ SV52 ) )
| ~ ( disjoint @ SV7 @ SV52 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(643,plain,
! [SV8: $i,SV53: $i] :
( ( ( SV53
!= ( singleton @ SV8 ) )
| ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV53 )
| ( SY330 = SV8 ) )
| ~ ( ( SY330 != SV8 )
| ( in @ SY330 @ SV53 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(644,plain,
! [SV8: $i,SV53: $i] :
( ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV53 )
| ( SY331 = SV8 ) )
| ~ ( ( SY331 != SV8 )
| ( in @ SY331 @ SV53 ) ) )
| ( SV53
= ( singleton @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(645,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( relation @ SV102 )
| ~ ( ~ ( ( SV102
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
| ! [SY455: $i,SY456: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 )
| ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 ) ) ) )
| ~ ( ~ ! [SY457: $i,SY458: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 )
| ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 ) ) )
| ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) ) ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(646,plain,
! [SV91: $i,SV78: $i,SV55: $i,SV10: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
| ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) )
| ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(647,plain,
! [SV14: $i] :
( ( ( ~ ~ ( empty @ SV14 ) )
= $true )
| ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(648,plain,
! [SV16: $i,SV92: $i] :
( ( ( ~ ( ( SV92
!= ( relation_rng @ SV16 ) )
| ! [SY408: $i] :
~ ( ~ ( ~ ( in @ SY408 @ SV92 )
| ~ ! [SY203: $i] :
~ ( in @ ( ordered_pair @ SY203 @ SY408 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY204: $i] :
~ ( in @ ( ordered_pair @ SY204 @ SY408 ) @ SV16 )
| ( in @ SY408 @ SV92 ) ) ) )
| ~ ( ~ ! [SY411: $i] :
~ ( ~ ( ~ ( in @ SY411 @ SV92 )
| ~ ! [SY206: $i] :
~ ( in @ ( ordered_pair @ SY206 @ SY411 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ ( ordered_pair @ SY207 @ SY411 ) @ SV16 )
| ( in @ SY411 @ SV92 ) ) )
| ( SV92
= ( relation_rng @ SV16 ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(649,plain,
! [SV58: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV58 ) )
= $true )
| ( ( ~ ( empty @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(650,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(651,plain,
( ( ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(652,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ! [SY209: $i,SY210: $i] :
~ ( ~ ( ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( SY210 = empty_set ) )
| ~ ( ( SY210 != empty_set )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(653,plain,
! [SV93: $i,SV79: $i,SV59: $i,SV20: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
| ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) )
| ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(654,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ~ ( ( SV80
!= ( unordered_pair @ SV21 @ SV60 ) )
| ! [SY380: $i] :
~ ( ~ ( ~ ( in @ SY380 @ SV80 )
| ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ~ ( ~ ( ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ( in @ SY380 @ SV80 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(655,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ~ ( ~ ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV80 )
| ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ~ ( ~ ( ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ( in @ SY381 @ SV80 ) ) )
| ( SV80
= ( unordered_pair @ SV21 @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(656,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ~ ( ( SV81
!= ( set_union2 @ SV22 @ SV61 ) )
| ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV81 )
| ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ~ ( ~ ( ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ( in @ SY382 @ SV81 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(657,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ~ ( ~ ! [SY383: $i] :
~ ( ~ ( ~ ( in @ SY383 @ SV81 )
| ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ~ ( ~ ( ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ( in @ SY383 @ SV81 ) ) )
| ( SV81
= ( set_union2 @ SV22 @ SV61 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(658,plain,
! [SV23: $i,SV62: $i] :
( ( ( in @ SV62 @ SV23 )
= $false )
| ( ( in @ SV23 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(659,plain,
! [SV63: $i,SV24: $i,SV82: $i] :
( ( ( relation @ SV82 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
| ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
| ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(660,plain,
! [SV64: $i,SV25: $i] :
( ( ~ ( subset @ SV25 @ SV64 )
| ! [SY348: $i] :
( ~ ( in @ SY348 @ SV25 )
| ( in @ SY348 @ SV64 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(661,plain,
! [SV64: $i,SV25: $i] :
( ( ~ ! [SY349: $i] :
( ~ ( in @ SY349 @ SV25 )
| ( in @ SY349 @ SV64 ) )
| ( subset @ SV25 @ SV64 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(662,plain,
( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
= $false )
| ( ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(663,plain,
! [SV65: $i,SV26: $i,SV83: $i] :
( ( ( relation @ SV83 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 )
| ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV83 ) )
| ~ ( in @ SV65 @ ( relation_rng @ SV83 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(664,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( relation @ SV94 ) )
= $true )
| ( ( ~ ( ~ ( ( SV27 != SV94 )
| ! [SY414: $i,SY415: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY416: $i,SY417: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 ) ) )
| ( SV27 = SV94 ) ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(665,plain,
( ( ~ ~ ( empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(666,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(667,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ~ ( ( SV84
!= ( set_intersection2 @ SV28 @ SV66 ) )
| ! [SY384: $i] :
~ ( ~ ( ~ ( in @ SY384 @ SV84 )
| ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) )
| ( in @ SY384 @ SV84 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(668,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ~ ( ~ ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV84 )
| ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) )
| ( in @ SY385 @ SV84 ) ) )
| ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(669,plain,
( ( ~ ( empty @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(670,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(671,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( ~ ( ~ ( ( SV103
!= ( relation_inverse_image @ SV30 @ SV95 ) )
| ! [SY459: $i] :
~ ( ~ ( ~ ( in @ SY459 @ SV103 )
| ~ ! [SY420: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY420 ) @ SV30 )
| ~ ( in @ SY420 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY421 ) @ SV30 )
| ~ ( in @ SY421 @ SV95 ) )
| ( in @ SY459 @ SV103 ) ) ) )
| ~ ( ~ ! [SY462: $i] :
~ ( ~ ( ~ ( in @ SY462 @ SV103 )
| ~ ! [SY423: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY423 ) @ SV30 )
| ~ ( in @ SY423 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY424: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY424 ) @ SV30 )
| ~ ( in @ SY424 @ SV95 ) )
| ( in @ SY462 @ SV103 ) ) )
| ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(672,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ~ ( ( SV85
!= ( cartesian_product2 @ SV31 @ SV67 ) )
| ! [SY386: $i] :
~ ( ~ ( ~ ( in @ SY386 @ SV85 )
| ~ ! [SY356: $i] :
~ ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY356 @ SV31 )
| ~ ( in @ SY357 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY356 @ SY357 ) ) ) )
| ~ ( ~ ~ ! [SY358: $i] :
~ ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY358 @ SV31 )
| ~ ( in @ SY359 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY358 @ SY359 ) ) )
| ( in @ SY386 @ SV85 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(673,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ~ ( ~ ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV85 )
| ~ ! [SY361: $i] :
~ ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY361 @ SV31 )
| ~ ( in @ SY362 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY361 @ SY362 ) ) ) )
| ~ ( ~ ~ ! [SY363: $i] :
~ ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV31 )
| ~ ( in @ SY364 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY363 @ SY364 ) ) )
| ( in @ SY391 @ SV85 ) ) )
| ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(674,plain,
! [SV32: $i,SV96: $i] :
( ( ( ~ ( relation @ SV96 ) )
= $true )
| ( ( ! [SY425: $i] :
( ~ ( relation @ SY425 )
| ~ ( ~ ( ( SY425
!= ( relation_composition @ SV32 @ SV96 ) )
| ! [SY426: $i,SY427: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY426 @ SY427 ) @ SY425 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY426 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY427 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY426 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY427 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY426 @ SY427 ) @ SY425 ) ) ) )
| ~ ( ~ ! [SY430: $i,SY431: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY430 @ SY431 ) @ SY425 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY430 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY431 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY430 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY431 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY430 @ SY431 ) @ SY425 ) ) )
| ( SY425
= ( relation_composition @ SV32 @ SV96 ) ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(675,plain,
! [SV97: $i,SV86: $i,SV68: $i,SV33: $i] :
( ( ( ( ordered_pair @ SV33 @ SV68 )
!= ( ordered_pair @ SV86 @ SV97 ) )
= $true )
| ( ( ~ ( ( SV33 != SV86 )
| ( SV68 != SV97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(676,plain,
! [SV34: $i,SV69: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) ) ) )
= $false )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[618]) ).
thf(677,plain,
! [SV35: $i,SV70: $i] :
( ( ( ~ ( ( SV70
!= ( identity_relation @ SV35 ) )
| ! [SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 )
| ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) )
| ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 ) ) ) )
| ~ ( ~ ! [SY370: $i,SY371: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 )
| ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) )
| ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV35 ) ) ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(678,plain,
! [SV36: $i] :
( ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY279
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(679,plain,
! [SV36: $i] :
( ( ( ~ ! [SY282: $i] :
~ ~ ( ~ ( in @ SY282 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY282
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(680,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ( relation @ SV38 )
| ~ ( relation @ SV72 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(681,plain,
! [SV39: $i] :
( ( ( SV39 != empty_set )
= $true )
| ( ( ! [SY287: $i] :
~ ( in @ SY287 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(682,plain,
! [SV39: $i] :
( ( ( ~ ! [SY288: $i] :
~ ( in @ SY288 @ SV39 ) )
= $true )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(683,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[626]) ).
thf(684,plain,
! [SV40: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[626]) ).
thf(685,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( ~ ( ~ ( ( SV98
!= ( relation_inverse @ SV41 ) )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 )
| ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 )
| ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 ) ) ) )
| ~ ( ~ ! [SY436: $i,SY437: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 )
| ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 )
| ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 ) ) )
| ( SV98
= ( relation_inverse @ SV41 ) ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(686,plain,
( ( ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(687,plain,
( ( ~ ( relation_empty_yielding @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(688,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ~ ( ( SV87
!= ( set_difference @ SV42 @ SV73 ) )
| ! [SY397: $i] :
~ ( ~ ( ~ ( in @ SY397 @ SV87 )
| ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) )
| ( in @ SY397 @ SV87 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(689,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ~ ( ~ ! [SY398: $i] :
~ ( ~ ( ~ ( in @ SY398 @ SV87 )
| ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) )
| ( in @ SY398 @ SV87 ) ) )
| ( SV87
= ( set_difference @ SV42 @ SV73 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(690,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( ~ ( ( SV104
!= ( relation_image @ SV43 @ SV99 ) )
| ! [SY465: $i] :
~ ( ~ ( ~ ( in @ SY465 @ SV104 )
| ~ ! [SY440: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY440 @ SY465 ) @ SV43 )
| ~ ( in @ SY440 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY441: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY441 @ SY465 ) @ SV43 )
| ~ ( in @ SY441 @ SV99 ) )
| ( in @ SY465 @ SV104 ) ) ) )
| ~ ( ~ ! [SY468: $i] :
~ ( ~ ( ~ ( in @ SY468 @ SV104 )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY443 @ SY468 ) @ SV43 )
| ~ ( in @ SY443 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY444 @ SY468 ) @ SV43 )
| ~ ( in @ SY444 @ SV99 ) )
| ( in @ SY468 @ SV104 ) ) )
| ( SV104
= ( relation_image @ SV43 @ SV99 ) ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(691,plain,
! [SV74: $i,SV44: $i] :
( ( ( ~ ( relation @ SV44 )
| ~ ( relation @ SV74 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV44 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(692,plain,
! [SV45: $i,SV100: $i] :
( ( ( ~ ( ( SV100
!= ( relation_dom @ SV45 ) )
| ! [SY445: $i] :
~ ( ~ ( ~ ( in @ SY445 @ SV100 )
| ~ ! [SY309: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY309 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY310: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY310 ) @ SV45 )
| ( in @ SY445 @ SV100 ) ) ) )
| ~ ( ~ ! [SY448: $i] :
~ ( ~ ( ~ ( in @ SY448 @ SV100 )
| ~ ! [SY312: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY312 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY313: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY313 ) @ SV45 )
| ( in @ SY448 @ SV100 ) ) )
| ( SV100
= ( relation_dom @ SV45 ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(693,plain,
! [SV75: $i,SV46: $i] :
( ( ( ~ ( relation @ SV46 )
| ~ ( relation @ SV75 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV46 @ SV75 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(694,plain,
! [SV47: $i] :
( ( ( ! [SY315: $i,SY316: $i] :
~ ( in @ ( ordered_pair @ SY315 @ SY316 ) @ SV47 ) )
= $false )
| ( ( SV47 = empty_set )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(695,plain,
! [SV76: $i,SV48: $i,SV88: $i] :
( ( ( relation @ SV88 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 )
| ~ ( ~ ( in @ SV48 @ ( relation_field @ SV88 ) )
| ~ ( in @ SV76 @ ( relation_field @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(696,plain,
! [SV3: $i,SV50: $i] :
( ( ( SV50
!= ( union @ SV3 ) )
= $true )
| ( ( ! [SY319: $i] :
~ ( ~ ( ~ ( in @ SY319 @ SV50 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ( in @ SY319 @ SY164 )
| ~ ( in @ SY164 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( in @ SY319 @ SY165 )
| ~ ( in @ SY165 @ SV3 ) )
| ( in @ SY319 @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(697,plain,
! [SV3: $i,SV50: $i] :
( ( ( ~ ! [SY322: $i] :
~ ( ~ ( ~ ( in @ SY322 @ SV50 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY322 @ SY167 )
| ~ ( in @ SY167 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY322 @ SY168 )
| ~ ( in @ SY168 @ SV3 ) )
| ( in @ SY322 @ SV50 ) ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(698,plain,
! [SV89: $i,SV4: $i,SV101: $i] :
( ( ( ~ ( relation @ SV101 ) )
= $true )
| ( ( ~ ( ~ ( ( SV101
!= ( relation_dom_restriction @ SV4 @ SV89 ) )
| ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 )
| ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 ) ) ) )
| ~ ( ~ ! [SY453: $i,SY454: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 )
| ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 ) ) )
| ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(699,plain,
! [SV51: $i,SV77: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY376 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY376 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY376 @ SV51 ) ) )
| ~ ( ~ ~ ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY377 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY377 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY377 @ SV51 ) )
| ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) ) ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(700,plain,
! [SV6: $i,SV90: $i] :
( ( ( relation @ SV90 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV6 @ SV90 )
| ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV6 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV90 ) ) )
| ~ ( ~ ! [SY406: $i,SY407: $i] :
( ~ ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV6 )
| ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV90 ) )
| ( subset @ SV6 @ SV90 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(701,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV7 @ SV52 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(702,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ( ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( in @ SY329 @ SV7 )
| ~ ( in @ SY329 @ SV52 ) )
| ~ ( disjoint @ SV7 @ SV52 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(703,plain,
! [SV8: $i,SV53: $i] :
( ( ( SV53
!= ( singleton @ SV8 ) )
= $true )
| ( ( ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV53 )
| ( SY330 = SV8 ) )
| ~ ( ( SY330 != SV8 )
| ( in @ SY330 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(704,plain,
! [SV8: $i,SV53: $i] :
( ( ( ~ ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV53 )
| ( SY331 = SV8 ) )
| ~ ( ( SY331 != SV8 )
| ( in @ SY331 @ SV53 ) ) ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(705,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( ~ ( ~ ( ( SV102
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
| ! [SY455: $i,SY456: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 )
| ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 ) ) ) )
| ~ ( ~ ! [SY457: $i,SY458: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 )
| ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 ) ) )
| ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) ) ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(706,plain,
! [SV91: $i,SV78: $i,SV55: $i,SV10: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
| ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(707,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) )
| ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(708,plain,
! [SV14: $i] :
( ( ( ~ ( empty @ SV14 ) )
= $false )
| ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(709,plain,
! [SV16: $i,SV92: $i] :
( ( ( ~ ( ( SV92
!= ( relation_rng @ SV16 ) )
| ! [SY408: $i] :
~ ( ~ ( ~ ( in @ SY408 @ SV92 )
| ~ ! [SY203: $i] :
~ ( in @ ( ordered_pair @ SY203 @ SY408 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY204: $i] :
~ ( in @ ( ordered_pair @ SY204 @ SY408 ) @ SV16 )
| ( in @ SY408 @ SV92 ) ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(710,plain,
! [SV16: $i,SV92: $i] :
( ( ( ~ ( ~ ! [SY411: $i] :
~ ( ~ ( ~ ( in @ SY411 @ SV92 )
| ~ ! [SY206: $i] :
~ ( in @ ( ordered_pair @ SY206 @ SY411 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ ( ordered_pair @ SY207 @ SY411 ) @ SV16 )
| ( in @ SY411 @ SV92 ) ) )
| ( SV92
= ( relation_rng @ SV16 ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(711,plain,
! [SV58: $i,SV17: $i] :
( ( ( in @ SV17 @ SV58 )
= $false )
| ( ( ~ ( empty @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(712,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(713,plain,
( ( function @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(714,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ! [SY209: $i,SY210: $i] :
~ ( ~ ( ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( SY210 = empty_set ) )
| ~ ( ( SY210 != empty_set )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(715,plain,
! [SV93: $i,SV79: $i,SV59: $i,SV20: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
| ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(716,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) )
| ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(717,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ( SV80
!= ( unordered_pair @ SV21 @ SV60 ) )
| ! [SY380: $i] :
~ ( ~ ( ~ ( in @ SY380 @ SV80 )
| ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ~ ( ~ ( ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ( in @ SY380 @ SV80 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(718,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ~ ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV80 )
| ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ~ ( ~ ( ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ( in @ SY381 @ SV80 ) ) )
| ( SV80
= ( unordered_pair @ SV21 @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(719,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ( SV81
!= ( set_union2 @ SV22 @ SV61 ) )
| ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV81 )
| ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ~ ( ~ ( ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ( in @ SY382 @ SV81 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(720,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ~ ! [SY383: $i] :
~ ( ~ ( ~ ( in @ SY383 @ SV81 )
| ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ~ ( ~ ( ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ( in @ SY383 @ SV81 ) ) )
| ( SV81
= ( set_union2 @ SV22 @ SV61 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(721,plain,
! [SV63: $i,SV82: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
| ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
| ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(722,plain,
! [SV64: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV64 ) )
= $true )
| ( ( ! [SY348: $i] :
( ~ ( in @ SY348 @ SV25 )
| ( in @ SY348 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(723,plain,
! [SV64: $i,SV25: $i] :
( ( ( ~ ! [SY349: $i] :
( ~ ( in @ SY349 @ SV25 )
| ( in @ SY349 @ SV64 ) ) )
= $true )
| ( ( subset @ SV25 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(724,plain,
( ( ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) )
= $false )
| ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(725,plain,
! [SV83: $i,SV65: $i,SV26: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV83 ) )
| ~ ( in @ SV65 @ ( relation_rng @ SV83 ) ) ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(726,plain,
! [SV27: $i,SV94: $i] :
( ( ( relation @ SV94 )
= $false )
| ( ( ~ ( ~ ( ( SV27 != SV94 )
| ! [SY414: $i,SY415: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY416: $i,SY417: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 ) ) )
| ( SV27 = SV94 ) ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(727,plain,
( ( ~ ( empty @ sK5_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[665]) ).
thf(728,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[666]) ).
thf(729,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ( SV84
!= ( set_intersection2 @ SV28 @ SV66 ) )
| ! [SY384: $i] :
~ ( ~ ( ~ ( in @ SY384 @ SV84 )
| ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) )
| ( in @ SY384 @ SV84 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(730,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ~ ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV84 )
| ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) )
| ( in @ SY385 @ SV84 ) ) )
| ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(731,plain,
( ( empty @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(732,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(733,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( ~ ( ( SV103
!= ( relation_inverse_image @ SV30 @ SV95 ) )
| ! [SY459: $i] :
~ ( ~ ( ~ ( in @ SY459 @ SV103 )
| ~ ! [SY420: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY420 ) @ SV30 )
| ~ ( in @ SY420 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY421 ) @ SV30 )
| ~ ( in @ SY421 @ SV95 ) )
| ( in @ SY459 @ SV103 ) ) ) )
| ~ ( ~ ! [SY462: $i] :
~ ( ~ ( ~ ( in @ SY462 @ SV103 )
| ~ ! [SY423: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY423 ) @ SV30 )
| ~ ( in @ SY423 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY424: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY424 ) @ SV30 )
| ~ ( in @ SY424 @ SV95 ) )
| ( in @ SY462 @ SV103 ) ) )
| ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(734,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ( SV85
!= ( cartesian_product2 @ SV31 @ SV67 ) )
| ! [SY386: $i] :
~ ( ~ ( ~ ( in @ SY386 @ SV85 )
| ~ ! [SY356: $i] :
~ ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY356 @ SV31 )
| ~ ( in @ SY357 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY356 @ SY357 ) ) ) )
| ~ ( ~ ~ ! [SY358: $i] :
~ ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY358 @ SV31 )
| ~ ( in @ SY359 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY358 @ SY359 ) ) )
| ( in @ SY386 @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[672]) ).
thf(735,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ~ ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV85 )
| ~ ! [SY361: $i] :
~ ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY361 @ SV31 )
| ~ ( in @ SY362 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY361 @ SY362 ) ) ) )
| ~ ( ~ ~ ! [SY363: $i] :
~ ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV31 )
| ~ ( in @ SY364 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY363 @ SY364 ) ) )
| ( in @ SY391 @ SV85 ) ) )
| ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[673]) ).
thf(736,plain,
! [SV32: $i,SV96: $i] :
( ( ( relation @ SV96 )
= $false )
| ( ( ! [SY425: $i] :
( ~ ( relation @ SY425 )
| ~ ( ~ ( ( SY425
!= ( relation_composition @ SV32 @ SV96 ) )
| ! [SY426: $i,SY427: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY426 @ SY427 ) @ SY425 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY426 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY427 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY426 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY427 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY426 @ SY427 ) @ SY425 ) ) ) )
| ~ ( ~ ! [SY430: $i,SY431: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY430 @ SY431 ) @ SY425 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY430 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY431 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY430 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY431 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY430 @ SY431 ) @ SY425 ) ) )
| ( SY425
= ( relation_composition @ SV32 @ SV96 ) ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(737,plain,
! [SV97: $i,SV86: $i,SV68: $i,SV33: $i] :
( ( ( ( ordered_pair @ SV33 @ SV68 )
= ( ordered_pair @ SV86 @ SV97 ) )
= $false )
| ( ( ~ ( ( SV33 != SV86 )
| ( SV68 != SV97 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(738,plain,
! [SV34: $i,SV69: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 ) )
| ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(739,plain,
! [SV35: $i,SV70: $i] :
( ( ( ~ ( ( SV70
!= ( identity_relation @ SV35 ) )
| ! [SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 )
| ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) )
| ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 ) ) ) ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(740,plain,
! [SV35: $i,SV70: $i] :
( ( ( ~ ( ~ ! [SY370: $i,SY371: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 )
| ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) )
| ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV35 ) ) ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(741,plain,
! [SV36: $i] :
( ( ( relation @ SV36 )
= $false )
| ( ( ! [SY279: $i] :
~ ~ ( ~ ( in @ SY279 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY279
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(742,plain,
! [SV36: $i] :
( ( ( ! [SY282: $i] :
~ ~ ( ~ ( in @ SY282 @ SV36 )
| ~ ! [SX2: $i,SX3: $i] :
( SY282
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(743,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ( relation @ SV38 ) )
= $true )
| ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(744,plain,
! [SV39: $i] :
( ( ( SV39 = empty_set )
= $false )
| ( ( ! [SY287: $i] :
~ ( in @ SY287 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(745,plain,
! [SV39: $i] :
( ( ( ! [SY288: $i] :
~ ( in @ SY288 @ SV39 ) )
= $false )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(746,plain,
! [SV40: $i] :
( ( ( empty @ ( relation_dom @ SV40 ) )
= $true )
| ( ( empty @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(747,plain,
! [SV40: $i] :
( ( ( relation @ ( relation_dom @ SV40 ) )
= $true )
| ( ( empty @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[684]) ).
thf(748,plain,
! [SV41: $i,SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( ~ ( ~ ( ( SV98
!= ( relation_inverse @ SV41 ) )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 )
| ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 )
| ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 ) ) ) )
| ~ ( ~ ! [SY436: $i,SY437: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 )
| ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 )
| ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 ) ) )
| ( SV98
= ( relation_inverse @ SV41 ) ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(749,plain,
( ( relation @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(750,plain,
( ( relation_empty_yielding @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(751,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ( SV87
!= ( set_difference @ SV42 @ SV73 ) )
| ! [SY397: $i] :
~ ( ~ ( ~ ( in @ SY397 @ SV87 )
| ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) )
| ( in @ SY397 @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(752,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ~ ! [SY398: $i] :
~ ( ~ ( ~ ( in @ SY398 @ SV87 )
| ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) )
| ( in @ SY398 @ SV87 ) ) )
| ( SV87
= ( set_difference @ SV42 @ SV73 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[689]) ).
thf(753,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( ( SV104
!= ( relation_image @ SV43 @ SV99 ) )
| ! [SY465: $i] :
~ ( ~ ( ~ ( in @ SY465 @ SV104 )
| ~ ! [SY440: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY440 @ SY465 ) @ SV43 )
| ~ ( in @ SY440 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY441: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY441 @ SY465 ) @ SV43 )
| ~ ( in @ SY441 @ SV99 ) )
| ( in @ SY465 @ SV104 ) ) ) )
| ~ ( ~ ! [SY468: $i] :
~ ( ~ ( ~ ( in @ SY468 @ SV104 )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY443 @ SY468 ) @ SV43 )
| ~ ( in @ SY443 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY444 @ SY468 ) @ SV43 )
| ~ ( in @ SY444 @ SV99 ) )
| ( in @ SY468 @ SV104 ) ) )
| ( SV104
= ( relation_image @ SV43 @ SV99 ) ) ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(754,plain,
! [SV74: $i,SV44: $i] :
( ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV44 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(755,plain,
! [SV45: $i,SV100: $i] :
( ( ( ~ ( ( SV100
!= ( relation_dom @ SV45 ) )
| ! [SY445: $i] :
~ ( ~ ( ~ ( in @ SY445 @ SV100 )
| ~ ! [SY309: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY309 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY310: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY310 ) @ SV45 )
| ( in @ SY445 @ SV100 ) ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(756,plain,
! [SV45: $i,SV100: $i] :
( ( ( ~ ( ~ ! [SY448: $i] :
~ ( ~ ( ~ ( in @ SY448 @ SV100 )
| ~ ! [SY312: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY312 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY313: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY313 ) @ SV45 )
| ( in @ SY448 @ SV100 ) ) )
| ( SV100
= ( relation_dom @ SV45 ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(757,plain,
! [SV75: $i,SV46: $i] :
( ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV46 @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(758,plain,
! [SV47: $i] :
( ( ( ! [SY471: $i] :
~ ( in @ ( ordered_pair @ ( sK9_SY315 @ SV47 ) @ SY471 ) @ SV47 ) )
= $false )
| ( ( SV47 = empty_set )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[694]) ).
thf(759,plain,
! [SV88: $i,SV76: $i,SV48: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV48 @ ( relation_field @ SV88 ) )
| ~ ( in @ SV76 @ ( relation_field @ SV88 ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(760,plain,
! [SV3: $i,SV50: $i] :
( ( ( SV50
= ( union @ SV3 ) )
= $false )
| ( ( ! [SY319: $i] :
~ ( ~ ( ~ ( in @ SY319 @ SV50 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ( in @ SY319 @ SY164 )
| ~ ( in @ SY164 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ( in @ SY319 @ SY165 )
| ~ ( in @ SY165 @ SV3 ) )
| ( in @ SY319 @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(761,plain,
! [SV3: $i,SV50: $i] :
( ( ( ! [SY322: $i] :
~ ( ~ ( ~ ( in @ SY322 @ SV50 )
| ~ ! [SY167: $i] :
~ ~ ( ~ ( in @ SY322 @ SY167 )
| ~ ( in @ SY167 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY322 @ SY168 )
| ~ ( in @ SY168 @ SV3 ) )
| ( in @ SY322 @ SV50 ) ) ) )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(762,plain,
! [SV89: $i,SV4: $i,SV101: $i] :
( ( ( relation @ SV101 )
= $false )
| ( ( ~ ( ~ ( ( SV101
!= ( relation_dom_restriction @ SV4 @ SV89 ) )
| ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 )
| ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 ) ) ) )
| ~ ( ~ ! [SY453: $i,SY454: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 )
| ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 ) ) )
| ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(763,plain,
! [SV51: $i,SV77: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY376 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY376 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY376 @ SV51 ) ) ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(764,plain,
! [SV51: $i,SV5: $i,SV77: $i] :
( ( ( ~ ( ~ ~ ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY377 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY377 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY377 @ SV51 ) )
| ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) ) ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(765,plain,
! [SV90: $i,SV6: $i] :
( ( ( ~ ( ~ ( subset @ SV6 @ SV90 )
| ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV6 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV90 ) ) )
| ~ ( ~ ! [SY406: $i,SY407: $i] :
( ~ ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV6 )
| ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV90 ) )
| ( subset @ SV6 @ SV90 ) ) )
= $false )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(766,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ~ ( disjoint @ SV7 @ SV52 )
| ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(767,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( in @ SY329 @ SV7 )
| ~ ( in @ SY329 @ SV52 ) )
| ~ ( disjoint @ SV7 @ SV52 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(768,plain,
! [SV8: $i,SV53: $i] :
( ( ( SV53
= ( singleton @ SV8 ) )
= $false )
| ( ( ! [SY330: $i] :
~ ( ~ ( ~ ( in @ SY330 @ SV53 )
| ( SY330 = SV8 ) )
| ~ ( ( SY330 != SV8 )
| ( in @ SY330 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(769,plain,
! [SV8: $i,SV53: $i] :
( ( ( ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ SV53 )
| ( SY331 = SV8 ) )
| ~ ( ( SY331 != SV8 )
| ( in @ SY331 @ SV53 ) ) ) )
= $false )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(770,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( relation @ SV102 )
= $false )
| ( ( ~ ( ~ ( ( SV102
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
| ! [SY455: $i,SY456: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 )
| ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 ) ) ) )
| ~ ( ~ ! [SY457: $i,SY458: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 )
| ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 ) ) )
| ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) ) ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(771,plain,
! [SV91: $i,SV78: $i,SV55: $i,SV10: $i] :
( ( ~ ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
| ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(772,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ~ ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) )
| ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(773,plain,
! [SV14: $i] :
( ( ( empty @ SV14 )
= $true )
| ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(774,plain,
! [SV16: $i,SV92: $i] :
( ( ( ( SV92
!= ( relation_rng @ SV16 ) )
| ! [SY408: $i] :
~ ( ~ ( ~ ( in @ SY408 @ SV92 )
| ~ ! [SY203: $i] :
~ ( in @ ( ordered_pair @ SY203 @ SY408 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY204: $i] :
~ ( in @ ( ordered_pair @ SY204 @ SY408 ) @ SV16 )
| ( in @ SY408 @ SV92 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(775,plain,
! [SV16: $i,SV92: $i] :
( ( ( ~ ! [SY411: $i] :
~ ( ~ ( ~ ( in @ SY411 @ SV92 )
| ~ ! [SY206: $i] :
~ ( in @ ( ordered_pair @ SY206 @ SY411 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ ( ordered_pair @ SY207 @ SY411 ) @ SV16 )
| ( in @ SY411 @ SV92 ) ) )
| ( SV92
= ( relation_rng @ SV16 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(776,plain,
! [SV17: $i,SV58: $i] :
( ( ( empty @ SV58 )
= $false )
| ( ( in @ SV17 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(777,plain,
! [SV19: $i] :
( ( ( function @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( ! [SY209: $i,SY210: $i] :
~ ( ~ ( ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY209 @ SY210 ) @ SV19 )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY209 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY210
!= ( apply @ SV19 @ SY209 ) )
| ( SY210 = empty_set ) )
| ~ ( ( SY210 != empty_set )
| ( SY210
= ( apply @ SV19 @ SY209 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(778,plain,
! [SV93: $i,SV79: $i,SV59: $i,SV20: $i] :
( ( ~ ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
| ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(779,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ~ ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) )
| ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(780,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ( SV80
!= ( unordered_pair @ SV21 @ SV60 ) )
= $true )
| ( ( ! [SY380: $i] :
~ ( ~ ( ~ ( in @ SY380 @ SV80 )
| ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ~ ( ~ ( ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ( in @ SY380 @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(781,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ( ~ ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV80 )
| ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ~ ( ~ ( ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ( in @ SY381 @ SV80 ) ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(782,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ( SV81
!= ( set_union2 @ SV22 @ SV61 ) )
= $true )
| ( ( ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV81 )
| ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ~ ( ~ ( ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ( in @ SY382 @ SV81 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(783,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ( ~ ! [SY383: $i] :
~ ( ~ ( ~ ( in @ SY383 @ SV81 )
| ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ~ ( ~ ( ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ( in @ SY383 @ SV81 ) ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(784,plain,
! [SV63: $i,SV82: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
| ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(785,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
| ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(786,plain,
! [SV64: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV64 )
= $false )
| ( ( ! [SY348: $i] :
( ~ ( in @ SY348 @ SV25 )
| ( in @ SY348 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(787,plain,
! [SV64: $i,SV25: $i] :
( ( ( ! [SY349: $i] :
( ~ ( in @ SY349 @ SV25 )
| ( in @ SY349 @ SV64 ) ) )
= $false )
| ( ( subset @ SV25 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(788,plain,
! [SV83: $i,SV65: $i,SV26: $i] :
( ( ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 )
= $false )
| ( ( ~ ( ~ ( in @ SV26 @ ( relation_dom @ SV83 ) )
| ~ ( in @ SV65 @ ( relation_rng @ SV83 ) ) ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(789,plain,
! [SV94: $i,SV27: $i] :
( ( ( ~ ( ( SV27 != SV94 )
| ! [SY414: $i,SY415: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY416: $i,SY417: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 ) ) )
| ( SV27 = SV94 ) ) )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(790,plain,
( ( empty @ sK5_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(791,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ( SV84
!= ( set_intersection2 @ SV28 @ SV66 ) )
= $true )
| ( ( ! [SY384: $i] :
~ ( ~ ( ~ ( in @ SY384 @ SV84 )
| ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) )
| ( in @ SY384 @ SV84 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(792,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ( ~ ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV84 )
| ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) )
| ( in @ SY385 @ SV84 ) ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(793,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( ~ ( ( SV103
!= ( relation_inverse_image @ SV30 @ SV95 ) )
| ! [SY459: $i] :
~ ( ~ ( ~ ( in @ SY459 @ SV103 )
| ~ ! [SY420: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY420 ) @ SV30 )
| ~ ( in @ SY420 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY421 ) @ SV30 )
| ~ ( in @ SY421 @ SV95 ) )
| ( in @ SY459 @ SV103 ) ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(794,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( ~ ( ~ ! [SY462: $i] :
~ ( ~ ( ~ ( in @ SY462 @ SV103 )
| ~ ! [SY423: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY423 ) @ SV30 )
| ~ ( in @ SY423 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY424: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY424 ) @ SV30 )
| ~ ( in @ SY424 @ SV95 ) )
| ( in @ SY462 @ SV103 ) ) )
| ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(795,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ( SV85
!= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true )
| ( ( ! [SY386: $i] :
~ ( ~ ( ~ ( in @ SY386 @ SV85 )
| ~ ! [SY356: $i] :
~ ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY356 @ SV31 )
| ~ ( in @ SY357 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY356 @ SY357 ) ) ) )
| ~ ( ~ ~ ! [SY358: $i] :
~ ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY358 @ SV31 )
| ~ ( in @ SY359 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY358 @ SY359 ) ) )
| ( in @ SY386 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(796,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ( ~ ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV85 )
| ~ ! [SY361: $i] :
~ ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY361 @ SV31 )
| ~ ( in @ SY362 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY361 @ SY362 ) ) ) )
| ~ ( ~ ~ ! [SY363: $i] :
~ ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV31 )
| ~ ( in @ SY364 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY363 @ SY364 ) ) )
| ( in @ SY391 @ SV85 ) ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(797,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ~ ( relation @ SV105 )
| ~ ( ~ ( ( SV105
!= ( relation_composition @ SV32 @ SV96 ) )
| ! [SY472: $i,SY473: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY473 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY473 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 ) ) ) )
| ~ ( ~ ! [SY476: $i,SY477: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY477 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY477 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 ) ) )
| ( SV105
= ( relation_composition @ SV32 @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(798,plain,
! [SV97: $i,SV68: $i,SV86: $i,SV33: $i] :
( ( ( ( SV33 != SV86 )
| ( SV68 != SV97 ) )
= $false )
| ( ( ( ordered_pair @ SV33 @ SV68 )
= ( ordered_pair @ SV86 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(799,plain,
! [SV34: $i,SV69: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(800,plain,
! [SV35: $i,SV70: $i] :
( ( ( ( SV70
!= ( identity_relation @ SV35 ) )
| ! [SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 )
| ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) )
| ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(801,plain,
! [SV35: $i,SV70: $i] :
( ( ( ~ ! [SY370: $i,SY371: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 )
| ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) )
| ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 ) ) )
| ( SV70
= ( identity_relation @ SV35 ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(802,plain,
! [SV36: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( in @ SV106 @ SV36 )
| ~ ! [SY480: $i,SY481: $i] :
( SV106
!= ( ordered_pair @ SY480 @ SY481 ) ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(803,plain,
! [SV36: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY282 @ SV36 ) @ SV36 )
| ~ ! [SY482: $i,SY483: $i] :
( ( sK10_SY282 @ SV36 )
!= ( ordered_pair @ SY482 @ SY483 ) ) ) )
= $false )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[742]) ).
thf(804,plain,
! [SV72: $i,SV38: $i] :
( ( ( relation @ SV38 )
= $false )
| ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(805,plain,
! [SV39: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV39 ) )
= $true )
| ( ( SV39 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(806,plain,
! [SV39: $i] :
( ( ( ~ ( in @ ( sK11_SY288 @ SV39 ) @ SV39 ) )
= $false )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[745]) ).
thf(807,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ( ( SV98
!= ( relation_inverse @ SV41 ) )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 )
| ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 )
| ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 ) ) ) )
| ~ ( ~ ! [SY436: $i,SY437: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 )
| ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 )
| ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 ) ) )
| ( SV98
= ( relation_inverse @ SV41 ) ) ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(808,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ( SV87
!= ( set_difference @ SV42 @ SV73 ) )
= $true )
| ( ( ! [SY397: $i] :
~ ( ~ ( ~ ( in @ SY397 @ SV87 )
| ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) )
| ( in @ SY397 @ SV87 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(809,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ( ~ ! [SY398: $i] :
~ ( ~ ( ~ ( in @ SY398 @ SV87 )
| ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) )
| ( in @ SY398 @ SV87 ) ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(810,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( ( SV104
!= ( relation_image @ SV43 @ SV99 ) )
| ! [SY465: $i] :
~ ( ~ ( ~ ( in @ SY465 @ SV104 )
| ~ ! [SY440: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY440 @ SY465 ) @ SV43 )
| ~ ( in @ SY440 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY441: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY441 @ SY465 ) @ SV43 )
| ~ ( in @ SY441 @ SV99 ) )
| ( in @ SY465 @ SV104 ) ) ) ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(811,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( ~ ! [SY468: $i] :
~ ( ~ ( ~ ( in @ SY468 @ SV104 )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY443 @ SY468 ) @ SV43 )
| ~ ( in @ SY443 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY444 @ SY468 ) @ SV43 )
| ~ ( in @ SY444 @ SV99 ) )
| ( in @ SY468 @ SV104 ) ) )
| ( SV104
= ( relation_image @ SV43 @ SV99 ) ) ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(812,plain,
! [SV74: $i,SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV44 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(813,plain,
! [SV45: $i,SV100: $i] :
( ( ( ( SV100
!= ( relation_dom @ SV45 ) )
| ! [SY445: $i] :
~ ( ~ ( ~ ( in @ SY445 @ SV100 )
| ~ ! [SY309: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY309 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY310: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY310 ) @ SV45 )
| ( in @ SY445 @ SV100 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(814,plain,
! [SV45: $i,SV100: $i] :
( ( ( ~ ! [SY448: $i] :
~ ( ~ ( ~ ( in @ SY448 @ SV100 )
| ~ ! [SY312: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY312 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY313: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY313 ) @ SV45 )
| ( in @ SY448 @ SV100 ) ) )
| ( SV100
= ( relation_dom @ SV45 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(815,plain,
! [SV75: $i,SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV46 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(816,plain,
! [SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_SY315 @ SV47 ) @ ( sK12_SY471 @ SV47 ) ) @ SV47 ) )
= $false )
| ( ( SV47 = empty_set )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[758]) ).
thf(817,plain,
! [SV88: $i,SV76: $i,SV48: $i] :
( ( ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 )
= $false )
| ( ( ~ ( ~ ( in @ SV48 @ ( relation_field @ SV88 ) )
| ~ ( in @ SV76 @ ( relation_field @ SV88 ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(818,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV108 @ SV50 )
| ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SV108 @ SY484 )
| ~ ( in @ SY484 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY485: $i] :
~ ~ ( ~ ( in @ SV108 @ SY485 )
| ~ ( in @ SY485 @ SV3 ) )
| ( in @ SV108 @ SV50 ) ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(819,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
| ~ ! [SY486: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY486 )
| ~ ( in @ SY486 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) ) )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[761]) ).
thf(820,plain,
! [SV89: $i,SV4: $i,SV101: $i] :
( ( ( ~ ( ( SV101
!= ( relation_dom_restriction @ SV4 @ SV89 ) )
| ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 )
| ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 ) ) ) )
| ~ ( ~ ! [SY453: $i,SY454: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 )
| ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 ) ) )
| ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) ) ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(821,plain,
! [SV51: $i,SV77: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY376 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY376 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY376 @ SV51 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[763]) ).
thf(822,plain,
! [SV51: $i,SV5: $i,SV77: $i] :
( ( ( ~ ~ ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY377 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY377 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY377 @ SV51 ) )
| ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[764]) ).
thf(823,plain,
! [SV90: $i,SV6: $i] :
( ( ( ~ ( ~ ( subset @ SV6 @ SV90 )
| ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV6 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV90 ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(824,plain,
! [SV90: $i,SV6: $i] :
( ( ( ~ ( ~ ! [SY406: $i,SY407: $i] :
( ~ ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV6 )
| ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV90 ) )
| ( subset @ SV6 @ SV90 ) ) )
= $false )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(825,plain,
! [SV52: $i,SV7: $i] :
( ( ( ~ ~ ( disjoint @ SV7 @ SV52 ) )
= $true )
| ( ( ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(826,plain,
! [SV52: $i,SV7: $i] :
( ( ( ~ ~ ! [SY329: $i] :
~ ~ ( ~ ( in @ SY329 @ SV7 )
| ~ ( in @ SY329 @ SV52 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(827,plain,
! [SV8: $i,SV53: $i,SV109: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV109 @ SV53 )
| ( SV109 = SV8 ) )
| ~ ( ( SV109 != SV8 )
| ( in @ SV109 @ SV53 ) ) ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(828,plain,
! [SV53: $i,SV8: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
| ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 ) )
| ~ ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
| ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) ) ) )
= $false )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[769]) ).
thf(829,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( ( SV102
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
| ! [SY455: $i,SY456: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 )
| ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 ) ) ) )
| ~ ( ~ ! [SY457: $i,SY458: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 )
| ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 ) ) )
| ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) ) ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(830,plain,
! [SV91: $i,SV78: $i,SV55: $i,SV10: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(831,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(832,plain,
! [SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( empty @ SV14 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(833,plain,
! [SV16: $i,SV92: $i] :
( ( ( SV92
!= ( relation_rng @ SV16 ) )
= $true )
| ( ( ! [SY408: $i] :
~ ( ~ ( ~ ( in @ SY408 @ SV92 )
| ~ ! [SY203: $i] :
~ ( in @ ( ordered_pair @ SY203 @ SY408 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY204: $i] :
~ ( in @ ( ordered_pair @ SY204 @ SY408 ) @ SV16 )
| ( in @ SY408 @ SV92 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(834,plain,
! [SV16: $i,SV92: $i] :
( ( ( ~ ! [SY411: $i] :
~ ( ~ ( ~ ( in @ SY411 @ SV92 )
| ~ ! [SY206: $i] :
~ ( in @ ( ordered_pair @ SY206 @ SY411 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ ( ordered_pair @ SY207 @ SY411 ) @ SV16 )
| ( in @ SY411 @ SV92 ) ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(835,plain,
! [SV19: $i,SV110: $i] :
( ( ( ! [SY488: $i] :
~ ( ~ ( ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY488
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SY488 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV110 @ SY488 ) @ SV19 )
| ( SY488
= ( apply @ SV19 @ SV110 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SY488
!= ( apply @ SV19 @ SV110 ) )
| ( SY488 = empty_set ) )
| ~ ( ( SY488 != empty_set )
| ( SY488
= ( apply @ SV19 @ SV110 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(836,plain,
! [SV93: $i,SV79: $i,SV59: $i,SV20: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(837,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(838,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( ~ ( ~ ( in @ SY380 @ SV80 )
| ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ~ ( ~ ( ( SY380 = SV21 )
| ( SY380 = SV60 ) )
| ( in @ SY380 @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(839,plain,
! [SV60: $i,SV21: $i,SV80: $i] :
( ( ( ! [SY381: $i] :
~ ( ~ ( ~ ( in @ SY381 @ SV80 )
| ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ~ ( ~ ( ( SY381 = SV21 )
| ( SY381 = SV60 ) )
| ( in @ SY381 @ SV80 ) ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(840,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false )
| ( ( ! [SY382: $i] :
~ ( ~ ( ~ ( in @ SY382 @ SV81 )
| ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ~ ( ~ ( ( in @ SY382 @ SV22 )
| ( in @ SY382 @ SV61 ) )
| ( in @ SY382 @ SV81 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(841,plain,
! [SV61: $i,SV22: $i,SV81: $i] :
( ( ( ! [SY383: $i] :
~ ( ~ ( ~ ( in @ SY383 @ SV81 )
| ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ~ ( ~ ( ( in @ SY383 @ SV22 )
| ( in @ SY383 @ SV61 ) )
| ( in @ SY383 @ SV81 ) ) ) )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(842,plain,
! [SV63: $i,SV82: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
| ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(843,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
| ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(844,plain,
! [SV64: $i,SV25: $i,SV111: $i] :
( ( ( ~ ( in @ SV111 @ SV25 )
| ( in @ SV111 @ SV64 ) )
= $true )
| ( ( subset @ SV25 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(845,plain,
! [SV25: $i,SV64: $i] :
( ( ( ~ ( in @ ( sK15_SY349 @ SV64 @ SV25 ) @ SV25 )
| ( in @ ( sK15_SY349 @ SV64 @ SV25 ) @ SV64 ) )
= $false )
| ( ( subset @ SV25 @ SV64 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[787]) ).
thf(846,plain,
! [SV65: $i,SV83: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( relation_dom @ SV83 ) )
| ~ ( in @ SV65 @ ( relation_rng @ SV83 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(847,plain,
! [SV94: $i,SV27: $i] :
( ( ( ~ ( ( SV27 != SV94 )
| ! [SY414: $i,SY415: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 ) ) ) ) )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(848,plain,
! [SV94: $i,SV27: $i] :
( ( ( ~ ( ~ ! [SY416: $i,SY417: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 ) ) )
| ( SV27 = SV94 ) ) )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(849,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false )
| ( ( ! [SY384: $i] :
~ ( ~ ( ~ ( in @ SY384 @ SV84 )
| ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY384 @ SV28 )
| ~ ( in @ SY384 @ SV66 ) )
| ( in @ SY384 @ SV84 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(850,plain,
! [SV66: $i,SV28: $i,SV84: $i] :
( ( ( ! [SY385: $i] :
~ ( ~ ( ~ ( in @ SY385 @ SV84 )
| ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY385 @ SV28 )
| ~ ( in @ SY385 @ SV66 ) )
| ( in @ SY385 @ SV84 ) ) ) )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(851,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( ( SV103
!= ( relation_inverse_image @ SV30 @ SV95 ) )
| ! [SY459: $i] :
~ ( ~ ( ~ ( in @ SY459 @ SV103 )
| ~ ! [SY420: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY420 ) @ SV30 )
| ~ ( in @ SY420 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY421 ) @ SV30 )
| ~ ( in @ SY421 @ SV95 ) )
| ( in @ SY459 @ SV103 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(852,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( ~ ! [SY462: $i] :
~ ( ~ ( ~ ( in @ SY462 @ SV103 )
| ~ ! [SY423: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY423 ) @ SV30 )
| ~ ( in @ SY423 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY424: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY424 ) @ SV30 )
| ~ ( in @ SY424 @ SV95 ) )
| ( in @ SY462 @ SV103 ) ) )
| ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(853,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false )
| ( ( ! [SY386: $i] :
~ ( ~ ( ~ ( in @ SY386 @ SV85 )
| ~ ! [SY356: $i] :
~ ~ ! [SY357: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY356 @ SV31 )
| ~ ( in @ SY357 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY356 @ SY357 ) ) ) )
| ~ ( ~ ~ ! [SY358: $i] :
~ ~ ! [SY359: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY358 @ SV31 )
| ~ ( in @ SY359 @ SV67 ) )
| ( SY386
!= ( ordered_pair @ SY358 @ SY359 ) ) )
| ( in @ SY386 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(854,plain,
! [SV67: $i,SV31: $i,SV85: $i] :
( ( ( ! [SY391: $i] :
~ ( ~ ( ~ ( in @ SY391 @ SV85 )
| ~ ! [SY361: $i] :
~ ~ ! [SY362: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY361 @ SV31 )
| ~ ( in @ SY362 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY361 @ SY362 ) ) ) )
| ~ ( ~ ~ ! [SY363: $i] :
~ ~ ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY363 @ SV31 )
| ~ ( in @ SY364 @ SV67 ) )
| ( SY391
!= ( ordered_pair @ SY363 @ SY364 ) ) )
| ( in @ SY391 @ SV85 ) ) ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(855,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ~ ( relation @ SV105 ) )
= $true )
| ( ( ~ ( ~ ( ( SV105
!= ( relation_composition @ SV32 @ SV96 ) )
| ! [SY472: $i,SY473: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY473 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY473 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 ) ) ) )
| ~ ( ~ ! [SY476: $i,SY477: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY477 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY477 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 ) ) )
| ( SV105
= ( relation_composition @ SV32 @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(856,plain,
! [SV97: $i,SV68: $i,SV86: $i,SV33: $i] :
( ( ( SV33 != SV86 )
= $false )
| ( ( ( ordered_pair @ SV33 @ SV68 )
= ( ordered_pair @ SV86 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(857,plain,
! [SV86: $i,SV33: $i,SV97: $i,SV68: $i] :
( ( ( SV68 != SV97 )
= $false )
| ( ( ( ordered_pair @ SV33 @ SV68 )
= ( ordered_pair @ SV86 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(858,plain,
! [SV34: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(859,plain,
! [SV35: $i,SV70: $i] :
( ( ( SV70
!= ( identity_relation @ SV35 ) )
= $true )
| ( ( ! [SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 )
| ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) )
| ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(860,plain,
! [SV35: $i,SV70: $i] :
( ( ( ~ ! [SY370: $i,SY371: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 )
| ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) )
| ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 ) ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(861,plain,
! [SV36: $i,SV106: $i] :
( ( ( ~ ( ~ ( in @ SV106 @ SV36 )
| ~ ! [SY480: $i,SY481: $i] :
( SV106
!= ( ordered_pair @ SY480 @ SY481 ) ) ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(862,plain,
! [SV36: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY282 @ SV36 ) @ SV36 )
| ~ ! [SY482: $i,SY483: $i] :
( ( sK10_SY282 @ SV36 )
!= ( ordered_pair @ SY482 @ SY483 ) ) ) )
= $true )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(863,plain,
! [SV38: $i,SV72: $i] :
( ( ( relation @ SV72 )
= $false )
| ( ( relation @ SV38 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(864,plain,
! [SV39: $i,SV107: $i] :
( ( ( in @ SV107 @ SV39 )
= $false )
| ( ( SV39 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(865,plain,
! [SV39: $i] :
( ( ( in @ ( sK11_SY288 @ SV39 ) @ SV39 )
= $true )
| ( ( SV39 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(866,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ( ( SV98
!= ( relation_inverse @ SV41 ) )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 )
| ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 )
| ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 ) ) ) ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(867,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ( ~ ! [SY436: $i,SY437: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 )
| ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 )
| ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 ) ) )
| ( SV98
= ( relation_inverse @ SV41 ) ) ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(868,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false )
| ( ( ! [SY397: $i] :
~ ( ~ ( ~ ( in @ SY397 @ SV87 )
| ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY397 @ SV42 )
| ~ ~ ( in @ SY397 @ SV73 ) )
| ( in @ SY397 @ SV87 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(869,plain,
! [SV73: $i,SV42: $i,SV87: $i] :
( ( ( ! [SY398: $i] :
~ ( ~ ( ~ ( in @ SY398 @ SV87 )
| ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY398 @ SV42 )
| ~ ~ ( in @ SY398 @ SV73 ) )
| ( in @ SY398 @ SV87 ) ) ) )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(870,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ( SV104
!= ( relation_image @ SV43 @ SV99 ) )
| ! [SY465: $i] :
~ ( ~ ( ~ ( in @ SY465 @ SV104 )
| ~ ! [SY440: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY440 @ SY465 ) @ SV43 )
| ~ ( in @ SY440 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY441: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY441 @ SY465 ) @ SV43 )
| ~ ( in @ SY441 @ SV99 ) )
| ( in @ SY465 @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(871,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ! [SY468: $i] :
~ ( ~ ( ~ ( in @ SY468 @ SV104 )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY443 @ SY468 ) @ SV43 )
| ~ ( in @ SY443 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY444 @ SY468 ) @ SV43 )
| ~ ( in @ SY444 @ SV99 ) )
| ( in @ SY468 @ SV104 ) ) )
| ( SV104
= ( relation_image @ SV43 @ SV99 ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(872,plain,
! [SV44: $i,SV74: $i] :
( ( ( relation @ SV74 )
= $false )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ ( relation_composition @ SV44 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(873,plain,
! [SV45: $i,SV100: $i] :
( ( ( SV100
!= ( relation_dom @ SV45 ) )
= $true )
| ( ( ! [SY445: $i] :
~ ( ~ ( ~ ( in @ SY445 @ SV100 )
| ~ ! [SY309: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY309 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY310: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY310 ) @ SV45 )
| ( in @ SY445 @ SV100 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(874,plain,
! [SV45: $i,SV100: $i] :
( ( ( ~ ! [SY448: $i] :
~ ( ~ ( ~ ( in @ SY448 @ SV100 )
| ~ ! [SY312: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY312 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY313: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY313 ) @ SV45 )
| ( in @ SY448 @ SV100 ) ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(875,plain,
! [SV46: $i,SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ ( set_union2 @ SV46 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(876,plain,
! [SV47: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_SY315 @ SV47 ) @ ( sK12_SY471 @ SV47 ) ) @ SV47 )
= $true )
| ( ( SV47 = empty_set )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(877,plain,
! [SV76: $i,SV88: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( relation_field @ SV88 ) )
| ~ ( in @ SV76 @ ( relation_field @ SV88 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(878,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ SV108 @ SV50 )
| ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SV108 @ SY484 )
| ~ ( in @ SY484 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY485: $i] :
~ ~ ( ~ ( in @ SV108 @ SY485 )
| ~ ( in @ SY485 @ SV3 ) )
| ( in @ SV108 @ SV50 ) ) )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(879,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
| ~ ! [SY486: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY486 )
| ~ ( in @ SY486 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(880,plain,
! [SV89: $i,SV4: $i,SV101: $i] :
( ( ( ~ ( ( SV101
!= ( relation_dom_restriction @ SV4 @ SV89 ) )
| ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 )
| ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 ) ) ) ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(881,plain,
! [SV4: $i,SV89: $i,SV101: $i] :
( ( ( ~ ( ~ ! [SY453: $i,SY454: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 )
| ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 ) ) )
| ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) ) ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(882,plain,
! [SV51: $i,SV77: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) ) )
= $true )
| ( ( ~ ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY376 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY376 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY376 @ SV51 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(883,plain,
! [SV51: $i,SV5: $i,SV77: $i] :
( ( ( ~ ~ ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY377 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY377 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY377 @ SV51 ) ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(884,plain,
! [SV90: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV90 )
| ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV6 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV90 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(885,plain,
! [SV90: $i,SV6: $i] :
( ( ( ~ ! [SY406: $i,SY407: $i] :
( ~ ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV6 )
| ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV90 ) )
| ( subset @ SV6 @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(886,plain,
! [SV52: $i,SV7: $i] :
( ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $false )
| ( ( ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(887,plain,
! [SV52: $i,SV7: $i] :
( ( ( ~ ! [SY329: $i] :
~ ~ ( ~ ( in @ SY329 @ SV7 )
| ~ ( in @ SY329 @ SV52 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(888,plain,
! [SV8: $i,SV53: $i,SV109: $i] :
( ( ( ~ ( ~ ( in @ SV109 @ SV53 )
| ( SV109 = SV8 ) )
| ~ ( ( SV109 != SV8 )
| ( in @ SV109 @ SV53 ) ) )
= $false )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(889,plain,
! [SV53: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
| ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 ) )
| ~ ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
| ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(890,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( ( SV102
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
| ! [SY455: $i,SY456: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 )
| ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 ) ) ) ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(891,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( ~ ! [SY457: $i,SY458: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 )
| ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 ) ) )
| ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) ) ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(892,plain,
! [SV91: $i,SV78: $i,SV55: $i,SV10: $i] :
( ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(893,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(894,plain,
! [SV14: $i] :
( ( ( empty @ ( relation_dom @ SV14 ) )
= $false )
| ( ( empty @ SV14 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(895,plain,
! [SV16: $i,SV92: $i] :
( ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( ! [SY408: $i] :
~ ( ~ ( ~ ( in @ SY408 @ SV92 )
| ~ ! [SY203: $i] :
~ ( in @ ( ordered_pair @ SY203 @ SY408 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY204: $i] :
~ ( in @ ( ordered_pair @ SY204 @ SY408 ) @ SV16 )
| ( in @ SY408 @ SV92 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(896,plain,
! [SV16: $i,SV92: $i] :
( ( ( ! [SY411: $i] :
~ ( ~ ( ~ ( in @ SY411 @ SV92 )
| ~ ! [SY206: $i] :
~ ( in @ ( ordered_pair @ SY206 @ SY411 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ( in @ ( ordered_pair @ SY207 @ SY411 ) @ SV16 )
| ( in @ SY411 @ SV92 ) ) ) )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(897,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(898,plain,
! [SV93: $i,SV79: $i,SV59: $i,SV20: $i] :
( ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(899,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(900,plain,
! [SV60: $i,SV21: $i,SV80: $i,SV113: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV113 @ SV80 )
| ( SV113 = SV21 )
| ( SV113 = SV60 ) )
| ~ ( ~ ( ( SV113 = SV21 )
| ( SV113 = SV60 ) )
| ( in @ SV113 @ SV80 ) ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(901,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ~ ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[839]) ).
thf(902,plain,
! [SV61: $i,SV22: $i,SV81: $i,SV114: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV114 @ SV81 )
| ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
| ~ ( ~ ( ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
| ( in @ SV114 @ SV81 ) ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(903,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ~ ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) ) ) )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[841]) ).
thf(904,plain,
! [SV63: $i,SV82: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(905,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) )
= $true )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(906,plain,
! [SV64: $i,SV25: $i,SV111: $i] :
( ( ( ~ ( in @ SV111 @ SV25 ) )
= $true )
| ( ( in @ SV111 @ SV64 )
= $true )
| ( ( subset @ SV25 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(907,plain,
! [SV25: $i,SV64: $i] :
( ( ( ~ ( in @ ( sK15_SY349 @ SV64 @ SV25 ) @ SV25 ) )
= $false )
| ( ( subset @ SV25 @ SV64 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(908,plain,
! [SV25: $i,SV64: $i] :
( ( ( in @ ( sK15_SY349 @ SV64 @ SV25 ) @ SV64 )
= $false )
| ( ( subset @ SV25 @ SV64 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(909,plain,
! [SV65: $i,SV83: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( relation_dom @ SV83 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(910,plain,
! [SV26: $i,SV83: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ ( relation_rng @ SV83 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(911,plain,
! [SV94: $i,SV27: $i] :
( ( ( ( SV27 != SV94 )
| ! [SY414: $i,SY415: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 ) ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(912,plain,
! [SV94: $i,SV27: $i] :
( ( ( ~ ! [SY416: $i,SY417: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 ) ) )
| ( SV27 = SV94 ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(913,plain,
! [SV66: $i,SV28: $i,SV84: $i,SV115: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV115 @ SV84 )
| ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) )
| ( in @ SV115 @ SV84 ) ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(914,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
| ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) ) )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[850]) ).
thf(915,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( SV103
!= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( ! [SY459: $i] :
~ ( ~ ( ~ ( in @ SY459 @ SV103 )
| ~ ! [SY420: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY420 ) @ SV30 )
| ~ ( in @ SY420 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY421 ) @ SV30 )
| ~ ( in @ SY421 @ SV95 ) )
| ( in @ SY459 @ SV103 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(916,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( ~ ! [SY462: $i] :
~ ( ~ ( ~ ( in @ SY462 @ SV103 )
| ~ ! [SY423: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY423 ) @ SV30 )
| ~ ( in @ SY423 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY424: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY424 ) @ SV30 )
| ~ ( in @ SY424 @ SV95 ) )
| ( in @ SY462 @ SV103 ) ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(917,plain,
! [SV67: $i,SV31: $i,SV85: $i,SV116: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV116 @ SV85 )
| ~ ! [SY489: $i] :
~ ~ ! [SY490: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY489 @ SV31 )
| ~ ( in @ SY490 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY489 @ SY490 ) ) ) )
| ~ ( ~ ~ ! [SY491: $i] :
~ ~ ! [SY492: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY491 @ SV31 )
| ~ ( in @ SY492 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY491 @ SY492 ) ) )
| ( in @ SV116 @ SV85 ) ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(918,plain,
! [SV85: $i,SV31: $i,SV67: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
| ~ ! [SY493: $i] :
~ ~ ! [SY494: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY493 @ SV31 )
| ~ ( in @ SY494 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY493 @ SY494 ) ) ) )
| ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[854]) ).
thf(919,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( relation @ SV105 )
= $false )
| ( ( ~ ( ~ ( ( SV105
!= ( relation_composition @ SV32 @ SV96 ) )
| ! [SY472: $i,SY473: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY473 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY473 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 ) ) ) )
| ~ ( ~ ! [SY476: $i,SY477: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY477 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY477 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 ) ) )
| ( SV105
= ( relation_composition @ SV32 @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(920,plain,
! [SV97: $i,SV68: $i,SV86: $i,SV33: $i] :
( ( ( SV33 = SV86 )
= $true )
| ( ( ( ordered_pair @ SV33 @ SV68 )
= ( ordered_pair @ SV86 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(921,plain,
! [SV86: $i,SV33: $i,SV97: $i,SV68: $i] :
( ( ( SV68 = SV97 )
= $true )
| ( ( ( ordered_pair @ SV33 @ SV68 )
= ( ordered_pair @ SV86 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(922,plain,
! [SV34: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(923,plain,
! [SV34: $i,SV69: $i] :
( ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(924,plain,
! [SV35: $i,SV70: $i] :
( ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( ! [SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 )
| ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY368 @ SV35 )
| ( SY368 != SY369 ) )
| ( in @ ( ordered_pair @ SY368 @ SY369 ) @ SV70 ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(925,plain,
! [SV35: $i,SV70: $i] :
( ( ( ! [SY370: $i,SY371: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 )
| ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY370 @ SV35 )
| ( SY370 != SY371 ) )
| ( in @ ( ordered_pair @ SY370 @ SY371 ) @ SV70 ) ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(926,plain,
! [SV36: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ SV36 )
| ~ ! [SY480: $i,SY481: $i] :
( SV106
!= ( ordered_pair @ SY480 @ SY481 ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(927,plain,
! [SV36: $i] :
( ( ( ~ ( in @ ( sK10_SY282 @ SV36 ) @ SV36 )
| ~ ! [SY482: $i,SY483: $i] :
( ( sK10_SY282 @ SV36 )
!= ( ordered_pair @ SY482 @ SY483 ) ) )
= $false )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(928,plain,
! [SV41: $i,SV98: $i] :
( ( ( ( SV98
!= ( relation_inverse @ SV41 ) )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 )
| ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 )
| ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 ) ) ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(929,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ! [SY436: $i,SY437: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 )
| ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 )
| ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 ) ) )
| ( SV98
= ( relation_inverse @ SV41 ) ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(930,plain,
! [SV73: $i,SV42: $i,SV87: $i,SV117: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV117 @ SV87 )
| ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) )
| ( in @ SV117 @ SV87 ) ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(931,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
| ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) ) )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[869]) ).
thf(932,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( SV104
!= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( ! [SY465: $i] :
~ ( ~ ( ~ ( in @ SY465 @ SV104 )
| ~ ! [SY440: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY440 @ SY465 ) @ SV43 )
| ~ ( in @ SY440 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY441: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY441 @ SY465 ) @ SV43 )
| ~ ( in @ SY441 @ SV99 ) )
| ( in @ SY465 @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(933,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ! [SY468: $i] :
~ ( ~ ( ~ ( in @ SY468 @ SV104 )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY443 @ SY468 ) @ SV43 )
| ~ ( in @ SY443 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY444 @ SY468 ) @ SV43 )
| ~ ( in @ SY444 @ SV99 ) )
| ( in @ SY468 @ SV104 ) ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(934,plain,
! [SV45: $i,SV100: $i] :
( ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( ! [SY445: $i] :
~ ( ~ ( ~ ( in @ SY445 @ SV100 )
| ~ ! [SY309: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY309 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY310: $i] :
~ ( in @ ( ordered_pair @ SY445 @ SY310 ) @ SV45 )
| ( in @ SY445 @ SV100 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(935,plain,
! [SV45: $i,SV100: $i] :
( ( ( ! [SY448: $i] :
~ ( ~ ( ~ ( in @ SY448 @ SV100 )
| ~ ! [SY312: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY312 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY313: $i] :
~ ( in @ ( ordered_pair @ SY448 @ SY313 ) @ SV45 )
| ( in @ SY448 @ SV100 ) ) ) )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(936,plain,
! [SV76: $i,SV88: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( relation_field @ SV88 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(937,plain,
! [SV48: $i,SV88: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( relation_field @ SV88 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(938,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ SV108 @ SV50 )
| ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SV108 @ SY484 )
| ~ ( in @ SY484 @ SV3 ) ) ) )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[878]) ).
thf(939,plain,
! [SV50: $i,SV3: $i,SV108: $i] :
( ( ( ~ ( ~ ~ ! [SY485: $i] :
~ ~ ( ~ ( in @ SV108 @ SY485 )
| ~ ( in @ SY485 @ SV3 ) )
| ( in @ SV108 @ SV50 ) ) )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[878]) ).
thf(940,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
| ~ ! [SY486: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY486 )
| ~ ( in @ SY486 @ SV3 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(941,plain,
! [SV89: $i,SV4: $i,SV101: $i] :
( ( ( ( SV101
!= ( relation_dom_restriction @ SV4 @ SV89 ) )
| ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 )
| ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 ) ) ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(942,plain,
! [SV4: $i,SV89: $i,SV101: $i] :
( ( ( ~ ! [SY453: $i,SY454: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 )
| ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 ) ) )
| ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[881]) ).
thf(943,plain,
! [SV51: $i,SV77: $i,SV5: $i] :
( ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( ~ ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY376 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY376 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY376 @ SV51 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(944,plain,
! [SV51: $i,SV5: $i,SV77: $i] :
( ( ( ~ ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY377 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY377 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY377 @ SV51 ) ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(945,plain,
! [SV90: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV90 ) )
= $true )
| ( ( ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV6 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV90 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(946,plain,
! [SV90: $i,SV6: $i] :
( ( ( ~ ! [SY406: $i,SY407: $i] :
( ~ ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV6 )
| ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV90 ) ) )
= $true )
| ( ( subset @ SV6 @ SV90 )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(947,plain,
! [SV52: $i,SV7: $i] :
( ( ( disjoint @ SV7 @ SV52 )
= $true )
| ( ( ~ ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(948,plain,
! [SV52: $i,SV7: $i] :
( ( ( ! [SY329: $i] :
~ ~ ( ~ ( in @ SY329 @ SV7 )
| ~ ( in @ SY329 @ SV52 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(949,plain,
! [SV8: $i,SV53: $i,SV109: $i] :
( ( ( ~ ( ~ ( in @ SV109 @ SV53 )
| ( SV109 = SV8 ) ) )
= $false )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(950,plain,
! [SV53: $i,SV8: $i,SV109: $i] :
( ( ( ~ ( ( SV109 != SV8 )
| ( in @ SV109 @ SV53 ) ) )
= $false )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(951,plain,
! [SV53: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
| ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 ) ) )
= $true )
| ( ( ~ ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
| ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(952,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ( SV102
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
| ! [SY455: $i,SY456: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 )
| ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 ) ) ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(953,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ! [SY457: $i,SY458: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 )
| ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 ) ) )
| ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(954,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(955,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV78 )
| ~ ( in @ SV55 @ SV91 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(956,plain,
! [SV16: $i,SV92: $i,SV118: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV118 @ SV92 )
| ~ ! [SY497: $i] :
~ ( in @ ( ordered_pair @ SY497 @ SV118 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY498: $i] :
~ ( in @ ( ordered_pair @ SY498 @ SV118 ) @ SV16 )
| ( in @ SV118 @ SV92 ) ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(957,plain,
! [SV92: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
| ~ ! [SY499: $i] :
~ ( in @ ( ordered_pair @ SY499 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
| ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) ) )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[896]) ).
thf(958,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( ~ ( ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(959,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(960,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV79 )
| ~ ( in @ SV59 @ SV93 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(961,plain,
! [SV60: $i,SV21: $i,SV80: $i,SV113: $i] :
( ( ( ~ ( ~ ( in @ SV113 @ SV80 )
| ( SV113 = SV21 )
| ( SV113 = SV60 ) )
| ~ ( ~ ( ( SV113 = SV21 )
| ( SV113 = SV60 ) )
| ( in @ SV113 @ SV80 ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(962,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ~ ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(963,plain,
! [SV61: $i,SV22: $i,SV81: $i,SV114: $i] :
( ( ( ~ ( ~ ( in @ SV114 @ SV81 )
| ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
| ~ ( ~ ( ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
| ( in @ SV114 @ SV81 ) ) )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(964,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ~ ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(965,plain,
! [SV63: $i,SV82: $i,SV24: $i] :
( ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(966,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) ) )
= $false )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(967,plain,
! [SV64: $i,SV25: $i,SV111: $i] :
( ( ( in @ SV111 @ SV25 )
= $false )
| ( ( in @ SV111 @ SV64 )
= $true )
| ( ( subset @ SV25 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(968,plain,
! [SV25: $i,SV64: $i] :
( ( ( in @ ( sK15_SY349 @ SV64 @ SV25 ) @ SV25 )
= $true )
| ( ( subset @ SV25 @ SV64 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(969,plain,
! [SV65: $i,SV83: $i,SV26: $i] :
( ( ( in @ SV26 @ ( relation_dom @ SV83 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[909]) ).
thf(970,plain,
! [SV26: $i,SV83: $i,SV65: $i] :
( ( ( in @ SV65 @ ( relation_rng @ SV83 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV26 @ SV65 ) @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(971,plain,
! [SV94: $i,SV27: $i] :
( ( ( SV27 != SV94 )
= $true )
| ( ( ! [SY414: $i,SY415: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 ) ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(972,plain,
! [SV94: $i,SV27: $i] :
( ( ( ~ ! [SY416: $i,SY417: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(973,plain,
! [SV66: $i,SV28: $i,SV84: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ SV115 @ SV84 )
| ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) )
| ( in @ SV115 @ SV84 ) ) )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(974,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
| ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(975,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( ! [SY459: $i] :
~ ( ~ ( ~ ( in @ SY459 @ SV103 )
| ~ ! [SY420: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY420 ) @ SV30 )
| ~ ( in @ SY420 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY421: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY459 @ SY421 ) @ SV30 )
| ~ ( in @ SY421 @ SV95 ) )
| ( in @ SY459 @ SV103 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(976,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( ! [SY462: $i] :
~ ( ~ ( ~ ( in @ SY462 @ SV103 )
| ~ ! [SY423: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY423 ) @ SV30 )
| ~ ( in @ SY423 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY424: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY462 @ SY424 ) @ SV30 )
| ~ ( in @ SY424 @ SV95 ) )
| ( in @ SY462 @ SV103 ) ) ) )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(977,plain,
! [SV67: $i,SV31: $i,SV85: $i,SV116: $i] :
( ( ( ~ ( ~ ( in @ SV116 @ SV85 )
| ~ ! [SY489: $i] :
~ ~ ! [SY490: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY489 @ SV31 )
| ~ ( in @ SY490 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY489 @ SY490 ) ) ) )
| ~ ( ~ ~ ! [SY491: $i] :
~ ~ ! [SY492: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY491 @ SV31 )
| ~ ( in @ SY492 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY491 @ SY492 ) ) )
| ( in @ SV116 @ SV85 ) ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(978,plain,
! [SV85: $i,SV31: $i,SV67: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
| ~ ! [SY493: $i] :
~ ~ ! [SY494: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY493 @ SV31 )
| ~ ( in @ SY494 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY493 @ SY494 ) ) ) )
| ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(979,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ~ ( ( SV105
!= ( relation_composition @ SV32 @ SV96 ) )
| ! [SY472: $i,SY473: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY473 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY473 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 ) ) ) )
| ~ ( ~ ! [SY476: $i,SY477: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY477 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY477 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 ) ) )
| ( SV105
= ( relation_composition @ SV32 @ SV96 ) ) ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(980,plain,
! [SV34: $i,SV69: $i] :
( ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(981,plain,
! [SV34: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) )
= $false )
| ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
= $false )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(982,plain,
! [SV35: $i,SV70: $i,SV119: $i] :
( ( ( ! [SY501: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV119 @ SY501 ) @ SV70 )
| ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SY501 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SY501 ) )
| ( in @ ( ordered_pair @ SV119 @ SY501 ) @ SV70 ) ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(983,plain,
! [SV70: $i,SV35: $i] :
( ( ( ! [SY502: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ SY502 ) @ SV70 )
| ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= SY502 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= SY502 ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ SY502 ) @ SV70 ) ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[925]) ).
thf(984,plain,
! [SV36: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ SV36 ) )
= $true )
| ( ( ~ ! [SY480: $i,SY481: $i] :
( SV106
!= ( ordered_pair @ SY480 @ SY481 ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(985,plain,
! [SV36: $i] :
( ( ( ~ ( in @ ( sK10_SY282 @ SV36 ) @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(986,plain,
! [SV36: $i] :
( ( ( ~ ! [SY482: $i,SY483: $i] :
( ( sK10_SY282 @ SV36 )
!= ( ordered_pair @ SY482 @ SY483 ) ) )
= $false )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(987,plain,
! [SV41: $i,SV98: $i] :
( ( ( SV98
!= ( relation_inverse @ SV41 ) )
= $true )
| ( ( ! [SY434: $i,SY435: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 )
| ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 )
| ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 ) ) ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(988,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ! [SY436: $i,SY437: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 )
| ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 )
| ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 ) ) ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(989,plain,
! [SV73: $i,SV42: $i,SV87: $i,SV117: $i] :
( ( ( ~ ( ~ ( in @ SV117 @ SV87 )
| ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) )
| ( in @ SV117 @ SV87 ) ) )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(990,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
| ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(991,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( ! [SY465: $i] :
~ ( ~ ( ~ ( in @ SY465 @ SV104 )
| ~ ! [SY440: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY440 @ SY465 ) @ SV43 )
| ~ ( in @ SY440 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY441: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY441 @ SY465 ) @ SV43 )
| ~ ( in @ SY441 @ SV99 ) )
| ( in @ SY465 @ SV104 ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(992,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ! [SY468: $i] :
~ ( ~ ( ~ ( in @ SY468 @ SV104 )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY443 @ SY468 ) @ SV43 )
| ~ ( in @ SY443 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY444 @ SY468 ) @ SV43 )
| ~ ( in @ SY444 @ SV99 ) )
| ( in @ SY468 @ SV104 ) ) ) )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(993,plain,
! [SV45: $i,SV100: $i,SV120: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV120 @ SV100 )
| ~ ! [SY503: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY503 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY504: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY504 ) @ SV45 )
| ( in @ SV120 @ SV100 ) ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(994,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
| ~ ! [SY505: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY505 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) ) )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[935]) ).
thf(995,plain,
! [SV76: $i,SV88: $i,SV48: $i] :
( ( ( in @ SV48 @ ( relation_field @ SV88 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[936]) ).
thf(996,plain,
! [SV48: $i,SV88: $i,SV76: $i] :
( ( ( in @ SV76 @ ( relation_field @ SV88 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV48 @ SV76 ) @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(997,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV50 )
| ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SV108 @ SY484 )
| ~ ( in @ SY484 @ SV3 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(998,plain,
! [SV50: $i,SV3: $i,SV108: $i] :
( ( ( ~ ~ ! [SY485: $i] :
~ ~ ( ~ ( in @ SV108 @ SY485 )
| ~ ( in @ SY485 @ SV3 ) )
| ( in @ SV108 @ SV50 ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[939]) ).
thf(999,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
| ~ ! [SY486: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY486 )
| ~ ( in @ SY486 @ SV3 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1000,plain,
! [SV89: $i,SV4: $i,SV101: $i] :
( ( ( SV101
!= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 )
| ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 ) ) ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1001,plain,
! [SV4: $i,SV89: $i,SV101: $i] :
( ( ( ~ ! [SY453: $i,SY454: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 )
| ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 ) ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1002,plain,
! [SV51: $i,SV5: $i,SV77: $i] :
( ( ( ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY376 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY376 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY376 @ SV51 ) ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1003,plain,
! [SV51: $i,SV5: $i,SV77: $i] :
( ( ( ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY377 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SY377 @ SV5 ) @ SV77 ) )
| ~ ( in @ SY377 @ SV51 ) ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(1004,plain,
! [SV90: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV90 )
= $false )
| ( ( ! [SY404: $i,SY405: $i] :
( ~ ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV6 )
| ( in @ ( ordered_pair @ SY404 @ SY405 ) @ SV90 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1005,plain,
! [SV90: $i,SV6: $i] :
( ( ( ! [SY406: $i,SY407: $i] :
( ~ ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV6 )
| ( in @ ( ordered_pair @ SY406 @ SY407 ) @ SV90 ) ) )
= $false )
| ( ( subset @ SV6 @ SV90 )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(1006,plain,
! [SV52: $i,SV7: $i] :
( ( ( ! [SY328: $i] :
~ ~ ( ~ ( in @ SY328 @ SV7 )
| ~ ( in @ SY328 @ SV52 ) ) )
= $false )
| ( ( disjoint @ SV7 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1007,plain,
! [SV52: $i,SV7: $i,SV121: $i] :
( ( ( ~ ~ ( ~ ( in @ SV121 @ SV7 )
| ~ ( in @ SV121 @ SV52 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1008,plain,
! [SV8: $i,SV53: $i,SV109: $i] :
( ( ( ~ ( in @ SV109 @ SV53 )
| ( SV109 = SV8 ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1009,plain,
! [SV53: $i,SV8: $i,SV109: $i] :
( ( ( ( SV109 != SV8 )
| ( in @ SV109 @ SV53 ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1010,plain,
! [SV53: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
| ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 ) )
= $false )
| ( ( ~ ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
| ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1011,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( SV102
!= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 )
| ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 ) ) ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1012,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ! [SY457: $i,SY458: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 )
| ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 ) ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1013,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV78 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1014,plain,
! [SV78: $i,SV10: $i,SV91: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV91 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1015,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV78 ) )
= $true )
| ( ( ~ ( in @ SV55 @ SV91 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1016,plain,
! [SV16: $i,SV92: $i,SV118: $i] :
( ( ( ~ ( ~ ( in @ SV118 @ SV92 )
| ~ ! [SY497: $i] :
~ ( in @ ( ordered_pair @ SY497 @ SV118 ) @ SV16 ) )
| ~ ( ~ ~ ! [SY498: $i] :
~ ( in @ ( ordered_pair @ SY498 @ SV118 ) @ SV16 )
| ( in @ SV118 @ SV92 ) ) )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1017,plain,
! [SV92: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
| ~ ! [SY499: $i] :
~ ( in @ ( ordered_pair @ SY499 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
| ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[957]) ).
thf(1018,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( ~ ( ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1019,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( ~ ( ~ ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1020,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV79 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1021,plain,
! [SV79: $i,SV20: $i,SV93: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV93 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1022,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV79 ) )
= $true )
| ( ( ~ ( in @ SV59 @ SV93 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1023,plain,
! [SV60: $i,SV21: $i,SV80: $i,SV113: $i] :
( ( ( ~ ( ~ ( in @ SV113 @ SV80 )
| ( SV113 = SV21 )
| ( SV113 = SV60 ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1024,plain,
! [SV80: $i,SV60: $i,SV21: $i,SV113: $i] :
( ( ( ~ ( ~ ( ( SV113 = SV21 )
| ( SV113 = SV60 ) )
| ( in @ SV113 @ SV80 ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1025,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1026,plain,
! [SV61: $i,SV22: $i,SV81: $i,SV114: $i] :
( ( ( ~ ( ~ ( in @ SV114 @ SV81 )
| ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) ) )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(1027,plain,
! [SV81: $i,SV61: $i,SV22: $i,SV114: $i] :
( ( ( ~ ( ~ ( ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
| ( in @ SV114 @ SV81 ) ) )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(1028,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1029,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
= $false )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1030,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV63 )
| ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
= $true )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1031,plain,
! [SV94: $i,SV27: $i] :
( ( ( SV27 = SV94 )
= $false )
| ( ( ! [SY414: $i,SY415: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV94 )
| ( in @ ( ordered_pair @ SY414 @ SY415 ) @ SV27 ) ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1032,plain,
! [SV94: $i,SV27: $i] :
( ( ( ! [SY416: $i,SY417: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV94 )
| ( in @ ( ordered_pair @ SY416 @ SY417 ) @ SV27 ) ) ) )
= $false )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1033,plain,
! [SV66: $i,SV28: $i,SV84: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ SV115 @ SV84 )
| ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) ) ) )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1034,plain,
! [SV84: $i,SV66: $i,SV28: $i,SV115: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) )
| ( in @ SV115 @ SV84 ) ) )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1035,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
| ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1036,plain,
! [SV95: $i,SV30: $i,SV103: $i,SV122: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV122 @ SV103 )
| ~ ! [SY507: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY507 ) @ SV30 )
| ~ ( in @ SY507 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY508: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY508 ) @ SV30 )
| ~ ( in @ SY508 @ SV95 ) )
| ( in @ SV122 @ SV103 ) ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1037,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
| ~ ! [SY509: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY509 ) @ SV30 )
| ~ ( in @ SY509 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) ) )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[976]) ).
thf(1038,plain,
! [SV67: $i,SV31: $i,SV85: $i,SV116: $i] :
( ( ( ~ ( ~ ( in @ SV116 @ SV85 )
| ~ ! [SY489: $i] :
~ ~ ! [SY490: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY489 @ SV31 )
| ~ ( in @ SY490 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY489 @ SY490 ) ) ) ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1039,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ! [SY491: $i] :
~ ~ ! [SY492: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY491 @ SV31 )
| ~ ( in @ SY492 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY491 @ SY492 ) ) )
| ( in @ SV116 @ SV85 ) ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1040,plain,
! [SV85: $i,SV31: $i,SV67: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
| ~ ! [SY493: $i] :
~ ~ ! [SY494: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY493 @ SV31 )
| ~ ( in @ SY494 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY493 @ SY494 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1041,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ~ ( ( SV105
!= ( relation_composition @ SV32 @ SV96 ) )
| ! [SY472: $i,SY473: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY473 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY473 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 ) ) ) ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1042,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ~ ( ~ ! [SY476: $i,SY477: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY477 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY477 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 ) ) )
| ( SV105
= ( relation_composition @ SV32 @ SV96 ) ) ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1043,plain,
! [SV34: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
| ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 ) )
= $false )
| ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1044,plain,
! [SV34: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 ) )
= $false )
| ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
= $false )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1045,plain,
! [SV34: $i,SV69: $i] :
( ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
= $false )
| ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
= $false )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1046,plain,
! [SV35: $i,SV70: $i,SV123: $i,SV119: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
| ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) )
| ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 ) ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1047,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
| ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[983]) ).
thf(1048,plain,
! [SV36: $i,SV106: $i] :
( ( ( in @ SV106 @ SV36 )
= $false )
| ( ( ~ ! [SY480: $i,SY481: $i] :
( SV106
!= ( ordered_pair @ SY480 @ SY481 ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1049,plain,
! [SV36: $i] :
( ( ( in @ ( sK10_SY282 @ SV36 ) @ SV36 )
= $true )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1050,plain,
! [SV36: $i] :
( ( ( ! [SY482: $i,SY483: $i] :
( ( sK10_SY282 @ SV36 )
!= ( ordered_pair @ SY482 @ SY483 ) ) )
= $true )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1051,plain,
! [SV41: $i,SV98: $i] :
( ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( ! [SY434: $i,SY435: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 )
| ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY435 @ SY434 ) @ SV41 )
| ( in @ ( ordered_pair @ SY434 @ SY435 ) @ SV98 ) ) ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1052,plain,
! [SV41: $i,SV98: $i] :
( ( ( ! [SY436: $i,SY437: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 )
| ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY437 @ SY436 ) @ SV41 )
| ( in @ ( ordered_pair @ SY436 @ SY437 ) @ SV98 ) ) ) )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1053,plain,
! [SV73: $i,SV42: $i,SV87: $i,SV117: $i] :
( ( ( ~ ( ~ ( in @ SV117 @ SV87 )
| ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) ) ) )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1054,plain,
! [SV87: $i,SV73: $i,SV42: $i,SV117: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) )
| ( in @ SV117 @ SV87 ) ) )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1055,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
| ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1056,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV124: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV124 @ SV104 )
| ~ ! [SY511: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY511 @ SV124 ) @ SV43 )
| ~ ( in @ SY511 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY512: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY512 @ SV124 ) @ SV43 )
| ~ ( in @ SY512 @ SV99 ) )
| ( in @ SV124 @ SV104 ) ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1057,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
| ~ ! [SY513: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY513 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) ) )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[992]) ).
thf(1058,plain,
! [SV45: $i,SV100: $i,SV120: $i] :
( ( ( ~ ( ~ ( in @ SV120 @ SV100 )
| ~ ! [SY503: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY503 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY504: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY504 ) @ SV45 )
| ( in @ SV120 @ SV100 ) ) )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1059,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
| ~ ! [SY505: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY505 ) @ SV45 ) )
| ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1060,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV50 ) )
= $true )
| ( ( ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SV108 @ SY484 )
| ~ ( in @ SY484 @ SV3 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1061,plain,
! [SV50: $i,SV3: $i,SV108: $i] :
( ( ( ~ ~ ! [SY485: $i] :
~ ~ ( ~ ( in @ SV108 @ SY485 )
| ~ ( in @ SY485 @ SV3 ) ) )
= $true )
| ( ( in @ SV108 @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1062,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1063,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ! [SY486: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY486 )
| ~ ( in @ SY486 @ SV3 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1064,plain,
! [SV89: $i,SV4: $i,SV101: $i] :
( ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( ! [SY451: $i,SY452: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 )
| ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY451 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY451 @ SY452 ) @ SV101 ) ) ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1065,plain,
! [SV4: $i,SV89: $i,SV101: $i] :
( ( ( ! [SY453: $i,SY454: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 )
| ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY453 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SY453 @ SY454 ) @ SV101 ) ) ) )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1066,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV5 ) @ SV77 ) )
| ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV51 ) ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1002]) ).
thf(1067,plain,
! [SV51: $i,SV5: $i,SV77: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV125 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 ) )
| ~ ( in @ SV125 @ SV51 ) ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1068,plain,
! [SV90: $i,SV6: $i,SV126: $i] :
( ( ( ! [SY515: $i] :
( ~ ( in @ ( ordered_pair @ SV126 @ SY515 ) @ SV6 )
| ( in @ ( ordered_pair @ SV126 @ SY515 ) @ SV90 ) ) )
= $true )
| ( ( subset @ SV6 @ SV90 )
= $false )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1069,plain,
! [SV6: $i,SV90: $i] :
( ( ( ! [SY516: $i] :
( ~ ( in @ ( ordered_pair @ ( sK28_SY406 @ SV90 @ SV6 ) @ SY516 ) @ SV6 )
| ( in @ ( ordered_pair @ ( sK28_SY406 @ SV90 @ SV6 ) @ SY516 ) @ SV90 ) ) )
= $false )
| ( ( subset @ SV6 @ SV90 )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1005]) ).
thf(1070,plain,
! [SV7: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV7 )
| ~ ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV52 ) ) )
= $false )
| ( ( disjoint @ SV7 @ SV52 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1006]) ).
thf(1071,plain,
! [SV52: $i,SV7: $i,SV121: $i] :
( ( ( ~ ( ~ ( in @ SV121 @ SV7 )
| ~ ( in @ SV121 @ SV52 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1072,plain,
! [SV8: $i,SV53: $i,SV109: $i] :
( ( ( ~ ( in @ SV109 @ SV53 ) )
= $true )
| ( ( SV109 = SV8 )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1073,plain,
! [SV53: $i,SV8: $i,SV109: $i] :
( ( ( SV109 != SV8 )
= $true )
| ( ( in @ SV109 @ SV53 )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1074,plain,
! [SV53: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) )
= $false )
| ( ( ~ ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
| ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1075,plain,
! [SV53: $i,SV8: $i] :
( ( ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 )
= $false )
| ( ( ~ ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
| ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1076,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 )
| ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY456 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY455 @ SY456 ) @ SV102 ) ) ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1077,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ! [SY457: $i,SY458: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 )
| ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY458 @ SV9 )
| ~ ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SY457 @ SY458 ) @ SV102 ) ) ) )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1078,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ( in @ SV10 @ SV78 )
= $true )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1079,plain,
! [SV78: $i,SV10: $i,SV91: $i,SV55: $i] :
( ( ( in @ SV55 @ SV91 )
= $true )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1080,plain,
! [SV91: $i,SV55: $i,SV78: $i,SV10: $i] :
( ( ( in @ SV10 @ SV78 )
= $false )
| ( ( ~ ( in @ SV55 @ SV91 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1081,plain,
! [SV16: $i,SV92: $i,SV118: $i] :
( ( ( ~ ( ~ ( in @ SV118 @ SV92 )
| ~ ! [SY497: $i] :
~ ( in @ ( ordered_pair @ SY497 @ SV118 ) @ SV16 ) ) )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1082,plain,
! [SV92: $i,SV16: $i,SV118: $i] :
( ( ( ~ ( ~ ~ ! [SY498: $i] :
~ ( in @ ( ordered_pair @ SY498 @ SV118 ) @ SV16 )
| ( in @ SV118 @ SV92 ) ) )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1083,plain,
! [SV92: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
| ~ ! [SY499: $i] :
~ ( in @ ( ordered_pair @ SY499 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1084,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1085,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( ~ ~ ( in @ SV110 @ ( relation_dom @ SV19 ) )
| ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1086,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ( in @ SV20 @ SV79 )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1087,plain,
! [SV79: $i,SV20: $i,SV93: $i,SV59: $i] :
( ( ( in @ SV59 @ SV93 )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1088,plain,
! [SV93: $i,SV59: $i,SV79: $i,SV20: $i] :
( ( ( in @ SV20 @ SV79 )
= $false )
| ( ( ~ ( in @ SV59 @ SV93 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1089,plain,
! [SV60: $i,SV21: $i,SV80: $i,SV113: $i] :
( ( ( ~ ( in @ SV113 @ SV80 )
| ( SV113 = SV21 )
| ( SV113 = SV60 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1023]) ).
thf(1090,plain,
! [SV80: $i,SV60: $i,SV21: $i,SV113: $i] :
( ( ( ~ ( ( SV113 = SV21 )
| ( SV113 = SV60 ) )
| ( in @ SV113 @ SV80 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1091,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1092,plain,
! [SV61: $i,SV22: $i,SV81: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV81 )
| ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1093,plain,
! [SV81: $i,SV61: $i,SV22: $i,SV114: $i] :
( ( ( ~ ( ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
| ( in @ SV114 @ SV81 ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1094,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1095,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV63 ) )
= $false )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1096,plain,
! [SV63: $i,SV82: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
= $false )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1097,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
= $true )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1098,plain,
! [SV94: $i,SV27: $i,SV127: $i] :
( ( ( ! [SY517: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV127 @ SY517 ) @ SV27 )
| ( in @ ( ordered_pair @ SV127 @ SY517 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV127 @ SY517 ) @ SV94 )
| ( in @ ( ordered_pair @ SV127 @ SY517 ) @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1099,plain,
! [SV27: $i,SV94: $i] :
( ( ( ! [SY518: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ SY518 ) @ SV27 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ SY518 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ SY518 ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ SY518 ) @ SV27 ) ) ) )
= $false )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1032]) ).
thf(1100,plain,
! [SV66: $i,SV28: $i,SV84: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV84 )
| ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1101,plain,
! [SV84: $i,SV66: $i,SV28: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) )
| ( in @ SV115 @ SV84 ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1102,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
| ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1103,plain,
! [SV95: $i,SV30: $i,SV103: $i,SV122: $i] :
( ( ( ~ ( ~ ( in @ SV122 @ SV103 )
| ~ ! [SY507: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY507 ) @ SV30 )
| ~ ( in @ SY507 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY508: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY508 ) @ SV30 )
| ~ ( in @ SY508 @ SV95 ) )
| ( in @ SV122 @ SV103 ) ) )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1104,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
| ~ ! [SY509: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY509 ) @ SV30 )
| ~ ( in @ SY509 @ SV95 ) ) )
| ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1105,plain,
! [SV67: $i,SV31: $i,SV85: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV85 )
| ~ ! [SY489: $i] :
~ ~ ! [SY490: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY489 @ SV31 )
| ~ ( in @ SY490 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY489 @ SY490 ) ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1038]) ).
thf(1106,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i] :
( ( ( ~ ~ ! [SY491: $i] :
~ ~ ! [SY492: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY491 @ SV31 )
| ~ ( in @ SY492 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY491 @ SY492 ) ) )
| ( in @ SV116 @ SV85 ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1107,plain,
! [SV85: $i,SV31: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
| ~ ! [SY493: $i] :
~ ~ ! [SY494: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY493 @ SV31 )
| ~ ( in @ SY494 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY493 @ SY494 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1108,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ( SV105
!= ( relation_composition @ SV32 @ SV96 ) )
| ! [SY472: $i,SY473: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY473 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY473 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 ) ) ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1109,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ~ ! [SY476: $i,SY477: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY477 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY477 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 ) ) )
| ( SV105
= ( relation_composition @ SV32 @ SV96 ) ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1110,plain,
! [SV34: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 ) )
= $false )
| ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1111,plain,
! [SV34: $i,SV69: $i] :
( ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
= $false )
| ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1112,plain,
! [SV34: $i,SV69: $i] :
( ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
= $true )
| ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
= $false )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1113,plain,
! [SV35: $i,SV70: $i,SV123: $i,SV119: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
| ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) )
| ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1114,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
| ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1115,plain,
! [SV36: $i,SV106: $i] :
( ( ( ! [SY480: $i,SY481: $i] :
( SV106
!= ( ordered_pair @ SY480 @ SY481 ) ) )
= $false )
| ( ( in @ SV106 @ SV36 )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1116,plain,
! [SV128: $i,SV36: $i] :
( ( ( ! [SY519: $i] :
( ( sK10_SY282 @ SV36 )
!= ( ordered_pair @ SV128 @ SY519 ) ) )
= $true )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1117,plain,
! [SV41: $i,SV98: $i,SV129: $i] :
( ( ( ! [SY520: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV129 @ SY520 ) @ SV98 )
| ( in @ ( ordered_pair @ SY520 @ SV129 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY520 @ SV129 ) @ SV41 )
| ( in @ ( ordered_pair @ SV129 @ SY520 ) @ SV98 ) ) ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1118,plain,
! [SV98: $i,SV41: $i] :
( ( ( ! [SY521: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ SY521 ) @ SV98 )
| ( in @ ( ordered_pair @ SY521 @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY521 @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ SY521 ) @ SV98 ) ) ) )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1052]) ).
thf(1119,plain,
! [SV73: $i,SV42: $i,SV87: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV87 )
| ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1120,plain,
! [SV87: $i,SV73: $i,SV42: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) )
| ( in @ SV117 @ SV87 ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1121,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
| ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1122,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ SV124 @ SV104 )
| ~ ! [SY511: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY511 @ SV124 ) @ SV43 )
| ~ ( in @ SY511 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY512: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY512 @ SV124 ) @ SV43 )
| ~ ( in @ SY512 @ SV99 ) )
| ( in @ SV124 @ SV104 ) ) )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1123,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
| ~ ! [SY513: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY513 @ SV99 ) ) )
| ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1124,plain,
! [SV45: $i,SV100: $i,SV120: $i] :
( ( ( ~ ( ~ ( in @ SV120 @ SV100 )
| ~ ! [SY503: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY503 ) @ SV45 ) ) )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1125,plain,
! [SV100: $i,SV45: $i,SV120: $i] :
( ( ( ~ ( ~ ~ ! [SY504: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY504 ) @ SV45 )
| ( in @ SV120 @ SV100 ) ) )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1126,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
| ~ ! [SY505: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY505 ) @ SV45 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1127,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( in @ SV108 @ SV50 )
= $false )
| ( ( ~ ! [SY484: $i] :
~ ~ ( ~ ( in @ SV108 @ SY484 )
| ~ ( in @ SY484 @ SV3 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1128,plain,
! [SV50: $i,SV3: $i,SV108: $i] :
( ( ( ~ ! [SY485: $i] :
~ ~ ( ~ ( in @ SV108 @ SY485 )
| ~ ( in @ SY485 @ SV3 ) ) )
= $false )
| ( ( in @ SV108 @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1129,plain,
! [SV50: $i,SV3: $i] :
( ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1130,plain,
! [SV50: $i,SV3: $i] :
( ( ( ! [SY486: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY486 )
| ~ ( in @ SY486 @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1131,plain,
! [SV4: $i,SV89: $i,SV101: $i,SV130: $i] :
( ( ( ! [SY522: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV130 @ SY522 ) @ SV101 )
| ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SY522 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SY522 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SV130 @ SY522 ) @ SV101 ) ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1132,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ! [SY523: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SY523 ) @ SV101 )
| ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SY523 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SY523 ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SY523 ) @ SV101 ) ) ) )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1065]) ).
thf(1133,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV5 ) @ SV77 ) )
| ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV51 ) ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1134,plain,
! [SV51: $i,SV5: $i,SV77: $i,SV125: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV125 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 ) )
| ~ ( in @ SV125 @ SV51 ) ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1135,plain,
! [SV90: $i,SV6: $i,SV131: $i,SV126: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV126 @ SV131 ) @ SV6 )
| ( in @ ( ordered_pair @ SV126 @ SV131 ) @ SV90 ) )
= $true )
| ( ( subset @ SV6 @ SV90 )
= $false )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1136,plain,
! [SV6: $i,SV90: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK28_SY406 @ SV90 @ SV6 ) @ ( sK33_SY516 @ SV6 @ SV90 ) ) @ SV6 )
| ( in @ ( ordered_pair @ ( sK28_SY406 @ SV90 @ SV6 ) @ ( sK33_SY516 @ SV6 @ SV90 ) ) @ SV90 ) )
= $false )
| ( ( subset @ SV6 @ SV90 )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1069]) ).
thf(1137,plain,
! [SV7: $i,SV52: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV7 )
| ~ ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV52 ) ) )
= $true )
| ( ( disjoint @ SV7 @ SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1138,plain,
! [SV52: $i,SV7: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ SV7 )
| ~ ( in @ SV121 @ SV52 ) )
= $true )
| ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1139,plain,
! [SV8: $i,SV53: $i,SV109: $i] :
( ( ( in @ SV109 @ SV53 )
= $false )
| ( ( SV109 = SV8 )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1140,plain,
! [SV53: $i,SV8: $i,SV109: $i] :
( ( ( SV109 = SV8 )
= $false )
| ( ( in @ SV109 @ SV53 )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1141,plain,
! [SV53: $i,SV8: $i] :
( ( ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
= $true )
| ( ( ~ ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
| ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) ) )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1142,plain,
! [SV53: $i,SV8: $i] :
( ( ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
| ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) )
= $false )
| ( ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 )
= $false )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1143,plain,
! [SV54: $i,SV9: $i,SV102: $i,SV132: $i] :
( ( ( ! [SY524: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV132 @ SY524 ) @ SV102 )
| ~ ( ~ ( in @ SY524 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SY524 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY524 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SY524 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SV132 @ SY524 ) @ SV102 ) ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1144,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( ! [SY525: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ SY525 ) @ SV102 )
| ~ ( ~ ( in @ SY525 @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ SY525 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY525 @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ SY525 ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ SY525 ) @ SV102 ) ) ) )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1077]) ).
thf(1145,plain,
! [SV78: $i,SV10: $i,SV91: $i,SV55: $i] :
( ( ( in @ SV55 @ SV91 )
= $false )
| ( ( in @ SV10 @ SV78 )
= $false )
| ( ( in @ ( ordered_pair @ SV10 @ SV55 ) @ ( cartesian_product2 @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1146,plain,
! [SV16: $i,SV92: $i,SV118: $i] :
( ( ( ~ ( in @ SV118 @ SV92 )
| ~ ! [SY497: $i] :
~ ( in @ ( ordered_pair @ SY497 @ SV118 ) @ SV16 ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1147,plain,
! [SV92: $i,SV16: $i,SV118: $i] :
( ( ( ~ ~ ! [SY498: $i] :
~ ( in @ ( ordered_pair @ SY498 @ SV118 ) @ SV16 )
| ( in @ SV118 @ SV92 ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1148,plain,
! [SV92: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
| ~ ! [SY499: $i] :
~ ( in @ ( ordered_pair @ SY499 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1149,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ ( relation_dom @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1150,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( ~ ~ ( in @ SV110 @ ( relation_dom @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1151,plain,
! [SV79: $i,SV20: $i,SV93: $i,SV59: $i] :
( ( ( in @ SV59 @ SV93 )
= $false )
| ( ( in @ SV20 @ SV79 )
= $false )
| ( ( in @ ( ordered_pair @ SV20 @ SV59 ) @ ( cartesian_product2 @ SV79 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1152,plain,
! [SV60: $i,SV21: $i,SV80: $i,SV113: $i] :
( ( ( ~ ( in @ SV113 @ SV80 ) )
= $true )
| ( ( ( SV113 = SV21 )
| ( SV113 = SV60 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1153,plain,
! [SV80: $i,SV60: $i,SV21: $i,SV113: $i] :
( ( ( ~ ( ( SV113 = SV21 )
| ( SV113 = SV60 ) ) )
= $true )
| ( ( in @ SV113 @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1154,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1155,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1156,plain,
! [SV61: $i,SV22: $i,SV81: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV81 ) )
= $true )
| ( ( ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1157,plain,
! [SV81: $i,SV61: $i,SV22: $i,SV114: $i] :
( ( ( ~ ( ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) ) )
= $true )
| ( ( in @ SV114 @ SV81 )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1158,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1159,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1160,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( in @ SV24 @ SV63 )
= $true )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1161,plain,
! [SV63: $i,SV82: $i,SV24: $i] :
( ( ( in @ SV24 @ ( relation_dom @ SV82 ) )
= $true )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1162,plain,
! [SV82: $i,SV63: $i,SV24: $i] :
( ( ( in @ SV24 @ SV63 )
= $false )
| ( ( ~ ( in @ SV24 @ ( relation_dom @ SV82 ) ) )
= $true )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1163,plain,
! [SV94: $i,SV27: $i,SV133: $i,SV127: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 )
| ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 )
| ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1164,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) ) ) )
= $false )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1099]) ).
thf(1165,plain,
! [SV66: $i,SV28: $i,SV84: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV84 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1166,plain,
! [SV84: $i,SV66: $i,SV28: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) ) )
= $true )
| ( ( in @ SV115 @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1167,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1168,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1169,plain,
! [SV95: $i,SV30: $i,SV103: $i,SV122: $i] :
( ( ( ~ ( ~ ( in @ SV122 @ SV103 )
| ~ ! [SY507: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY507 ) @ SV30 )
| ~ ( in @ SY507 @ SV95 ) ) ) )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1170,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV122: $i] :
( ( ( ~ ( ~ ~ ! [SY508: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY508 ) @ SV30 )
| ~ ( in @ SY508 @ SV95 ) )
| ( in @ SV122 @ SV103 ) ) )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1171,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
| ~ ! [SY509: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY509 ) @ SV30 )
| ~ ( in @ SY509 @ SV95 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1172,plain,
! [SV67: $i,SV31: $i,SV85: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV85 ) )
= $true )
| ( ( ~ ! [SY489: $i] :
~ ~ ! [SY490: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY489 @ SV31 )
| ~ ( in @ SY490 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY489 @ SY490 ) ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1173,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i] :
( ( ( ~ ~ ! [SY491: $i] :
~ ~ ! [SY492: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY491 @ SV31 )
| ~ ( in @ SY492 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY491 @ SY492 ) ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1174,plain,
! [SV85: $i,SV31: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1175,plain,
! [SV85: $i,SV67: $i,SV31: $i] :
( ( ( ~ ! [SY493: $i] :
~ ~ ! [SY494: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY493 @ SV31 )
| ~ ( in @ SY494 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY493 @ SY494 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1176,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( SV105
!= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( ! [SY472: $i,SY473: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY473 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY473 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 ) ) ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1177,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ~ ! [SY476: $i,SY477: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY477 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY477 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 ) ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1178,plain,
! [SV34: $i,SV69: $i] :
( ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV69 )
= $true )
| ( ( in @ ( sK8_SY367 @ SV69 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1179,plain,
! [SV35: $i,SV70: $i,SV123: $i,SV119: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
| ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1180,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) )
| ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 ) ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1181,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
| ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1182,plain,
! [SV36: $i,SV106: $i] :
( ( ( ! [SY526: $i] :
( SV106
!= ( ordered_pair @ ( sK36_SY480 @ SV36 @ SV106 ) @ SY526 ) ) )
= $false )
| ( ( in @ SV106 @ SV36 )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1115]) ).
thf(1183,plain,
! [SV134: $i,SV128: $i,SV36: $i] :
( ( ( ( sK10_SY282 @ SV36 )
!= ( ordered_pair @ SV128 @ SV134 ) )
= $true )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1184,plain,
! [SV41: $i,SV98: $i,SV135: $i,SV129: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 )
| ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 )
| ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 ) ) ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1185,plain,
! [SV98: $i,SV41: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
| ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) ) ) )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1118]) ).
thf(1186,plain,
! [SV73: $i,SV42: $i,SV87: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV87 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1187,plain,
! [SV87: $i,SV73: $i,SV42: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) ) )
= $true )
| ( ( in @ SV117 @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1188,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1189,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1190,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ SV124 @ SV104 )
| ~ ! [SY511: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY511 @ SV124 ) @ SV43 )
| ~ ( in @ SY511 @ SV99 ) ) ) )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1191,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i] :
( ( ( ~ ( ~ ~ ! [SY512: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY512 @ SV124 ) @ SV43 )
| ~ ( in @ SY512 @ SV99 ) )
| ( in @ SV124 @ SV104 ) ) )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1192,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
| ~ ! [SY513: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY513 @ SV99 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1193,plain,
! [SV45: $i,SV100: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV100 )
| ~ ! [SY503: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY503 ) @ SV45 ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1194,plain,
! [SV100: $i,SV45: $i,SV120: $i] :
( ( ( ~ ~ ! [SY504: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY504 ) @ SV45 )
| ( in @ SV120 @ SV100 ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1195,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
| ~ ! [SY505: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY505 ) @ SV45 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1196,plain,
! [SV50: $i,SV3: $i,SV108: $i] :
( ( ( ! [SY484: $i] :
~ ~ ( ~ ( in @ SV108 @ SY484 )
| ~ ( in @ SY484 @ SV3 ) ) )
= $false )
| ( ( in @ SV108 @ SV50 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1197,plain,
! [SV50: $i,SV3: $i,SV108: $i] :
( ( ( ! [SY485: $i] :
~ ~ ( ~ ( in @ SV108 @ SY485 )
| ~ ( in @ SY485 @ SV3 ) ) )
= $true )
| ( ( in @ SV108 @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1198,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1199,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
| ~ ( in @ SV136 @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1200,plain,
! [SV4: $i,SV89: $i,SV101: $i,SV137: $i,SV130: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
| ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 ) ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1201,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
| ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) ) )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1132]) ).
thf(1202,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV5 ) @ SV77 ) )
| ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV51 ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1203,plain,
! [SV51: $i,SV5: $i,SV77: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ( in @ SV125 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 ) )
| ~ ( in @ SV125 @ SV51 ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1204,plain,
! [SV90: $i,SV6: $i,SV131: $i,SV126: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV126 @ SV131 ) @ SV6 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV126 @ SV131 ) @ SV90 )
= $true )
| ( ( subset @ SV6 @ SV90 )
= $false )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1205,plain,
! [SV6: $i,SV90: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK28_SY406 @ SV90 @ SV6 ) @ ( sK33_SY516 @ SV6 @ SV90 ) ) @ SV6 ) )
= $false )
| ( ( subset @ SV6 @ SV90 )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1206,plain,
! [SV6: $i,SV90: $i] :
( ( ( in @ ( ordered_pair @ ( sK28_SY406 @ SV90 @ SV6 ) @ ( sK33_SY516 @ SV6 @ SV90 ) ) @ SV90 )
= $false )
| ( ( subset @ SV6 @ SV90 )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1207,plain,
! [SV7: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV7 )
| ~ ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV52 ) )
= $false )
| ( ( disjoint @ SV7 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1208,plain,
! [SV52: $i,SV7: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV121 @ SV52 ) )
= $true )
| ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1209,plain,
! [SV53: $i,SV8: $i] :
( ( ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
| ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 ) )
= $false )
| ( ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1210,plain,
! [SV53: $i,SV8: $i] :
( ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
= $false )
| ( ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 )
= $false )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1211,plain,
! [SV53: $i,SV8: $i] :
( ( ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
= $false )
| ( ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 )
= $false )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1212,plain,
! [SV54: $i,SV9: $i,SV102: $i,SV138: $i,SV132: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
| ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 ) ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1213,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
| ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) ) )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1144]) ).
thf(1214,plain,
! [SV16: $i,SV92: $i,SV118: $i] :
( ( ( ~ ( in @ SV118 @ SV92 ) )
= $true )
| ( ( ~ ! [SY497: $i] :
~ ( in @ ( ordered_pair @ SY497 @ SV118 ) @ SV16 ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1215,plain,
! [SV92: $i,SV16: $i,SV118: $i] :
( ( ( ~ ~ ! [SY498: $i] :
~ ( in @ ( ordered_pair @ SY498 @ SV118 ) @ SV16 ) )
= $true )
| ( ( in @ SV118 @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1216,plain,
! [SV92: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1217,plain,
! [SV92: $i,SV16: $i] :
( ( ( ~ ! [SY499: $i] :
~ ( in @ ( ordered_pair @ SY499 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1218,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1219,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ ( relation_dom @ SV19 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1220,plain,
! [SV60: $i,SV21: $i,SV80: $i,SV113: $i] :
( ( ( in @ SV113 @ SV80 )
= $false )
| ( ( ( SV113 = SV21 )
| ( SV113 = SV60 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1221,plain,
! [SV80: $i,SV60: $i,SV21: $i,SV113: $i] :
( ( ( ( SV113 = SV21 )
| ( SV113 = SV60 ) )
= $false )
| ( ( in @ SV113 @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1222,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
= $true )
| ( ( ~ ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1223,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
= $false )
| ( ( ~ ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1155]) ).
thf(1224,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 )
= $false )
| ( ( ~ ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1155]) ).
thf(1225,plain,
! [SV61: $i,SV22: $i,SV81: $i,SV114: $i] :
( ( ( in @ SV114 @ SV81 )
= $false )
| ( ( ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1226,plain,
! [SV81: $i,SV61: $i,SV22: $i,SV114: $i] :
( ( ( ( in @ SV114 @ SV22 )
| ( in @ SV114 @ SV61 ) )
= $false )
| ( ( in @ SV114 @ SV81 )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1227,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1228,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1229,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) ) )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1230,plain,
! [SV63: $i,SV82: $i,SV24: $i] :
( ( ( in @ SV24 @ ( relation_dom @ SV82 ) )
= $false )
| ( ( in @ SV24 @ SV63 )
= $false )
| ( ( in @ SV24 @ ( relation_dom @ ( relation_dom_restriction @ SV82 @ SV63 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1231,plain,
! [SV94: $i,SV27: $i,SV133: $i,SV127: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 )
| ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 )
| ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 ) ) )
= $false )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1232,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) ) )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1233,plain,
! [SV66: $i,SV28: $i,SV84: $i,SV115: $i] :
( ( ( in @ SV115 @ SV84 )
= $false )
| ( ( ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1234,plain,
! [SV84: $i,SV66: $i,SV28: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) ) )
= $false )
| ( ( in @ SV115 @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1235,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1167]) ).
thf(1236,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1237,plain,
! [SV95: $i,SV30: $i,SV103: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV103 )
| ~ ! [SY507: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY507 ) @ SV30 )
| ~ ( in @ SY507 @ SV95 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1238,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV122: $i] :
( ( ( ~ ~ ! [SY508: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY508 ) @ SV30 )
| ~ ( in @ SY508 @ SV95 ) )
| ( in @ SV122 @ SV103 ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1239,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
| ~ ! [SY509: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY509 ) @ SV30 )
| ~ ( in @ SY509 @ SV95 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1240,plain,
! [SV67: $i,SV31: $i,SV85: $i,SV116: $i] :
( ( ( in @ SV116 @ SV85 )
= $false )
| ( ( ~ ! [SY489: $i] :
~ ~ ! [SY490: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY489 @ SV31 )
| ~ ( in @ SY490 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY489 @ SY490 ) ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1241,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i] :
( ( ( ~ ! [SY491: $i] :
~ ~ ! [SY492: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY491 @ SV31 )
| ~ ( in @ SY492 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY491 @ SY492 ) ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1242,plain,
! [SV85: $i,SV31: $i,SV67: $i] :
( ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1174]) ).
thf(1243,plain,
! [SV85: $i,SV67: $i,SV31: $i] :
( ( ( ! [SY493: $i] :
~ ~ ! [SY494: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY493 @ SV31 )
| ~ ( in @ SY494 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY493 @ SY494 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1244,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( ! [SY472: $i,SY473: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 )
| ~ ! [SY428: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY428 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY428 @ SY473 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY429: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY472 @ SY429 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY429 @ SY473 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY472 @ SY473 ) @ SV105 ) ) ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1245,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ! [SY476: $i,SY477: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY432 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY432 @ SY477 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY476 @ SY433 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY433 @ SY477 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SY476 @ SY477 ) @ SV105 ) ) ) )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1246,plain,
! [SV35: $i,SV70: $i,SV123: $i,SV119: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
| ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1247,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( ~ ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) )
| ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1248,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
| ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1249,plain,
! [SV36: $i,SV106: $i] :
( ( ( SV106
!= ( ordered_pair @ ( sK36_SY480 @ SV36 @ SV106 ) @ ( sK40_SY526 @ SV36 @ SV106 ) ) )
= $false )
| ( ( in @ SV106 @ SV36 )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1182]) ).
thf(1250,plain,
! [SV134: $i,SV128: $i,SV36: $i] :
( ( ( ( sK10_SY282 @ SV36 )
= ( ordered_pair @ SV128 @ SV134 ) )
= $false )
| ( ( relation @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1251,plain,
! [SV41: $i,SV98: $i,SV135: $i,SV129: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 )
| ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 )
| ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 ) ) )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1252,plain,
! [SV98: $i,SV41: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
| ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1185]) ).
thf(1253,plain,
! [SV73: $i,SV42: $i,SV87: $i,SV117: $i] :
( ( ( in @ SV117 @ SV87 )
= $false )
| ( ( ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1254,plain,
! [SV87: $i,SV73: $i,SV42: $i,SV117: $i] :
( ( ( ~ ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) ) )
= $false )
| ( ( in @ SV117 @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1255,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1256,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1257,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV104 )
| ~ ! [SY511: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY511 @ SV124 ) @ SV43 )
| ~ ( in @ SY511 @ SV99 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1258,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i] :
( ( ( ~ ~ ! [SY512: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY512 @ SV124 ) @ SV43 )
| ~ ( in @ SY512 @ SV99 ) )
| ( in @ SV124 @ SV104 ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1259,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
| ~ ! [SY513: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY513 @ SV99 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1260,plain,
! [SV45: $i,SV100: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV100 ) )
= $true )
| ( ( ~ ! [SY503: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY503 ) @ SV45 ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1261,plain,
! [SV100: $i,SV45: $i,SV120: $i] :
( ( ( ~ ~ ! [SY504: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY504 ) @ SV45 ) )
= $true )
| ( ( in @ SV120 @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1262,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1263,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ! [SY505: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY505 ) @ SV45 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1264,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ( in @ SV108 @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) )
| ~ ( in @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) @ SV3 ) ) )
= $false )
| ( ( in @ SV108 @ SV50 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1196]) ).
thf(1265,plain,
! [SV50: $i,SV3: $i,SV139: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ( in @ SV108 @ SV139 )
| ~ ( in @ SV139 @ SV3 ) ) )
= $true )
| ( ( in @ SV108 @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1266,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1267,plain,
! [SV50: $i,SV3: $i] :
( ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1268,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
| ~ ( in @ SV136 @ SV3 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1269,plain,
! [SV4: $i,SV89: $i,SV101: $i,SV137: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
| ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 ) ) )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1270,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
| ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1271,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV5 ) @ SV77 ) ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1272,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV51 ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1273,plain,
! [SV51: $i,SV5: $i,SV77: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ( in @ SV125 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 ) ) )
= $true )
| ( ( ~ ( in @ SV125 @ SV51 ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1274,plain,
! [SV90: $i,SV6: $i,SV131: $i,SV126: $i] :
( ( ( in @ ( ordered_pair @ SV126 @ SV131 ) @ SV6 )
= $false )
| ( ( in @ ( ordered_pair @ SV126 @ SV131 ) @ SV90 )
= $true )
| ( ( subset @ SV6 @ SV90 )
= $false )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1275,plain,
! [SV6: $i,SV90: $i] :
( ( ( in @ ( ordered_pair @ ( sK28_SY406 @ SV90 @ SV6 ) @ ( sK33_SY516 @ SV6 @ SV90 ) ) @ SV6 )
= $true )
| ( ( subset @ SV6 @ SV90 )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1276,plain,
! [SV7: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV7 ) )
= $false )
| ( ( disjoint @ SV7 @ SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1277,plain,
! [SV7: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV52 ) )
= $false )
| ( ( disjoint @ SV7 @ SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1278,plain,
! [SV52: $i,SV7: $i,SV121: $i] :
( ( ( in @ SV121 @ SV7 )
= $false )
| ( ( ~ ( in @ SV121 @ SV52 ) )
= $true )
| ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1279,plain,
! [SV53: $i,SV8: $i] :
( ( ( ( sK14_SY331 @ SV8 @ SV53 )
!= SV8 )
= $false )
| ( ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1280,plain,
! [SV53: $i,SV8: $i] :
( ( ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
= $false )
| ( ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1281,plain,
! [SV53: $i,SV8: $i] :
( ( ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 )
= $true )
| ( ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 )
= $false )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1282,plain,
! [SV54: $i,SV9: $i,SV102: $i,SV138: $i,SV132: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
| ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 ) ) )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1283,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
| ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1284,plain,
! [SV16: $i,SV92: $i,SV118: $i] :
( ( ( in @ SV118 @ SV92 )
= $false )
| ( ( ~ ! [SY497: $i] :
~ ( in @ ( ordered_pair @ SY497 @ SV118 ) @ SV16 ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1285,plain,
! [SV92: $i,SV16: $i,SV118: $i] :
( ( ( ~ ! [SY498: $i] :
~ ( in @ ( ordered_pair @ SY498 @ SV118 ) @ SV16 ) )
= $false )
| ( ( in @ SV118 @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1286,plain,
! [SV92: $i,SV16: $i] :
( ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $true )
| ( ( ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1287,plain,
! [SV92: $i,SV16: $i] :
( ( ( ! [SY499: $i] :
~ ( in @ ( ordered_pair @ SY499 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1217]) ).
thf(1288,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) )
= $false )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1289,plain,
! [SV112: $i,SV19: $i,SV110: $i] :
( ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1290,plain,
! [SV80: $i,SV60: $i,SV21: $i,SV113: $i] :
( ( ( SV113 = SV21 )
= $true )
| ( ( SV113 = SV60 )
= $true )
| ( ( in @ SV113 @ SV80 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1291,plain,
! [SV60: $i,SV80: $i,SV21: $i,SV113: $i] :
( ( ( SV113 = SV21 )
= $false )
| ( ( in @ SV113 @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1292,plain,
! [SV21: $i,SV80: $i,SV60: $i,SV113: $i] :
( ( ( SV113 = SV60 )
= $false )
| ( ( in @ SV113 @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1293,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) )
= $false )
| ( ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1294,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) )
= $false )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1295,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
| ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 ) )
= $false )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1296,plain,
! [SV81: $i,SV61: $i,SV22: $i,SV114: $i] :
( ( ( in @ SV114 @ SV22 )
= $true )
| ( ( in @ SV114 @ SV61 )
= $true )
| ( ( in @ SV114 @ SV81 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1297,plain,
! [SV61: $i,SV81: $i,SV22: $i,SV114: $i] :
( ( ( in @ SV114 @ SV22 )
= $false )
| ( ( in @ SV114 @ SV81 )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1298,plain,
! [SV22: $i,SV81: $i,SV61: $i,SV114: $i] :
( ( ( in @ SV114 @ SV61 )
= $false )
| ( ( in @ SV114 @ SV81 )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1299,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) )
= $false )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1300,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) )
= $false )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1301,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 ) )
= $false )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1302,plain,
! [SV94: $i,SV27: $i,SV133: $i,SV127: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 )
| ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 ) ) )
= $false )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1303,plain,
! [SV27: $i,SV94: $i,SV133: $i,SV127: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 )
| ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 ) ) )
= $false )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1304,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) ) )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1305,plain,
! [SV84: $i,SV66: $i,SV28: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) )
= $false )
| ( ( in @ SV115 @ SV84 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1306,plain,
! [SV84: $i,SV66: $i,SV28: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV28 )
| ~ ( in @ SV115 @ SV66 ) )
= $true )
| ( ( in @ SV115 @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1307,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1308,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 ) )
= $true )
| ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1309,plain,
! [SV95: $i,SV30: $i,SV103: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV103 ) )
= $true )
| ( ( ~ ! [SY507: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY507 ) @ SV30 )
| ~ ( in @ SY507 @ SV95 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1310,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV122: $i] :
( ( ( ~ ~ ! [SY508: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY508 ) @ SV30 )
| ~ ( in @ SY508 @ SV95 ) ) )
= $true )
| ( ( in @ SV122 @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1311,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1239]) ).
thf(1312,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ! [SY509: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY509 ) @ SV30 )
| ~ ( in @ SY509 @ SV95 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1239]) ).
thf(1313,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i] :
( ( ( ! [SY489: $i] :
~ ~ ! [SY490: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY489 @ SV31 )
| ~ ( in @ SY490 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY489 @ SY490 ) ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1314,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i] :
( ( ( ! [SY491: $i] :
~ ~ ! [SY492: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY491 @ SV31 )
| ~ ( in @ SY492 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SY491 @ SY492 ) ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1315,plain,
! [SV85: $i,SV67: $i,SV31: $i] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1316,plain,
! [SV85: $i,SV67: $i,SV31: $i,SV140: $i] :
( ( ( ~ ~ ! [SY527: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV140 @ SV31 )
| ~ ( in @ SY527 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SY527 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1317,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV141: $i] :
( ( ( ! [SY528: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY528 ) @ SV105 )
| ~ ! [SY529: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY529 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY529 @ SY528 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY530: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY530 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY530 @ SY528 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SV141 @ SY528 ) @ SV105 ) ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1318,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ! [SY531: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY531 ) @ SV105 )
| ~ ! [SY532: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY532 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY532 @ SY531 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY533 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY533 @ SY531 ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY531 ) @ SV105 ) ) ) )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1245]) ).
thf(1319,plain,
! [SV35: $i,SV70: $i,SV123: $i,SV119: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1320,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( ~ ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1321,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1322,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1323,plain,
! [SV36: $i,SV106: $i] :
( ( ( SV106
= ( ordered_pair @ ( sK36_SY480 @ SV36 @ SV106 ) @ ( sK40_SY526 @ SV36 @ SV106 ) ) )
= $true )
| ( ( in @ SV106 @ SV36 )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1324,plain,
! [SV41: $i,SV98: $i,SV135: $i,SV129: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 )
| ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 ) ) )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1251]) ).
thf(1325,plain,
! [SV98: $i,SV41: $i,SV129: $i,SV135: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 )
| ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 ) ) )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1251]) ).
thf(1326,plain,
! [SV98: $i,SV41: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
| ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1327,plain,
! [SV87: $i,SV73: $i,SV42: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) )
= $false )
| ( ( in @ SV117 @ SV87 )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1328,plain,
! [SV87: $i,SV73: $i,SV42: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV42 )
| ~ ~ ( in @ SV117 @ SV73 ) )
= $true )
| ( ( in @ SV117 @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1329,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1330,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1331,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV104 ) )
= $true )
| ( ( ~ ! [SY511: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY511 @ SV124 ) @ SV43 )
| ~ ( in @ SY511 @ SV99 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1332,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i] :
( ( ( ~ ~ ! [SY512: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY512 @ SV124 ) @ SV43 )
| ~ ( in @ SY512 @ SV99 ) ) )
= $true )
| ( ( in @ SV124 @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1333,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1334,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ! [SY513: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY513 @ SV99 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1335,plain,
! [SV45: $i,SV100: $i,SV120: $i] :
( ( ( in @ SV120 @ SV100 )
= $false )
| ( ( ~ ! [SY503: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY503 ) @ SV45 ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1336,plain,
! [SV100: $i,SV45: $i,SV120: $i] :
( ( ( ~ ! [SY504: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY504 ) @ SV45 ) )
= $false )
| ( ( in @ SV120 @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1337,plain,
! [SV100: $i,SV45: $i] :
( ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $true )
| ( ( ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1338,plain,
! [SV100: $i,SV45: $i] :
( ( ( ! [SY505: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY505 ) @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1339,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ SV108 @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) )
| ~ ( in @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) @ SV3 ) ) )
= $true )
| ( ( in @ SV108 @ SV50 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1340,plain,
! [SV50: $i,SV3: $i,SV139: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ SV108 @ SV139 )
| ~ ( in @ SV139 @ SV3 ) ) )
= $false )
| ( ( in @ SV108 @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1341,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) ) )
= $true )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1342,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
| ~ ( in @ SV136 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1268]) ).
thf(1343,plain,
! [SV4: $i,SV89: $i,SV101: $i,SV137: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
| ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) ) ) )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1344,plain,
! [SV101: $i,SV4: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 ) ) )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1269]) ).
thf(1345,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
| ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1346,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV5 ) @ SV77 ) ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1271]) ).
thf(1347,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV51 )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1348,plain,
! [SV51: $i,SV5: $i,SV77: $i,SV125: $i] :
( ( ( ~ ( ~ ( in @ SV125 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 ) ) )
= $false )
| ( ( ~ ( in @ SV125 @ SV51 ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1349,plain,
! [SV7: $i,SV52: $i] :
( ( ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV7 )
= $true )
| ( ( disjoint @ SV7 @ SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1276]) ).
thf(1350,plain,
! [SV7: $i,SV52: $i] :
( ( ( in @ ( sK29_SY328 @ SV52 @ SV7 ) @ SV52 )
= $true )
| ( ( disjoint @ SV7 @ SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1277]) ).
thf(1351,plain,
! [SV7: $i,SV52: $i,SV121: $i] :
( ( ( in @ SV121 @ SV52 )
= $false )
| ( ( in @ SV121 @ SV7 )
= $false )
| ( ( ~ ( disjoint @ SV7 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1352,plain,
! [SV53: $i,SV8: $i] :
( ( ( ( sK14_SY331 @ SV8 @ SV53 )
= SV8 )
= $true )
| ( ( in @ ( sK14_SY331 @ SV8 @ SV53 ) @ SV53 )
= $true )
| ( ( SV53
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1353,plain,
! [SV54: $i,SV9: $i,SV102: $i,SV138: $i,SV132: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
| ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) ) ) )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1354,plain,
! [SV102: $i,SV54: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 ) ) )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1355,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
| ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1356,plain,
! [SV92: $i,SV16: $i,SV118: $i] :
( ( ( ! [SY497: $i] :
~ ( in @ ( ordered_pair @ SY497 @ SV118 ) @ SV16 ) )
= $false )
| ( ( in @ SV118 @ SV92 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1357,plain,
! [SV92: $i,SV16: $i,SV118: $i] :
( ( ( ! [SY498: $i] :
~ ( in @ ( ordered_pair @ SY498 @ SV118 ) @ SV16 ) )
= $true )
| ( ( in @ SV118 @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1358,plain,
! [SV92: $i,SV16: $i] :
( ( ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) )
= $false )
| ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1359,plain,
! [SV92: $i,SV16: $i,SV142: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV142 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1360,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) ) )
= $false )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1288]) ).
thf(1361,plain,
! [SV19: $i,SV112: $i,SV110: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) )
= $false )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1288]) ).
thf(1362,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) )
= $false )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1363,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) ) )
= $false )
| ( ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1364,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
= $false )
| ( ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1365,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) ) )
= $false )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1366,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
= $false )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1367,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ~ ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) ) )
= $false )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1368,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
= $false )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1369,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) ) )
= $false )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1370,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
= $false )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1371,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) ) )
= $false )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1372,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
= $false )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1373,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ~ ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) ) )
= $false )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1301]) ).
thf(1374,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
= $false )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1301]) ).
thf(1375,plain,
! [SV94: $i,SV27: $i,SV133: $i,SV127: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 )
| ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 ) )
= $true )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1302]) ).
thf(1376,plain,
! [SV27: $i,SV94: $i,SV133: $i,SV127: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 )
| ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 ) )
= $true )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1377,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) ) )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1378,plain,
! [SV66: $i,SV84: $i,SV28: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV28 ) )
= $false )
| ( ( in @ SV115 @ SV84 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1305]) ).
thf(1379,plain,
! [SV28: $i,SV84: $i,SV66: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV66 ) )
= $false )
| ( ( in @ SV115 @ SV84 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1305]) ).
thf(1380,plain,
! [SV84: $i,SV66: $i,SV28: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV28 ) )
= $true )
| ( ( ~ ( in @ SV115 @ SV66 ) )
= $true )
| ( ( in @ SV115 @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1381,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1307]) ).
thf(1382,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1307]) ).
thf(1383,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1384,plain,
! [SV95: $i,SV30: $i,SV103: $i,SV122: $i] :
( ( ( in @ SV122 @ SV103 )
= $false )
| ( ( ~ ! [SY507: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY507 ) @ SV30 )
| ~ ( in @ SY507 @ SV95 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1385,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV122: $i] :
( ( ( ~ ! [SY508: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY508 ) @ SV30 )
| ~ ( in @ SY508 @ SV95 ) ) )
= $false )
| ( ( in @ SV122 @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1386,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1311]) ).
thf(1387,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ! [SY509: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY509 ) @ SV30 )
| ~ ( in @ SY509 @ SV95 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1388,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ~ ~ ! [SY534: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ SY534 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SY534 ) ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1313]) ).
thf(1389,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i,SV143: $i] :
( ( ( ~ ~ ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV143 @ SV31 )
| ~ ( in @ SY535 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SV143 @ SY535 ) ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1390,plain,
! [SV85: $i,SV67: $i,SV31: $i] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1391,plain,
! [SV85: $i,SV31: $i,SV67: $i] :
( ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1392,plain,
! [SV85: $i,SV67: $i,SV31: $i,SV140: $i] :
( ( ( ~ ! [SY527: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV140 @ SV31 )
| ~ ( in @ SY527 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SY527 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1393,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV144: $i,SV141: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
| ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY536 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY536 @ SV144 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY537 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY537 @ SV144 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 ) ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1394,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
| ~ ! [SY538: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY538 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY538 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) ) )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1318]) ).
thf(1395,plain,
! [SV35: $i,SV70: $i,SV123: $i,SV119: $i] :
( ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $false )
| ( ( ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1396,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( ~ ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1397,plain,
! [SV70: $i,SV35: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1398,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1322]) ).
thf(1399,plain,
! [SV41: $i,SV98: $i,SV135: $i,SV129: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 )
| ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1324]) ).
thf(1400,plain,
! [SV98: $i,SV41: $i,SV129: $i,SV135: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 )
| ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1401,plain,
! [SV98: $i,SV41: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
| ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1402,plain,
! [SV73: $i,SV87: $i,SV42: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV42 ) )
= $false )
| ( ( in @ SV117 @ SV87 )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1327]) ).
thf(1403,plain,
! [SV42: $i,SV87: $i,SV73: $i,SV117: $i] :
( ( ( ~ ~ ( in @ SV117 @ SV73 ) )
= $false )
| ( ( in @ SV117 @ SV87 )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1327]) ).
thf(1404,plain,
! [SV87: $i,SV73: $i,SV42: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV42 ) )
= $true )
| ( ( ~ ~ ( in @ SV117 @ SV73 ) )
= $true )
| ( ( in @ SV117 @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1405,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1406,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1407,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1408,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV124: $i] :
( ( ( in @ SV124 @ SV104 )
= $false )
| ( ( ~ ! [SY511: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY511 @ SV124 ) @ SV43 )
| ~ ( in @ SY511 @ SV99 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1409,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i] :
( ( ( ~ ! [SY512: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY512 @ SV124 ) @ SV43 )
| ~ ( in @ SY512 @ SV99 ) ) )
= $false )
| ( ( in @ SV124 @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1410,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1411,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ! [SY513: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY513 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY513 @ SV99 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1412,plain,
! [SV100: $i,SV45: $i,SV120: $i] :
( ( ( ! [SY503: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY503 ) @ SV45 ) )
= $false )
| ( ( in @ SV120 @ SV100 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1413,plain,
! [SV100: $i,SV45: $i,SV120: $i] :
( ( ( ! [SY504: $i] :
~ ( in @ ( ordered_pair @ SV120 @ SY504 ) @ SV45 ) )
= $true )
| ( ( in @ SV120 @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1336]) ).
thf(1414,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) )
= $false )
| ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1415,plain,
! [SV145: $i,SV100: $i,SV45: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV145 ) @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1416,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) )
| ~ ( in @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) @ SV3 ) )
= $false )
| ( ( in @ SV108 @ SV50 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1417,plain,
! [SV50: $i,SV3: $i,SV139: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV139 )
| ~ ( in @ SV139 @ SV3 ) )
= $true )
| ( ( in @ SV108 @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1418,plain,
! [SV50: $i,SV3: $i] :
( ( ( ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1419,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 ) )
= $true )
| ( ( ~ ( in @ SV136 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1420,plain,
! [SV4: $i,SV89: $i,SV101: $i,SV137: $i,SV130: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
| ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1421,plain,
! [SV101: $i,SV4: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( ~ ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) )
| ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1344]) ).
thf(1422,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
| ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1423,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV5 ) @ SV77 ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1424,plain,
! [SV51: $i,SV5: $i,SV77: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ ( relation_dom @ SV77 ) )
| ~ ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ SV125 @ SV51 ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1425,plain,
! [SV121: $i,SV52: $i,SV7: $i] :
( ( ( disjoint @ SV7 @ SV52 )
= $false )
| ( ( in @ SV121 @ SV7 )
= $false )
| ( ( in @ SV121 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1426,plain,
! [SV54: $i,SV9: $i,SV102: $i,SV138: $i,SV132: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
| ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1427,plain,
! [SV102: $i,SV54: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) )
| ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1354]) ).
thf(1428,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
| ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1429,plain,
! [SV118: $i,SV16: $i,SV92: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK45_SY497 @ SV92 @ SV16 @ SV118 ) @ SV118 ) @ SV16 ) )
= $false )
| ( ( in @ SV118 @ SV92 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1356]) ).
thf(1430,plain,
! [SV92: $i,SV16: $i,SV118: $i,SV146: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV146 @ SV118 ) @ SV16 ) )
= $true )
| ( ( in @ SV118 @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1431,plain,
! [SV92: $i,SV16: $i] :
( ( ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $false )
| ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1432,plain,
! [SV92: $i,SV16: $i] :
( ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $false )
| ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1433,plain,
! [SV92: $i,SV16: $i,SV142: $i] :
( ( ( in @ ( ordered_pair @ SV142 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $false )
| ( ( ~ ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) ) )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1434,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1435,plain,
! [SV19: $i,SV112: $i,SV110: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1436,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( ~ ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) ) )
= $false )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1437,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( ~ ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) ) )
= $false )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1438,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
= $true )
| ( ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1363]) ).
thf(1439,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
= $true )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1440,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
| ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 ) )
= $true )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1441,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
= $true )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1442,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
= $true )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1443,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
| ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 ) )
= $true )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1373]) ).
thf(1444,plain,
! [SV94: $i,SV27: $i,SV133: $i,SV127: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 )
= $true )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1445,plain,
! [SV27: $i,SV94: $i,SV133: $i,SV127: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 )
= $true )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1446,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) ) )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1447,plain,
! [SV27: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) ) )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1448,plain,
! [SV66: $i,SV84: $i,SV28: $i,SV115: $i] :
( ( ( in @ SV115 @ SV28 )
= $true )
| ( ( in @ SV115 @ SV84 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1449,plain,
! [SV28: $i,SV84: $i,SV66: $i,SV115: $i] :
( ( ( in @ SV115 @ SV66 )
= $true )
| ( ( in @ SV115 @ SV84 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1450,plain,
! [SV84: $i,SV66: $i,SV28: $i,SV115: $i] :
( ( ( in @ SV115 @ SV28 )
= $false )
| ( ( ~ ( in @ SV115 @ SV66 ) )
= $true )
| ( ( in @ SV115 @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1451,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) ) )
= $true )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1381]) ).
thf(1452,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1453,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV122: $i] :
( ( ( ! [SY507: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY507 ) @ SV30 )
| ~ ( in @ SY507 @ SV95 ) ) )
= $false )
| ( ( in @ SV122 @ SV103 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1454,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV122: $i] :
( ( ( ! [SY508: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SY508 ) @ SV30 )
| ~ ( in @ SY508 @ SV95 ) ) )
= $true )
| ( ( in @ SV122 @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1455,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) )
= $false )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1456,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
| ~ ( in @ SV147 @ SV95 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1457,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ~ ! [SY534: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ SY534 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SY534 ) ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1388]) ).
thf(1458,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i,SV143: $i] :
( ( ( ~ ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV143 @ SV31 )
| ~ ( in @ SY535 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SV143 @ SY535 ) ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1459,plain,
! [SV85: $i,SV67: $i,SV31: $i] :
( ( ( ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) ) )
= $true )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1390]) ).
thf(1460,plain,
! [SV85: $i,SV67: $i,SV31: $i,SV140: $i] :
( ( ( ! [SY527: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV140 @ SV31 )
| ~ ( in @ SY527 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SY527 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1392]) ).
thf(1461,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV144: $i,SV141: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
| ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY536 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY536 @ SV144 ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY537 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY537 @ SV144 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 ) ) )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1462,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
| ~ ! [SY538: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY538 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY538 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
| ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1463,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1464,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV35 )
| ( SV119 != SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1465,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1466,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 ) )
= $true )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1467,plain,
! [SV41: $i,SV98: $i,SV135: $i,SV129: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1468,plain,
! [SV98: $i,SV41: $i,SV129: $i,SV135: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1469,plain,
! [SV98: $i,SV41: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1470,plain,
! [SV41: $i,SV98: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1471,plain,
! [SV73: $i,SV87: $i,SV42: $i,SV117: $i] :
( ( ( in @ SV117 @ SV42 )
= $true )
| ( ( in @ SV117 @ SV87 )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1472,plain,
! [SV42: $i,SV87: $i,SV73: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV73 ) )
= $true )
| ( ( in @ SV117 @ SV87 )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1473,plain,
! [SV87: $i,SV73: $i,SV42: $i,SV117: $i] :
( ( ( in @ SV117 @ SV42 )
= $false )
| ( ( ~ ~ ( in @ SV117 @ SV73 ) )
= $true )
| ( ( in @ SV117 @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1474,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) ) )
= $true )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1475,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1476,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i] :
( ( ( ! [SY511: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY511 @ SV124 ) @ SV43 )
| ~ ( in @ SY511 @ SV99 ) ) )
= $false )
| ( ( in @ SV124 @ SV104 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1477,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i] :
( ( ( ! [SY512: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY512 @ SV124 ) @ SV43 )
| ~ ( in @ SY512 @ SV99 ) ) )
= $true )
| ( ( in @ SV124 @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1409]) ).
thf(1478,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) )
= $false )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1479,plain,
! [SV104: $i,SV43: $i,SV99: $i,SV148: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SV148 @ SV99 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1480,plain,
! [SV45: $i,SV100: $i,SV120: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV120 @ ( sK46_SY503 @ SV100 @ SV45 @ SV120 ) ) @ SV45 ) )
= $false )
| ( ( in @ SV120 @ SV100 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1412]) ).
thf(1481,plain,
! [SV100: $i,SV45: $i,SV149: $i,SV120: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV120 @ SV149 ) @ SV45 ) )
= $true )
| ( ( in @ SV120 @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1482,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 ) )
= $false )
| ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1483,plain,
! [SV100: $i,SV45: $i] :
( ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $false )
| ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1484,plain,
! [SV145: $i,SV100: $i,SV45: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV145 ) @ SV45 )
= $false )
| ( ( ~ ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1485,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) ) )
= $false )
| ( ( in @ SV108 @ SV50 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1486,plain,
! [SV108: $i,SV3: $i,SV50: $i] :
( ( ( ~ ( in @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) @ SV3 ) )
= $false )
| ( ( in @ SV108 @ SV50 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1487,plain,
! [SV50: $i,SV3: $i,SV139: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV139 ) )
= $true )
| ( ( ~ ( in @ SV139 @ SV3 ) )
= $true )
| ( ( in @ SV108 @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1488,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK47_SY487 @ SV50 @ SV3 ) )
| ~ ( in @ ( sK47_SY487 @ SV50 @ SV3 ) @ SV3 ) ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1418]) ).
thf(1489,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( ~ ( in @ SV136 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1490,plain,
! [SV4: $i,SV89: $i,SV101: $i,SV137: $i,SV130: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1491,plain,
! [SV101: $i,SV4: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( ~ ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1492,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1493,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1494,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ ( relation_dom @ SV77 ) ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1495,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV5 ) @ SV77 ) )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1496,plain,
! [SV51: $i,SV5: $i,SV77: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ ( relation_dom @ SV77 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ SV125 @ SV51 ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1497,plain,
! [SV54: $i,SV9: $i,SV102: $i,SV138: $i,SV132: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1498,plain,
! [SV102: $i,SV54: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1499,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1500,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1501,plain,
! [SV118: $i,SV16: $i,SV92: $i] :
( ( ( in @ ( ordered_pair @ ( sK45_SY497 @ SV92 @ SV16 @ SV118 ) @ SV118 ) @ SV16 )
= $true )
| ( ( in @ SV118 @ SV92 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1502,plain,
! [SV92: $i,SV16: $i,SV118: $i,SV146: $i] :
( ( ( in @ ( ordered_pair @ SV146 @ SV118 ) @ SV16 )
= $false )
| ( ( in @ SV118 @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1503,plain,
! [SV92: $i,SV16: $i] :
( ( ( ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $true )
| ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1431]) ).
thf(1504,plain,
! [SV142: $i,SV92: $i,SV16: $i] :
( ( ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
| ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV142 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1505,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1506,plain,
! [SV19: $i,SV112: $i,SV110: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 ) )
= $true )
| ( ( SV112
= ( apply @ SV19 @ SV110 ) )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1507,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
| ( SV112 = empty_set ) )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1508,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( ( SV112 != empty_set )
| ( SV112
= ( apply @ SV19 @ SV110 ) ) )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1509,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
= $true )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 )
= $true )
| ( ( in @ ( sK16_SY381 @ SV60 @ SV21 @ SV80 ) @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1510,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
= $true )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 )
= $true )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1511,plain,
! [SV80: $i,SV21: $i,SV60: $i] :
( ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV21 )
= $true )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 )
= $true )
| ( ( ( sK16_SY381 @ SV60 @ SV21 @ SV80 )
= SV60 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1512,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
= $true )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 )
= $true )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV81 )
= $true )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1513,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
= $true )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 )
= $true )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1514,plain,
! [SV81: $i,SV22: $i,SV61: $i] :
( ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV22 )
= $true )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 )
= $true )
| ( ( in @ ( sK17_SY383 @ SV61 @ SV22 @ SV81 ) @ SV61 )
= $false )
| ( ( SV81
= ( set_union2 @ SV22 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1515,plain,
! [SV94: $i,SV27: $i,SV133: $i,SV127: $i] :
( ( ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 )
= $false )
| ( ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 )
= $true )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1516,plain,
! [SV27: $i,SV94: $i,SV133: $i,SV127: $i] :
( ( ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV94 )
= $false )
| ( ( in @ ( ordered_pair @ SV127 @ SV133 ) @ SV27 )
= $true )
| ( ( SV27 = SV94 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1517,plain,
! [SV27: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) ) )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1446]) ).
thf(1518,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
= $false )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1519,plain,
! [SV84: $i,SV28: $i,SV66: $i,SV115: $i] :
( ( ( in @ SV115 @ SV66 )
= $false )
| ( ( in @ SV115 @ SV28 )
= $false )
| ( ( in @ SV115 @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1520,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1521,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
| ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1522,plain,
! [SV30: $i,SV95: $i,SV103: $i,SV122: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) ) @ SV30 )
| ~ ( in @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) @ SV95 ) ) )
= $false )
| ( ( in @ SV122 @ SV103 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1453]) ).
thf(1523,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV150: $i,SV122: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SV150 ) @ SV30 )
| ~ ( in @ SV150 @ SV95 ) ) )
= $true )
| ( ( in @ SV122 @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1524,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1525,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $false )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1526,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
| ~ ( in @ SV147 @ SV95 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1527,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ! [SY534: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ SY534 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SY534 ) ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1528,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i,SV143: $i] :
( ( ( ! [SY535: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV143 @ SV31 )
| ~ ( in @ SY535 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SV143 @ SY535 ) ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1458]) ).
thf(1529,plain,
! [SV85: $i,SV67: $i,SV31: $i] :
( ( ( ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1530,plain,
! [SV85: $i,SV67: $i,SV151: $i,SV31: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV140 @ SV31 )
| ~ ( in @ SV151 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SV151 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1531,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV144: $i,SV141: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
| ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY536 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY536 @ SV144 ) @ SV96 ) ) ) )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1532,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV141: $i] :
( ( ( ~ ( ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY537 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY537 @ SV144 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 ) ) )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1533,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
| ~ ! [SY538: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY538 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY538 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1534,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV35 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1535,plain,
! [SV35: $i,SV70: $i,SV123: $i,SV119: $i] :
( ( ( SV119 != SV123 )
= $false )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1536,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV35 ) )
= $true )
| ( ( SV119 != SV123 )
= $true )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1537,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1538,plain,
! [SV70: $i,SV35: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1539,plain,
! [SV70: $i,SV35: $i] :
( ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1540,plain,
! [SV41: $i,SV98: $i,SV135: $i,SV129: $i] :
( ( ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 )
= $false )
| ( ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1541,plain,
! [SV98: $i,SV41: $i,SV129: $i,SV135: $i] :
( ( ( in @ ( ordered_pair @ SV135 @ SV129 ) @ SV41 )
= $false )
| ( ( in @ ( ordered_pair @ SV129 @ SV135 ) @ SV98 )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $false )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1542,plain,
! [SV98: $i,SV41: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) ) )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1543,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1544,plain,
! [SV42: $i,SV87: $i,SV73: $i,SV117: $i] :
( ( ( in @ SV117 @ SV73 )
= $false )
| ( ( in @ SV117 @ SV87 )
= $false )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1545,plain,
! [SV87: $i,SV42: $i,SV73: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV73 ) )
= $false )
| ( ( in @ SV117 @ SV42 )
= $false )
| ( ( in @ SV117 @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1546,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1547,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) ) )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1548,plain,
! [SV124: $i,SV43: $i,SV99: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV124 ) @ SV43 )
| ~ ( in @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV99 ) ) )
= $false )
| ( ( in @ SV124 @ SV104 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1476]) ).
thf(1549,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV152 @ SV124 ) @ SV43 )
| ~ ( in @ SV152 @ SV99 ) ) )
= $true )
| ( ( in @ SV124 @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1550,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) ) )
= $false )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1551,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $false )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1552,plain,
! [SV104: $i,SV43: $i,SV99: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SV148 @ SV99 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1553,plain,
! [SV45: $i,SV100: $i,SV120: $i] :
( ( ( in @ ( ordered_pair @ SV120 @ ( sK46_SY503 @ SV100 @ SV45 @ SV120 ) ) @ SV45 )
= $true )
| ( ( in @ SV120 @ SV100 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1554,plain,
! [SV100: $i,SV45: $i,SV149: $i,SV120: $i] :
( ( ( in @ ( ordered_pair @ SV120 @ SV149 ) @ SV45 )
= $false )
| ( ( in @ SV120 @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1555,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 ) )
= $true )
| ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1556,plain,
! [SV145: $i,SV100: $i,SV45: $i] :
( ( ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 )
| ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV145 ) @ SV45 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1557,plain,
! [SV3: $i,SV50: $i,SV108: $i] :
( ( ( in @ SV108 @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) )
= $true )
| ( ( in @ SV108 @ SV50 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1558,plain,
! [SV108: $i,SV3: $i,SV50: $i] :
( ( ( in @ ( sK41_SY484 @ SV50 @ SV3 @ SV108 ) @ SV3 )
= $true )
| ( ( in @ SV108 @ SV50 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1559,plain,
! [SV50: $i,SV3: $i,SV139: $i,SV108: $i] :
( ( ( in @ SV108 @ SV139 )
= $false )
| ( ( ~ ( in @ SV139 @ SV3 ) )
= $true )
| ( ( in @ SV108 @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1560,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK47_SY487 @ SV50 @ SV3 ) )
| ~ ( in @ ( sK47_SY487 @ SV50 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1561,plain,
! [SV50: $i,SV3: $i,SV136: $i] :
( ( ( in @ SV136 @ SV3 )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( ~ ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) ) )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1562,plain,
! [SV4: $i,SV89: $i,SV101: $i,SV137: $i,SV130: $i] :
( ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $false )
| ( ( ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1563,plain,
! [SV101: $i,SV4: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1564,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1492]) ).
thf(1565,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1493]) ).
thf(1566,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( in @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ ( relation_dom @ SV77 ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1567,plain,
! [SV77: $i,SV5: $i,SV51: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_SY376 @ SV51 @ SV5 @ SV77 ) @ SV5 ) @ SV77 )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1568,plain,
! [SV51: $i,SV5: $i,SV77: $i,SV125: $i] :
( ( ( in @ SV125 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ SV125 @ SV51 ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1569,plain,
! [SV54: $i,SV9: $i,SV102: $i,SV138: $i,SV132: $i] :
( ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $false )
| ( ( ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1570,plain,
! [SV102: $i,SV54: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( ~ ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1571,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1572,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1573,plain,
! [SV92: $i,SV16: $i] :
( ( ( ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $false )
| ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1574,plain,
! [SV142: $i,SV92: $i,SV16: $i] :
( ( ( ~ ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV142 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1575,plain,
! [SV142: $i,SV92: $i,SV16: $i] :
( ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $false )
| ( ( in @ ( ordered_pair @ SV142 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1576,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( SV112
= ( apply @ SV19 @ SV110 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1577,plain,
! [SV19: $i,SV112: $i,SV110: $i] :
( ( ( in @ ( ordered_pair @ SV110 @ SV112 ) @ SV19 )
= $false )
| ( ( SV112
= ( apply @ SV19 @ SV110 ) )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1578,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( SV112
!= ( apply @ SV19 @ SV110 ) )
= $true )
| ( ( SV112 = empty_set )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1507]) ).
thf(1579,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( SV112 != empty_set )
= $true )
| ( ( SV112
= ( apply @ SV19 @ SV110 ) )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1580,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
| ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1581,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
= $false )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1582,plain,
! [SV27: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
= $false )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1583,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1520]) ).
thf(1584,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1520]) ).
thf(1585,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1521]) ).
thf(1586,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1521]) ).
thf(1587,plain,
! [SV30: $i,SV95: $i,SV103: $i,SV122: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV122 @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) ) @ SV30 )
| ~ ( in @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) @ SV95 ) ) )
= $true )
| ( ( in @ SV122 @ SV103 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1522]) ).
thf(1588,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV150: $i,SV122: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV122 @ SV150 ) @ SV30 )
| ~ ( in @ SV150 @ SV95 ) ) )
= $false )
| ( ( in @ SV122 @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1589,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) ) )
= $true )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1524]) ).
thf(1590,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
| ~ ( in @ SV147 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1591,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) @ SV67 ) )
| ( SV116
!= ( ordered_pair @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) ) ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1527]) ).
thf(1592,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV153: $i,SV31: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV143 @ SV31 )
| ~ ( in @ SV153 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SV143 @ SV153 ) ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1593,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ~ ~ ! [SY540: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ SY540 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SY540 ) ) ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1529]) ).
thf(1594,plain,
! [SV85: $i,SV67: $i,SV151: $i,SV31: $i,SV140: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV140 @ SV31 )
| ~ ( in @ SV151 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SV151 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1595,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV144: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
| ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY536 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY536 @ SV144 ) @ SV96 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1596,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV141: $i] :
( ( ( ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY537 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY537 @ SV144 ) @ SV96 ) )
| ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1532]) ).
thf(1597,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
| ~ ! [SY538: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY538 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY538 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1598,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( in @ SV119 @ SV35 )
= $true )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1534]) ).
thf(1599,plain,
! [SV35: $i,SV70: $i,SV123: $i,SV119: $i] :
( ( ( SV119 = SV123 )
= $true )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1600,plain,
! [SV70: $i,SV123: $i,SV35: $i,SV119: $i] :
( ( ( in @ SV119 @ SV35 )
= $false )
| ( ( SV119 != SV123 )
= $true )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1601,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1537]) ).
thf(1602,plain,
! [SV70: $i,SV35: $i] :
( ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) ) )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1603,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
| ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1604,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1543]) ).
thf(1605,plain,
! [SV98: $i,SV41: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1543]) ).
thf(1606,plain,
! [SV87: $i,SV42: $i,SV73: $i,SV117: $i] :
( ( ( in @ SV117 @ SV73 )
= $true )
| ( ( in @ SV117 @ SV42 )
= $false )
| ( ( in @ SV117 @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1607,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1608,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1609,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
| ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1610,plain,
! [SV124: $i,SV43: $i,SV99: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV124 ) @ SV43 )
| ~ ( in @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV99 ) ) )
= $true )
| ( ( in @ SV124 @ SV104 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1548]) ).
thf(1611,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i,SV152: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV152 @ SV124 ) @ SV43 )
| ~ ( in @ SV152 @ SV99 ) ) )
= $false )
| ( ( in @ SV124 @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1612,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) ) )
= $true )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1613,plain,
! [SV104: $i,SV43: $i,SV99: $i,SV148: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SV148 @ SV99 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1614,plain,
! [SV100: $i,SV45: $i] :
( ( ( ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 ) )
= $false )
| ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1615,plain,
! [SV145: $i,SV100: $i,SV45: $i] :
( ( ( ~ ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV145 ) @ SV45 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1616,plain,
! [SV145: $i,SV100: $i,SV45: $i] :
( ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV145 ) @ SV45 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1617,plain,
! [SV50: $i,SV108: $i,SV3: $i,SV139: $i] :
( ( ( in @ SV139 @ SV3 )
= $false )
| ( ( in @ SV108 @ SV139 )
= $false )
| ( ( in @ SV108 @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1618,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK47_SY487 @ SV50 @ SV3 ) )
| ~ ( in @ ( sK47_SY487 @ SV50 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1619,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) )
| ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1620,plain,
! [SV101: $i,SV4: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1621,plain,
! [SV101: $i,SV4: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1622,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1623,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1624,plain,
! [SV51: $i,SV77: $i,SV5: $i,SV125: $i] :
( ( ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 )
= $false )
| ( ( in @ SV125 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( ~ ( in @ SV125 @ SV51 ) )
= $true )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1625,plain,
! [SV102: $i,SV54: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1626,plain,
! [SV102: $i,SV54: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ SV9 )
| ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1627,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1628,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1629,plain,
! [SV16: $i,SV92: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_SY500 @ SV92 @ SV16 ) @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $false )
| ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1573]) ).
thf(1630,plain,
! [SV142: $i,SV92: $i,SV16: $i] :
( ( ( ~ ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV142 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1631,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( SV112
= ( apply @ SV19 @ SV110 ) )
= $false )
| ( ( SV112 = empty_set )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1632,plain,
! [SV110: $i,SV19: $i,SV112: $i] :
( ( ( SV112 = empty_set )
= $false )
| ( ( SV112
= ( apply @ SV19 @ SV110 ) )
= $true )
| ( ( in @ SV110 @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1633,plain,
! [SV27: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1634,plain,
! [SV27: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1635,plain,
! [SV27: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
= $false )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1636,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $true )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1637,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $true )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1638,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) ) )
= $true )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1639,plain,
! [SV30: $i,SV95: $i,SV103: $i,SV122: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV122 @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) ) @ SV30 )
| ~ ( in @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) @ SV95 ) )
= $false )
| ( ( in @ SV122 @ SV103 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1640,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV150: $i,SV122: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV122 @ SV150 ) @ SV30 )
| ~ ( in @ SV150 @ SV95 ) )
= $true )
| ( ( in @ SV122 @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1641,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) ) )
= $false )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1642,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV147 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1643,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) @ SV67 ) )
| ( SV116
!= ( ordered_pair @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) ) ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1644,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV153: $i,SV31: $i,SV143: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV143 @ SV31 )
| ~ ( in @ SV153 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SV143 @ SV153 ) ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1645,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ~ ! [SY540: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ SY540 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SY540 ) ) ) )
= $true )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1646,plain,
! [SV85: $i,SV67: $i,SV151: $i,SV31: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ( in @ SV140 @ SV31 )
| ~ ( in @ SV151 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SV151 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1594]) ).
thf(1647,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV144: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 ) )
= $true )
| ( ( ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY536 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY536 @ SV144 ) @ SV96 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1648,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV141: $i] :
( ( ( ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY537 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY537 @ SV144 ) @ SV96 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1649,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1597]) ).
thf(1650,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ! [SY538: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY538 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY538 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1597]) ).
thf(1651,plain,
! [SV70: $i,SV35: $i,SV123: $i,SV119: $i] :
( ( ( SV119 = SV123 )
= $false )
| ( ( in @ SV119 @ SV35 )
= $false )
| ( ( in @ ( ordered_pair @ SV119 @ SV123 ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1652,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1653,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
| ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 ) )
= $false )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1654,plain,
! [SV41: $i,SV98: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1655,plain,
! [SV98: $i,SV41: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1656,plain,
! [SV41: $i,SV98: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
= $false )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1657,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $true )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1658,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $true )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1659,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1660,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1661,plain,
! [SV124: $i,SV43: $i,SV99: $i,SV104: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV124 ) @ SV43 )
| ~ ( in @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV99 ) )
= $false )
| ( ( in @ SV124 @ SV104 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1662,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i,SV152: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV152 @ SV124 ) @ SV43 )
| ~ ( in @ SV152 @ SV99 ) )
= $true )
| ( ( in @ SV124 @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1663,plain,
! [SV104: $i,SV43: $i,SV99: $i] :
( ( ( ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) ) )
= $false )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1664,plain,
! [SV104: $i,SV43: $i,SV99: $i,SV148: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 ) )
= $true )
| ( ( ~ ( in @ SV148 @ SV99 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1665,plain,
! [SV100: $i,SV45: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ ( sK53_SY506 @ SV100 @ SV45 ) ) @ SV45 ) )
= $false )
| ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1614]) ).
thf(1666,plain,
! [SV145: $i,SV100: $i,SV45: $i] :
( ( ( ~ ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV145 ) @ SV45 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1615]) ).
thf(1667,plain,
! [SV50: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK47_SY487 @ SV50 @ SV3 ) ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1668,plain,
! [SV3: $i,SV50: $i] :
( ( ( ~ ( in @ ( sK47_SY487 @ SV50 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1669,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1670,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1671,plain,
! [SV4: $i,SV101: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV89 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1672,plain,
! [SV89: $i,SV101: $i,SV4: $i,SV137: $i,SV130: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1673,plain,
! [SV101: $i,SV4: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV89 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1674,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1675,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1676,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1677,plain,
! [SV5: $i,SV77: $i,SV51: $i,SV125: $i] :
( ( ( in @ SV125 @ SV51 )
= $false )
| ( ( in @ SV125 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV125 @ SV5 ) @ SV77 )
= $false )
| ( ( in @ SV5 @ ( relation_image @ SV77 @ SV51 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1678,plain,
! [SV54: $i,SV102: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ SV9 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1679,plain,
! [SV9: $i,SV102: $i,SV54: $i,SV138: $i,SV132: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1680,plain,
! [SV102: $i,SV54: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ SV9 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1681,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1682,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1683,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1684,plain,
! [SV16: $i,SV92: $i] :
( ( ( in @ ( ordered_pair @ ( sK52_SY500 @ SV92 @ SV16 ) @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $true )
| ( ( in @ ( sK21_SY411 @ SV16 @ SV92 ) @ SV92 )
= $true )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1685,plain,
! [SV142: $i,SV92: $i,SV16: $i] :
( ( ( ! [SY500: $i] :
~ ( in @ ( ordered_pair @ SY500 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV142 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1686,plain,
! [SV27: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV94 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK30_SY416 @ SV94 @ SV27 ) @ ( sK35_SY518 @ SV27 @ SV94 ) ) @ SV27 )
= $true )
| ( ( SV27 = SV94 )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1687,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
| ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1688,plain,
! [SV30: $i,SV95: $i,SV103: $i,SV122: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV122 @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) ) @ SV30 ) )
= $false )
| ( ( in @ SV122 @ SV103 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1689,plain,
! [SV122: $i,SV30: $i,SV95: $i,SV103: $i] :
( ( ( ~ ( in @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) @ SV95 ) )
= $false )
| ( ( in @ SV122 @ SV103 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1690,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV150: $i,SV122: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV122 @ SV150 ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV150 @ SV95 ) )
= $true )
| ( ( in @ SV122 @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1691,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) ) @ SV30 )
| ~ ( in @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) @ SV95 ) ) )
= $false )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1641]) ).
thf(1692,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( ~ ( in @ SV147 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1693,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) @ SV67 ) )
| ( SV116
!= ( ordered_pair @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1694,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV153: $i,SV31: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ SV143 @ SV31 )
| ~ ( in @ SV153 @ SV67 ) )
| ( SV116
!= ( ordered_pair @ SV143 @ SV153 ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1695,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ! [SY540: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ SY540 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SY540 ) ) ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1696,plain,
! [SV85: $i,SV67: $i,SV151: $i,SV31: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ( in @ SV140 @ SV31 )
| ~ ( in @ SV151 @ SV67 ) ) )
= $true )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SV151 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1697,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV144: $i,SV141: $i] :
( ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $false )
| ( ( ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY536 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY536 @ SV144 ) @ SV96 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1698,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV141: $i] :
( ( ( ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY537 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY537 @ SV144 ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1699,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1700,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ! [SY538: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY538 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY538 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1701,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1702,plain,
! [SV70: $i,SV35: $i] :
( ( ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1703,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) ) )
= $false )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1704,plain,
! [SV70: $i,SV35: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $false )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1705,plain,
! [SV41: $i,SV98: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_SY521 @ SV98 @ SV41 ) @ ( sK31_SY436 @ SV41 @ SV98 ) ) @ SV41 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY436 @ SV41 @ SV98 ) @ ( sK37_SY521 @ SV98 @ SV41 ) ) @ SV98 )
= $true )
| ( ( SV98
= ( relation_inverse @ SV41 ) )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1706,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1707,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) ) )
= $true )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1708,plain,
! [SV124: $i,SV43: $i,SV99: $i,SV104: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV124 ) @ SV43 ) )
= $false )
| ( ( in @ SV124 @ SV104 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1709,plain,
! [SV124: $i,SV43: $i,SV99: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV99 ) )
= $false )
| ( ( in @ SV124 @ SV104 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1710,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i,SV152: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV152 @ SV124 ) @ SV43 ) )
= $true )
| ( ( ~ ( in @ SV152 @ SV99 ) )
= $true )
| ( ( in @ SV124 @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1711,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ SV99 ) ) )
= $false )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1663]) ).
thf(1712,plain,
! [SV104: $i,SV43: $i,SV99: $i,SV148: $i] :
( ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( ~ ( in @ SV148 @ SV99 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1713,plain,
! [SV100: $i,SV45: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ ( sK53_SY506 @ SV100 @ SV45 ) ) @ SV45 )
= $true )
| ( ( in @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1714,plain,
! [SV145: $i,SV100: $i,SV45: $i] :
( ( ( ! [SY506: $i] :
~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SY506 ) @ SV45 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV145 ) @ SV45 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1666]) ).
thf(1715,plain,
! [SV50: $i,SV3: $i] :
( ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK47_SY487 @ SV50 @ SV3 ) )
= $true )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1716,plain,
! [SV3: $i,SV50: $i] :
( ( ( in @ ( sK47_SY487 @ SV50 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV50 )
= $true )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1717,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) ) )
= $true )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1718,plain,
! [SV4: $i,SV101: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( in @ SV130 @ SV89 )
= $true )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1719,plain,
! [SV89: $i,SV101: $i,SV4: $i,SV137: $i,SV130: $i] :
( ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 )
= $true )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1720,plain,
! [SV101: $i,SV4: $i,SV137: $i,SV89: $i,SV130: $i] :
( ( ( in @ SV130 @ SV89 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1721,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1722,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) ) )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1723,plain,
! [SV54: $i,SV102: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( in @ SV138 @ SV9 )
= $true )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1724,plain,
! [SV9: $i,SV102: $i,SV54: $i,SV138: $i,SV132: $i] :
( ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 )
= $true )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1725,plain,
! [SV102: $i,SV54: $i,SV132: $i,SV9: $i,SV138: $i] :
( ( ( in @ SV138 @ SV9 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1726,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1727,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) ) )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1728,plain,
! [SV16: $i,SV92: $i,SV142: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK56_SY500 @ SV142 @ SV92 @ SV16 ) @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV142 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1685]) ).
thf(1729,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1730,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1731,plain,
! [SV30: $i,SV95: $i,SV103: $i,SV122: $i] :
( ( ( in @ ( ordered_pair @ SV122 @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) ) @ SV30 )
= $true )
| ( ( in @ SV122 @ SV103 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1732,plain,
! [SV122: $i,SV30: $i,SV95: $i,SV103: $i] :
( ( ( in @ ( sK48_SY507 @ SV103 @ SV95 @ SV30 @ SV122 ) @ SV95 )
= $true )
| ( ( in @ SV122 @ SV103 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1733,plain,
! [SV103: $i,SV95: $i,SV30: $i,SV150: $i,SV122: $i] :
( ( ( in @ ( ordered_pair @ SV122 @ SV150 ) @ SV30 )
= $false )
| ( ( ~ ( in @ SV150 @ SV95 ) )
= $true )
| ( ( in @ SV122 @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1734,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) ) @ SV30 )
| ~ ( in @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1735,plain,
! [SV103: $i,SV30: $i,SV95: $i,SV147: $i] :
( ( ( in @ SV147 @ SV95 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( ~ ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1736,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) @ SV67 ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1737,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV116: $i] :
( ( ( SV116
!= ( ordered_pair @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1738,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV153: $i,SV31: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ SV143 @ SV31 )
| ~ ( in @ SV153 @ SV67 ) ) )
= $true )
| ( ( SV116
!= ( ordered_pair @ SV143 @ SV153 ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1739,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) ) ) ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1695]) ).
thf(1740,plain,
! [SV85: $i,SV67: $i,SV151: $i,SV31: $i,SV140: $i] :
( ( ( ~ ( ~ ( in @ SV140 @ SV31 )
| ~ ( in @ SV151 @ SV67 ) ) )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SV151 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1741,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV141: $i] :
( ( ( ! [SY536: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY536 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY536 @ SV144 ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1742,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV141: $i] :
( ( ( ! [SY537: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SY537 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY537 @ SV144 ) @ SV96 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1743,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1744,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(1745,plain,
! [SV70: $i,SV35: $i] :
( ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1746,plain,
! [SV70: $i,SV35: $i] :
( ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK22_SY370 @ SV35 @ SV70 ) @ ( sK25_SY502 @ SV70 @ SV35 ) ) @ SV70 )
= $true )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1747,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) ) )
= $true )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1748,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
| ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1749,plain,
! [SV124: $i,SV43: $i,SV99: $i,SV104: $i] :
( ( ( in @ ( ordered_pair @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV124 ) @ SV43 )
= $true )
| ( ( in @ SV124 @ SV104 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1750,plain,
! [SV124: $i,SV43: $i,SV99: $i,SV104: $i] :
( ( ( in @ ( sK49_SY511 @ SV104 @ SV99 @ SV43 @ SV124 ) @ SV99 )
= $true )
| ( ( in @ SV124 @ SV104 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1751,plain,
! [SV104: $i,SV99: $i,SV43: $i,SV124: $i,SV152: $i] :
( ( ( in @ ( ordered_pair @ SV152 @ SV124 ) @ SV43 )
= $false )
| ( ( ~ ( in @ SV152 @ SV99 ) )
= $true )
| ( ( in @ SV124 @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1752,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(1753,plain,
! [SV104: $i,SV43: $i,SV99: $i,SV148: $i] :
( ( ( in @ SV148 @ SV99 )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( ~ ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) ) )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1754,plain,
! [SV145: $i,SV100: $i,SV45: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ ( sK58_SY506 @ SV145 @ SV100 @ SV45 ) ) @ SV45 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV145 ) @ SV45 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1714]) ).
thf(1755,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ! [SY487: $i] :
~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SY487 )
| ~ ( in @ SY487 @ SV3 ) ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1756,plain,
! [SV101: $i,SV89: $i,SV4: $i,SV137: $i,SV130: $i] :
( ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV4 )
= $false )
| ( ( in @ SV130 @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ SV130 @ SV137 ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1757,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1758,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
| ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 ) )
= $false )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1759,plain,
! [SV102: $i,SV9: $i,SV54: $i,SV138: $i,SV132: $i] :
( ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV54 )
= $false )
| ( ( in @ SV138 @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ SV132 @ SV138 ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $false )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1760,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1761,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
| ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 ) )
= $false )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1762,plain,
! [SV16: $i,SV92: $i,SV142: $i] :
( ( ( in @ ( ordered_pair @ ( sK56_SY500 @ SV142 @ SV92 @ SV16 ) @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $true )
| ( ( in @ ( ordered_pair @ SV142 @ ( sK21_SY411 @ SV16 @ SV92 ) ) @ SV16 )
= $false )
| ( ( SV92
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(1763,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $true )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1764,plain,
! [SV84: $i,SV28: $i,SV66: $i] :
( ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $true )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV28 )
= $false )
| ( ( in @ ( sK18_SY385 @ SV66 @ SV28 @ SV84 ) @ SV66 )
= $false )
| ( ( SV84
= ( set_intersection2 @ SV28 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1765,plain,
! [SV103: $i,SV30: $i,SV122: $i,SV95: $i,SV150: $i] :
( ( ( in @ SV150 @ SV95 )
= $false )
| ( ( in @ ( ordered_pair @ SV122 @ SV150 ) @ SV30 )
= $false )
| ( ( in @ SV122 @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1766,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) ) @ SV30 )
| ~ ( in @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) @ SV95 ) )
= $false )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1767,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) )
| ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1768,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) @ SV67 ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1769,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV116: $i] :
( ( ( SV116
= ( ordered_pair @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1770,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV153: $i,SV31: $i,SV143: $i] :
( ( ( ~ ( ~ ( in @ SV143 @ SV31 )
| ~ ( in @ SV153 @ SV67 ) ) )
= $false )
| ( ( SV116
!= ( ordered_pair @ SV143 @ SV153 ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1771,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) ) ) ) )
= $true )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1772,plain,
! [SV85: $i,SV67: $i,SV151: $i,SV31: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ SV31 )
| ~ ( in @ SV151 @ SV67 ) )
= $true )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SV151 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1773,plain,
! [SV32: $i,SV144: $i,SV96: $i,SV105: $i,SV141: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) @ SV144 ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1741]) ).
thf(1774,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV155: $i,SV141: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SV155 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SV155 @ SV144 ) @ SV96 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(1775,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1776,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1777,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1778,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
| ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) ) )
= $false )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1779,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1780,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1781,plain,
! [SV104: $i,SV43: $i,SV124: $i,SV99: $i,SV152: $i] :
( ( ( in @ SV152 @ SV99 )
= $false )
| ( ( in @ ( ordered_pair @ SV152 @ SV124 ) @ SV43 )
= $false )
| ( ( in @ SV124 @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1782,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ SV99 ) )
= $false )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1783,plain,
! [SV148: $i,SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) )
| ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1784,plain,
! [SV145: $i,SV100: $i,SV45: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ ( sK58_SY506 @ SV145 @ SV100 @ SV45 ) ) @ SV45 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY448 @ SV45 @ SV100 ) @ SV145 ) @ SV45 )
= $false )
| ( ( SV100
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1785,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) )
| ~ ( in @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) @ SV3 ) ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1755]) ).
thf(1786,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1757]) ).
thf(1787,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1757]) ).
thf(1788,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) ) )
= $false )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1789,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $false )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1790,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1791,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1792,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) ) )
= $false )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1793,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $false )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1794,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) ) @ SV30 ) )
= $false )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1795,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( ~ ( in @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) @ SV95 ) )
= $false )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1796,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1797,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1798,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) @ SV67 ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1799,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV153: $i,SV31: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV31 )
| ~ ( in @ SV153 @ SV67 ) )
= $true )
| ( ( SV116
!= ( ordered_pair @ SV143 @ SV153 ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1770]) ).
thf(1800,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) ) ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1801,plain,
! [SV85: $i,SV67: $i,SV151: $i,SV31: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ SV31 ) )
= $true )
| ( ( ~ ( in @ SV151 @ SV67 ) )
= $true )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SV151 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1802,plain,
! [SV32: $i,SV144: $i,SV96: $i,SV105: $i,SV141: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV141 @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) @ SV144 ) @ SV96 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1803,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV155: $i,SV141: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV141 @ SV155 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SV155 @ SV144 ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1804,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1805,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1806,plain,
! [SV70: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 ) )
= $false )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1807,plain,
! [SV70: $i,SV35: $i] :
( ( ( ( sK22_SY370 @ SV35 @ SV70 )
!= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1808,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $true )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1809,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 ) )
= $true )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1780]) ).
thf(1810,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 ) )
= $false )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1782]) ).
thf(1811,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( ~ ( in @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ SV99 ) )
= $false )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1782]) ).
thf(1812,plain,
! [SV148: $i,SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1783]) ).
thf(1813,plain,
! [SV148: $i,SV104: $i,SV43: $i,SV99: $i] :
( ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1783]) ).
thf(1814,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) )
| ~ ( in @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1815,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1816,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV101 )
= $true )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1817,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) ) )
= $true )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1818,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1819,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV102 )
= $true )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1820,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) ) )
= $true )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1821,plain,
! [SV103: $i,SV30: $i,SV95: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) ) @ SV30 )
= $true )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1822,plain,
! [SV95: $i,SV30: $i,SV103: $i] :
( ( ( in @ ( sK54_SY510 @ SV103 @ SV30 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV103 )
= $true )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1823,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1796]) ).
thf(1824,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1825,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) @ SV67 ) )
= $false )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1826,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV153: $i,SV31: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV31 ) )
= $true )
| ( ( ~ ( in @ SV153 @ SV67 ) )
= $true )
| ( ( SV116
!= ( ordered_pair @ SV143 @ SV153 ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1827,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) @ SV67 ) ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1800]) ).
thf(1828,plain,
! [SV85: $i,SV31: $i,SV67: $i] :
( ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1800]) ).
thf(1829,plain,
! [SV85: $i,SV67: $i,SV151: $i,SV31: $i,SV140: $i] :
( ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ~ ( in @ SV151 @ SV67 ) )
= $true )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SV151 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1830,plain,
! [SV32: $i,SV144: $i,SV96: $i,SV105: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV141 @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) @ SV144 ) @ SV96 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1831,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV155: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV141 @ SV155 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SV155 @ SV144 ) @ SV96 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1832,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1833,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(1834,plain,
! [SV70: $i,SV35: $i] :
( ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $true )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1835,plain,
! [SV70: $i,SV35: $i] :
( ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $true )
| ( ( in @ ( sK22_SY370 @ SV35 @ SV70 ) @ SV35 )
= $false )
| ( ( ( sK22_SY370 @ SV35 @ SV70 )
= ( sK25_SY502 @ SV70 @ SV35 ) )
= $false )
| ( ( SV70
= ( identity_relation @ SV35 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1836,plain,
! [SV87: $i,SV42: $i,SV73: $i] :
( ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV42 )
= $false )
| ( ( in @ ( sK20_SY398 @ SV73 @ SV42 @ SV87 ) @ SV73 )
= $true )
| ( ( SV87
= ( set_difference @ SV42 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1837,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( in @ ( ordered_pair @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $true )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1810]) ).
thf(1838,plain,
! [SV99: $i,SV43: $i,SV104: $i] :
( ( ( in @ ( sK55_SY514 @ SV104 @ SV43 @ SV99 ) @ SV99 )
= $true )
| ( ( in @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1839,plain,
! [SV148: $i,SV104: $i,SV43: $i,SV99: $i] :
( ( ( ~ ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1840,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) )
| ~ ( in @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1841,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
= $false )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1842,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
| ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1843,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ! [SY510: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SY510 ) @ SV30 )
| ~ ( in @ SY510 @ SV95 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1844,plain,
! [SV31: $i,SV67: $i,SV116: $i,SV85: $i] :
( ( ( in @ ( sK43_SY489 @ SV85 @ SV116 @ SV67 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1824]) ).
thf(1845,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV31: $i] :
( ( ( in @ ( sK50_SY534 @ SV31 @ SV67 @ SV116 @ SV85 ) @ SV67 )
= $true )
| ( ( in @ SV116 @ SV85 )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(1846,plain,
! [SV85: $i,SV116: $i,SV67: $i,SV153: $i,SV31: $i,SV143: $i] :
( ( ( in @ SV143 @ SV31 )
= $false )
| ( ( ~ ( in @ SV153 @ SV67 ) )
= $true )
| ( ( SV116
!= ( ordered_pair @ SV143 @ SV153 ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1847,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ~ ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) @ SV67 ) ) )
= $true )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1848,plain,
! [SV85: $i,SV31: $i,SV67: $i] :
( ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) ) )
= $true )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1828]) ).
thf(1849,plain,
! [SV85: $i,SV31: $i,SV140: $i,SV67: $i,SV151: $i] :
( ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SV140 @ SV151 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1850,plain,
! [SV32: $i,SV144: $i,SV96: $i,SV105: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV141 @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) ) @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1851,plain,
! [SV141: $i,SV32: $i,SV144: $i,SV96: $i,SV105: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) @ SV144 ) @ SV96 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1852,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV155: $i,SV141: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV141 @ SV155 ) @ SV32 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV155 @ SV144 ) @ SV96 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(1853,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1832]) ).
thf(1854,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1855,plain,
! [SV148: $i,SV104: $i,SV43: $i,SV99: $i] :
( ( ( ! [SY514: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY514 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ SY514 @ SV99 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(1856,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1857,plain,
! [SV3: $i,SV50: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1858,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 ) )
= $false )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1859,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 ) )
= $false )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1860,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 ) )
= $false )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1842]) ).
thf(1861,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1842]) ).
thf(1862,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) ) @ SV30 )
| ~ ( in @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) @ SV95 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1843]) ).
thf(1863,plain,
! [SV85: $i,SV116: $i,SV31: $i,SV143: $i,SV67: $i,SV153: $i] :
( ( ( in @ SV153 @ SV67 )
= $false )
| ( ( in @ SV143 @ SV31 )
= $false )
| ( ( SV116
!= ( ordered_pair @ SV143 @ SV153 ) )
= $true )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1864,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) @ SV67 ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1865,plain,
! [SV151: $i,SV140: $i,SV85: $i,SV31: $i,SV67: $i] :
( ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(1866,plain,
! [SV32: $i,SV144: $i,SV96: $i,SV105: $i,SV141: $i] :
( ( ( in @ ( ordered_pair @ SV141 @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) ) @ SV32 )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1867,plain,
! [SV141: $i,SV32: $i,SV144: $i,SV96: $i,SV105: $i] :
( ( ( in @ ( ordered_pair @ ( sK59_SY536 @ SV105 @ SV96 @ SV144 @ SV32 @ SV141 ) @ SV144 ) @ SV96 )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1851]) ).
thf(1868,plain,
! [SV105: $i,SV96: $i,SV144: $i,SV32: $i,SV155: $i,SV141: $i] :
( ( ( in @ ( ordered_pair @ SV141 @ SV155 ) @ SV32 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV155 @ SV144 ) @ SV96 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(1869,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1870,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV154: $i] :
( ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( ~ ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) ) )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1871,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV148: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ SV99 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1855]) ).
thf(1872,plain,
! [SV136: $i,SV50: $i,SV3: $i] :
( ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) )
= $true )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1873,plain,
! [SV3: $i,SV50: $i,SV136: $i] :
( ( ( in @ ( sK60_SY487 @ SV136 @ SV50 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ ( sK13_SY322 @ SV3 @ SV50 ) @ SV136 )
= $false )
| ( ( in @ SV136 @ SV3 )
= $false )
| ( ( SV50
= ( union @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(1874,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $true )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(1875,plain,
! [SV101: $i,SV89: $i,SV4: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $true )
| ( ( in @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_SY453 @ SV4 @ SV89 @ SV101 ) @ ( sK38_SY523 @ SV101 @ SV89 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV101
= ( relation_dom_restriction @ SV4 @ SV89 ) )
= $true )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1859]) ).
thf(1876,plain,
! [SV54: $i,SV9: $i,SV102: $i] :
( ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $true )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1860]) ).
thf(1877,plain,
! [SV102: $i,SV9: $i,SV54: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $true )
| ( ( in @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) @ SV9 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_SY457 @ SV54 @ SV9 @ SV102 ) @ ( sK39_SY525 @ SV102 @ SV9 @ SV54 ) ) @ SV54 )
= $false )
| ( ( SV102
= ( relation_rng_restriction @ SV9 @ SV54 ) )
= $true )
| ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(1878,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) ) @ SV30 )
| ~ ( in @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(1879,plain,
! [SV85: $i,SV67: $i,SV31: $i,SV153: $i,SV143: $i,SV116: $i] :
( ( ( SV116
= ( ordered_pair @ SV143 @ SV153 ) )
= $false )
| ( ( in @ SV143 @ SV31 )
= $false )
| ( ( in @ SV153 @ SV67 )
= $false )
| ( ( in @ SV116 @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(1880,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1864]) ).
thf(1881,plain,
! [SV85: $i,SV67: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) @ SV67 ) )
= $false )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1864]) ).
thf(1882,plain,
! [SV140: $i,SV151: $i,SV85: $i,SV67: $i,SV31: $i] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(1883,plain,
! [SV105: $i,SV32: $i,SV141: $i,SV96: $i,SV144: $i,SV155: $i] :
( ( ( in @ ( ordered_pair @ SV155 @ SV144 ) @ SV96 )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV155 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV141 @ SV144 ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $false )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1884,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1885,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
| ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1886,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ SV99 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1887,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) ) @ SV30 )
| ~ ( in @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) @ SV95 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1888,plain,
! [SV31: $i,SV67: $i,SV85: $i] :
( ( ( in @ ( sK51_SY495 @ SV85 @ SV67 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1880]) ).
thf(1889,plain,
! [SV85: $i,SV67: $i,SV31: $i] :
( ( ( in @ ( sK57_SY540 @ SV31 @ SV67 @ SV85 ) @ SV67 )
= $true )
| ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1881]) ).
thf(1890,plain,
! [SV140: $i,SV151: $i,SV85: $i,SV67: $i,SV31: $i] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(1891,plain,
! [SV140: $i,SV151: $i,SV85: $i,SV31: $i,SV67: $i] :
( ( ( in @ ( sK19_SY391 @ SV67 @ SV31 @ SV85 ) @ SV85 )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(1892,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) ) @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1884]) ).
thf(1893,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1884]) ).
thf(1894,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1885]) ).
thf(1895,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1885]) ).
thf(1896,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV148: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
| ~ ( in @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ SV99 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(1897,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) ) @ SV30 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(1898,plain,
! [SV95: $i,SV30: $i,SV103: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) @ SV95 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(1899,plain,
! [SV140: $i,SV151: $i,SV85: $i,SV67: $i,SV31: $i] :
( ( ( ~ ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) ) )
= $true )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(1900,plain,
! [SV105: $i,SV32: $i,SV96: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) ) @ SV32 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1892]) ).
thf(1901,plain,
! [SV96: $i,SV32: $i,SV105: $i] :
( ( ( in @ ( ordered_pair @ ( sK61_SY539 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV105 )
= $true )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(1902,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(1903,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV148: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1904,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV148: $i] :
( ( ( ~ ( in @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ SV99 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1905,plain,
! [SV147: $i,SV103: $i,SV30: $i,SV95: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) ) @ SV30 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(1906,plain,
! [SV95: $i,SV30: $i,SV103: $i,SV147: $i] :
( ( ( in @ ( sK62_SY510 @ SV147 @ SV103 @ SV30 @ SV95 ) @ SV95 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY462 @ SV95 @ SV30 @ SV103 ) @ SV147 ) @ SV30 )
= $false )
| ( ( in @ SV147 @ SV95 )
= $false )
| ( ( SV103
= ( relation_inverse_image @ SV30 @ SV95 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(1907,plain,
! [SV140: $i,SV151: $i,SV85: $i,SV67: $i,SV31: $i] :
( ( ( ! [SY495: $i] :
~ ~ ! [SY496: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY495 @ SV31 )
| ~ ( in @ SY496 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ SY495 @ SY496 ) ) ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(1908,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ! [SY539: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SY539 ) @ SV32 )
| ~ ( in @ ( ordered_pair @ SY539 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(1909,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV148: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $true )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(1910,plain,
! [SV99: $i,SV43: $i,SV104: $i,SV148: $i] :
( ( ( in @ ( sK63_SY514 @ SV148 @ SV104 @ SV43 @ SV99 ) @ SV99 )
= $true )
| ( ( in @ ( ordered_pair @ SV148 @ ( sK26_SY468 @ SV99 @ SV43 @ SV104 ) ) @ SV43 )
= $false )
| ( ( in @ SV148 @ SV99 )
= $false )
| ( ( SV104
= ( relation_image @ SV43 @ SV99 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(1911,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ~ ~ ! [SY541: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ SY541 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SY541 ) ) ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1907]) ).
thf(1912,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1908]) ).
thf(1913,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ~ ! [SY541: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ SY541 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SY541 ) ) ) )
= $true )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1911]) ).
thf(1914,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1915,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ! [SY541: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ SY541 @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SY541 ) ) ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1916,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1917,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) ) ) ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1915]) ).
thf(1918,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) ) @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1916]) ).
thf(1919,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV154: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1916]) ).
thf(1920,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) ) ) ) )
= $true )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1917]) ).
thf(1921,plain,
! [SV154: $i,SV105: $i,SV32: $i,SV96: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) ) @ SV32 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(1922,plain,
! [SV96: $i,SV32: $i,SV105: $i,SV154: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_SY539 @ SV154 @ SV105 @ SV32 @ SV96 ) @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY476 @ SV96 @ SV32 @ SV105 ) @ SV154 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ ( sK44_SY531 @ SV105 @ SV32 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV105
= ( relation_composition @ SV32 @ SV96 ) )
= $true )
| ( ( relation @ SV105 )
= $false )
| ( ( relation @ SV96 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(1923,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) @ SV67 ) )
| ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) ) ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(1924,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) @ SV67 ) ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(1925,plain,
! [SV151: $i,SV140: $i,SV85: $i,SV31: $i,SV67: $i] :
( ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
!= ( ordered_pair @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(1926,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ~ ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) @ SV67 ) ) )
= $true )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(1927,plain,
! [SV151: $i,SV140: $i,SV85: $i,SV31: $i,SV67: $i] :
( ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) ) )
= $true )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(1928,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) @ SV67 ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(1929,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(1930,plain,
! [SV140: $i,SV151: $i,SV85: $i,SV67: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) @ SV67 ) )
= $false )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(1931,plain,
! [SV31: $i,SV67: $i,SV85: $i,SV151: $i,SV140: $i] :
( ( ( in @ ( sK64_SY495 @ SV140 @ SV151 @ SV85 @ SV67 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(1932,plain,
! [SV140: $i,SV151: $i,SV85: $i,SV67: $i,SV31: $i] :
( ( ( in @ ( sK66_SY541 @ SV31 @ SV67 @ SV85 @ SV151 @ SV140 ) @ SV67 )
= $true )
| ( ( in @ SV151 @ SV67 )
= $false )
| ( ( in @ SV140 @ SV31 )
= $false )
| ( ( ( sK19_SY391 @ SV67 @ SV31 @ SV85 )
= ( ordered_pair @ SV140 @ SV151 ) )
= $false )
| ( ( SV85
= ( cartesian_product2 @ SV31 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(1933,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[332,1932,1931,1927,1922,1921,1910,1909,1906,1905,1901,1900,1895,1891,1889,1888,1883,1879,1877,1876,1875,1874,1873,1872,1867,1866,1848,1845,1844,1838,1837,1836,1835,1834,1822,1821,1819,1818,1816,1815,1813,1808,1797,1793,1789,1784,1781,1776,1769,1765,1764,1763,1762,1759,1756,1750,1749,1746,1745,1732,1731,1724,1723,1719,1718,1716,1715,1713,1706,1705,1704,1686,1684,1682,1677,1675,1670,1660,1657,1656,1655,1651,1637,1636,1635,1634,1632,1631,1617,1616,1606,1605,1599,1598,1586,1582,1577,1576,1575,1567,1566,1558,1557,1554,1553,1551,1544,1541,1540,1538,1525,1519,1516,1515,1514,1513,1512,1511,1510,1509,1502,1501,1483,1471,1449,1448,1432,1425,1406,1391,1382,1374,1372,1370,1368,1366,1364,1352,1350,1349,1347,1323,1298,1297,1296,1292,1291,1290,1281,1280,1275,1274,1267,1250,1230,1211,1206,1178,1161,1160,1151,1145,1140,1139,1112,1111,1087,1086,1079,1078,1049,1045,996,995,970,969,968,967,921,920,908,894,876,875,872,865,864,863,790,776,750,749,747,746,732,731,728,724,713,712,658,622,596,594,560,553,545,539,537,528,422,369,368,354,353,348,347,345,344,343,342,341,340,339,338,337,336,335,334,333]) ).
thf(1934,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(copy,[status(thm)],[287]) ).
thf(1935,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(copy,[status(thm)],[286]) ).
thf(1936,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(copy,[status(thm)],[285]) ).
thf(1937,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(copy,[status(thm)],[284]) ).
thf(1938,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(copy,[status(thm)],[283]) ).
thf(1939,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(1940,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(copy,[status(thm)],[281]) ).
thf(1941,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(1942,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(copy,[status(thm)],[279]) ).
thf(1943,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(1944,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(1945,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(1946,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(copy,[status(thm)],[275]) ).
thf(1947,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(copy,[status(thm)],[274]) ).
thf(1948,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(copy,[status(thm)],[273]) ).
thf(1949,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(copy,[status(thm)],[272]) ).
thf(1950,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(copy,[status(thm)],[271]) ).
thf(1951,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(1952,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(1953,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(1954,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(copy,[status(thm)],[267]) ).
thf(1955,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(1956,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(copy,[status(thm)],[265]) ).
thf(1957,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(copy,[status(thm)],[264]) ).
thf(1958,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(copy,[status(thm)],[263]) ).
thf(1959,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(1960,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(copy,[status(thm)],[261]) ).
thf(1961,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(copy,[status(thm)],[260]) ).
thf(1962,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(copy,[status(thm)],[259]) ).
thf(1963,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(1964,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(copy,[status(thm)],[257]) ).
thf(1965,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(copy,[status(thm)],[256]) ).
thf(1966,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(copy,[status(thm)],[255]) ).
thf(1967,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(copy,[status(thm)],[254]) ).
thf(1968,plain,
$true = $true,
inference(copy,[status(thm)],[253]) ).
thf(1969,plain,
$true = $true,
inference(copy,[status(thm)],[252]) ).
thf(1970,plain,
$true = $true,
inference(copy,[status(thm)],[251]) ).
thf(1971,plain,
$true = $true,
inference(copy,[status(thm)],[250]) ).
thf(1972,plain,
$true = $true,
inference(copy,[status(thm)],[249]) ).
thf(1973,plain,
$true = $true,
inference(copy,[status(thm)],[248]) ).
thf(1974,plain,
$true = $true,
inference(copy,[status(thm)],[247]) ).
thf(1975,plain,
$true = $true,
inference(copy,[status(thm)],[246]) ).
thf(1976,plain,
$true = $true,
inference(copy,[status(thm)],[245]) ).
thf(1977,plain,
$true = $true,
inference(copy,[status(thm)],[244]) ).
thf(1978,plain,
$true = $true,
inference(copy,[status(thm)],[243]) ).
thf(1979,plain,
$true = $true,
inference(copy,[status(thm)],[242]) ).
thf(1980,plain,
$true = $true,
inference(copy,[status(thm)],[241]) ).
thf(1981,plain,
$true = $true,
inference(copy,[status(thm)],[240]) ).
thf(1982,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(1983,plain,
$true = $true,
inference(copy,[status(thm)],[238]) ).
thf(1984,plain,
$true = $true,
inference(copy,[status(thm)],[237]) ).
thf(1985,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(1986,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(1987,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(1988,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(1989,plain,
$true = $true,
inference(copy,[status(thm)],[232]) ).
thf(1990,plain,
$true = $true,
inference(copy,[status(thm)],[231]) ).
thf(1991,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(1992,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(1993,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(1994,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(1995,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(1996,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(1997,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(1998,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(1999,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(2000,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(2001,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(2002,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(2003,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(2004,plain,
( ( function @ sK3_SY160 )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(2005,plain,
( ( relation @ sK3_SY160 )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(2006,plain,
( ( ~ ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
& ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(2007,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ ( relation_field @ SX2 ) )
| ~ ( in @ SX1 @ ( relation_field @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1938]) ).
thf(2008,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1935]) ).
thf(2009,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1953]) ).
thf(2010,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1991]) ).
thf(2011,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX3 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX3 @ SX0 ) @ SX2 ) )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX3 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX3 @ SX0 ) @ SX2 ) )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1936]) ).
thf(2012,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1945]) ).
thf(2013,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1988]) ).
thf(2014,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1963]) ).
thf(2015,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) )
| ( SX0 = SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1954]) ).
thf(2016,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1965]) ).
thf(2017,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1985]) ).
thf(2018,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2003]) ).
thf(2019,plain,
( ( ~ ( ~ ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
| ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) ) )
| ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2006]) ).
thf(2020,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1952]) ).
thf(2021,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1957]) ).
thf(2022,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1996]) ).
thf(2023,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2001]) ).
thf(2024,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1959]) ).
thf(2025,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ 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 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1966]) ).
thf(2026,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1999]) ).
thf(2027,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1982]) ).
thf(2028,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1942]) ).
thf(2029,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1943]) ).
thf(2030,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1940]) ).
thf(2031,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1939]) ).
thf(2032,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1994]) ).
thf(2033,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2002]) ).
thf(2034,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1960]) ).
thf(2035,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1934]) ).
thf(2036,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1995]) ).
thf(2037,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_rng_restriction @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( 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 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_rng_restriction @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1948]) ).
thf(2038,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( relation_inverse_image @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( relation_inverse_image @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1950]) ).
thf(2039,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1987]) ).
thf(2040,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1955]) ).
thf(2041,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_dom_restriction @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( 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 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1947]) ).
thf(2042,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( ~ ( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ( ~ ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( ~ ( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) )
| ~ ( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1961]) ).
thf(2043,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i,SX3: $i] :
( SX1
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1951]) ).
thf(2044,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1949]) ).
thf(2045,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1962]) ).
thf(2046,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1997]) ).
thf(2047,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2000]) ).
thf(2048,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1998]) ).
thf(2049,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ( SX2 != SX3 ) )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1946]) ).
thf(2050,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1993]) ).
thf(2051,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1944]) ).
thf(2052,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1956]) ).
thf(2053,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ! [SX1: $i,SX2: $i] :
~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1941]) ).
thf(2054,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ~ ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1937]) ).
thf(2055,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( subset @ 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 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1958]) ).
thf(2056,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1964]) ).
thf(2057,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_composition @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [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 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_composition @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1967]) ).
thf(2058,plain,
! [SV156: $i] :
( ( relation @ ( identity_relation @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2059,plain,
! [SV157: $i] :
( ( ! [SY542: $i] :
~ ( empty @ ( ordered_pair @ SV157 @ SY542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2060,plain,
! [SV158: $i] :
( ( ! [SY543: $i,SY544: $i] :
( ~ ( relation @ SY544 )
| ~ ( in @ ( ordered_pair @ SV158 @ SY543 ) @ SY544 )
| ~ ( ~ ( in @ SV158 @ ( relation_field @ SY544 ) )
| ~ ( in @ SY543 @ ( relation_field @ SY544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2061,plain,
! [SV159: $i] :
( ( ! [SY545: $i,SY546: $i,SY547: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV159 @ SY545 ) @ ( cartesian_product2 @ SY546 @ SY547 ) )
| ~ ( ~ ( in @ SV159 @ SY546 )
| ~ ( in @ SY545 @ SY547 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV159 @ SY546 )
| ~ ( in @ SY545 @ SY547 ) )
| ( in @ ( ordered_pair @ SV159 @ SY545 ) @ ( cartesian_product2 @ SY546 @ SY547 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2062,plain,
! [SV160: $i] :
( ( ~ ( ~ ( ( SV160 != empty_set )
| ! [SY548: $i] :
~ ( in @ SY548 @ SV160 ) )
| ~ ( ~ ! [SY549: $i] :
~ ( in @ SY549 @ SV160 )
| ( SV160 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2063,plain,
! [SV161: $i] :
( ( ! [SY550: $i] :
( ~ ~ ( ~ ( relation @ SV161 )
| ~ ( relation @ SY550 ) )
| ( relation @ ( set_intersection2 @ SV161 @ SY550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2064,plain,
! [SV162: $i] :
( ( ! [SY551: $i,SY552: $i] :
( ~ ( relation @ SY552 )
| ~ ( ~ ( ~ ( in @ SV162 @ ( relation_image @ SY552 @ SY551 ) )
| ~ ! [SY553: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY553 @ ( relation_dom @ SY552 ) )
| ~ ( in @ ( ordered_pair @ SY553 @ SV162 ) @ SY552 ) )
| ~ ( in @ SY553 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY554: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY554 @ ( relation_dom @ SY552 ) )
| ~ ( in @ ( ordered_pair @ SY554 @ SV162 ) @ SY552 ) )
| ~ ( in @ SY554 @ SY551 ) )
| ( in @ SV162 @ ( relation_image @ SY552 @ SY551 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2065,plain,
! [SV163: $i] :
( ( ~ ( empty @ SV163 )
| ( relation @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2066,plain,
! [SV164: $i] :
( ( ! [SY555: $i] :
( ~ ( relation @ SY555 )
| ( relation @ ( relation_rng_restriction @ SV164 @ SY555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2067,plain,
! [SV165: $i] :
( ( ! [SY556: $i] :
~ ( ~ ( ( SY556
!= ( union @ SV165 ) )
| ! [SY557: $i] :
~ ( ~ ( ~ ( in @ SY557 @ SY556 )
| ~ ! [SY558: $i] :
~ ~ ( ~ ( in @ SY557 @ SY558 )
| ~ ( in @ SY558 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ~ ( ~ ( in @ SY557 @ SY559 )
| ~ ( in @ SY559 @ SV165 ) )
| ( in @ SY557 @ SY556 ) ) ) )
| ~ ( ~ ! [SY560: $i] :
~ ( ~ ( ~ ( in @ SY560 @ SY556 )
| ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY560 @ SY561 )
| ~ ( in @ SY561 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY562: $i] :
~ ~ ( ~ ( in @ SY560 @ SY562 )
| ~ ( in @ SY562 @ SV165 ) )
| ( in @ SY560 @ SY556 ) ) )
| ( SY556
= ( union @ SV165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2068,plain,
! [SV166: $i] :
( ( ~ ( relation @ SV166 )
| ! [SY563: $i] :
( ~ ( relation @ SY563 )
| ~ ( ~ ( ( SV166 != SY563 )
| ! [SY564: $i,SY565: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SV166 )
| ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SY563 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SY563 )
| ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SV166 ) ) ) )
| ~ ( ~ ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV166 )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SY563 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SY563 )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV166 ) ) )
| ( SV166 = SY563 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2069,plain,
! [SV167: $i] :
( ( ~ ( relation @ SV167 )
| ! [SY568: $i] :
~ ( ~ ( ( SY568
!= ( relation_rng @ SV167 ) )
| ! [SY569: $i] :
~ ( ~ ( ~ ( in @ SY569 @ SY568 )
| ~ ! [SY570: $i] :
~ ( in @ ( ordered_pair @ SY570 @ SY569 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY571: $i] :
~ ( in @ ( ordered_pair @ SY571 @ SY569 ) @ SV167 )
| ( in @ SY569 @ SY568 ) ) ) )
| ~ ( ~ ! [SY572: $i] :
~ ( ~ ( ~ ( in @ SY572 @ SY568 )
| ~ ! [SY573: $i] :
~ ( in @ ( ordered_pair @ SY573 @ SY572 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ SY572 ) @ SV167 )
| ( in @ SY572 @ SY568 ) ) )
| ( SY568
= ( relation_rng @ SV167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2070,plain,
! [SV168: $i] :
( ( ! [SY575: $i] :
( ~ ~ ( ~ ( relation @ SV168 )
| ~ ( relation @ SY575 ) )
| ( relation @ ( relation_composition @ SV168 @ SY575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2071,plain,
! [SV169: $i] :
( ( ! [SY576: $i] :
~ ~ ( ~ ( in @ SV169 @ SY576 )
| ~ ( empty @ SY576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2072,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
| ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) ) )
| ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2073,plain,
! [SV170: $i] :
( ( ! [SY577: $i] :
~ ( ~ ( ( SY577
!= ( singleton @ SV170 ) )
| ! [SY578: $i] :
~ ( ~ ( ~ ( in @ SY578 @ SY577 )
| ( SY578 = SV170 ) )
| ~ ( ( SY578 != SV170 )
| ( in @ SY578 @ SY577 ) ) ) )
| ~ ( ~ ! [SY579: $i] :
~ ( ~ ( ~ ( in @ SY579 @ SY577 )
| ( SY579 = SV170 ) )
| ~ ( ( SY579 != SV170 )
| ( in @ SY579 @ SY577 ) ) )
| ( SY577
= ( singleton @ SV170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2074,plain,
! [SV171: $i] :
( ( ! [SY580: $i,SY581: $i] :
~ ( ~ ( ( SY581
!= ( cartesian_product2 @ SV171 @ SY580 ) )
| ! [SY582: $i] :
~ ( ~ ( ~ ( in @ SY582 @ SY581 )
| ~ ! [SY583: $i] :
~ ~ ! [SY584: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY583 @ SV171 )
| ~ ( in @ SY584 @ SY580 ) )
| ( SY582
!= ( ordered_pair @ SY583 @ SY584 ) ) ) )
| ~ ( ~ ~ ! [SY585: $i] :
~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY585 @ SV171 )
| ~ ( in @ SY586 @ SY580 ) )
| ( SY582
!= ( ordered_pair @ SY585 @ SY586 ) ) )
| ( in @ SY582 @ SY581 ) ) ) )
| ~ ( ~ ! [SY587: $i] :
~ ( ~ ( ~ ( in @ SY587 @ SY581 )
| ~ ! [SY588: $i] :
~ ~ ! [SY589: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY588 @ SV171 )
| ~ ( in @ SY589 @ SY580 ) )
| ( SY587
!= ( ordered_pair @ SY588 @ SY589 ) ) ) )
| ~ ( ~ ~ ! [SY590: $i] :
~ ~ ! [SY591: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY590 @ SV171 )
| ~ ( in @ SY591 @ SY580 ) )
| ( SY587
!= ( ordered_pair @ SY590 @ SY591 ) ) )
| ( in @ SY587 @ SY581 ) ) )
| ( SY581
= ( cartesian_product2 @ SV171 @ SY580 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2075,plain,
! [SV172: $i] :
( ( ~ ( relation @ SV172 )
| ( ( relation_inverse @ ( relation_inverse @ SV172 ) )
= SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2076,plain,
! [SV173: $i] :
( ( ! [SY592: $i] :
( ~ ( in @ SV173 @ SY592 )
| ( element @ SV173 @ SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2077,plain,
! [SV174: $i] :
( ( ! [SY593: $i] :
~ ( ~ ( ~ ( subset @ SV174 @ SY593 )
| ! [SY594: $i] :
( ~ ( in @ SY594 @ SV174 )
| ( in @ SY594 @ SY593 ) ) )
| ~ ( ~ ! [SY595: $i] :
( ~ ( in @ SY595 @ SV174 )
| ( in @ SY595 @ SY593 ) )
| ( subset @ SV174 @ SY593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2078,plain,
! [SV175: $i] :
( ( ~ ( relation @ SV175 )
| ! [SY596: $i] :
( ~ ( relation @ SY596 )
| ~ ( ~ ( ( SY596
!= ( relation_inverse @ SV175 ) )
| ! [SY597: $i,SY598: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY597 @ SY598 ) @ SY596 )
| ( in @ ( ordered_pair @ SY598 @ SY597 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY598 @ SY597 ) @ SV175 )
| ( in @ ( ordered_pair @ SY597 @ SY598 ) @ SY596 ) ) ) )
| ~ ( ~ ! [SY599: $i,SY600: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY599 @ SY600 ) @ SY596 )
| ( in @ ( ordered_pair @ SY600 @ SY599 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY600 @ SY599 ) @ SV175 )
| ( in @ ( ordered_pair @ SY599 @ SY600 ) @ SY596 ) ) )
| ( SY596
= ( relation_inverse @ SV175 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2079,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2080,plain,
! [SV176: $i] :
( ( ~ ( relation @ SV176 )
| ( relation @ ( relation_inverse @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2081,plain,
! [SV177: $i] :
( ( ! [SY601: $i,SY602: $i] :
( ~ ( relation @ SY602 )
| ~ ( ~ ( ~ ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SY602 @ SY601 ) ) )
| ~ ( ~ ( in @ SV177 @ SY601 )
| ~ ( in @ SV177 @ ( relation_dom @ SY602 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV177 @ SY601 )
| ~ ( in @ SV177 @ ( relation_dom @ SY602 ) ) )
| ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SY602 @ SY601 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2082,plain,
! [SV178: $i] :
( ( ! [SY603: $i] :
( ~ ( in @ SV178 @ SY603 )
| ~ ( in @ SY603 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2083,plain,
! [SV179: $i] :
( ( ! [SY604: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV179 @ SY604 )
| ~ ! [SY605: $i] :
~ ~ ( ~ ( in @ SY605 @ SV179 )
| ~ ( in @ SY605 @ SY604 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY606: $i] :
~ ~ ( ~ ( in @ SY606 @ SV179 )
| ~ ( in @ SY606 @ SY604 ) )
| ~ ( disjoint @ SV179 @ SY604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2084,plain,
! [SV180: $i] :
( ( ! [SY607: $i,SY608: $i,SY609: $i] :
( ( ( ordered_pair @ SV180 @ SY607 )
!= ( ordered_pair @ SY608 @ SY609 ) )
| ~ ( ( SV180 != SY608 )
| ( SY607 != SY609 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2085,plain,
! [SV181: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV181 )
| ~ ( relation @ SV181 ) )
| ~ ( empty @ ( relation_dom @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2086,plain,
! [SV182: $i] :
( ( ! [SY610: $i] :
( ~ ! [SY611: $i] :
~ ( ~ ( ~ ( in @ SY611 @ SV182 )
| ( in @ SY611 @ SY610 ) )
| ~ ( ~ ( in @ SY611 @ SY610 )
| ( in @ SY611 @ SV182 ) ) )
| ( SV182 = SY610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2087,plain,
! [SV183: $i] :
( ( ! [SY612: $i,SY613: $i] :
~ ( ~ ( ( SY613
!= ( set_intersection2 @ SV183 @ SY612 ) )
| ! [SY614: $i] :
~ ( ~ ( ~ ( in @ SY614 @ SY613 )
| ~ ( ~ ( in @ SY614 @ SV183 )
| ~ ( in @ SY614 @ SY612 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY614 @ SV183 )
| ~ ( in @ SY614 @ SY612 ) )
| ( in @ SY614 @ SY613 ) ) ) )
| ~ ( ~ ! [SY615: $i] :
~ ( ~ ( ~ ( in @ SY615 @ SY613 )
| ~ ( ~ ( in @ SY615 @ SV183 )
| ~ ( in @ SY615 @ SY612 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY615 @ SV183 )
| ~ ( in @ SY615 @ SY612 ) )
| ( in @ SY615 @ SY613 ) ) )
| ( SY613
= ( set_intersection2 @ SV183 @ SY612 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2088,plain,
! [SV184: $i] :
( ( ! [SY616: $i,SY617: $i,SY618: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV184 @ SY616 ) @ ( cartesian_product2 @ SY617 @ SY618 ) )
| ~ ( ~ ( in @ SV184 @ SY617 )
| ~ ( in @ SY616 @ SY618 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV184 @ SY617 )
| ~ ( in @ SY616 @ SY618 ) )
| ( in @ ( ordered_pair @ SV184 @ SY616 ) @ ( cartesian_product2 @ SY617 @ SY618 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2089,plain,
! [SV185: $i] :
( ( ~ ( empty @ SV185 )
| ~ ( ~ ( empty @ ( relation_dom @ SV185 ) )
| ~ ( relation @ ( relation_dom @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2090,plain,
! [SV186: $i] :
( ( ! [SY619: $i] :
( ~ ( relation @ SY619 )
| ! [SY620: $i] :
( ~ ( relation @ SY620 )
| ~ ( ~ ( ( SY620
!= ( relation_rng_restriction @ SV186 @ SY619 ) )
| ! [SY621: $i,SY622: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY621 @ SY622 ) @ SY620 )
| ~ ( ~ ( in @ SY622 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY621 @ SY622 ) @ SY619 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY622 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY621 @ SY622 ) @ SY619 ) )
| ( in @ ( ordered_pair @ SY621 @ SY622 ) @ SY620 ) ) ) )
| ~ ( ~ ! [SY623: $i,SY624: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY623 @ SY624 ) @ SY620 )
| ~ ( ~ ( in @ SY624 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY623 @ SY624 ) @ SY619 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY624 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY623 @ SY624 ) @ SY619 ) )
| ( in @ ( ordered_pair @ SY623 @ SY624 ) @ SY620 ) ) )
| ( SY620
= ( relation_rng_restriction @ SV186 @ SY619 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2091,plain,
! [SV187: $i] :
( ( ~ ( relation @ SV187 )
| ! [SY625: $i,SY626: $i] :
~ ( ~ ( ( SY626
!= ( relation_inverse_image @ SV187 @ SY625 ) )
| ! [SY627: $i] :
~ ( ~ ( ~ ( in @ SY627 @ SY626 )
| ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY627 @ SY628 ) @ SV187 )
| ~ ( in @ SY628 @ SY625 ) ) )
| ~ ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY627 @ SY629 ) @ SV187 )
| ~ ( in @ SY629 @ SY625 ) )
| ( in @ SY627 @ SY626 ) ) ) )
| ~ ( ~ ! [SY630: $i] :
~ ( ~ ( ~ ( in @ SY630 @ SY626 )
| ~ ! [SY631: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SV187 )
| ~ ( in @ SY631 @ SY625 ) ) )
| ~ ( ~ ~ ! [SY632: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY630 @ SY632 ) @ SV187 )
| ~ ( in @ SY632 @ SY625 ) )
| ( in @ SY630 @ SY626 ) ) )
| ( SY626
= ( relation_inverse_image @ SV187 @ SY625 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2092,plain,
! [SV188: $i] :
( ( ! [SY633: $i] :
( ~ ( relation @ SV188 )
| ( relation @ ( relation_dom_restriction @ SV188 @ SY633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2093,plain,
! [SV189: $i] :
( ( ! [SY634: $i,SY635: $i] :
~ ( ~ ( ( SY635
!= ( unordered_pair @ SV189 @ SY634 ) )
| ! [SY636: $i] :
~ ( ~ ( ~ ( in @ SY636 @ SY635 )
| ( SY636 = SV189 )
| ( SY636 = SY634 ) )
| ~ ( ~ ( ( SY636 = SV189 )
| ( SY636 = SY634 ) )
| ( in @ SY636 @ SY635 ) ) ) )
| ~ ( ~ ! [SY637: $i] :
~ ( ~ ( ~ ( in @ SY637 @ SY635 )
| ( SY637 = SV189 )
| ( SY637 = SY634 ) )
| ~ ( ~ ( ( SY637 = SV189 )
| ( SY637 = SY634 ) )
| ( in @ SY637 @ SY635 ) ) )
| ( SY635
= ( unordered_pair @ SV189 @ SY634 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2094,plain,
! [SV190: $i] :
( ( ~ ( relation @ SV190 )
| ! [SY638: $i,SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( ~ ( ( SY639
!= ( relation_dom_restriction @ SV190 @ SY638 ) )
| ! [SY640: $i,SY641: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SY639 )
| ~ ( ~ ( in @ SY640 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY640 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SY639 ) ) ) )
| ~ ( ~ ! [SY642: $i,SY643: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY639 )
| ~ ( ~ ( in @ SY642 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY642 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY639 ) ) )
| ( SY639
= ( relation_dom_restriction @ SV190 @ SY638 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2095,plain,
! [SV191: $i] :
( ( ~ ~ ( ~ ( relation @ SV191 )
| ~ ( function @ SV191 ) )
| ! [SY644: $i,SY645: $i] :
~ ( ~ ( ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( SY645 = empty_set ) )
| ~ ( ( SY645 != empty_set )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2096,plain,
! [SV192: $i] :
( ( ~ ( ~ ( ~ ( relation @ SV192 )
| ! [SY646: $i] :
~ ~ ( ~ ( in @ SY646 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY646
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY649: $i] :
~ ~ ( ~ ( in @ SY649 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY649
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2097,plain,
! [SV193: $i] :
( ( ~ ( relation @ SV193 )
| ! [SY652: $i,SY653: $i] :
~ ( ~ ( ( SY653
!= ( relation_image @ SV193 @ SY652 ) )
| ! [SY654: $i] :
~ ( ~ ( ~ ( in @ SY654 @ SY653 )
| ~ ! [SY655: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY655 @ SY654 ) @ SV193 )
| ~ ( in @ SY655 @ SY652 ) ) )
| ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY656 @ SY654 ) @ SV193 )
| ~ ( in @ SY656 @ SY652 ) )
| ( in @ SY654 @ SY653 ) ) ) )
| ~ ( ~ ! [SY657: $i] :
~ ( ~ ( ~ ( in @ SY657 @ SY653 )
| ~ ! [SY658: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY658 @ SY657 ) @ SV193 )
| ~ ( in @ SY658 @ SY652 ) ) )
| ~ ( ~ ~ ! [SY659: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY659 @ SY657 ) @ SV193 )
| ~ ( in @ SY659 @ SY652 ) )
| ( in @ SY657 @ SY653 ) ) )
| ( SY653
= ( relation_image @ SV193 @ SY652 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2098,plain,
! [SV194: $i] :
( ( ~ ( relation @ SV194 )
| ! [SY660: $i] :
~ ( ~ ( ( SY660
!= ( relation_dom @ SV194 ) )
| ! [SY661: $i] :
~ ( ~ ( ~ ( in @ SY661 @ SY660 )
| ~ ! [SY662: $i] :
~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY663: $i] :
~ ( in @ ( ordered_pair @ SY661 @ SY663 ) @ SV194 )
| ( in @ SY661 @ SY660 ) ) ) )
| ~ ( ~ ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ SY660 )
| ~ ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY665 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY666: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY666 ) @ SV194 )
| ( in @ SY664 @ SY660 ) ) )
| ( SY660
= ( relation_dom @ SV194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2099,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2100,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2101,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2102,plain,
! [SV195: $i] :
( ( ! [SY667: $i] :
( ~ ( relation @ SY667 )
| ~ ( ~ ( ( SY667
!= ( identity_relation @ SV195 ) )
| ! [SY668: $i,SY669: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY668 @ SY669 ) @ SY667 )
| ~ ( ~ ( in @ SY668 @ SV195 )
| ( SY668 != SY669 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY668 @ SV195 )
| ( SY668 != SY669 ) )
| ( in @ ( ordered_pair @ SY668 @ SY669 ) @ SY667 ) ) ) )
| ~ ( ~ ! [SY670: $i,SY671: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY670 @ SY671 ) @ SY667 )
| ~ ( ~ ( in @ SY670 @ SV195 )
| ( SY670 != SY671 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY670 @ SV195 )
| ( SY670 != SY671 ) )
| ( in @ ( ordered_pair @ SY670 @ SY671 ) @ SY667 ) ) )
| ( SY667
= ( identity_relation @ SV195 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2103,plain,
! [SV196: $i] :
( ( ! [SY672: $i] :
( ~ ~ ( ~ ( relation @ SV196 )
| ~ ( relation @ SY672 ) )
| ( relation @ ( set_union2 @ SV196 @ SY672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2104,plain,
! [SV197: $i] :
( ( ~ ( empty @ SV197 )
| ( function @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2105,plain,
! [SV198: $i] :
( ( ! [SY673: $i,SY674: $i] :
~ ( ~ ( ( SY674
!= ( set_union2 @ SV198 @ SY673 ) )
| ! [SY675: $i] :
~ ( ~ ( ~ ( in @ SY675 @ SY674 )
| ( in @ SY675 @ SV198 )
| ( in @ SY675 @ SY673 ) )
| ~ ( ~ ( ( in @ SY675 @ SV198 )
| ( in @ SY675 @ SY673 ) )
| ( in @ SY675 @ SY674 ) ) ) )
| ~ ( ~ ! [SY676: $i] :
~ ( ~ ( ~ ( in @ SY676 @ SY674 )
| ( in @ SY676 @ SV198 )
| ( in @ SY676 @ SY673 ) )
| ~ ( ~ ( ( in @ SY676 @ SV198 )
| ( in @ SY676 @ SY673 ) )
| ( in @ SY676 @ SY674 ) ) )
| ( SY674
= ( set_union2 @ SV198 @ SY673 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2106,plain,
! [SV199: $i] :
( ( ~ ( relation @ SV199 )
| ~ ! [SY677: $i,SY678: $i] :
~ ( in @ ( ordered_pair @ SY677 @ SY678 ) @ SV199 )
| ( SV199 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2107,plain,
! [SV200: $i] :
( ( ! [SY679: $i,SY680: $i] :
( ~ ( relation @ SY680 )
| ~ ( in @ ( ordered_pair @ SV200 @ SY679 ) @ SY680 )
| ~ ( ~ ( in @ SV200 @ ( relation_dom @ SY680 ) )
| ~ ( in @ SY679 @ ( relation_rng @ SY680 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2108,plain,
! [SV201: $i] :
( ( ~ ( relation @ SV201 )
| ! [SY681: $i] :
( ~ ( relation @ SY681 )
| ~ ( ~ ( ~ ( subset @ SV201 @ SY681 )
| ! [SY682: $i,SY683: $i] :
( ~ ( in @ ( ordered_pair @ SY682 @ SY683 ) @ SV201 )
| ( in @ ( ordered_pair @ SY682 @ SY683 ) @ SY681 ) ) )
| ~ ( ~ ! [SY684: $i,SY685: $i] :
( ~ ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SV201 )
| ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SY681 ) )
| ( subset @ SV201 @ SY681 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2109,plain,
! [SV202: $i] :
( ( ! [SY686: $i,SY687: $i] :
~ ( ~ ( ( SY687
!= ( set_difference @ SV202 @ SY686 ) )
| ! [SY688: $i] :
~ ( ~ ( ~ ( in @ SY688 @ SY687 )
| ~ ( ~ ( in @ SY688 @ SV202 )
| ~ ~ ( in @ SY688 @ SY686 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY688 @ SV202 )
| ~ ~ ( in @ SY688 @ SY686 ) )
| ( in @ SY688 @ SY687 ) ) ) )
| ~ ( ~ ! [SY689: $i] :
~ ( ~ ( ~ ( in @ SY689 @ SY687 )
| ~ ( ~ ( in @ SY689 @ SV202 )
| ~ ~ ( in @ SY689 @ SY686 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY689 @ SV202 )
| ~ ~ ( in @ SY689 @ SY686 ) )
| ( in @ SY689 @ SY687 ) ) )
| ( SY687
= ( set_difference @ SV202 @ SY686 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2110,plain,
! [SV203: $i] :
( ( ~ ( relation @ SV203 )
| ! [SY690: $i] :
( ~ ( relation @ SY690 )
| ! [SY691: $i] :
( ~ ( relation @ SY691 )
| ~ ( ~ ( ( SY691
!= ( relation_composition @ SV203 @ SY690 ) )
| ! [SY692: $i,SY693: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SY691 )
| ~ ! [SY694: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY692 @ SY694 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY694 @ SY693 ) @ SY690 ) ) )
| ~ ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY692 @ SY695 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY695 @ SY693 ) @ SY690 ) )
| ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SY691 ) ) ) )
| ~ ( ~ ! [SY696: $i,SY697: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY696 @ SY697 ) @ SY691 )
| ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY696 @ SY698 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY698 @ SY697 ) @ SY690 ) ) )
| ~ ( ~ ~ ! [SY699: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY696 @ SY699 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY699 @ SY697 ) @ SY690 ) )
| ( in @ ( ordered_pair @ SY696 @ SY697 ) @ SY691 ) ) )
| ( SY691
= ( relation_composition @ SV203 @ SY690 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2111,plain,
! [SV204: $i,SV157: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV157 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2112,plain,
! [SV205: $i,SV158: $i] :
( ( ! [SY700: $i] :
( ~ ( relation @ SY700 )
| ~ ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SY700 )
| ~ ( ~ ( in @ SV158 @ ( relation_field @ SY700 ) )
| ~ ( in @ SV205 @ ( relation_field @ SY700 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2113,plain,
! [SV206: $i,SV159: $i] :
( ( ! [SY701: $i,SY702: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SY701 @ SY702 ) )
| ~ ( ~ ( in @ SV159 @ SY701 )
| ~ ( in @ SV206 @ SY702 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV159 @ SY701 )
| ~ ( in @ SV206 @ SY702 ) )
| ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SY701 @ SY702 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2114,plain,
! [SV160: $i] :
( ( ~ ( ( SV160 != empty_set )
| ! [SY548: $i] :
~ ( in @ SY548 @ SV160 ) )
| ~ ( ~ ! [SY549: $i] :
~ ( in @ SY549 @ SV160 )
| ( SV160 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2115,plain,
! [SV207: $i,SV161: $i] :
( ( ~ ~ ( ~ ( relation @ SV161 )
| ~ ( relation @ SV207 ) )
| ( relation @ ( set_intersection2 @ SV161 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2116,plain,
! [SV208: $i,SV162: $i] :
( ( ! [SY703: $i] :
( ~ ( relation @ SY703 )
| ~ ( ~ ( ~ ( in @ SV162 @ ( relation_image @ SY703 @ SV208 ) )
| ~ ! [SY704: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY704 @ ( relation_dom @ SY703 ) )
| ~ ( in @ ( ordered_pair @ SY704 @ SV162 ) @ SY703 ) )
| ~ ( in @ SY704 @ SV208 ) ) )
| ~ ( ~ ~ ! [SY705: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY705 @ ( relation_dom @ SY703 ) )
| ~ ( in @ ( ordered_pair @ SY705 @ SV162 ) @ SY703 ) )
| ~ ( in @ SY705 @ SV208 ) )
| ( in @ SV162 @ ( relation_image @ SY703 @ SV208 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2117,plain,
! [SV163: $i] :
( ( ( ~ ( empty @ SV163 ) )
= $true )
| ( ( relation @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2065]) ).
thf(2118,plain,
! [SV164: $i,SV209: $i] :
( ( ~ ( relation @ SV209 )
| ( relation @ ( relation_rng_restriction @ SV164 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2119,plain,
! [SV165: $i,SV210: $i] :
( ( ~ ( ~ ( ( SV210
!= ( union @ SV165 ) )
| ! [SY706: $i] :
~ ( ~ ( ~ ( in @ SY706 @ SV210 )
| ~ ! [SY558: $i] :
~ ~ ( ~ ( in @ SY706 @ SY558 )
| ~ ( in @ SY558 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ~ ( ~ ( in @ SY706 @ SY559 )
| ~ ( in @ SY559 @ SV165 ) )
| ( in @ SY706 @ SV210 ) ) ) )
| ~ ( ~ ! [SY709: $i] :
~ ( ~ ( ~ ( in @ SY709 @ SV210 )
| ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY709 @ SY561 )
| ~ ( in @ SY561 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY562: $i] :
~ ~ ( ~ ( in @ SY709 @ SY562 )
| ~ ( in @ SY562 @ SV165 ) )
| ( in @ SY709 @ SV210 ) ) )
| ( SV210
= ( union @ SV165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2120,plain,
! [SV166: $i] :
( ( ( ~ ( relation @ SV166 ) )
= $true )
| ( ( ! [SY563: $i] :
( ~ ( relation @ SY563 )
| ~ ( ~ ( ( SV166 != SY563 )
| ! [SY564: $i,SY565: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SV166 )
| ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SY563 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SY563 )
| ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SV166 ) ) ) )
| ~ ( ~ ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV166 )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SY563 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SY563 )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV166 ) ) )
| ( SV166 = SY563 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2068]) ).
thf(2121,plain,
! [SV167: $i] :
( ( ( ~ ( relation @ SV167 ) )
= $true )
| ( ( ! [SY568: $i] :
~ ( ~ ( ( SY568
!= ( relation_rng @ SV167 ) )
| ! [SY569: $i] :
~ ( ~ ( ~ ( in @ SY569 @ SY568 )
| ~ ! [SY570: $i] :
~ ( in @ ( ordered_pair @ SY570 @ SY569 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY571: $i] :
~ ( in @ ( ordered_pair @ SY571 @ SY569 ) @ SV167 )
| ( in @ SY569 @ SY568 ) ) ) )
| ~ ( ~ ! [SY572: $i] :
~ ( ~ ( ~ ( in @ SY572 @ SY568 )
| ~ ! [SY573: $i] :
~ ( in @ ( ordered_pair @ SY573 @ SY572 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ SY572 ) @ SV167 )
| ( in @ SY572 @ SY568 ) ) )
| ( SY568
= ( relation_rng @ SV167 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2069]) ).
thf(2122,plain,
! [SV211: $i,SV168: $i] :
( ( ~ ~ ( ~ ( relation @ SV168 )
| ~ ( relation @ SV211 ) )
| ( relation @ ( relation_composition @ SV168 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2123,plain,
! [SV212: $i,SV169: $i] :
( ( ~ ~ ( ~ ( in @ SV169 @ SV212 )
| ~ ( empty @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2124,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
| ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2125,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY158 ) @ sK3_SY160 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2126,plain,
! [SV170: $i,SV213: $i] :
( ( ~ ( ~ ( ( SV213
!= ( singleton @ SV170 ) )
| ! [SY712: $i] :
~ ( ~ ( ~ ( in @ SY712 @ SV213 )
| ( SY712 = SV170 ) )
| ~ ( ( SY712 != SV170 )
| ( in @ SY712 @ SV213 ) ) ) )
| ~ ( ~ ! [SY713: $i] :
~ ( ~ ( ~ ( in @ SY713 @ SV213 )
| ( SY713 = SV170 ) )
| ~ ( ( SY713 != SV170 )
| ( in @ SY713 @ SV213 ) ) )
| ( SV213
= ( singleton @ SV170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2127,plain,
! [SV214: $i,SV171: $i] :
( ( ! [SY714: $i] :
~ ( ~ ( ( SY714
!= ( cartesian_product2 @ SV171 @ SV214 ) )
| ! [SY715: $i] :
~ ( ~ ( ~ ( in @ SY715 @ SY714 )
| ~ ! [SY716: $i] :
~ ~ ! [SY717: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY716 @ SV171 )
| ~ ( in @ SY717 @ SV214 ) )
| ( SY715
!= ( ordered_pair @ SY716 @ SY717 ) ) ) )
| ~ ( ~ ~ ! [SY718: $i] :
~ ~ ! [SY719: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY718 @ SV171 )
| ~ ( in @ SY719 @ SV214 ) )
| ( SY715
!= ( ordered_pair @ SY718 @ SY719 ) ) )
| ( in @ SY715 @ SY714 ) ) ) )
| ~ ( ~ ! [SY720: $i] :
~ ( ~ ( ~ ( in @ SY720 @ SY714 )
| ~ ! [SY721: $i] :
~ ~ ! [SY722: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY721 @ SV171 )
| ~ ( in @ SY722 @ SV214 ) )
| ( SY720
!= ( ordered_pair @ SY721 @ SY722 ) ) ) )
| ~ ( ~ ~ ! [SY723: $i] :
~ ~ ! [SY724: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY723 @ SV171 )
| ~ ( in @ SY724 @ SV214 ) )
| ( SY720
!= ( ordered_pair @ SY723 @ SY724 ) ) )
| ( in @ SY720 @ SY714 ) ) )
| ( SY714
= ( cartesian_product2 @ SV171 @ SV214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2128,plain,
! [SV172: $i] :
( ( ( ~ ( relation @ SV172 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV172 ) )
= SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2129,plain,
! [SV215: $i,SV173: $i] :
( ( ~ ( in @ SV173 @ SV215 )
| ( element @ SV173 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2130,plain,
! [SV216: $i,SV174: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV174 @ SV216 )
| ! [SY725: $i] :
( ~ ( in @ SY725 @ SV174 )
| ( in @ SY725 @ SV216 ) ) )
| ~ ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV174 )
| ( in @ SY726 @ SV216 ) )
| ( subset @ SV174 @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2131,plain,
! [SV175: $i] :
( ( ( ~ ( relation @ SV175 ) )
= $true )
| ( ( ! [SY596: $i] :
( ~ ( relation @ SY596 )
| ~ ( ~ ( ( SY596
!= ( relation_inverse @ SV175 ) )
| ! [SY597: $i,SY598: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY597 @ SY598 ) @ SY596 )
| ( in @ ( ordered_pair @ SY598 @ SY597 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY598 @ SY597 ) @ SV175 )
| ( in @ ( ordered_pair @ SY597 @ SY598 ) @ SY596 ) ) ) )
| ~ ( ~ ! [SY599: $i,SY600: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY599 @ SY600 ) @ SY596 )
| ( in @ ( ordered_pair @ SY600 @ SY599 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY600 @ SY599 ) @ SV175 )
| ( in @ ( ordered_pair @ SY599 @ SY600 ) @ SY596 ) ) )
| ( SY596
= ( relation_inverse @ SV175 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2132,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK67_SX0 )
| ~ ( relation @ sK67_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2079]) ).
thf(2133,plain,
! [SV176: $i] :
( ( ( ~ ( relation @ SV176 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2080]) ).
thf(2134,plain,
! [SV217: $i,SV177: $i] :
( ( ! [SY727: $i] :
( ~ ( relation @ SY727 )
| ~ ( ~ ( ~ ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SY727 @ SV217 ) ) )
| ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SY727 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SY727 ) ) )
| ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SY727 @ SV217 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2135,plain,
! [SV218: $i,SV178: $i] :
( ( ~ ( in @ SV178 @ SV218 )
| ~ ( in @ SV218 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2136,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV179 @ SV219 )
| ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY729: $i] :
~ ~ ( ~ ( in @ SY729 @ SV179 )
| ~ ( in @ SY729 @ SV219 ) )
| ~ ( disjoint @ SV179 @ SV219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2137,plain,
! [SV220: $i,SV180: $i] :
( ( ! [SY730: $i,SY731: $i] :
( ( ( ordered_pair @ SV180 @ SV220 )
!= ( ordered_pair @ SY730 @ SY731 ) )
| ~ ( ( SV180 != SY730 )
| ( SV220 != SY731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2138,plain,
! [SV181: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV181 )
| ~ ( relation @ SV181 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2085]) ).
thf(2139,plain,
! [SV221: $i,SV182: $i] :
( ( ~ ! [SY732: $i] :
~ ( ~ ( ~ ( in @ SY732 @ SV182 )
| ( in @ SY732 @ SV221 ) )
| ~ ( ~ ( in @ SY732 @ SV221 )
| ( in @ SY732 @ SV182 ) ) )
| ( SV182 = SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2140,plain,
! [SV222: $i,SV183: $i] :
( ( ! [SY733: $i] :
~ ( ~ ( ( SY733
!= ( set_intersection2 @ SV183 @ SV222 ) )
| ! [SY734: $i] :
~ ( ~ ( ~ ( in @ SY734 @ SY733 )
| ~ ( ~ ( in @ SY734 @ SV183 )
| ~ ( in @ SY734 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY734 @ SV183 )
| ~ ( in @ SY734 @ SV222 ) )
| ( in @ SY734 @ SY733 ) ) ) )
| ~ ( ~ ! [SY735: $i] :
~ ( ~ ( ~ ( in @ SY735 @ SY733 )
| ~ ( ~ ( in @ SY735 @ SV183 )
| ~ ( in @ SY735 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY735 @ SV183 )
| ~ ( in @ SY735 @ SV222 ) )
| ( in @ SY735 @ SY733 ) ) )
| ( SY733
= ( set_intersection2 @ SV183 @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2141,plain,
! [SV223: $i,SV184: $i] :
( ( ! [SY736: $i,SY737: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SY736 @ SY737 ) )
| ~ ( ~ ( in @ SV184 @ SY736 )
| ~ ( in @ SV223 @ SY737 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV184 @ SY736 )
| ~ ( in @ SV223 @ SY737 ) )
| ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SY736 @ SY737 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2142,plain,
! [SV185: $i] :
( ( ( ~ ( empty @ SV185 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV185 ) )
| ~ ( relation @ ( relation_dom @ SV185 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2143,plain,
! [SV186: $i,SV224: $i] :
( ( ~ ( relation @ SV224 )
| ! [SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( ~ ( ( SY738
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
| ! [SY739: $i,SY740: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SY738 )
| ~ ( ~ ( in @ SY740 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY740 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SY738 ) ) ) )
| ~ ( ~ ! [SY741: $i,SY742: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SY738 )
| ~ ( ~ ( in @ SY742 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY742 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SY738 ) ) )
| ( SY738
= ( relation_rng_restriction @ SV186 @ SV224 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2144,plain,
! [SV187: $i] :
( ( ( ~ ( relation @ SV187 ) )
= $true )
| ( ( ! [SY625: $i,SY626: $i] :
~ ( ~ ( ( SY626
!= ( relation_inverse_image @ SV187 @ SY625 ) )
| ! [SY627: $i] :
~ ( ~ ( ~ ( in @ SY627 @ SY626 )
| ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY627 @ SY628 ) @ SV187 )
| ~ ( in @ SY628 @ SY625 ) ) )
| ~ ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY627 @ SY629 ) @ SV187 )
| ~ ( in @ SY629 @ SY625 ) )
| ( in @ SY627 @ SY626 ) ) ) )
| ~ ( ~ ! [SY630: $i] :
~ ( ~ ( ~ ( in @ SY630 @ SY626 )
| ~ ! [SY631: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SV187 )
| ~ ( in @ SY631 @ SY625 ) ) )
| ~ ( ~ ~ ! [SY632: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY630 @ SY632 ) @ SV187 )
| ~ ( in @ SY632 @ SY625 ) )
| ( in @ SY630 @ SY626 ) ) )
| ( SY626
= ( relation_inverse_image @ SV187 @ SY625 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2145,plain,
! [SV225: $i,SV188: $i] :
( ( ~ ( relation @ SV188 )
| ( relation @ ( relation_dom_restriction @ SV188 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2146,plain,
! [SV226: $i,SV189: $i] :
( ( ! [SY743: $i] :
~ ( ~ ( ( SY743
!= ( unordered_pair @ SV189 @ SV226 ) )
| ! [SY744: $i] :
~ ( ~ ( ~ ( in @ SY744 @ SY743 )
| ( SY744 = SV189 )
| ( SY744 = SV226 ) )
| ~ ( ~ ( ( SY744 = SV189 )
| ( SY744 = SV226 ) )
| ( in @ SY744 @ SY743 ) ) ) )
| ~ ( ~ ! [SY745: $i] :
~ ( ~ ( ~ ( in @ SY745 @ SY743 )
| ( SY745 = SV189 )
| ( SY745 = SV226 ) )
| ~ ( ~ ( ( SY745 = SV189 )
| ( SY745 = SV226 ) )
| ( in @ SY745 @ SY743 ) ) )
| ( SY743
= ( unordered_pair @ SV189 @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2147,plain,
! [SV190: $i] :
( ( ( ~ ( relation @ SV190 ) )
= $true )
| ( ( ! [SY638: $i,SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( ~ ( ( SY639
!= ( relation_dom_restriction @ SV190 @ SY638 ) )
| ! [SY640: $i,SY641: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SY639 )
| ~ ( ~ ( in @ SY640 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY640 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SY639 ) ) ) )
| ~ ( ~ ! [SY642: $i,SY643: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY639 )
| ~ ( ~ ( in @ SY642 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY642 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY639 ) ) )
| ( SY639
= ( relation_dom_restriction @ SV190 @ SY638 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2148,plain,
! [SV191: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV191 )
| ~ ( function @ SV191 ) ) )
= $true )
| ( ( ! [SY644: $i,SY645: $i] :
~ ( ~ ( ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( SY645 = empty_set ) )
| ~ ( ( SY645 != empty_set )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2149,plain,
! [SV192: $i] :
( ( ~ ( ~ ( relation @ SV192 )
| ! [SY646: $i] :
~ ~ ( ~ ( in @ SY646 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY646
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ! [SY649: $i] :
~ ~ ( ~ ( in @ SY649 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY649
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV192 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2150,plain,
! [SV193: $i] :
( ( ( ~ ( relation @ SV193 ) )
= $true )
| ( ( ! [SY652: $i,SY653: $i] :
~ ( ~ ( ( SY653
!= ( relation_image @ SV193 @ SY652 ) )
| ! [SY654: $i] :
~ ( ~ ( ~ ( in @ SY654 @ SY653 )
| ~ ! [SY655: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY655 @ SY654 ) @ SV193 )
| ~ ( in @ SY655 @ SY652 ) ) )
| ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY656 @ SY654 ) @ SV193 )
| ~ ( in @ SY656 @ SY652 ) )
| ( in @ SY654 @ SY653 ) ) ) )
| ~ ( ~ ! [SY657: $i] :
~ ( ~ ( ~ ( in @ SY657 @ SY653 )
| ~ ! [SY658: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY658 @ SY657 ) @ SV193 )
| ~ ( in @ SY658 @ SY652 ) ) )
| ~ ( ~ ~ ! [SY659: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY659 @ SY657 ) @ SV193 )
| ~ ( in @ SY659 @ SY652 ) )
| ( in @ SY657 @ SY653 ) ) )
| ( SY653
= ( relation_image @ SV193 @ SY652 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2097]) ).
thf(2151,plain,
! [SV194: $i] :
( ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ! [SY660: $i] :
~ ( ~ ( ( SY660
!= ( relation_dom @ SV194 ) )
| ! [SY661: $i] :
~ ( ~ ( ~ ( in @ SY661 @ SY660 )
| ~ ! [SY662: $i] :
~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY663: $i] :
~ ( in @ ( ordered_pair @ SY661 @ SY663 ) @ SV194 )
| ( in @ SY661 @ SY660 ) ) ) )
| ~ ( ~ ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ SY660 )
| ~ ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY665 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY666: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY666 ) @ SV194 )
| ( in @ SY664 @ SY660 ) ) )
| ( SY660
= ( relation_dom @ SV194 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2152,plain,
( ( ~ ~ ( ~ ( relation @ sK68_SX0 )
| ~ ( function @ sK68_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2099]) ).
thf(2153,plain,
( ( ~ ~ ( ~ ( relation @ sK69_SX0 )
| ~ ( relation_empty_yielding @ sK69_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2100]) ).
thf(2154,plain,
( ( ~ ~ ( ~ ( empty @ sK70_SX0 )
| ~ ( relation @ sK70_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2101]) ).
thf(2155,plain,
! [SV195: $i,SV227: $i] :
( ( ~ ( relation @ SV227 )
| ~ ( ~ ( ( SV227
!= ( identity_relation @ SV195 ) )
| ! [SY746: $i,SY747: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 )
| ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 ) ) ) )
| ~ ( ~ ! [SY748: $i,SY749: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 )
| ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) )
| ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 ) ) )
| ( SV227
= ( identity_relation @ SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2156,plain,
! [SV228: $i,SV196: $i] :
( ( ~ ~ ( ~ ( relation @ SV196 )
| ~ ( relation @ SV228 ) )
| ( relation @ ( set_union2 @ SV196 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2157,plain,
! [SV197: $i] :
( ( ( ~ ( empty @ SV197 ) )
= $true )
| ( ( function @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2158,plain,
! [SV229: $i,SV198: $i] :
( ( ! [SY750: $i] :
~ ( ~ ( ( SY750
!= ( set_union2 @ SV198 @ SV229 ) )
| ! [SY751: $i] :
~ ( ~ ( ~ ( in @ SY751 @ SY750 )
| ( in @ SY751 @ SV198 )
| ( in @ SY751 @ SV229 ) )
| ~ ( ~ ( ( in @ SY751 @ SV198 )
| ( in @ SY751 @ SV229 ) )
| ( in @ SY751 @ SY750 ) ) ) )
| ~ ( ~ ! [SY752: $i] :
~ ( ~ ( ~ ( in @ SY752 @ SY750 )
| ( in @ SY752 @ SV198 )
| ( in @ SY752 @ SV229 ) )
| ~ ( ~ ( ( in @ SY752 @ SV198 )
| ( in @ SY752 @ SV229 ) )
| ( in @ SY752 @ SY750 ) ) )
| ( SY750
= ( set_union2 @ SV198 @ SV229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2159,plain,
! [SV199: $i] :
( ( ( ~ ( relation @ SV199 ) )
= $true )
| ( ( ~ ! [SY677: $i,SY678: $i] :
~ ( in @ ( ordered_pair @ SY677 @ SY678 ) @ SV199 )
| ( SV199 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2160,plain,
! [SV230: $i,SV200: $i] :
( ( ! [SY753: $i] :
( ~ ( relation @ SY753 )
| ~ ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SY753 )
| ~ ( ~ ( in @ SV200 @ ( relation_dom @ SY753 ) )
| ~ ( in @ SV230 @ ( relation_rng @ SY753 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2161,plain,
! [SV201: $i] :
( ( ( ~ ( relation @ SV201 ) )
= $true )
| ( ( ! [SY681: $i] :
( ~ ( relation @ SY681 )
| ~ ( ~ ( ~ ( subset @ SV201 @ SY681 )
| ! [SY682: $i,SY683: $i] :
( ~ ( in @ ( ordered_pair @ SY682 @ SY683 ) @ SV201 )
| ( in @ ( ordered_pair @ SY682 @ SY683 ) @ SY681 ) ) )
| ~ ( ~ ! [SY684: $i,SY685: $i] :
( ~ ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SV201 )
| ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SY681 ) )
| ( subset @ SV201 @ SY681 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2162,plain,
! [SV231: $i,SV202: $i] :
( ( ! [SY754: $i] :
~ ( ~ ( ( SY754
!= ( set_difference @ SV202 @ SV231 ) )
| ! [SY755: $i] :
~ ( ~ ( ~ ( in @ SY755 @ SY754 )
| ~ ( ~ ( in @ SY755 @ SV202 )
| ~ ~ ( in @ SY755 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY755 @ SV202 )
| ~ ~ ( in @ SY755 @ SV231 ) )
| ( in @ SY755 @ SY754 ) ) ) )
| ~ ( ~ ! [SY756: $i] :
~ ( ~ ( ~ ( in @ SY756 @ SY754 )
| ~ ( ~ ( in @ SY756 @ SV202 )
| ~ ~ ( in @ SY756 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY756 @ SV202 )
| ~ ~ ( in @ SY756 @ SV231 ) )
| ( in @ SY756 @ SY754 ) ) )
| ( SY754
= ( set_difference @ SV202 @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2163,plain,
! [SV203: $i] :
( ( ( ~ ( relation @ SV203 ) )
= $true )
| ( ( ! [SY690: $i] :
( ~ ( relation @ SY690 )
| ! [SY691: $i] :
( ~ ( relation @ SY691 )
| ~ ( ~ ( ( SY691
!= ( relation_composition @ SV203 @ SY690 ) )
| ! [SY692: $i,SY693: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SY691 )
| ~ ! [SY694: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY692 @ SY694 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY694 @ SY693 ) @ SY690 ) ) )
| ~ ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY692 @ SY695 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY695 @ SY693 ) @ SY690 ) )
| ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SY691 ) ) ) )
| ~ ( ~ ! [SY696: $i,SY697: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY696 @ SY697 ) @ SY691 )
| ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY696 @ SY698 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY698 @ SY697 ) @ SY690 ) ) )
| ~ ( ~ ~ ! [SY699: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY696 @ SY699 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY699 @ SY697 ) @ SY690 ) )
| ( in @ ( ordered_pair @ SY696 @ SY697 ) @ SY691 ) ) )
| ( SY691
= ( relation_composition @ SV203 @ SY690 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2164,plain,
! [SV204: $i,SV157: $i] :
( ( empty @ ( ordered_pair @ SV157 @ SV204 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2165,plain,
! [SV205: $i,SV158: $i,SV232: $i] :
( ( ~ ( relation @ SV232 )
| ~ ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 )
| ~ ( ~ ( in @ SV158 @ ( relation_field @ SV232 ) )
| ~ ( in @ SV205 @ ( relation_field @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2166,plain,
! [SV233: $i,SV206: $i,SV159: $i] :
( ( ! [SY757: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SY757 ) )
| ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SY757 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SY757 ) )
| ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SY757 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2167,plain,
! [SV160: $i] :
( ( ~ ( ( SV160 != empty_set )
| ! [SY548: $i] :
~ ( in @ SY548 @ SV160 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2168,plain,
! [SV160: $i] :
( ( ~ ( ~ ! [SY549: $i] :
~ ( in @ SY549 @ SV160 )
| ( SV160 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2169,plain,
! [SV207: $i,SV161: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV161 )
| ~ ( relation @ SV207 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV161 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2170,plain,
! [SV208: $i,SV162: $i,SV234: $i] :
( ( ~ ( relation @ SV234 )
| ~ ( ~ ( ~ ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
| ~ ! [SY758: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY758 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY758 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY758 @ SV208 ) ) )
| ~ ( ~ ~ ! [SY759: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY759 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY759 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY759 @ SV208 ) )
| ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2171,plain,
! [SV163: $i] :
( ( ( empty @ SV163 )
= $false )
| ( ( relation @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2172,plain,
! [SV164: $i,SV209: $i] :
( ( ( ~ ( relation @ SV209 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV164 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2118]) ).
thf(2173,plain,
! [SV165: $i,SV210: $i] :
( ( ~ ( ( SV210
!= ( union @ SV165 ) )
| ! [SY706: $i] :
~ ( ~ ( ~ ( in @ SY706 @ SV210 )
| ~ ! [SY558: $i] :
~ ~ ( ~ ( in @ SY706 @ SY558 )
| ~ ( in @ SY558 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ~ ( ~ ( in @ SY706 @ SY559 )
| ~ ( in @ SY559 @ SV165 ) )
| ( in @ SY706 @ SV210 ) ) ) )
| ~ ( ~ ! [SY709: $i] :
~ ( ~ ( ~ ( in @ SY709 @ SV210 )
| ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY709 @ SY561 )
| ~ ( in @ SY561 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY562: $i] :
~ ~ ( ~ ( in @ SY709 @ SY562 )
| ~ ( in @ SY562 @ SV165 ) )
| ( in @ SY709 @ SV210 ) ) )
| ( SV210
= ( union @ SV165 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2174,plain,
! [SV166: $i] :
( ( ( relation @ SV166 )
= $false )
| ( ( ! [SY563: $i] :
( ~ ( relation @ SY563 )
| ~ ( ~ ( ( SV166 != SY563 )
| ! [SY564: $i,SY565: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SV166 )
| ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SY563 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SY563 )
| ( in @ ( ordered_pair @ SY564 @ SY565 ) @ SV166 ) ) ) )
| ~ ( ~ ! [SY566: $i,SY567: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV166 )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SY563 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SY563 )
| ( in @ ( ordered_pair @ SY566 @ SY567 ) @ SV166 ) ) )
| ( SV166 = SY563 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2175,plain,
! [SV167: $i] :
( ( ( relation @ SV167 )
= $false )
| ( ( ! [SY568: $i] :
~ ( ~ ( ( SY568
!= ( relation_rng @ SV167 ) )
| ! [SY569: $i] :
~ ( ~ ( ~ ( in @ SY569 @ SY568 )
| ~ ! [SY570: $i] :
~ ( in @ ( ordered_pair @ SY570 @ SY569 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY571: $i] :
~ ( in @ ( ordered_pair @ SY571 @ SY569 ) @ SV167 )
| ( in @ SY569 @ SY568 ) ) ) )
| ~ ( ~ ! [SY572: $i] :
~ ( ~ ( ~ ( in @ SY572 @ SY568 )
| ~ ! [SY573: $i] :
~ ( in @ ( ordered_pair @ SY573 @ SY572 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ SY572 ) @ SV167 )
| ( in @ SY572 @ SY568 ) ) )
| ( SY568
= ( relation_rng @ SV167 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2176,plain,
! [SV211: $i,SV168: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV168 )
| ~ ( relation @ SV211 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV168 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2122]) ).
thf(2177,plain,
! [SV212: $i,SV169: $i] :
( ( ~ ( ~ ( in @ SV169 @ SV212 )
| ~ ( empty @ SV212 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2178,plain,
( ( ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
| ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2124]) ).
thf(2179,plain,
! [SV170: $i,SV213: $i] :
( ( ~ ( ( SV213
!= ( singleton @ SV170 ) )
| ! [SY712: $i] :
~ ( ~ ( ~ ( in @ SY712 @ SV213 )
| ( SY712 = SV170 ) )
| ~ ( ( SY712 != SV170 )
| ( in @ SY712 @ SV213 ) ) ) )
| ~ ( ~ ! [SY713: $i] :
~ ( ~ ( ~ ( in @ SY713 @ SV213 )
| ( SY713 = SV170 ) )
| ~ ( ( SY713 != SV170 )
| ( in @ SY713 @ SV213 ) ) )
| ( SV213
= ( singleton @ SV170 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2180,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ~ ( ~ ( ( SV235
!= ( cartesian_product2 @ SV171 @ SV214 ) )
| ! [SY760: $i] :
~ ( ~ ( ~ ( in @ SY760 @ SV235 )
| ~ ! [SY716: $i] :
~ ~ ! [SY717: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY716 @ SV171 )
| ~ ( in @ SY717 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY716 @ SY717 ) ) ) )
| ~ ( ~ ~ ! [SY718: $i] :
~ ~ ! [SY719: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY718 @ SV171 )
| ~ ( in @ SY719 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY718 @ SY719 ) ) )
| ( in @ SY760 @ SV235 ) ) ) )
| ~ ( ~ ! [SY765: $i] :
~ ( ~ ( ~ ( in @ SY765 @ SV235 )
| ~ ! [SY721: $i] :
~ ~ ! [SY722: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY721 @ SV171 )
| ~ ( in @ SY722 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY721 @ SY722 ) ) ) )
| ~ ( ~ ~ ! [SY723: $i] :
~ ~ ! [SY724: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY723 @ SV171 )
| ~ ( in @ SY724 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY723 @ SY724 ) ) )
| ( in @ SY765 @ SV235 ) ) )
| ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2181,plain,
! [SV172: $i] :
( ( ( relation @ SV172 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV172 ) )
= SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2182,plain,
! [SV215: $i,SV173: $i] :
( ( ( ~ ( in @ SV173 @ SV215 ) )
= $true )
| ( ( element @ SV173 @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2183,plain,
! [SV216: $i,SV174: $i] :
( ( ~ ( ~ ( subset @ SV174 @ SV216 )
| ! [SY725: $i] :
( ~ ( in @ SY725 @ SV174 )
| ( in @ SY725 @ SV216 ) ) )
| ~ ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV174 )
| ( in @ SY726 @ SV216 ) )
| ( subset @ SV174 @ SV216 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2184,plain,
! [SV175: $i] :
( ( ( relation @ SV175 )
= $false )
| ( ( ! [SY596: $i] :
( ~ ( relation @ SY596 )
| ~ ( ~ ( ( SY596
!= ( relation_inverse @ SV175 ) )
| ! [SY597: $i,SY598: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY597 @ SY598 ) @ SY596 )
| ( in @ ( ordered_pair @ SY598 @ SY597 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY598 @ SY597 ) @ SV175 )
| ( in @ ( ordered_pair @ SY597 @ SY598 ) @ SY596 ) ) ) )
| ~ ( ~ ! [SY599: $i,SY600: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY599 @ SY600 ) @ SY596 )
| ( in @ ( ordered_pair @ SY600 @ SY599 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY600 @ SY599 ) @ SV175 )
| ( in @ ( ordered_pair @ SY599 @ SY600 ) @ SY596 ) ) )
| ( SY596
= ( relation_inverse @ SV175 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2185,plain,
( ( ~ ( ~ ~ ( empty @ sK67_SX0 )
| ~ ( relation @ sK67_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2132]) ).
thf(2186,plain,
! [SV176: $i] :
( ( ( relation @ SV176 )
= $false )
| ( ( relation @ ( relation_inverse @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2187,plain,
! [SV217: $i,SV177: $i,SV236: $i] :
( ( ~ ( relation @ SV236 )
| ~ ( ~ ( ~ ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
| ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
| ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2188,plain,
! [SV218: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ SV218 ) )
= $true )
| ( ( ~ ( in @ SV218 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2189,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV179 @ SV219 )
| ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY729: $i] :
~ ~ ( ~ ( in @ SY729 @ SV179 )
| ~ ( in @ SY729 @ SV219 ) )
| ~ ( disjoint @ SV179 @ SV219 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2190,plain,
! [SV237: $i,SV220: $i,SV180: $i] :
( ( ! [SY770: $i] :
( ( ( ordered_pair @ SV180 @ SV220 )
!= ( ordered_pair @ SV237 @ SY770 ) )
| ~ ( ( SV180 != SV237 )
| ( SV220 != SY770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2191,plain,
! [SV181: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV181 )
| ~ ( relation @ SV181 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2192,plain,
! [SV221: $i,SV182: $i] :
( ( ( ~ ! [SY732: $i] :
~ ( ~ ( ~ ( in @ SY732 @ SV182 )
| ( in @ SY732 @ SV221 ) )
| ~ ( ~ ( in @ SY732 @ SV221 )
| ( in @ SY732 @ SV182 ) ) ) )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2193,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ~ ( ~ ( ( SV238
!= ( set_intersection2 @ SV183 @ SV222 ) )
| ! [SY771: $i] :
~ ( ~ ( ~ ( in @ SY771 @ SV238 )
| ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) )
| ( in @ SY771 @ SV238 ) ) ) )
| ~ ( ~ ! [SY772: $i] :
~ ( ~ ( ~ ( in @ SY772 @ SV238 )
| ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) )
| ( in @ SY772 @ SV238 ) ) )
| ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2194,plain,
! [SV239: $i,SV223: $i,SV184: $i] :
( ( ! [SY773: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SY773 ) )
| ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SY773 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SY773 ) )
| ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SY773 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2195,plain,
! [SV185: $i] :
( ( ( empty @ SV185 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV185 ) )
| ~ ( relation @ ( relation_dom @ SV185 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2196,plain,
! [SV186: $i,SV224: $i] :
( ( ( ~ ( relation @ SV224 ) )
= $true )
| ( ( ! [SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( ~ ( ( SY738
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
| ! [SY739: $i,SY740: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SY738 )
| ~ ( ~ ( in @ SY740 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY740 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SY738 ) ) ) )
| ~ ( ~ ! [SY741: $i,SY742: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SY738 )
| ~ ( ~ ( in @ SY742 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY742 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SY738 ) ) )
| ( SY738
= ( relation_rng_restriction @ SV186 @ SV224 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2143]) ).
thf(2197,plain,
! [SV187: $i] :
( ( ( relation @ SV187 )
= $false )
| ( ( ! [SY625: $i,SY626: $i] :
~ ( ~ ( ( SY626
!= ( relation_inverse_image @ SV187 @ SY625 ) )
| ! [SY627: $i] :
~ ( ~ ( ~ ( in @ SY627 @ SY626 )
| ~ ! [SY628: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY627 @ SY628 ) @ SV187 )
| ~ ( in @ SY628 @ SY625 ) ) )
| ~ ( ~ ~ ! [SY629: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY627 @ SY629 ) @ SV187 )
| ~ ( in @ SY629 @ SY625 ) )
| ( in @ SY627 @ SY626 ) ) ) )
| ~ ( ~ ! [SY630: $i] :
~ ( ~ ( ~ ( in @ SY630 @ SY626 )
| ~ ! [SY631: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SV187 )
| ~ ( in @ SY631 @ SY625 ) ) )
| ~ ( ~ ~ ! [SY632: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY630 @ SY632 ) @ SV187 )
| ~ ( in @ SY632 @ SY625 ) )
| ( in @ SY630 @ SY626 ) ) )
| ( SY626
= ( relation_inverse_image @ SV187 @ SY625 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2198,plain,
! [SV225: $i,SV188: $i] :
( ( ( ~ ( relation @ SV188 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV188 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2199,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ~ ( ~ ( ( SV240
!= ( unordered_pair @ SV189 @ SV226 ) )
| ! [SY774: $i] :
~ ( ~ ( ~ ( in @ SY774 @ SV240 )
| ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ~ ( ~ ( ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ( in @ SY774 @ SV240 ) ) ) )
| ~ ( ~ ! [SY775: $i] :
~ ( ~ ( ~ ( in @ SY775 @ SV240 )
| ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ~ ( ~ ( ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ( in @ SY775 @ SV240 ) ) )
| ( SV240
= ( unordered_pair @ SV189 @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2200,plain,
! [SV190: $i] :
( ( ( relation @ SV190 )
= $false )
| ( ( ! [SY638: $i,SY639: $i] :
( ~ ( relation @ SY639 )
| ~ ( ~ ( ( SY639
!= ( relation_dom_restriction @ SV190 @ SY638 ) )
| ! [SY640: $i,SY641: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SY639 )
| ~ ( ~ ( in @ SY640 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY640 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY640 @ SY641 ) @ SY639 ) ) ) )
| ~ ( ~ ! [SY642: $i,SY643: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY639 )
| ~ ( ~ ( in @ SY642 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY642 @ SY638 )
| ~ ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY642 @ SY643 ) @ SY639 ) ) )
| ( SY639
= ( relation_dom_restriction @ SV190 @ SY638 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2201,plain,
! [SV191: $i] :
( ( ( ~ ( ~ ( relation @ SV191 )
| ~ ( function @ SV191 ) ) )
= $false )
| ( ( ! [SY644: $i,SY645: $i] :
~ ( ~ ( ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( SY645 = empty_set ) )
| ~ ( ( SY645 != empty_set )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2202,plain,
! [SV192: $i] :
( ( ~ ( ~ ( relation @ SV192 )
| ! [SY646: $i] :
~ ~ ( ~ ( in @ SY646 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY646
!= ( ordered_pair @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2203,plain,
! [SV192: $i] :
( ( ~ ( ~ ! [SY649: $i] :
~ ~ ( ~ ( in @ SY649 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY649
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV192 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2204,plain,
! [SV193: $i] :
( ( ( relation @ SV193 )
= $false )
| ( ( ! [SY652: $i,SY653: $i] :
~ ( ~ ( ( SY653
!= ( relation_image @ SV193 @ SY652 ) )
| ! [SY654: $i] :
~ ( ~ ( ~ ( in @ SY654 @ SY653 )
| ~ ! [SY655: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY655 @ SY654 ) @ SV193 )
| ~ ( in @ SY655 @ SY652 ) ) )
| ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY656 @ SY654 ) @ SV193 )
| ~ ( in @ SY656 @ SY652 ) )
| ( in @ SY654 @ SY653 ) ) ) )
| ~ ( ~ ! [SY657: $i] :
~ ( ~ ( ~ ( in @ SY657 @ SY653 )
| ~ ! [SY658: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY658 @ SY657 ) @ SV193 )
| ~ ( in @ SY658 @ SY652 ) ) )
| ~ ( ~ ~ ! [SY659: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY659 @ SY657 ) @ SV193 )
| ~ ( in @ SY659 @ SY652 ) )
| ( in @ SY657 @ SY653 ) ) )
| ( SY653
= ( relation_image @ SV193 @ SY652 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2205,plain,
! [SV194: $i] :
( ( ( relation @ SV194 )
= $false )
| ( ( ! [SY660: $i] :
~ ( ~ ( ( SY660
!= ( relation_dom @ SV194 ) )
| ! [SY661: $i] :
~ ( ~ ( ~ ( in @ SY661 @ SY660 )
| ~ ! [SY662: $i] :
~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY663: $i] :
~ ( in @ ( ordered_pair @ SY661 @ SY663 ) @ SV194 )
| ( in @ SY661 @ SY660 ) ) ) )
| ~ ( ~ ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ SY660 )
| ~ ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY665 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY666: $i] :
~ ( in @ ( ordered_pair @ SY664 @ SY666 ) @ SV194 )
| ( in @ SY664 @ SY660 ) ) )
| ( SY660
= ( relation_dom @ SV194 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2206,plain,
( ( ~ ( ~ ( relation @ sK68_SX0 )
| ~ ( function @ sK68_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2152]) ).
thf(2207,plain,
( ( ~ ( ~ ( relation @ sK69_SX0 )
| ~ ( relation_empty_yielding @ sK69_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2153]) ).
thf(2208,plain,
( ( ~ ( ~ ( empty @ sK70_SX0 )
| ~ ( relation @ sK70_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2154]) ).
thf(2209,plain,
! [SV195: $i,SV227: $i] :
( ( ( ~ ( relation @ SV227 ) )
= $true )
| ( ( ~ ( ~ ( ( SV227
!= ( identity_relation @ SV195 ) )
| ! [SY746: $i,SY747: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 )
| ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 ) ) ) )
| ~ ( ~ ! [SY748: $i,SY749: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 )
| ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) )
| ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 ) ) )
| ( SV227
= ( identity_relation @ SV195 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2210,plain,
! [SV228: $i,SV196: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV196 )
| ~ ( relation @ SV228 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV196 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2211,plain,
! [SV197: $i] :
( ( ( empty @ SV197 )
= $false )
| ( ( function @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2212,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ~ ( ~ ( ( SV241
!= ( set_union2 @ SV198 @ SV229 ) )
| ! [SY776: $i] :
~ ( ~ ( ~ ( in @ SY776 @ SV241 )
| ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ~ ( ~ ( ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ( in @ SY776 @ SV241 ) ) ) )
| ~ ( ~ ! [SY777: $i] :
~ ( ~ ( ~ ( in @ SY777 @ SV241 )
| ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ~ ( ~ ( ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ( in @ SY777 @ SV241 ) ) )
| ( SV241
= ( set_union2 @ SV198 @ SV229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2213,plain,
! [SV199: $i] :
( ( ( relation @ SV199 )
= $false )
| ( ( ~ ! [SY677: $i,SY678: $i] :
~ ( in @ ( ordered_pair @ SY677 @ SY678 ) @ SV199 )
| ( SV199 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2214,plain,
! [SV230: $i,SV200: $i,SV242: $i] :
( ( ~ ( relation @ SV242 )
| ~ ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 )
| ~ ( ~ ( in @ SV200 @ ( relation_dom @ SV242 ) )
| ~ ( in @ SV230 @ ( relation_rng @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2215,plain,
! [SV201: $i] :
( ( ( relation @ SV201 )
= $false )
| ( ( ! [SY681: $i] :
( ~ ( relation @ SY681 )
| ~ ( ~ ( ~ ( subset @ SV201 @ SY681 )
| ! [SY682: $i,SY683: $i] :
( ~ ( in @ ( ordered_pair @ SY682 @ SY683 ) @ SV201 )
| ( in @ ( ordered_pair @ SY682 @ SY683 ) @ SY681 ) ) )
| ~ ( ~ ! [SY684: $i,SY685: $i] :
( ~ ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SV201 )
| ( in @ ( ordered_pair @ SY684 @ SY685 ) @ SY681 ) )
| ( subset @ SV201 @ SY681 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2216,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ~ ( ~ ( ( SV243
!= ( set_difference @ SV202 @ SV231 ) )
| ! [SY778: $i] :
~ ( ~ ( ~ ( in @ SY778 @ SV243 )
| ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) )
| ( in @ SY778 @ SV243 ) ) ) )
| ~ ( ~ ! [SY779: $i] :
~ ( ~ ( ~ ( in @ SY779 @ SV243 )
| ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) )
| ( in @ SY779 @ SV243 ) ) )
| ( SV243
= ( set_difference @ SV202 @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2217,plain,
! [SV203: $i] :
( ( ( relation @ SV203 )
= $false )
| ( ( ! [SY690: $i] :
( ~ ( relation @ SY690 )
| ! [SY691: $i] :
( ~ ( relation @ SY691 )
| ~ ( ~ ( ( SY691
!= ( relation_composition @ SV203 @ SY690 ) )
| ! [SY692: $i,SY693: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SY691 )
| ~ ! [SY694: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY692 @ SY694 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY694 @ SY693 ) @ SY690 ) ) )
| ~ ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY692 @ SY695 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY695 @ SY693 ) @ SY690 ) )
| ( in @ ( ordered_pair @ SY692 @ SY693 ) @ SY691 ) ) ) )
| ~ ( ~ ! [SY696: $i,SY697: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY696 @ SY697 ) @ SY691 )
| ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY696 @ SY698 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY698 @ SY697 ) @ SY690 ) ) )
| ~ ( ~ ~ ! [SY699: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY696 @ SY699 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY699 @ SY697 ) @ SY690 ) )
| ( in @ ( ordered_pair @ SY696 @ SY697 ) @ SY691 ) ) )
| ( SY691
= ( relation_composition @ SV203 @ SY690 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2218,plain,
! [SV205: $i,SV158: $i,SV232: $i] :
( ( ( ~ ( relation @ SV232 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 )
| ~ ( ~ ( in @ SV158 @ ( relation_field @ SV232 ) )
| ~ ( in @ SV205 @ ( relation_field @ SV232 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2219,plain,
! [SV244: $i,SV233: $i,SV206: $i,SV159: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
| ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) )
| ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2220,plain,
! [SV160: $i] :
( ( ( SV160 != empty_set )
| ! [SY548: $i] :
~ ( in @ SY548 @ SV160 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2167]) ).
thf(2221,plain,
! [SV160: $i] :
( ( ~ ! [SY549: $i] :
~ ( in @ SY549 @ SV160 )
| ( SV160 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2168]) ).
thf(2222,plain,
! [SV207: $i,SV161: $i] :
( ( ( ~ ( ~ ( relation @ SV161 )
| ~ ( relation @ SV207 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV161 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2223,plain,
! [SV208: $i,SV162: $i,SV234: $i] :
( ( ( ~ ( relation @ SV234 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
| ~ ! [SY758: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY758 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY758 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY758 @ SV208 ) ) )
| ~ ( ~ ~ ! [SY759: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY759 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY759 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY759 @ SV208 ) )
| ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2224,plain,
! [SV164: $i,SV209: $i] :
( ( ( relation @ SV209 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV164 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2225,plain,
! [SV165: $i,SV210: $i] :
( ( ~ ( ( SV210
!= ( union @ SV165 ) )
| ! [SY706: $i] :
~ ( ~ ( ~ ( in @ SY706 @ SV210 )
| ~ ! [SY558: $i] :
~ ~ ( ~ ( in @ SY706 @ SY558 )
| ~ ( in @ SY558 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ~ ( ~ ( in @ SY706 @ SY559 )
| ~ ( in @ SY559 @ SV165 ) )
| ( in @ SY706 @ SV210 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2226,plain,
! [SV165: $i,SV210: $i] :
( ( ~ ( ~ ! [SY709: $i] :
~ ( ~ ( ~ ( in @ SY709 @ SV210 )
| ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY709 @ SY561 )
| ~ ( in @ SY561 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY562: $i] :
~ ~ ( ~ ( in @ SY709 @ SY562 )
| ~ ( in @ SY562 @ SV165 ) )
| ( in @ SY709 @ SV210 ) ) )
| ( SV210
= ( union @ SV165 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2227,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( relation @ SV245 )
| ~ ( ~ ( ( SV166 != SV245 )
| ! [SY780: $i,SY781: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 ) ) ) )
| ~ ( ~ ! [SY782: $i,SY783: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 ) ) )
| ( SV166 = SV245 ) ) ) )
= $true )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2228,plain,
! [SV167: $i,SV246: $i] :
( ( ( ~ ( ~ ( ( SV246
!= ( relation_rng @ SV167 ) )
| ! [SY784: $i] :
~ ( ~ ( ~ ( in @ SY784 @ SV246 )
| ~ ! [SY570: $i] :
~ ( in @ ( ordered_pair @ SY570 @ SY784 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY571: $i] :
~ ( in @ ( ordered_pair @ SY571 @ SY784 ) @ SV167 )
| ( in @ SY784 @ SV246 ) ) ) )
| ~ ( ~ ! [SY787: $i] :
~ ( ~ ( ~ ( in @ SY787 @ SV246 )
| ~ ! [SY573: $i] :
~ ( in @ ( ordered_pair @ SY573 @ SY787 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ SY787 ) @ SV167 )
| ( in @ SY787 @ SV246 ) ) )
| ( SV246
= ( relation_rng @ SV167 ) ) ) ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2229,plain,
! [SV211: $i,SV168: $i] :
( ( ( ~ ( ~ ( relation @ SV168 )
| ~ ( relation @ SV211 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV168 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2230,plain,
! [SV212: $i,SV169: $i] :
( ( ~ ( in @ SV169 @ SV212 )
| ~ ( empty @ SV212 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2177]) ).
thf(2231,plain,
( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
| ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2232,plain,
! [SV170: $i,SV213: $i] :
( ( ~ ( ( SV213
!= ( singleton @ SV170 ) )
| ! [SY712: $i] :
~ ( ~ ( ~ ( in @ SY712 @ SV213 )
| ( SY712 = SV170 ) )
| ~ ( ( SY712 != SV170 )
| ( in @ SY712 @ SV213 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2179]) ).
thf(2233,plain,
! [SV170: $i,SV213: $i] :
( ( ~ ( ~ ! [SY713: $i] :
~ ( ~ ( ~ ( in @ SY713 @ SV213 )
| ( SY713 = SV170 ) )
| ~ ( ( SY713 != SV170 )
| ( in @ SY713 @ SV213 ) ) )
| ( SV213
= ( singleton @ SV170 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2179]) ).
thf(2234,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ~ ( ( SV235
!= ( cartesian_product2 @ SV171 @ SV214 ) )
| ! [SY760: $i] :
~ ( ~ ( ~ ( in @ SY760 @ SV235 )
| ~ ! [SY716: $i] :
~ ~ ! [SY717: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY716 @ SV171 )
| ~ ( in @ SY717 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY716 @ SY717 ) ) ) )
| ~ ( ~ ~ ! [SY718: $i] :
~ ~ ! [SY719: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY718 @ SV171 )
| ~ ( in @ SY719 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY718 @ SY719 ) ) )
| ( in @ SY760 @ SV235 ) ) ) )
| ~ ( ~ ! [SY765: $i] :
~ ( ~ ( ~ ( in @ SY765 @ SV235 )
| ~ ! [SY721: $i] :
~ ~ ! [SY722: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY721 @ SV171 )
| ~ ( in @ SY722 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY721 @ SY722 ) ) ) )
| ~ ( ~ ~ ! [SY723: $i] :
~ ~ ! [SY724: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY723 @ SV171 )
| ~ ( in @ SY724 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY723 @ SY724 ) ) )
| ( in @ SY765 @ SV235 ) ) )
| ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2235,plain,
! [SV215: $i,SV173: $i] :
( ( ( in @ SV173 @ SV215 )
= $false )
| ( ( element @ SV173 @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2236,plain,
! [SV216: $i,SV174: $i] :
( ( ~ ( ~ ( subset @ SV174 @ SV216 )
| ! [SY725: $i] :
( ~ ( in @ SY725 @ SV174 )
| ( in @ SY725 @ SV216 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2183]) ).
thf(2237,plain,
! [SV216: $i,SV174: $i] :
( ( ~ ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV174 )
| ( in @ SY726 @ SV216 ) )
| ( subset @ SV174 @ SV216 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2183]) ).
thf(2238,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ( relation @ SV247 )
| ~ ( ~ ( ( SV247
!= ( relation_inverse @ SV175 ) )
| ! [SY790: $i,SY791: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 )
| ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 ) ) ) )
| ~ ( ~ ! [SY792: $i,SY793: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 )
| ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 )
| ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 ) ) )
| ( SV247
= ( relation_inverse @ SV175 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2239,plain,
( ( ~ ~ ( empty @ sK67_SX0 )
| ~ ( relation @ sK67_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2240,plain,
! [SV217: $i,SV177: $i,SV236: $i] :
( ( ( ~ ( relation @ SV236 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
| ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
| ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2187]) ).
thf(2241,plain,
! [SV218: $i,SV178: $i] :
( ( ( in @ SV178 @ SV218 )
= $false )
| ( ( ~ ( in @ SV218 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2242,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV179 @ SV219 )
| ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2243,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY729: $i] :
~ ~ ( ~ ( in @ SY729 @ SV179 )
| ~ ( in @ SY729 @ SV219 ) )
| ~ ( disjoint @ SV179 @ SV219 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2244,plain,
! [SV248: $i,SV237: $i,SV220: $i,SV180: $i] :
( ( ( ( ordered_pair @ SV180 @ SV220 )
!= ( ordered_pair @ SV237 @ SV248 ) )
| ~ ( ( SV180 != SV237 )
| ( SV220 != SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2245,plain,
! [SV181: $i] :
( ( ( ~ ~ ( empty @ SV181 )
| ~ ( relation @ SV181 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2246,plain,
! [SV221: $i,SV182: $i] :
( ( ( ! [SY732: $i] :
~ ( ~ ( ~ ( in @ SY732 @ SV182 )
| ( in @ SY732 @ SV221 ) )
| ~ ( ~ ( in @ SY732 @ SV221 )
| ( in @ SY732 @ SV182 ) ) ) )
= $false )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2247,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ~ ( ( SV238
!= ( set_intersection2 @ SV183 @ SV222 ) )
| ! [SY771: $i] :
~ ( ~ ( ~ ( in @ SY771 @ SV238 )
| ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) )
| ( in @ SY771 @ SV238 ) ) ) )
| ~ ( ~ ! [SY772: $i] :
~ ( ~ ( ~ ( in @ SY772 @ SV238 )
| ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) )
| ( in @ SY772 @ SV238 ) ) )
| ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2248,plain,
! [SV249: $i,SV239: $i,SV223: $i,SV184: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
| ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) )
| ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2249,plain,
! [SV185: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV185 ) )
| ~ ( relation @ ( relation_dom @ SV185 ) ) )
= $false )
| ( ( empty @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2250,plain,
! [SV186: $i,SV224: $i] :
( ( ( relation @ SV224 )
= $false )
| ( ( ! [SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( ~ ( ( SY738
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
| ! [SY739: $i,SY740: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SY738 )
| ~ ( ~ ( in @ SY740 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY740 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY739 @ SY740 ) @ SY738 ) ) ) )
| ~ ( ~ ! [SY741: $i,SY742: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SY738 )
| ~ ( ~ ( in @ SY742 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY742 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY741 @ SY742 ) @ SY738 ) ) )
| ( SY738
= ( relation_rng_restriction @ SV186 @ SV224 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2251,plain,
! [SV250: $i,SV187: $i] :
( ( ( ! [SY794: $i] :
~ ( ~ ( ( SY794
!= ( relation_inverse_image @ SV187 @ SV250 ) )
| ! [SY795: $i] :
~ ( ~ ( ~ ( in @ SY795 @ SY794 )
| ~ ! [SY796: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY795 @ SY796 ) @ SV187 )
| ~ ( in @ SY796 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY797: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY795 @ SY797 ) @ SV187 )
| ~ ( in @ SY797 @ SV250 ) )
| ( in @ SY795 @ SY794 ) ) ) )
| ~ ( ~ ! [SY798: $i] :
~ ( ~ ( ~ ( in @ SY798 @ SY794 )
| ~ ! [SY799: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY798 @ SY799 ) @ SV187 )
| ~ ( in @ SY799 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY800: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY798 @ SY800 ) @ SV187 )
| ~ ( in @ SY800 @ SV250 ) )
| ( in @ SY798 @ SY794 ) ) )
| ( SY794
= ( relation_inverse_image @ SV187 @ SV250 ) ) ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2252,plain,
! [SV225: $i,SV188: $i] :
( ( ( relation @ SV188 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV188 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2253,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ~ ( ( SV240
!= ( unordered_pair @ SV189 @ SV226 ) )
| ! [SY774: $i] :
~ ( ~ ( ~ ( in @ SY774 @ SV240 )
| ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ~ ( ~ ( ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ( in @ SY774 @ SV240 ) ) ) )
| ~ ( ~ ! [SY775: $i] :
~ ( ~ ( ~ ( in @ SY775 @ SV240 )
| ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ~ ( ~ ( ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ( in @ SY775 @ SV240 ) ) )
| ( SV240
= ( unordered_pair @ SV189 @ SV226 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2254,plain,
! [SV251: $i,SV190: $i] :
( ( ( ! [SY801: $i] :
( ~ ( relation @ SY801 )
| ~ ( ~ ( ( SY801
!= ( relation_dom_restriction @ SV190 @ SV251 ) )
| ! [SY802: $i,SY803: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY802 @ SY803 ) @ SY801 )
| ~ ( ~ ( in @ SY802 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY802 @ SY803 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY802 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY802 @ SY803 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY802 @ SY803 ) @ SY801 ) ) ) )
| ~ ( ~ ! [SY804: $i,SY805: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SY801 )
| ~ ( ~ ( in @ SY804 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY804 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SY801 ) ) )
| ( SY801
= ( relation_dom_restriction @ SV190 @ SV251 ) ) ) ) ) )
= $true )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2255,plain,
! [SV191: $i] :
( ( ( ~ ( relation @ SV191 )
| ~ ( function @ SV191 ) )
= $true )
| ( ( ! [SY644: $i,SY645: $i] :
~ ( ~ ( ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( SY645 = empty_set ) )
| ~ ( ( SY645 != empty_set )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2256,plain,
! [SV192: $i] :
( ( ~ ( relation @ SV192 )
| ! [SY646: $i] :
~ ~ ( ~ ( in @ SY646 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY646
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2257,plain,
! [SV192: $i] :
( ( ~ ! [SY649: $i] :
~ ~ ( ~ ( in @ SY649 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY649
!= ( ordered_pair @ SX2 @ SX3 ) ) )
| ( relation @ SV192 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2203]) ).
thf(2258,plain,
! [SV252: $i,SV193: $i] :
( ( ( ! [SY806: $i] :
~ ( ~ ( ( SY806
!= ( relation_image @ SV193 @ SV252 ) )
| ! [SY807: $i] :
~ ( ~ ( ~ ( in @ SY807 @ SY806 )
| ~ ! [SY808: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY808 @ SY807 ) @ SV193 )
| ~ ( in @ SY808 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY809: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY809 @ SY807 ) @ SV193 )
| ~ ( in @ SY809 @ SV252 ) )
| ( in @ SY807 @ SY806 ) ) ) )
| ~ ( ~ ! [SY810: $i] :
~ ( ~ ( ~ ( in @ SY810 @ SY806 )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY811 @ SY810 ) @ SV193 )
| ~ ( in @ SY811 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY812 @ SY810 ) @ SV193 )
| ~ ( in @ SY812 @ SV252 ) )
| ( in @ SY810 @ SY806 ) ) )
| ( SY806
= ( relation_image @ SV193 @ SV252 ) ) ) ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2259,plain,
! [SV194: $i,SV253: $i] :
( ( ( ~ ( ~ ( ( SV253
!= ( relation_dom @ SV194 ) )
| ! [SY813: $i] :
~ ( ~ ( ~ ( in @ SY813 @ SV253 )
| ~ ! [SY662: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY662 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY663: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY663 ) @ SV194 )
| ( in @ SY813 @ SV253 ) ) ) )
| ~ ( ~ ! [SY816: $i] :
~ ( ~ ( ~ ( in @ SY816 @ SV253 )
| ~ ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY665 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY666: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY666 ) @ SV194 )
| ( in @ SY816 @ SV253 ) ) )
| ( SV253
= ( relation_dom @ SV194 ) ) ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2260,plain,
( ( ~ ( relation @ sK68_SX0 )
| ~ ( function @ sK68_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2261,plain,
( ( ~ ( relation @ sK69_SX0 )
| ~ ( relation_empty_yielding @ sK69_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2262,plain,
( ( ~ ( empty @ sK70_SX0 )
| ~ ( relation @ sK70_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2263,plain,
! [SV195: $i,SV227: $i] :
( ( ( relation @ SV227 )
= $false )
| ( ( ~ ( ~ ( ( SV227
!= ( identity_relation @ SV195 ) )
| ! [SY746: $i,SY747: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 )
| ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 ) ) ) )
| ~ ( ~ ! [SY748: $i,SY749: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 )
| ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) )
| ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 ) ) )
| ( SV227
= ( identity_relation @ SV195 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2264,plain,
! [SV228: $i,SV196: $i] :
( ( ( ~ ( ~ ( relation @ SV196 )
| ~ ( relation @ SV228 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV196 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2265,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ~ ( ( SV241
!= ( set_union2 @ SV198 @ SV229 ) )
| ! [SY776: $i] :
~ ( ~ ( ~ ( in @ SY776 @ SV241 )
| ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ~ ( ~ ( ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ( in @ SY776 @ SV241 ) ) ) )
| ~ ( ~ ! [SY777: $i] :
~ ( ~ ( ~ ( in @ SY777 @ SV241 )
| ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ~ ( ~ ( ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ( in @ SY777 @ SV241 ) ) )
| ( SV241
= ( set_union2 @ SV198 @ SV229 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2266,plain,
! [SV199: $i] :
( ( ( ~ ! [SY677: $i,SY678: $i] :
~ ( in @ ( ordered_pair @ SY677 @ SY678 ) @ SV199 ) )
= $true )
| ( ( SV199 = empty_set )
= $true )
| ( ( relation @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2267,plain,
! [SV230: $i,SV200: $i,SV242: $i] :
( ( ( ~ ( relation @ SV242 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 )
| ~ ( ~ ( in @ SV200 @ ( relation_dom @ SV242 ) )
| ~ ( in @ SV230 @ ( relation_rng @ SV242 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2268,plain,
! [SV201: $i,SV254: $i] :
( ( ( ~ ( relation @ SV254 )
| ~ ( ~ ( ~ ( subset @ SV201 @ SV254 )
| ! [SY819: $i,SY820: $i] :
( ~ ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV201 )
| ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV254 ) ) )
| ~ ( ~ ! [SY821: $i,SY822: $i] :
( ~ ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV201 )
| ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV254 ) )
| ( subset @ SV201 @ SV254 ) ) ) )
= $true )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2269,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ~ ( ( SV243
!= ( set_difference @ SV202 @ SV231 ) )
| ! [SY778: $i] :
~ ( ~ ( ~ ( in @ SY778 @ SV243 )
| ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) )
| ( in @ SY778 @ SV243 ) ) ) )
| ~ ( ~ ! [SY779: $i] :
~ ( ~ ( ~ ( in @ SY779 @ SV243 )
| ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) )
| ( in @ SY779 @ SV243 ) ) )
| ( SV243
= ( set_difference @ SV202 @ SV231 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2270,plain,
! [SV203: $i,SV255: $i] :
( ( ( ~ ( relation @ SV255 )
| ! [SY823: $i] :
( ~ ( relation @ SY823 )
| ~ ( ~ ( ( SY823
!= ( relation_composition @ SV203 @ SV255 ) )
| ! [SY824: $i,SY825: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY824 @ SY825 ) @ SY823 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY824 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY825 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY824 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY825 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY824 @ SY825 ) @ SY823 ) ) ) )
| ~ ( ~ ! [SY828: $i,SY829: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY828 @ SY829 ) @ SY823 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY828 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY828 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY829 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY828 @ SY829 ) @ SY823 ) ) )
| ( SY823
= ( relation_composition @ SV203 @ SV255 ) ) ) ) ) )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2271,plain,
! [SV205: $i,SV158: $i,SV232: $i] :
( ( ( relation @ SV232 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 )
| ~ ( ~ ( in @ SV158 @ ( relation_field @ SV232 ) )
| ~ ( in @ SV205 @ ( relation_field @ SV232 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2272,plain,
! [SV244: $i,SV233: $i,SV206: $i,SV159: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
| ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) )
| ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2273,plain,
! [SV160: $i] :
( ( ( SV160 != empty_set )
= $true )
| ( ( ! [SY548: $i] :
~ ( in @ SY548 @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2274,plain,
! [SV160: $i] :
( ( ( ~ ! [SY549: $i] :
~ ( in @ SY549 @ SV160 ) )
= $true )
| ( ( SV160 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2275,plain,
! [SV207: $i,SV161: $i] :
( ( ( ~ ( relation @ SV161 )
| ~ ( relation @ SV207 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV161 @ SV207 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2276,plain,
! [SV208: $i,SV162: $i,SV234: $i] :
( ( ( relation @ SV234 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
| ~ ! [SY758: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY758 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY758 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY758 @ SV208 ) ) )
| ~ ( ~ ~ ! [SY759: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY759 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY759 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY759 @ SV208 ) )
| ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2277,plain,
! [SV165: $i,SV210: $i] :
( ( ( SV210
!= ( union @ SV165 ) )
| ! [SY706: $i] :
~ ( ~ ( ~ ( in @ SY706 @ SV210 )
| ~ ! [SY558: $i] :
~ ~ ( ~ ( in @ SY706 @ SY558 )
| ~ ( in @ SY558 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ~ ( ~ ( in @ SY706 @ SY559 )
| ~ ( in @ SY559 @ SV165 ) )
| ( in @ SY706 @ SV210 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2278,plain,
! [SV165: $i,SV210: $i] :
( ( ~ ! [SY709: $i] :
~ ( ~ ( ~ ( in @ SY709 @ SV210 )
| ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY709 @ SY561 )
| ~ ( in @ SY561 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY562: $i] :
~ ~ ( ~ ( in @ SY709 @ SY562 )
| ~ ( in @ SY562 @ SV165 ) )
| ( in @ SY709 @ SV210 ) ) )
| ( SV210
= ( union @ SV165 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2226]) ).
thf(2279,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( relation @ SV245 ) )
= $true )
| ( ( ~ ( ~ ( ( SV166 != SV245 )
| ! [SY780: $i,SY781: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 ) ) ) )
| ~ ( ~ ! [SY782: $i,SY783: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 ) ) )
| ( SV166 = SV245 ) ) ) )
= $true )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2280,plain,
! [SV167: $i,SV246: $i] :
( ( ( ~ ( ( SV246
!= ( relation_rng @ SV167 ) )
| ! [SY784: $i] :
~ ( ~ ( ~ ( in @ SY784 @ SV246 )
| ~ ! [SY570: $i] :
~ ( in @ ( ordered_pair @ SY570 @ SY784 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY571: $i] :
~ ( in @ ( ordered_pair @ SY571 @ SY784 ) @ SV167 )
| ( in @ SY784 @ SV246 ) ) ) )
| ~ ( ~ ! [SY787: $i] :
~ ( ~ ( ~ ( in @ SY787 @ SV246 )
| ~ ! [SY573: $i] :
~ ( in @ ( ordered_pair @ SY573 @ SY787 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ SY787 ) @ SV167 )
| ( in @ SY787 @ SV246 ) ) )
| ( SV246
= ( relation_rng @ SV167 ) ) ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2281,plain,
! [SV211: $i,SV168: $i] :
( ( ( ~ ( relation @ SV168 )
| ~ ( relation @ SV211 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV168 @ SV211 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2229]) ).
thf(2282,plain,
! [SV212: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ SV212 ) )
= $true )
| ( ( ~ ( empty @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2283,plain,
( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2231]) ).
thf(2284,plain,
( ( sK2_SY158
!= ( apply @ sK3_SY160 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2231]) ).
thf(2285,plain,
! [SV170: $i,SV213: $i] :
( ( ( SV213
!= ( singleton @ SV170 ) )
| ! [SY712: $i] :
~ ( ~ ( ~ ( in @ SY712 @ SV213 )
| ( SY712 = SV170 ) )
| ~ ( ( SY712 != SV170 )
| ( in @ SY712 @ SV213 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2232]) ).
thf(2286,plain,
! [SV170: $i,SV213: $i] :
( ( ~ ! [SY713: $i] :
~ ( ~ ( ~ ( in @ SY713 @ SV213 )
| ( SY713 = SV170 ) )
| ~ ( ( SY713 != SV170 )
| ( in @ SY713 @ SV213 ) ) )
| ( SV213
= ( singleton @ SV170 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2233]) ).
thf(2287,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ~ ( ( SV235
!= ( cartesian_product2 @ SV171 @ SV214 ) )
| ! [SY760: $i] :
~ ( ~ ( ~ ( in @ SY760 @ SV235 )
| ~ ! [SY716: $i] :
~ ~ ! [SY717: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY716 @ SV171 )
| ~ ( in @ SY717 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY716 @ SY717 ) ) ) )
| ~ ( ~ ~ ! [SY718: $i] :
~ ~ ! [SY719: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY718 @ SV171 )
| ~ ( in @ SY719 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY718 @ SY719 ) ) )
| ( in @ SY760 @ SV235 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2288,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ~ ( ~ ! [SY765: $i] :
~ ( ~ ( ~ ( in @ SY765 @ SV235 )
| ~ ! [SY721: $i] :
~ ~ ! [SY722: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY721 @ SV171 )
| ~ ( in @ SY722 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY721 @ SY722 ) ) ) )
| ~ ( ~ ~ ! [SY723: $i] :
~ ~ ! [SY724: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY723 @ SV171 )
| ~ ( in @ SY724 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY723 @ SY724 ) ) )
| ( in @ SY765 @ SV235 ) ) )
| ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2289,plain,
! [SV216: $i,SV174: $i] :
( ( ~ ( subset @ SV174 @ SV216 )
| ! [SY725: $i] :
( ~ ( in @ SY725 @ SV174 )
| ( in @ SY725 @ SV216 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2236]) ).
thf(2290,plain,
! [SV216: $i,SV174: $i] :
( ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV174 )
| ( in @ SY726 @ SV216 ) )
| ( subset @ SV174 @ SV216 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2237]) ).
thf(2291,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ( relation @ SV247 ) )
= $true )
| ( ( ~ ( ~ ( ( SV247
!= ( relation_inverse @ SV175 ) )
| ! [SY790: $i,SY791: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 )
| ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 ) ) ) )
| ~ ( ~ ! [SY792: $i,SY793: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 )
| ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 )
| ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 ) ) )
| ( SV247
= ( relation_inverse @ SV175 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2292,plain,
( ( ~ ~ ( empty @ sK67_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2293,plain,
( ( ~ ( relation @ sK67_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2294,plain,
! [SV217: $i,SV177: $i,SV236: $i] :
( ( ( relation @ SV236 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
| ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
| ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2295,plain,
! [SV178: $i,SV218: $i] :
( ( ( in @ SV218 @ SV178 )
= $false )
| ( ( in @ SV178 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2296,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV179 @ SV219 )
| ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2297,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ~ ( ~ ~ ! [SY729: $i] :
~ ~ ( ~ ( in @ SY729 @ SV179 )
| ~ ( in @ SY729 @ SV219 ) )
| ~ ( disjoint @ SV179 @ SV219 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2243]) ).
thf(2298,plain,
! [SV248: $i,SV237: $i,SV220: $i,SV180: $i] :
( ( ( ( ordered_pair @ SV180 @ SV220 )
!= ( ordered_pair @ SV237 @ SV248 ) )
= $true )
| ( ( ~ ( ( SV180 != SV237 )
| ( SV220 != SV248 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2299,plain,
! [SV181: $i] :
( ( ( ~ ~ ( empty @ SV181 ) )
= $true )
| ( ( ~ ( relation @ SV181 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2300,plain,
! [SV182: $i,SV221: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 ) )
| ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) ) ) )
= $false )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2246]) ).
thf(2301,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ~ ( ( SV238
!= ( set_intersection2 @ SV183 @ SV222 ) )
| ! [SY771: $i] :
~ ( ~ ( ~ ( in @ SY771 @ SV238 )
| ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) )
| ( in @ SY771 @ SV238 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2302,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ~ ( ~ ! [SY772: $i] :
~ ( ~ ( ~ ( in @ SY772 @ SV238 )
| ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) )
| ( in @ SY772 @ SV238 ) ) )
| ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2303,plain,
! [SV249: $i,SV239: $i,SV223: $i,SV184: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
| ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) )
| ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2304,plain,
! [SV185: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV185 ) ) )
= $false )
| ( ( empty @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2249]) ).
thf(2305,plain,
! [SV185: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV185 ) ) )
= $false )
| ( ( empty @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2249]) ).
thf(2306,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( relation @ SV256 )
| ~ ( ~ ( ( SV256
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
| ! [SY832: $i,SY833: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 )
| ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 ) ) ) )
| ~ ( ~ ! [SY834: $i,SY835: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 )
| ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 ) ) )
| ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) ) ) ) )
= $true )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2307,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( ~ ( ~ ( ( SV257
!= ( relation_inverse_image @ SV187 @ SV250 ) )
| ! [SY836: $i] :
~ ( ~ ( ~ ( in @ SY836 @ SV257 )
| ~ ! [SY796: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY796 ) @ SV187 )
| ~ ( in @ SY796 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY797: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY797 ) @ SV187 )
| ~ ( in @ SY797 @ SV250 ) )
| ( in @ SY836 @ SV257 ) ) ) )
| ~ ( ~ ! [SY839: $i] :
~ ( ~ ( ~ ( in @ SY839 @ SV257 )
| ~ ! [SY799: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY799 ) @ SV187 )
| ~ ( in @ SY799 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY800: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY800 ) @ SV187 )
| ~ ( in @ SY800 @ SV250 ) )
| ( in @ SY839 @ SV257 ) ) )
| ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) ) ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2308,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ~ ( ( SV240
!= ( unordered_pair @ SV189 @ SV226 ) )
| ! [SY774: $i] :
~ ( ~ ( ~ ( in @ SY774 @ SV240 )
| ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ~ ( ~ ( ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ( in @ SY774 @ SV240 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2253]) ).
thf(2309,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ~ ( ~ ! [SY775: $i] :
~ ( ~ ( ~ ( in @ SY775 @ SV240 )
| ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ~ ( ~ ( ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ( in @ SY775 @ SV240 ) ) )
| ( SV240
= ( unordered_pair @ SV189 @ SV226 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2253]) ).
thf(2310,plain,
! [SV251: $i,SV190: $i,SV258: $i] :
( ( ( ~ ( relation @ SV258 )
| ~ ( ~ ( ( SV258
!= ( relation_dom_restriction @ SV190 @ SV251 ) )
| ! [SY842: $i,SY843: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 )
| ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 ) ) ) )
| ~ ( ~ ! [SY844: $i,SY845: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 )
| ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 ) ) )
| ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) ) ) ) )
= $true )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2311,plain,
! [SV191: $i] :
( ( ( ~ ( relation @ SV191 ) )
= $true )
| ( ( ~ ( function @ SV191 ) )
= $true )
| ( ( ! [SY644: $i,SY645: $i] :
~ ( ~ ( ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( SY645 = empty_set ) )
| ~ ( ( SY645 != empty_set )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2312,plain,
! [SV192: $i] :
( ( ( ~ ( relation @ SV192 ) )
= $true )
| ( ( ! [SY646: $i] :
~ ~ ( ~ ( in @ SY646 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY646
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2313,plain,
! [SV192: $i] :
( ( ( ~ ! [SY649: $i] :
~ ~ ( ~ ( in @ SY649 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY649
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2314,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ( ~ ( ( SV259
!= ( relation_image @ SV193 @ SV252 ) )
| ! [SY846: $i] :
~ ( ~ ( ~ ( in @ SY846 @ SV259 )
| ~ ! [SY808: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY808 @ SY846 ) @ SV193 )
| ~ ( in @ SY808 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY809: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY809 @ SY846 ) @ SV193 )
| ~ ( in @ SY809 @ SV252 ) )
| ( in @ SY846 @ SV259 ) ) ) )
| ~ ( ~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SV259 )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY811 @ SY849 ) @ SV193 )
| ~ ( in @ SY811 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY812 @ SY849 ) @ SV193 )
| ~ ( in @ SY812 @ SV252 ) )
| ( in @ SY849 @ SV259 ) ) )
| ( SV259
= ( relation_image @ SV193 @ SV252 ) ) ) ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2315,plain,
! [SV194: $i,SV253: $i] :
( ( ( ~ ( ( SV253
!= ( relation_dom @ SV194 ) )
| ! [SY813: $i] :
~ ( ~ ( ~ ( in @ SY813 @ SV253 )
| ~ ! [SY662: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY662 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY663: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY663 ) @ SV194 )
| ( in @ SY813 @ SV253 ) ) ) )
| ~ ( ~ ! [SY816: $i] :
~ ( ~ ( ~ ( in @ SY816 @ SV253 )
| ~ ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY665 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY666: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY666 ) @ SV194 )
| ( in @ SY816 @ SV253 ) ) )
| ( SV253
= ( relation_dom @ SV194 ) ) ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2316,plain,
( ( ~ ( relation @ sK68_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2317,plain,
( ( ~ ( function @ sK68_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2318,plain,
( ( ~ ( relation @ sK69_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2261]) ).
thf(2319,plain,
( ( ~ ( relation_empty_yielding @ sK69_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2261]) ).
thf(2320,plain,
( ( ~ ( empty @ sK70_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2321,plain,
( ( ~ ( relation @ sK70_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2322,plain,
! [SV195: $i,SV227: $i] :
( ( ( ~ ( ( SV227
!= ( identity_relation @ SV195 ) )
| ! [SY746: $i,SY747: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 )
| ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 ) ) ) )
| ~ ( ~ ! [SY748: $i,SY749: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 )
| ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) )
| ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 ) ) )
| ( SV227
= ( identity_relation @ SV195 ) ) ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2323,plain,
! [SV228: $i,SV196: $i] :
( ( ( ~ ( relation @ SV196 )
| ~ ( relation @ SV228 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV196 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2264]) ).
thf(2324,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ~ ( ( SV241
!= ( set_union2 @ SV198 @ SV229 ) )
| ! [SY776: $i] :
~ ( ~ ( ~ ( in @ SY776 @ SV241 )
| ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ~ ( ~ ( ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ( in @ SY776 @ SV241 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2265]) ).
thf(2325,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ~ ( ~ ! [SY777: $i] :
~ ( ~ ( ~ ( in @ SY777 @ SV241 )
| ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ~ ( ~ ( ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ( in @ SY777 @ SV241 ) ) )
| ( SV241
= ( set_union2 @ SV198 @ SV229 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2265]) ).
thf(2326,plain,
! [SV199: $i] :
( ( ( ! [SY677: $i,SY678: $i] :
~ ( in @ ( ordered_pair @ SY677 @ SY678 ) @ SV199 ) )
= $false )
| ( ( SV199 = empty_set )
= $true )
| ( ( relation @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2327,plain,
! [SV230: $i,SV200: $i,SV242: $i] :
( ( ( relation @ SV242 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 )
| ~ ( ~ ( in @ SV200 @ ( relation_dom @ SV242 ) )
| ~ ( in @ SV230 @ ( relation_rng @ SV242 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2328,plain,
! [SV201: $i,SV254: $i] :
( ( ( ~ ( relation @ SV254 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV201 @ SV254 )
| ! [SY819: $i,SY820: $i] :
( ~ ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV201 )
| ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV254 ) ) )
| ~ ( ~ ! [SY821: $i,SY822: $i] :
( ~ ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV201 )
| ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV254 ) )
| ( subset @ SV201 @ SV254 ) ) ) )
= $true )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2329,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ~ ( ( SV243
!= ( set_difference @ SV202 @ SV231 ) )
| ! [SY778: $i] :
~ ( ~ ( ~ ( in @ SY778 @ SV243 )
| ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) )
| ( in @ SY778 @ SV243 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2269]) ).
thf(2330,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ~ ( ~ ! [SY779: $i] :
~ ( ~ ( ~ ( in @ SY779 @ SV243 )
| ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) )
| ( in @ SY779 @ SV243 ) ) )
| ( SV243
= ( set_difference @ SV202 @ SV231 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2269]) ).
thf(2331,plain,
! [SV203: $i,SV255: $i] :
( ( ( ~ ( relation @ SV255 ) )
= $true )
| ( ( ! [SY823: $i] :
( ~ ( relation @ SY823 )
| ~ ( ~ ( ( SY823
!= ( relation_composition @ SV203 @ SV255 ) )
| ! [SY824: $i,SY825: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY824 @ SY825 ) @ SY823 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY824 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY825 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY824 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY825 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY824 @ SY825 ) @ SY823 ) ) ) )
| ~ ( ~ ! [SY828: $i,SY829: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY828 @ SY829 ) @ SY823 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY828 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY828 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY829 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY828 @ SY829 ) @ SY823 ) ) )
| ( SY823
= ( relation_composition @ SV203 @ SV255 ) ) ) ) ) )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2332,plain,
! [SV232: $i,SV205: $i,SV158: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV158 @ ( relation_field @ SV232 ) )
| ~ ( in @ SV205 @ ( relation_field @ SV232 ) ) ) )
= $true )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2333,plain,
! [SV244: $i,SV233: $i,SV206: $i,SV159: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
| ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2334,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) )
| ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2335,plain,
! [SV160: $i] :
( ( ( SV160 = empty_set )
= $false )
| ( ( ! [SY548: $i] :
~ ( in @ SY548 @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2336,plain,
! [SV160: $i] :
( ( ( ! [SY549: $i] :
~ ( in @ SY549 @ SV160 ) )
= $false )
| ( ( SV160 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2337,plain,
! [SV207: $i,SV161: $i] :
( ( ( ~ ( relation @ SV161 ) )
= $true )
| ( ( ~ ( relation @ SV207 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV161 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2338,plain,
! [SV208: $i,SV234: $i,SV162: $i] :
( ( ( ~ ( ~ ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
| ~ ! [SY758: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY758 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY758 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY758 @ SV208 ) ) )
| ~ ( ~ ~ ! [SY759: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY759 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY759 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY759 @ SV208 ) )
| ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) ) ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2339,plain,
! [SV165: $i,SV210: $i] :
( ( ( SV210
!= ( union @ SV165 ) )
= $true )
| ( ( ! [SY706: $i] :
~ ( ~ ( ~ ( in @ SY706 @ SV210 )
| ~ ! [SY558: $i] :
~ ~ ( ~ ( in @ SY706 @ SY558 )
| ~ ( in @ SY558 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ~ ( ~ ( in @ SY706 @ SY559 )
| ~ ( in @ SY559 @ SV165 ) )
| ( in @ SY706 @ SV210 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2340,plain,
! [SV165: $i,SV210: $i] :
( ( ( ~ ! [SY709: $i] :
~ ( ~ ( ~ ( in @ SY709 @ SV210 )
| ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY709 @ SY561 )
| ~ ( in @ SY561 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY562: $i] :
~ ~ ( ~ ( in @ SY709 @ SY562 )
| ~ ( in @ SY562 @ SV165 ) )
| ( in @ SY709 @ SV210 ) ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2341,plain,
! [SV166: $i,SV245: $i] :
( ( ( relation @ SV245 )
= $false )
| ( ( ~ ( ~ ( ( SV166 != SV245 )
| ! [SY780: $i,SY781: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 ) ) ) )
| ~ ( ~ ! [SY782: $i,SY783: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 ) ) )
| ( SV166 = SV245 ) ) ) )
= $true )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2342,plain,
! [SV167: $i,SV246: $i] :
( ( ( ~ ( ( SV246
!= ( relation_rng @ SV167 ) )
| ! [SY784: $i] :
~ ( ~ ( ~ ( in @ SY784 @ SV246 )
| ~ ! [SY570: $i] :
~ ( in @ ( ordered_pair @ SY570 @ SY784 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY571: $i] :
~ ( in @ ( ordered_pair @ SY571 @ SY784 ) @ SV167 )
| ( in @ SY784 @ SV246 ) ) ) ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2280]) ).
thf(2343,plain,
! [SV167: $i,SV246: $i] :
( ( ( ~ ( ~ ! [SY787: $i] :
~ ( ~ ( ~ ( in @ SY787 @ SV246 )
| ~ ! [SY573: $i] :
~ ( in @ ( ordered_pair @ SY573 @ SY787 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ SY787 ) @ SV167 )
| ( in @ SY787 @ SV246 ) ) )
| ( SV246
= ( relation_rng @ SV167 ) ) ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2280]) ).
thf(2344,plain,
! [SV211: $i,SV168: $i] :
( ( ( ~ ( relation @ SV168 ) )
= $true )
| ( ( ~ ( relation @ SV211 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV168 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2345,plain,
! [SV212: $i,SV169: $i] :
( ( ( in @ SV169 @ SV212 )
= $false )
| ( ( ~ ( empty @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2346,plain,
( ( in @ sK1_A @ ( relation_dom @ sK3_SY160 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2283]) ).
thf(2347,plain,
( ( sK2_SY158
= ( apply @ sK3_SY160 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2284]) ).
thf(2348,plain,
! [SV170: $i,SV213: $i] :
( ( ( SV213
!= ( singleton @ SV170 ) )
= $true )
| ( ( ! [SY712: $i] :
~ ( ~ ( ~ ( in @ SY712 @ SV213 )
| ( SY712 = SV170 ) )
| ~ ( ( SY712 != SV170 )
| ( in @ SY712 @ SV213 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2349,plain,
! [SV170: $i,SV213: $i] :
( ( ( ~ ! [SY713: $i] :
~ ( ~ ( ~ ( in @ SY713 @ SV213 )
| ( SY713 = SV170 ) )
| ~ ( ( SY713 != SV170 )
| ( in @ SY713 @ SV213 ) ) ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2350,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ( SV235
!= ( cartesian_product2 @ SV171 @ SV214 ) )
| ! [SY760: $i] :
~ ( ~ ( ~ ( in @ SY760 @ SV235 )
| ~ ! [SY716: $i] :
~ ~ ! [SY717: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY716 @ SV171 )
| ~ ( in @ SY717 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY716 @ SY717 ) ) ) )
| ~ ( ~ ~ ! [SY718: $i] :
~ ~ ! [SY719: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY718 @ SV171 )
| ~ ( in @ SY719 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY718 @ SY719 ) ) )
| ( in @ SY760 @ SV235 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2287]) ).
thf(2351,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ~ ! [SY765: $i] :
~ ( ~ ( ~ ( in @ SY765 @ SV235 )
| ~ ! [SY721: $i] :
~ ~ ! [SY722: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY721 @ SV171 )
| ~ ( in @ SY722 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY721 @ SY722 ) ) ) )
| ~ ( ~ ~ ! [SY723: $i] :
~ ~ ! [SY724: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY723 @ SV171 )
| ~ ( in @ SY724 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY723 @ SY724 ) ) )
| ( in @ SY765 @ SV235 ) ) )
| ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2288]) ).
thf(2352,plain,
! [SV216: $i,SV174: $i] :
( ( ( ~ ( subset @ SV174 @ SV216 ) )
= $true )
| ( ( ! [SY725: $i] :
( ~ ( in @ SY725 @ SV174 )
| ( in @ SY725 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2353,plain,
! [SV216: $i,SV174: $i] :
( ( ( ~ ! [SY726: $i] :
( ~ ( in @ SY726 @ SV174 )
| ( in @ SY726 @ SV216 ) ) )
= $true )
| ( ( subset @ SV174 @ SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2354,plain,
! [SV175: $i,SV247: $i] :
( ( ( relation @ SV247 )
= $false )
| ( ( ~ ( ~ ( ( SV247
!= ( relation_inverse @ SV175 ) )
| ! [SY790: $i,SY791: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 )
| ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 ) ) ) )
| ~ ( ~ ! [SY792: $i,SY793: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 )
| ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 )
| ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 ) ) )
| ( SV247
= ( relation_inverse @ SV175 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2355,plain,
( ( ~ ( empty @ sK67_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2292]) ).
thf(2356,plain,
( ( relation @ sK67_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2357,plain,
! [SV217: $i,SV236: $i,SV177: $i] :
( ( ( ~ ( ~ ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
| ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
| ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) ) ) )
= $false )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2358,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV179 @ SV219 )
| ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2359,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ( ~ ~ ! [SY729: $i] :
~ ~ ( ~ ( in @ SY729 @ SV179 )
| ~ ( in @ SY729 @ SV219 ) )
| ~ ( disjoint @ SV179 @ SV219 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2360,plain,
! [SV248: $i,SV237: $i,SV220: $i,SV180: $i] :
( ( ( ( ordered_pair @ SV180 @ SV220 )
= ( ordered_pair @ SV237 @ SV248 ) )
= $false )
| ( ( ~ ( ( SV180 != SV237 )
| ( SV220 != SV248 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2361,plain,
! [SV181: $i] :
( ( ( ~ ( empty @ SV181 ) )
= $false )
| ( ( ~ ( relation @ SV181 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2362,plain,
! [SV182: $i,SV221: $i] :
( ( ( ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 ) )
| ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) ) )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2300]) ).
thf(2363,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ( SV238
!= ( set_intersection2 @ SV183 @ SV222 ) )
| ! [SY771: $i] :
~ ( ~ ( ~ ( in @ SY771 @ SV238 )
| ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) )
| ( in @ SY771 @ SV238 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2301]) ).
thf(2364,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ~ ! [SY772: $i] :
~ ( ~ ( ~ ( in @ SY772 @ SV238 )
| ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) )
| ( in @ SY772 @ SV238 ) ) )
| ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2302]) ).
thf(2365,plain,
! [SV249: $i,SV239: $i,SV223: $i,SV184: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
| ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2366,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) )
| ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2367,plain,
! [SV185: $i] :
( ( ( empty @ ( relation_dom @ SV185 ) )
= $true )
| ( ( empty @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2304]) ).
thf(2368,plain,
! [SV185: $i] :
( ( ( relation @ ( relation_dom @ SV185 ) )
= $true )
| ( ( empty @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2305]) ).
thf(2369,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( relation @ SV256 ) )
= $true )
| ( ( ~ ( ~ ( ( SV256
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
| ! [SY832: $i,SY833: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 )
| ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 ) ) ) )
| ~ ( ~ ! [SY834: $i,SY835: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 )
| ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 ) ) )
| ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) ) ) ) )
= $true )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2370,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( ~ ( ( SV257
!= ( relation_inverse_image @ SV187 @ SV250 ) )
| ! [SY836: $i] :
~ ( ~ ( ~ ( in @ SY836 @ SV257 )
| ~ ! [SY796: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY796 ) @ SV187 )
| ~ ( in @ SY796 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY797: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY797 ) @ SV187 )
| ~ ( in @ SY797 @ SV250 ) )
| ( in @ SY836 @ SV257 ) ) ) )
| ~ ( ~ ! [SY839: $i] :
~ ( ~ ( ~ ( in @ SY839 @ SV257 )
| ~ ! [SY799: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY799 ) @ SV187 )
| ~ ( in @ SY799 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY800: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY800 ) @ SV187 )
| ~ ( in @ SY800 @ SV250 ) )
| ( in @ SY839 @ SV257 ) ) )
| ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) ) ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2371,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ( SV240
!= ( unordered_pair @ SV189 @ SV226 ) )
| ! [SY774: $i] :
~ ( ~ ( ~ ( in @ SY774 @ SV240 )
| ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ~ ( ~ ( ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ( in @ SY774 @ SV240 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2308]) ).
thf(2372,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ~ ! [SY775: $i] :
~ ( ~ ( ~ ( in @ SY775 @ SV240 )
| ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ~ ( ~ ( ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ( in @ SY775 @ SV240 ) ) )
| ( SV240
= ( unordered_pair @ SV189 @ SV226 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2373,plain,
! [SV251: $i,SV190: $i,SV258: $i] :
( ( ( ~ ( relation @ SV258 ) )
= $true )
| ( ( ~ ( ~ ( ( SV258
!= ( relation_dom_restriction @ SV190 @ SV251 ) )
| ! [SY842: $i,SY843: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 )
| ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 ) ) ) )
| ~ ( ~ ! [SY844: $i,SY845: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 )
| ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 ) ) )
| ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) ) ) ) )
= $true )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2374,plain,
! [SV191: $i] :
( ( ( relation @ SV191 )
= $false )
| ( ( ~ ( function @ SV191 ) )
= $true )
| ( ( ! [SY644: $i,SY645: $i] :
~ ( ~ ( ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( SY645 = empty_set ) )
| ~ ( ( SY645 != empty_set )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2375,plain,
! [SV192: $i] :
( ( ( relation @ SV192 )
= $false )
| ( ( ! [SY646: $i] :
~ ~ ( ~ ( in @ SY646 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY646
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2376,plain,
! [SV192: $i] :
( ( ( ! [SY649: $i] :
~ ~ ( ~ ( in @ SY649 @ SV192 )
| ~ ! [SX2: $i,SX3: $i] :
( SY649
!= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2377,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ( ( SV259
!= ( relation_image @ SV193 @ SV252 ) )
| ! [SY846: $i] :
~ ( ~ ( ~ ( in @ SY846 @ SV259 )
| ~ ! [SY808: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY808 @ SY846 ) @ SV193 )
| ~ ( in @ SY808 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY809: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY809 @ SY846 ) @ SV193 )
| ~ ( in @ SY809 @ SV252 ) )
| ( in @ SY846 @ SV259 ) ) ) )
| ~ ( ~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SV259 )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY811 @ SY849 ) @ SV193 )
| ~ ( in @ SY811 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY812 @ SY849 ) @ SV193 )
| ~ ( in @ SY812 @ SV252 ) )
| ( in @ SY849 @ SV259 ) ) )
| ( SV259
= ( relation_image @ SV193 @ SV252 ) ) ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2378,plain,
! [SV194: $i,SV253: $i] :
( ( ( ~ ( ( SV253
!= ( relation_dom @ SV194 ) )
| ! [SY813: $i] :
~ ( ~ ( ~ ( in @ SY813 @ SV253 )
| ~ ! [SY662: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY662 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY663: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY663 ) @ SV194 )
| ( in @ SY813 @ SV253 ) ) ) ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2379,plain,
! [SV194: $i,SV253: $i] :
( ( ( ~ ( ~ ! [SY816: $i] :
~ ( ~ ( ~ ( in @ SY816 @ SV253 )
| ~ ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY665 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY666: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY666 ) @ SV194 )
| ( in @ SY816 @ SV253 ) ) )
| ( SV253
= ( relation_dom @ SV194 ) ) ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2380,plain,
( ( relation @ sK68_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2316]) ).
thf(2381,plain,
( ( function @ sK68_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2317]) ).
thf(2382,plain,
( ( relation @ sK69_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2318]) ).
thf(2383,plain,
( ( relation_empty_yielding @ sK69_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2319]) ).
thf(2384,plain,
( ( empty @ sK70_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2320]) ).
thf(2385,plain,
( ( relation @ sK70_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2321]) ).
thf(2386,plain,
! [SV195: $i,SV227: $i] :
( ( ( ~ ( ( SV227
!= ( identity_relation @ SV195 ) )
| ! [SY746: $i,SY747: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 )
| ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 ) ) ) ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2322]) ).
thf(2387,plain,
! [SV195: $i,SV227: $i] :
( ( ( ~ ( ~ ! [SY748: $i,SY749: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 )
| ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) )
| ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 ) ) )
| ( SV227
= ( identity_relation @ SV195 ) ) ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2322]) ).
thf(2388,plain,
! [SV228: $i,SV196: $i] :
( ( ( ~ ( relation @ SV196 ) )
= $true )
| ( ( ~ ( relation @ SV228 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV196 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2389,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ( SV241
!= ( set_union2 @ SV198 @ SV229 ) )
| ! [SY776: $i] :
~ ( ~ ( ~ ( in @ SY776 @ SV241 )
| ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ~ ( ~ ( ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ( in @ SY776 @ SV241 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2324]) ).
thf(2390,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ~ ! [SY777: $i] :
~ ( ~ ( ~ ( in @ SY777 @ SV241 )
| ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ~ ( ~ ( ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ( in @ SY777 @ SV241 ) ) )
| ( SV241
= ( set_union2 @ SV198 @ SV229 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2325]) ).
thf(2391,plain,
! [SV199: $i] :
( ( ( ! [SY852: $i] :
~ ( in @ ( ordered_pair @ ( sK72_SY677 @ SV199 ) @ SY852 ) @ SV199 ) )
= $false )
| ( ( SV199 = empty_set )
= $true )
| ( ( relation @ SV199 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2326]) ).
thf(2392,plain,
! [SV242: $i,SV230: $i,SV200: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV200 @ ( relation_dom @ SV242 ) )
| ~ ( in @ SV230 @ ( relation_rng @ SV242 ) ) ) )
= $true )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2393,plain,
! [SV201: $i,SV254: $i] :
( ( ( relation @ SV254 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV201 @ SV254 )
| ! [SY819: $i,SY820: $i] :
( ~ ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV201 )
| ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV254 ) ) )
| ~ ( ~ ! [SY821: $i,SY822: $i] :
( ~ ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV201 )
| ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV254 ) )
| ( subset @ SV201 @ SV254 ) ) ) )
= $true )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2394,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ( SV243
!= ( set_difference @ SV202 @ SV231 ) )
| ! [SY778: $i] :
~ ( ~ ( ~ ( in @ SY778 @ SV243 )
| ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) )
| ( in @ SY778 @ SV243 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2329]) ).
thf(2395,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ~ ! [SY779: $i] :
~ ( ~ ( ~ ( in @ SY779 @ SV243 )
| ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) )
| ( in @ SY779 @ SV243 ) ) )
| ( SV243
= ( set_difference @ SV202 @ SV231 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2330]) ).
thf(2396,plain,
! [SV203: $i,SV255: $i] :
( ( ( relation @ SV255 )
= $false )
| ( ( ! [SY823: $i] :
( ~ ( relation @ SY823 )
| ~ ( ~ ( ( SY823
!= ( relation_composition @ SV203 @ SV255 ) )
| ! [SY824: $i,SY825: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY824 @ SY825 ) @ SY823 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY824 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY825 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY824 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY825 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY824 @ SY825 ) @ SY823 ) ) ) )
| ~ ( ~ ! [SY828: $i,SY829: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY828 @ SY829 ) @ SY823 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY828 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY829 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY828 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY829 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY828 @ SY829 ) @ SY823 ) ) )
| ( SY823
= ( relation_composition @ SV203 @ SV255 ) ) ) ) ) )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2397,plain,
! [SV232: $i,SV205: $i,SV158: $i] :
( ( ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 )
= $false )
| ( ( ~ ( ~ ( in @ SV158 @ ( relation_field @ SV232 ) )
| ~ ( in @ SV205 @ ( relation_field @ SV232 ) ) ) )
= $true )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2398,plain,
! [SV244: $i,SV233: $i,SV206: $i,SV159: $i] :
( ( ~ ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
| ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2399,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ~ ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) )
| ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2400,plain,
! [SV160: $i,SV260: $i] :
( ( ( ~ ( in @ SV260 @ SV160 ) )
= $true )
| ( ( SV160 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2401,plain,
! [SV160: $i] :
( ( ( ~ ( in @ ( sK73_SY549 @ SV160 ) @ SV160 ) )
= $false )
| ( ( SV160 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2336]) ).
thf(2402,plain,
! [SV207: $i,SV161: $i] :
( ( ( relation @ SV161 )
= $false )
| ( ( ~ ( relation @ SV207 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV161 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2403,plain,
! [SV208: $i,SV234: $i,SV162: $i] :
( ( ( ~ ( ~ ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
| ~ ! [SY758: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY758 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY758 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY758 @ SV208 ) ) ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2338]) ).
thf(2404,plain,
! [SV208: $i,SV162: $i,SV234: $i] :
( ( ( ~ ( ~ ~ ! [SY759: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY759 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY759 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY759 @ SV208 ) )
| ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) ) ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2338]) ).
thf(2405,plain,
! [SV165: $i,SV210: $i] :
( ( ( SV210
= ( union @ SV165 ) )
= $false )
| ( ( ! [SY706: $i] :
~ ( ~ ( ~ ( in @ SY706 @ SV210 )
| ~ ! [SY558: $i] :
~ ~ ( ~ ( in @ SY706 @ SY558 )
| ~ ( in @ SY558 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY559: $i] :
~ ~ ( ~ ( in @ SY706 @ SY559 )
| ~ ( in @ SY559 @ SV165 ) )
| ( in @ SY706 @ SV210 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2406,plain,
! [SV165: $i,SV210: $i] :
( ( ( ! [SY709: $i] :
~ ( ~ ( ~ ( in @ SY709 @ SV210 )
| ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY709 @ SY561 )
| ~ ( in @ SY561 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY562: $i] :
~ ~ ( ~ ( in @ SY709 @ SY562 )
| ~ ( in @ SY562 @ SV165 ) )
| ( in @ SY709 @ SV210 ) ) ) )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2407,plain,
! [SV245: $i,SV166: $i] :
( ( ( ~ ( ( SV166 != SV245 )
| ! [SY780: $i,SY781: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 ) ) ) )
| ~ ( ~ ! [SY782: $i,SY783: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 ) ) )
| ( SV166 = SV245 ) ) )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2408,plain,
! [SV167: $i,SV246: $i] :
( ( ( ( SV246
!= ( relation_rng @ SV167 ) )
| ! [SY784: $i] :
~ ( ~ ( ~ ( in @ SY784 @ SV246 )
| ~ ! [SY570: $i] :
~ ( in @ ( ordered_pair @ SY570 @ SY784 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY571: $i] :
~ ( in @ ( ordered_pair @ SY571 @ SY784 ) @ SV167 )
| ( in @ SY784 @ SV246 ) ) ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2409,plain,
! [SV167: $i,SV246: $i] :
( ( ( ~ ! [SY787: $i] :
~ ( ~ ( ~ ( in @ SY787 @ SV246 )
| ~ ! [SY573: $i] :
~ ( in @ ( ordered_pair @ SY573 @ SY787 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ SY787 ) @ SV167 )
| ( in @ SY787 @ SV246 ) ) )
| ( SV246
= ( relation_rng @ SV167 ) ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2343]) ).
thf(2410,plain,
! [SV211: $i,SV168: $i] :
( ( ( relation @ SV168 )
= $false )
| ( ( ~ ( relation @ SV211 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV168 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2411,plain,
! [SV169: $i,SV212: $i] :
( ( ( empty @ SV212 )
= $false )
| ( ( in @ SV169 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2412,plain,
! [SV170: $i,SV213: $i] :
( ( ( SV213
= ( singleton @ SV170 ) )
= $false )
| ( ( ! [SY712: $i] :
~ ( ~ ( ~ ( in @ SY712 @ SV213 )
| ( SY712 = SV170 ) )
| ~ ( ( SY712 != SV170 )
| ( in @ SY712 @ SV213 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2413,plain,
! [SV170: $i,SV213: $i] :
( ( ( ! [SY713: $i] :
~ ( ~ ( ~ ( in @ SY713 @ SV213 )
| ( SY713 = SV170 ) )
| ~ ( ( SY713 != SV170 )
| ( in @ SY713 @ SV213 ) ) ) )
= $false )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2414,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ( SV235
!= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true )
| ( ( ! [SY760: $i] :
~ ( ~ ( ~ ( in @ SY760 @ SV235 )
| ~ ! [SY716: $i] :
~ ~ ! [SY717: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY716 @ SV171 )
| ~ ( in @ SY717 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY716 @ SY717 ) ) ) )
| ~ ( ~ ~ ! [SY718: $i] :
~ ~ ! [SY719: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY718 @ SV171 )
| ~ ( in @ SY719 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY718 @ SY719 ) ) )
| ( in @ SY760 @ SV235 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2415,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ( ~ ! [SY765: $i] :
~ ( ~ ( ~ ( in @ SY765 @ SV235 )
| ~ ! [SY721: $i] :
~ ~ ! [SY722: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY721 @ SV171 )
| ~ ( in @ SY722 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY721 @ SY722 ) ) ) )
| ~ ( ~ ~ ! [SY723: $i] :
~ ~ ! [SY724: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY723 @ SV171 )
| ~ ( in @ SY724 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY723 @ SY724 ) ) )
| ( in @ SY765 @ SV235 ) ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2416,plain,
! [SV216: $i,SV174: $i] :
( ( ( subset @ SV174 @ SV216 )
= $false )
| ( ( ! [SY725: $i] :
( ~ ( in @ SY725 @ SV174 )
| ( in @ SY725 @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2417,plain,
! [SV216: $i,SV174: $i] :
( ( ( ! [SY726: $i] :
( ~ ( in @ SY726 @ SV174 )
| ( in @ SY726 @ SV216 ) ) )
= $false )
| ( ( subset @ SV174 @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2418,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ( ( SV247
!= ( relation_inverse @ SV175 ) )
| ! [SY790: $i,SY791: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 )
| ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 ) ) ) )
| ~ ( ~ ! [SY792: $i,SY793: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 )
| ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 )
| ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 ) ) )
| ( SV247
= ( relation_inverse @ SV175 ) ) ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2419,plain,
( ( empty @ sK67_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2420,plain,
! [SV217: $i,SV236: $i,SV177: $i] :
( ( ( ~ ( ~ ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
| ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) ) )
= $false )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2357]) ).
thf(2421,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
| ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) ) ) )
= $false )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2357]) ).
thf(2422,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ~ ( disjoint @ SV179 @ SV219 )
| ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2423,plain,
! [SV219: $i,SV179: $i] :
( ( ~ ~ ! [SY729: $i] :
~ ~ ( ~ ( in @ SY729 @ SV179 )
| ~ ( in @ SY729 @ SV219 ) )
| ~ ( disjoint @ SV179 @ SV219 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2359]) ).
thf(2424,plain,
! [SV248: $i,SV220: $i,SV237: $i,SV180: $i] :
( ( ( ( SV180 != SV237 )
| ( SV220 != SV248 ) )
= $false )
| ( ( ( ordered_pair @ SV180 @ SV220 )
= ( ordered_pair @ SV237 @ SV248 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2425,plain,
! [SV181: $i] :
( ( ( empty @ SV181 )
= $true )
| ( ( ~ ( relation @ SV181 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2361]) ).
thf(2426,plain,
! [SV182: $i,SV221: $i] :
( ( ( ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) ) )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2427,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ( SV238
!= ( set_intersection2 @ SV183 @ SV222 ) )
= $true )
| ( ( ! [SY771: $i] :
~ ( ~ ( ~ ( in @ SY771 @ SV238 )
| ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) )
| ( in @ SY771 @ SV238 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2428,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ( ~ ! [SY772: $i] :
~ ( ~ ( ~ ( in @ SY772 @ SV238 )
| ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) )
| ( in @ SY772 @ SV238 ) ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2429,plain,
! [SV249: $i,SV239: $i,SV223: $i,SV184: $i] :
( ( ~ ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
| ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2365]) ).
thf(2430,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ~ ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) )
| ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2366]) ).
thf(2431,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( relation @ SV256 )
= $false )
| ( ( ~ ( ~ ( ( SV256
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
| ! [SY832: $i,SY833: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 )
| ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 ) ) ) )
| ~ ( ~ ! [SY834: $i,SY835: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 )
| ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 ) ) )
| ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) ) ) ) )
= $true )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2432,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( ~ ( ( SV257
!= ( relation_inverse_image @ SV187 @ SV250 ) )
| ! [SY836: $i] :
~ ( ~ ( ~ ( in @ SY836 @ SV257 )
| ~ ! [SY796: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY796 ) @ SV187 )
| ~ ( in @ SY796 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY797: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY797 ) @ SV187 )
| ~ ( in @ SY797 @ SV250 ) )
| ( in @ SY836 @ SV257 ) ) ) ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2370]) ).
thf(2433,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( ~ ( ~ ! [SY839: $i] :
~ ( ~ ( ~ ( in @ SY839 @ SV257 )
| ~ ! [SY799: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY799 ) @ SV187 )
| ~ ( in @ SY799 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY800: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY800 ) @ SV187 )
| ~ ( in @ SY800 @ SV250 ) )
| ( in @ SY839 @ SV257 ) ) )
| ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) ) ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2370]) ).
thf(2434,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ( SV240
!= ( unordered_pair @ SV189 @ SV226 ) )
= $true )
| ( ( ! [SY774: $i] :
~ ( ~ ( ~ ( in @ SY774 @ SV240 )
| ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ~ ( ~ ( ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ( in @ SY774 @ SV240 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2435,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ( ~ ! [SY775: $i] :
~ ( ~ ( ~ ( in @ SY775 @ SV240 )
| ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ~ ( ~ ( ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ( in @ SY775 @ SV240 ) ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2436,plain,
! [SV251: $i,SV190: $i,SV258: $i] :
( ( ( relation @ SV258 )
= $false )
| ( ( ~ ( ~ ( ( SV258
!= ( relation_dom_restriction @ SV190 @ SV251 ) )
| ! [SY842: $i,SY843: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 )
| ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 ) ) ) )
| ~ ( ~ ! [SY844: $i,SY845: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 )
| ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 ) ) )
| ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) ) ) ) )
= $true )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2437,plain,
! [SV191: $i] :
( ( ( function @ SV191 )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( ! [SY644: $i,SY645: $i] :
~ ( ~ ( ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY644 @ SY645 ) @ SV191 )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY644 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY645
!= ( apply @ SV191 @ SY644 ) )
| ( SY645 = empty_set ) )
| ~ ( ( SY645 != empty_set )
| ( SY645
= ( apply @ SV191 @ SY644 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2438,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ~ ( ~ ( in @ SV261 @ SV192 )
| ~ ! [SY853: $i,SY854: $i] :
( SV261
!= ( ordered_pair @ SY853 @ SY854 ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2439,plain,
! [SV192: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK74_SY649 @ SV192 ) @ SV192 )
| ~ ! [SY855: $i,SY856: $i] :
( ( sK74_SY649 @ SV192 )
!= ( ordered_pair @ SY855 @ SY856 ) ) ) )
= $false )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2376]) ).
thf(2440,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ( ( SV259
!= ( relation_image @ SV193 @ SV252 ) )
| ! [SY846: $i] :
~ ( ~ ( ~ ( in @ SY846 @ SV259 )
| ~ ! [SY808: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY808 @ SY846 ) @ SV193 )
| ~ ( in @ SY808 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY809: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY809 @ SY846 ) @ SV193 )
| ~ ( in @ SY809 @ SV252 ) )
| ( in @ SY846 @ SV259 ) ) ) ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2441,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ( ~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SV259 )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY811 @ SY849 ) @ SV193 )
| ~ ( in @ SY811 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY812 @ SY849 ) @ SV193 )
| ~ ( in @ SY812 @ SV252 ) )
| ( in @ SY849 @ SV259 ) ) )
| ( SV259
= ( relation_image @ SV193 @ SV252 ) ) ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2442,plain,
! [SV194: $i,SV253: $i] :
( ( ( ( SV253
!= ( relation_dom @ SV194 ) )
| ! [SY813: $i] :
~ ( ~ ( ~ ( in @ SY813 @ SV253 )
| ~ ! [SY662: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY662 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY663: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY663 ) @ SV194 )
| ( in @ SY813 @ SV253 ) ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2443,plain,
! [SV194: $i,SV253: $i] :
( ( ( ~ ! [SY816: $i] :
~ ( ~ ( ~ ( in @ SY816 @ SV253 )
| ~ ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY665 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY666: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY666 ) @ SV194 )
| ( in @ SY816 @ SV253 ) ) )
| ( SV253
= ( relation_dom @ SV194 ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2379]) ).
thf(2444,plain,
! [SV195: $i,SV227: $i] :
( ( ( ( SV227
!= ( identity_relation @ SV195 ) )
| ! [SY746: $i,SY747: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 )
| ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 ) ) ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2386]) ).
thf(2445,plain,
! [SV195: $i,SV227: $i] :
( ( ( ~ ! [SY748: $i,SY749: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 )
| ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) )
| ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 ) ) )
| ( SV227
= ( identity_relation @ SV195 ) ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2387]) ).
thf(2446,plain,
! [SV228: $i,SV196: $i] :
( ( ( relation @ SV196 )
= $false )
| ( ( ~ ( relation @ SV228 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV196 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2447,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ( SV241
!= ( set_union2 @ SV198 @ SV229 ) )
= $true )
| ( ( ! [SY776: $i] :
~ ( ~ ( ~ ( in @ SY776 @ SV241 )
| ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ~ ( ~ ( ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ( in @ SY776 @ SV241 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2448,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ( ~ ! [SY777: $i] :
~ ( ~ ( ~ ( in @ SY777 @ SV241 )
| ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ~ ( ~ ( ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ( in @ SY777 @ SV241 ) ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2390]) ).
thf(2449,plain,
! [SV199: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK72_SY677 @ SV199 ) @ ( sK75_SY852 @ SV199 ) ) @ SV199 ) )
= $false )
| ( ( SV199 = empty_set )
= $true )
| ( ( relation @ SV199 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2391]) ).
thf(2450,plain,
! [SV242: $i,SV230: $i,SV200: $i] :
( ( ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 )
= $false )
| ( ( ~ ( ~ ( in @ SV200 @ ( relation_dom @ SV242 ) )
| ~ ( in @ SV230 @ ( relation_rng @ SV242 ) ) ) )
= $true )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2451,plain,
! [SV254: $i,SV201: $i] :
( ( ( ~ ( ~ ( subset @ SV201 @ SV254 )
| ! [SY819: $i,SY820: $i] :
( ~ ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV201 )
| ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV254 ) ) )
| ~ ( ~ ! [SY821: $i,SY822: $i] :
( ~ ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV201 )
| ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV254 ) )
| ( subset @ SV201 @ SV254 ) ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2452,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ( SV243
!= ( set_difference @ SV202 @ SV231 ) )
= $true )
| ( ( ! [SY778: $i] :
~ ( ~ ( ~ ( in @ SY778 @ SV243 )
| ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) )
| ( in @ SY778 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2453,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ( ~ ! [SY779: $i] :
~ ( ~ ( ~ ( in @ SY779 @ SV243 )
| ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) )
| ( in @ SY779 @ SV243 ) ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2454,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ~ ( relation @ SV262 )
| ~ ( ~ ( ( SV262
!= ( relation_composition @ SV203 @ SV255 ) )
| ! [SY857: $i,SY858: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY858 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY858 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 ) ) ) )
| ~ ( ~ ! [SY861: $i,SY862: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY862 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY862 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 ) ) )
| ( SV262
= ( relation_composition @ SV203 @ SV255 ) ) ) ) )
= $true )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2455,plain,
! [SV205: $i,SV232: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ ( relation_field @ SV232 ) )
| ~ ( in @ SV205 @ ( relation_field @ SV232 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 )
= $false )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2456,plain,
! [SV244: $i,SV233: $i,SV206: $i,SV159: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2457,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ( ~ ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2399]) ).
thf(2458,plain,
! [SV160: $i,SV260: $i] :
( ( ( in @ SV260 @ SV160 )
= $false )
| ( ( SV160 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2459,plain,
! [SV160: $i] :
( ( ( in @ ( sK73_SY549 @ SV160 ) @ SV160 )
= $true )
| ( ( SV160 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2401]) ).
thf(2460,plain,
! [SV161: $i,SV207: $i] :
( ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV161 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2461,plain,
! [SV208: $i,SV234: $i,SV162: $i] :
( ( ( ~ ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
| ~ ! [SY758: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY758 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY758 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY758 @ SV208 ) ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2403]) ).
thf(2462,plain,
! [SV208: $i,SV162: $i,SV234: $i] :
( ( ( ~ ~ ! [SY759: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY759 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY759 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY759 @ SV208 ) )
| ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2404]) ).
thf(2463,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV263 @ SV210 )
| ~ ! [SY865: $i] :
~ ~ ( ~ ( in @ SV263 @ SY865 )
| ~ ( in @ SY865 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY866: $i] :
~ ~ ( ~ ( in @ SV263 @ SY866 )
| ~ ( in @ SY866 @ SV165 ) )
| ( in @ SV263 @ SV210 ) ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2464,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
| ~ ! [SY867: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY867 )
| ~ ( in @ SY867 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) ) )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2406]) ).
thf(2465,plain,
! [SV245: $i,SV166: $i] :
( ( ( ~ ( ( SV166 != SV245 )
| ! [SY780: $i,SY781: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 ) ) ) ) )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2407]) ).
thf(2466,plain,
! [SV245: $i,SV166: $i] :
( ( ( ~ ( ~ ! [SY782: $i,SY783: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 ) ) )
| ( SV166 = SV245 ) ) )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2407]) ).
thf(2467,plain,
! [SV167: $i,SV246: $i] :
( ( ( SV246
!= ( relation_rng @ SV167 ) )
= $true )
| ( ( ! [SY784: $i] :
~ ( ~ ( ~ ( in @ SY784 @ SV246 )
| ~ ! [SY570: $i] :
~ ( in @ ( ordered_pair @ SY570 @ SY784 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY571: $i] :
~ ( in @ ( ordered_pair @ SY571 @ SY784 ) @ SV167 )
| ( in @ SY784 @ SV246 ) ) ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2468,plain,
! [SV167: $i,SV246: $i] :
( ( ( ~ ! [SY787: $i] :
~ ( ~ ( ~ ( in @ SY787 @ SV246 )
| ~ ! [SY573: $i] :
~ ( in @ ( ordered_pair @ SY573 @ SY787 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ SY787 ) @ SV167 )
| ( in @ SY787 @ SV246 ) ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2469,plain,
! [SV168: $i,SV211: $i] :
( ( ( relation @ SV211 )
= $false )
| ( ( relation @ SV168 )
= $false )
| ( ( relation @ ( relation_composition @ SV168 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2470,plain,
! [SV170: $i,SV213: $i,SV264: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV264 @ SV213 )
| ( SV264 = SV170 ) )
| ~ ( ( SV264 != SV170 )
| ( in @ SV264 @ SV213 ) ) ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2471,plain,
! [SV213: $i,SV170: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
| ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 ) )
| ~ ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
| ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) ) ) )
= $false )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2413]) ).
thf(2472,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false )
| ( ( ! [SY760: $i] :
~ ( ~ ( ~ ( in @ SY760 @ SV235 )
| ~ ! [SY716: $i] :
~ ~ ! [SY717: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY716 @ SV171 )
| ~ ( in @ SY717 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY716 @ SY717 ) ) ) )
| ~ ( ~ ~ ! [SY718: $i] :
~ ~ ! [SY719: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY718 @ SV171 )
| ~ ( in @ SY719 @ SV214 ) )
| ( SY760
!= ( ordered_pair @ SY718 @ SY719 ) ) )
| ( in @ SY760 @ SV235 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2473,plain,
! [SV214: $i,SV171: $i,SV235: $i] :
( ( ( ! [SY765: $i] :
~ ( ~ ( ~ ( in @ SY765 @ SV235 )
| ~ ! [SY721: $i] :
~ ~ ! [SY722: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY721 @ SV171 )
| ~ ( in @ SY722 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY721 @ SY722 ) ) ) )
| ~ ( ~ ~ ! [SY723: $i] :
~ ~ ! [SY724: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY723 @ SV171 )
| ~ ( in @ SY724 @ SV214 ) )
| ( SY765
!= ( ordered_pair @ SY723 @ SY724 ) ) )
| ( in @ SY765 @ SV235 ) ) ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2474,plain,
! [SV216: $i,SV174: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ SV174 )
| ( in @ SV265 @ SV216 ) )
= $true )
| ( ( subset @ SV174 @ SV216 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2475,plain,
! [SV174: $i,SV216: $i] :
( ( ( ~ ( in @ ( sK78_SY726 @ SV216 @ SV174 ) @ SV174 )
| ( in @ ( sK78_SY726 @ SV216 @ SV174 ) @ SV216 ) )
= $false )
| ( ( subset @ SV174 @ SV216 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2417]) ).
thf(2476,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ( ( SV247
!= ( relation_inverse @ SV175 ) )
| ! [SY790: $i,SY791: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 )
| ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 ) ) ) ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2418]) ).
thf(2477,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ( ~ ! [SY792: $i,SY793: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 )
| ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 )
| ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 ) ) )
| ( SV247
= ( relation_inverse @ SV175 ) ) ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2418]) ).
thf(2478,plain,
! [SV217: $i,SV236: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
| ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2420]) ).
thf(2479,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( ~ ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
| ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2421]) ).
thf(2480,plain,
! [SV219: $i,SV179: $i] :
( ( ( ~ ~ ( disjoint @ SV179 @ SV219 ) )
= $true )
| ( ( ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2481,plain,
! [SV219: $i,SV179: $i] :
( ( ( ~ ~ ! [SY729: $i] :
~ ~ ( ~ ( in @ SY729 @ SV179 )
| ~ ( in @ SY729 @ SV219 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2482,plain,
! [SV248: $i,SV220: $i,SV237: $i,SV180: $i] :
( ( ( SV180 != SV237 )
= $false )
| ( ( ( ordered_pair @ SV180 @ SV220 )
= ( ordered_pair @ SV237 @ SV248 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2424]) ).
thf(2483,plain,
! [SV237: $i,SV180: $i,SV248: $i,SV220: $i] :
( ( ( SV220 != SV248 )
= $false )
| ( ( ( ordered_pair @ SV180 @ SV220 )
= ( ordered_pair @ SV237 @ SV248 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2424]) ).
thf(2484,plain,
! [SV181: $i] :
( ( ( relation @ SV181 )
= $false )
| ( ( empty @ SV181 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2485,plain,
! [SV182: $i,SV221: $i] :
( ( ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) ) )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2486,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false )
| ( ( ! [SY771: $i] :
~ ( ~ ( ~ ( in @ SY771 @ SV238 )
| ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY771 @ SV183 )
| ~ ( in @ SY771 @ SV222 ) )
| ( in @ SY771 @ SV238 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2487,plain,
! [SV222: $i,SV183: $i,SV238: $i] :
( ( ( ! [SY772: $i] :
~ ( ~ ( ~ ( in @ SY772 @ SV238 )
| ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY772 @ SV183 )
| ~ ( in @ SY772 @ SV222 ) )
| ( in @ SY772 @ SV238 ) ) ) )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2488,plain,
! [SV249: $i,SV239: $i,SV223: $i,SV184: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2489,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ( ~ ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2490,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( ( SV256
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
| ! [SY832: $i,SY833: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 )
| ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 ) ) ) )
| ~ ( ~ ! [SY834: $i,SY835: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 )
| ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 ) ) )
| ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) ) ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2491,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( ( SV257
!= ( relation_inverse_image @ SV187 @ SV250 ) )
| ! [SY836: $i] :
~ ( ~ ( ~ ( in @ SY836 @ SV257 )
| ~ ! [SY796: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY796 ) @ SV187 )
| ~ ( in @ SY796 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY797: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY797 ) @ SV187 )
| ~ ( in @ SY797 @ SV250 ) )
| ( in @ SY836 @ SV257 ) ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2432]) ).
thf(2492,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( ~ ! [SY839: $i] :
~ ( ~ ( ~ ( in @ SY839 @ SV257 )
| ~ ! [SY799: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY799 ) @ SV187 )
| ~ ( in @ SY799 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY800: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY800 ) @ SV187 )
| ~ ( in @ SY800 @ SV250 ) )
| ( in @ SY839 @ SV257 ) ) )
| ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2433]) ).
thf(2493,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false )
| ( ( ! [SY774: $i] :
~ ( ~ ( ~ ( in @ SY774 @ SV240 )
| ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ~ ( ~ ( ( SY774 = SV189 )
| ( SY774 = SV226 ) )
| ( in @ SY774 @ SV240 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2494,plain,
! [SV226: $i,SV189: $i,SV240: $i] :
( ( ( ! [SY775: $i] :
~ ( ~ ( ~ ( in @ SY775 @ SV240 )
| ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ~ ( ~ ( ( SY775 = SV189 )
| ( SY775 = SV226 ) )
| ( in @ SY775 @ SV240 ) ) ) )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2495,plain,
! [SV251: $i,SV190: $i,SV258: $i] :
( ( ( ~ ( ( SV258
!= ( relation_dom_restriction @ SV190 @ SV251 ) )
| ! [SY842: $i,SY843: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 )
| ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 ) ) ) )
| ~ ( ~ ! [SY844: $i,SY845: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 )
| ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 ) ) )
| ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) ) ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2496,plain,
! [SV191: $i,SV266: $i] :
( ( ( ! [SY869: $i] :
~ ( ~ ( ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY869
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SY869 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV266 @ SY869 ) @ SV191 )
| ( SY869
= ( apply @ SV191 @ SV266 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SY869
!= ( apply @ SV191 @ SV266 ) )
| ( SY869 = empty_set ) )
| ~ ( ( SY869 != empty_set )
| ( SY869
= ( apply @ SV191 @ SV266 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(2497,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ( ~ ( in @ SV261 @ SV192 )
| ~ ! [SY853: $i,SY854: $i] :
( SV261
!= ( ordered_pair @ SY853 @ SY854 ) ) ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2498,plain,
! [SV192: $i] :
( ( ( ~ ( ~ ( in @ ( sK74_SY649 @ SV192 ) @ SV192 )
| ~ ! [SY855: $i,SY856: $i] :
( ( sK74_SY649 @ SV192 )
!= ( ordered_pair @ SY855 @ SY856 ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2439]) ).
thf(2499,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ( SV259
!= ( relation_image @ SV193 @ SV252 ) )
| ! [SY846: $i] :
~ ( ~ ( ~ ( in @ SY846 @ SV259 )
| ~ ! [SY808: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY808 @ SY846 ) @ SV193 )
| ~ ( in @ SY808 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY809: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY809 @ SY846 ) @ SV193 )
| ~ ( in @ SY809 @ SV252 ) )
| ( in @ SY846 @ SV259 ) ) ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2440]) ).
thf(2500,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SV259 )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY811 @ SY849 ) @ SV193 )
| ~ ( in @ SY811 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY812 @ SY849 ) @ SV193 )
| ~ ( in @ SY812 @ SV252 ) )
| ( in @ SY849 @ SV259 ) ) )
| ( SV259
= ( relation_image @ SV193 @ SV252 ) ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2441]) ).
thf(2501,plain,
! [SV194: $i,SV253: $i] :
( ( ( SV253
!= ( relation_dom @ SV194 ) )
= $true )
| ( ( ! [SY813: $i] :
~ ( ~ ( ~ ( in @ SY813 @ SV253 )
| ~ ! [SY662: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY662 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY663: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY663 ) @ SV194 )
| ( in @ SY813 @ SV253 ) ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2502,plain,
! [SV194: $i,SV253: $i] :
( ( ( ~ ! [SY816: $i] :
~ ( ~ ( ~ ( in @ SY816 @ SV253 )
| ~ ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY665 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY666: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY666 ) @ SV194 )
| ( in @ SY816 @ SV253 ) ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2503,plain,
! [SV195: $i,SV227: $i] :
( ( ( SV227
!= ( identity_relation @ SV195 ) )
= $true )
| ( ( ! [SY746: $i,SY747: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 )
| ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 ) ) ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2504,plain,
! [SV195: $i,SV227: $i] :
( ( ( ~ ! [SY748: $i,SY749: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 )
| ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) )
| ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 ) ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2505,plain,
! [SV196: $i,SV228: $i] :
( ( ( relation @ SV228 )
= $false )
| ( ( relation @ SV196 )
= $false )
| ( ( relation @ ( set_union2 @ SV196 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2506,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false )
| ( ( ! [SY776: $i] :
~ ( ~ ( ~ ( in @ SY776 @ SV241 )
| ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ~ ( ~ ( ( in @ SY776 @ SV198 )
| ( in @ SY776 @ SV229 ) )
| ( in @ SY776 @ SV241 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2507,plain,
! [SV229: $i,SV198: $i,SV241: $i] :
( ( ( ! [SY777: $i] :
~ ( ~ ( ~ ( in @ SY777 @ SV241 )
| ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ~ ( ~ ( ( in @ SY777 @ SV198 )
| ( in @ SY777 @ SV229 ) )
| ( in @ SY777 @ SV241 ) ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2508,plain,
! [SV199: $i] :
( ( ( in @ ( ordered_pair @ ( sK72_SY677 @ SV199 ) @ ( sK75_SY852 @ SV199 ) ) @ SV199 )
= $true )
| ( ( SV199 = empty_set )
= $true )
| ( ( relation @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2449]) ).
thf(2509,plain,
! [SV230: $i,SV242: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ ( relation_dom @ SV242 ) )
| ~ ( in @ SV230 @ ( relation_rng @ SV242 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2510,plain,
! [SV254: $i,SV201: $i] :
( ( ( ~ ( ~ ( subset @ SV201 @ SV254 )
| ! [SY819: $i,SY820: $i] :
( ~ ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV201 )
| ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV254 ) ) ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2451]) ).
thf(2511,plain,
! [SV254: $i,SV201: $i] :
( ( ( ~ ( ~ ! [SY821: $i,SY822: $i] :
( ~ ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV201 )
| ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV254 ) )
| ( subset @ SV201 @ SV254 ) ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2451]) ).
thf(2512,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false )
| ( ( ! [SY778: $i] :
~ ( ~ ( ~ ( in @ SY778 @ SV243 )
| ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY778 @ SV202 )
| ~ ~ ( in @ SY778 @ SV231 ) )
| ( in @ SY778 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2513,plain,
! [SV231: $i,SV202: $i,SV243: $i] :
( ( ( ! [SY779: $i] :
~ ( ~ ( ~ ( in @ SY779 @ SV243 )
| ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY779 @ SV202 )
| ~ ~ ( in @ SY779 @ SV231 ) )
| ( in @ SY779 @ SV243 ) ) ) )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2514,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ~ ( relation @ SV262 ) )
= $true )
| ( ( ~ ( ~ ( ( SV262
!= ( relation_composition @ SV203 @ SV255 ) )
| ! [SY857: $i,SY858: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY858 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY858 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 ) ) ) )
| ~ ( ~ ! [SY861: $i,SY862: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY862 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY862 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 ) ) )
| ( SV262
= ( relation_composition @ SV203 @ SV255 ) ) ) ) )
= $true )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2515,plain,
! [SV205: $i,SV232: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ ( relation_field @ SV232 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 )
= $false )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2516,plain,
! [SV158: $i,SV232: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ ( relation_field @ SV232 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 )
= $false )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2517,plain,
! [SV244: $i,SV233: $i,SV206: $i,SV159: $i] :
( ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2518,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ( ~ ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(2519,plain,
! [SV208: $i,SV234: $i,SV162: $i] :
( ( ( ~ ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) ) )
= $true )
| ( ( ~ ! [SY758: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY758 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY758 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY758 @ SV208 ) ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2520,plain,
! [SV208: $i,SV162: $i,SV234: $i] :
( ( ( ~ ~ ! [SY759: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY759 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY759 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY759 @ SV208 ) ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2521,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ SV263 @ SV210 )
| ~ ! [SY865: $i] :
~ ~ ( ~ ( in @ SV263 @ SY865 )
| ~ ( in @ SY865 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY866: $i] :
~ ~ ( ~ ( in @ SV263 @ SY866 )
| ~ ( in @ SY866 @ SV165 ) )
| ( in @ SV263 @ SV210 ) ) )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2522,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
| ~ ! [SY867: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY867 )
| ~ ( in @ SY867 @ SV165 ) ) )
| ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2464]) ).
thf(2523,plain,
! [SV245: $i,SV166: $i] :
( ( ( ( SV166 != SV245 )
| ! [SY780: $i,SY781: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 ) ) ) )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2465]) ).
thf(2524,plain,
! [SV245: $i,SV166: $i] :
( ( ( ~ ! [SY782: $i,SY783: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 ) ) )
| ( SV166 = SV245 ) )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2525,plain,
! [SV167: $i,SV246: $i] :
( ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( ! [SY784: $i] :
~ ( ~ ( ~ ( in @ SY784 @ SV246 )
| ~ ! [SY570: $i] :
~ ( in @ ( ordered_pair @ SY570 @ SY784 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY571: $i] :
~ ( in @ ( ordered_pair @ SY571 @ SY784 ) @ SV167 )
| ( in @ SY784 @ SV246 ) ) ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2526,plain,
! [SV167: $i,SV246: $i] :
( ( ( ! [SY787: $i] :
~ ( ~ ( ~ ( in @ SY787 @ SV246 )
| ~ ! [SY573: $i] :
~ ( in @ ( ordered_pair @ SY573 @ SY787 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ SY787 ) @ SV167 )
| ( in @ SY787 @ SV246 ) ) ) )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2527,plain,
! [SV170: $i,SV213: $i,SV264: $i] :
( ( ( ~ ( ~ ( in @ SV264 @ SV213 )
| ( SV264 = SV170 ) )
| ~ ( ( SV264 != SV170 )
| ( in @ SV264 @ SV213 ) ) )
= $false )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2528,plain,
! [SV213: $i,SV170: $i] :
( ( ( ~ ( ~ ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
| ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 ) )
| ~ ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
| ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2471]) ).
thf(2529,plain,
! [SV214: $i,SV171: $i,SV235: $i,SV267: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV267 @ SV235 )
| ~ ! [SY870: $i] :
~ ~ ! [SY871: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY870 @ SV171 )
| ~ ( in @ SY871 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY870 @ SY871 ) ) ) )
| ~ ( ~ ~ ! [SY872: $i] :
~ ~ ! [SY873: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY872 @ SV171 )
| ~ ( in @ SY873 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY872 @ SY873 ) ) )
| ( in @ SV267 @ SV235 ) ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2530,plain,
! [SV235: $i,SV171: $i,SV214: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
| ~ ! [SY874: $i] :
~ ~ ! [SY875: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY874 @ SV171 )
| ~ ( in @ SY875 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY874 @ SY875 ) ) ) )
| ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2473]) ).
thf(2531,plain,
! [SV216: $i,SV174: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ SV174 ) )
= $true )
| ( ( in @ SV265 @ SV216 )
= $true )
| ( ( subset @ SV174 @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2532,plain,
! [SV174: $i,SV216: $i] :
( ( ( ~ ( in @ ( sK78_SY726 @ SV216 @ SV174 ) @ SV174 ) )
= $false )
| ( ( subset @ SV174 @ SV216 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2475]) ).
thf(2533,plain,
! [SV174: $i,SV216: $i] :
( ( ( in @ ( sK78_SY726 @ SV216 @ SV174 ) @ SV216 )
= $false )
| ( ( subset @ SV174 @ SV216 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2475]) ).
thf(2534,plain,
! [SV175: $i,SV247: $i] :
( ( ( ( SV247
!= ( relation_inverse @ SV175 ) )
| ! [SY790: $i,SY791: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 )
| ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 ) ) ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2476]) ).
thf(2535,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ! [SY792: $i,SY793: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 )
| ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 )
| ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 ) ) )
| ( SV247
= ( relation_inverse @ SV175 ) ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2477]) ).
thf(2536,plain,
! [SV217: $i,SV236: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2537,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( ~ ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) )
= $true )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2479]) ).
thf(2538,plain,
! [SV219: $i,SV179: $i] :
( ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $false )
| ( ( ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2539,plain,
! [SV219: $i,SV179: $i] :
( ( ( ~ ! [SY729: $i] :
~ ~ ( ~ ( in @ SY729 @ SV179 )
| ~ ( in @ SY729 @ SV219 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2540,plain,
! [SV248: $i,SV220: $i,SV237: $i,SV180: $i] :
( ( ( SV180 = SV237 )
= $true )
| ( ( ( ordered_pair @ SV180 @ SV220 )
= ( ordered_pair @ SV237 @ SV248 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2482]) ).
thf(2541,plain,
! [SV237: $i,SV180: $i,SV248: $i,SV220: $i] :
( ( ( SV220 = SV248 )
= $true )
| ( ( ( ordered_pair @ SV180 @ SV220 )
= ( ordered_pair @ SV237 @ SV248 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2542,plain,
! [SV181: $i] :
( ( ( empty @ ( relation_dom @ SV181 ) )
= $false )
| ( ( empty @ SV181 )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2543,plain,
! [SV182: $i,SV221: $i] :
( ( ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) ) )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2544,plain,
! [SV182: $i,SV221: $i] :
( ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) ) )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2545,plain,
! [SV222: $i,SV183: $i,SV238: $i,SV268: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV268 @ SV238 )
| ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) )
| ( in @ SV268 @ SV238 ) ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2546,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
| ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) ) )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2487]) ).
thf(2547,plain,
! [SV249: $i,SV239: $i,SV223: $i,SV184: $i] :
( ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2548,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ( ~ ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2549,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( ( SV256
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
| ! [SY832: $i,SY833: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 )
| ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 ) ) ) ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2490]) ).
thf(2550,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( ~ ! [SY834: $i,SY835: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 )
| ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 ) ) )
| ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) ) ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2490]) ).
thf(2551,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( SV257
!= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( ! [SY836: $i] :
~ ( ~ ( ~ ( in @ SY836 @ SV257 )
| ~ ! [SY796: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY796 ) @ SV187 )
| ~ ( in @ SY796 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY797: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY797 ) @ SV187 )
| ~ ( in @ SY797 @ SV250 ) )
| ( in @ SY836 @ SV257 ) ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2552,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( ~ ! [SY839: $i] :
~ ( ~ ( ~ ( in @ SY839 @ SV257 )
| ~ ! [SY799: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY799 ) @ SV187 )
| ~ ( in @ SY799 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY800: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY800 ) @ SV187 )
| ~ ( in @ SY800 @ SV250 ) )
| ( in @ SY839 @ SV257 ) ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2553,plain,
! [SV226: $i,SV189: $i,SV240: $i,SV269: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV269 @ SV240 )
| ( SV269 = SV189 )
| ( SV269 = SV226 ) )
| ~ ( ~ ( ( SV269 = SV189 )
| ( SV269 = SV226 ) )
| ( in @ SV269 @ SV240 ) ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(2554,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ~ ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) ) ) )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2494]) ).
thf(2555,plain,
! [SV251: $i,SV190: $i,SV258: $i] :
( ( ( ~ ( ( SV258
!= ( relation_dom_restriction @ SV190 @ SV251 ) )
| ! [SY842: $i,SY843: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 )
| ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 ) ) ) ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2556,plain,
! [SV190: $i,SV251: $i,SV258: $i] :
( ( ( ~ ( ~ ! [SY844: $i,SY845: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 )
| ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 ) ) )
| ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) ) ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2557,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) )
| ~ ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(2558,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ SV192 )
| ~ ! [SY853: $i,SY854: $i] :
( SV261
!= ( ordered_pair @ SY853 @ SY854 ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2497]) ).
thf(2559,plain,
! [SV192: $i] :
( ( ( ~ ( in @ ( sK74_SY649 @ SV192 ) @ SV192 )
| ~ ! [SY855: $i,SY856: $i] :
( ( sK74_SY649 @ SV192 )
!= ( ordered_pair @ SY855 @ SY856 ) ) )
= $false )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2560,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( SV259
!= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( ! [SY846: $i] :
~ ( ~ ( ~ ( in @ SY846 @ SV259 )
| ~ ! [SY808: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY808 @ SY846 ) @ SV193 )
| ~ ( in @ SY808 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY809: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY809 @ SY846 ) @ SV193 )
| ~ ( in @ SY809 @ SV252 ) )
| ( in @ SY846 @ SV259 ) ) ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2499]) ).
thf(2561,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SV259 )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY811 @ SY849 ) @ SV193 )
| ~ ( in @ SY811 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY812 @ SY849 ) @ SV193 )
| ~ ( in @ SY812 @ SV252 ) )
| ( in @ SY849 @ SV259 ) ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2562,plain,
! [SV194: $i,SV253: $i] :
( ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( ! [SY813: $i] :
~ ( ~ ( ~ ( in @ SY813 @ SV253 )
| ~ ! [SY662: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY662 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY663: $i] :
~ ( in @ ( ordered_pair @ SY813 @ SY663 ) @ SV194 )
| ( in @ SY813 @ SV253 ) ) ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2563,plain,
! [SV194: $i,SV253: $i] :
( ( ( ! [SY816: $i] :
~ ( ~ ( ~ ( in @ SY816 @ SV253 )
| ~ ! [SY665: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY665 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY666: $i] :
~ ( in @ ( ordered_pair @ SY816 @ SY666 ) @ SV194 )
| ( in @ SY816 @ SV253 ) ) ) )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2564,plain,
! [SV195: $i,SV227: $i] :
( ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( ! [SY746: $i,SY747: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 )
| ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY746 @ SV195 )
| ( SY746 != SY747 ) )
| ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV227 ) ) ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2565,plain,
! [SV195: $i,SV227: $i] :
( ( ( ! [SY748: $i,SY749: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 )
| ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY748 @ SV195 )
| ( SY748 != SY749 ) )
| ( in @ ( ordered_pair @ SY748 @ SY749 ) @ SV227 ) ) ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2566,plain,
! [SV229: $i,SV198: $i,SV241: $i,SV271: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV271 @ SV241 )
| ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
| ~ ( ~ ( ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
| ( in @ SV271 @ SV241 ) ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2567,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ~ ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2507]) ).
thf(2568,plain,
! [SV230: $i,SV242: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ ( relation_dom @ SV242 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2509]) ).
thf(2569,plain,
! [SV200: $i,SV242: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ ( relation_rng @ SV242 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2509]) ).
thf(2570,plain,
! [SV254: $i,SV201: $i] :
( ( ( ~ ( subset @ SV201 @ SV254 )
| ! [SY819: $i,SY820: $i] :
( ~ ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV201 )
| ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV254 ) ) )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2510]) ).
thf(2571,plain,
! [SV254: $i,SV201: $i] :
( ( ( ~ ! [SY821: $i,SY822: $i] :
( ~ ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV201 )
| ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV254 ) )
| ( subset @ SV201 @ SV254 ) )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2511]) ).
thf(2572,plain,
! [SV231: $i,SV202: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV272 @ SV243 )
| ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) )
| ( in @ SV272 @ SV243 ) ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2573,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
| ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) ) )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2513]) ).
thf(2574,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( relation @ SV262 )
= $false )
| ( ( ~ ( ~ ( ( SV262
!= ( relation_composition @ SV203 @ SV255 ) )
| ! [SY857: $i,SY858: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY858 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY858 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 ) ) ) )
| ~ ( ~ ! [SY861: $i,SY862: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY862 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY862 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 ) ) )
| ( SV262
= ( relation_composition @ SV203 @ SV255 ) ) ) ) )
= $true )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2575,plain,
! [SV205: $i,SV232: $i,SV158: $i] :
( ( ( in @ SV158 @ ( relation_field @ SV232 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 )
= $false )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2515]) ).
thf(2576,plain,
! [SV158: $i,SV232: $i,SV205: $i] :
( ( ( in @ SV205 @ ( relation_field @ SV232 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV158 @ SV205 ) @ SV232 )
= $false )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2516]) ).
thf(2577,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2578,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV233 )
| ~ ( in @ SV206 @ SV244 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2518]) ).
thf(2579,plain,
! [SV208: $i,SV234: $i,SV162: $i] :
( ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( ~ ! [SY758: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY758 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY758 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY758 @ SV208 ) ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2580,plain,
! [SV208: $i,SV162: $i,SV234: $i] :
( ( ( ~ ! [SY759: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY759 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY759 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY759 @ SV208 ) ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2581,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ SV263 @ SV210 )
| ~ ! [SY865: $i] :
~ ~ ( ~ ( in @ SV263 @ SY865 )
| ~ ( in @ SY865 @ SV165 ) ) ) )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2521]) ).
thf(2582,plain,
! [SV210: $i,SV165: $i,SV263: $i] :
( ( ( ~ ( ~ ~ ! [SY866: $i] :
~ ~ ( ~ ( in @ SV263 @ SY866 )
| ~ ( in @ SY866 @ SV165 ) )
| ( in @ SV263 @ SV210 ) ) )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2521]) ).
thf(2583,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
| ~ ! [SY867: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY867 )
| ~ ( in @ SY867 @ SV165 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2584,plain,
! [SV245: $i,SV166: $i] :
( ( ( SV166 != SV245 )
= $true )
| ( ( ! [SY780: $i,SY781: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 ) ) ) )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2585,plain,
! [SV245: $i,SV166: $i] :
( ( ( ~ ! [SY782: $i,SY783: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 ) ) ) )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2586,plain,
! [SV167: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV273 @ SV246 )
| ~ ! [SY878: $i] :
~ ( in @ ( ordered_pair @ SY878 @ SV273 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY879: $i] :
~ ( in @ ( ordered_pair @ SY879 @ SV273 ) @ SV167 )
| ( in @ SV273 @ SV246 ) ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(2587,plain,
! [SV246: $i,SV167: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
| ~ ! [SY880: $i] :
~ ( in @ ( ordered_pair @ SY880 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
| ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) ) )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2526]) ).
thf(2588,plain,
! [SV170: $i,SV213: $i,SV264: $i] :
( ( ( ~ ( ~ ( in @ SV264 @ SV213 )
| ( SV264 = SV170 ) ) )
= $false )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2589,plain,
! [SV213: $i,SV170: $i,SV264: $i] :
( ( ( ~ ( ( SV264 != SV170 )
| ( in @ SV264 @ SV213 ) ) )
= $false )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2590,plain,
! [SV213: $i,SV170: $i] :
( ( ( ~ ( ~ ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
| ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 ) ) )
= $true )
| ( ( ~ ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
| ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2591,plain,
! [SV214: $i,SV171: $i,SV235: $i,SV267: $i] :
( ( ( ~ ( ~ ( in @ SV267 @ SV235 )
| ~ ! [SY870: $i] :
~ ~ ! [SY871: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY870 @ SV171 )
| ~ ( in @ SY871 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY870 @ SY871 ) ) ) )
| ~ ( ~ ~ ! [SY872: $i] :
~ ~ ! [SY873: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY872 @ SV171 )
| ~ ( in @ SY873 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY872 @ SY873 ) ) )
| ( in @ SV267 @ SV235 ) ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2592,plain,
! [SV235: $i,SV171: $i,SV214: $i] :
( ( ( ~ ( ~ ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
| ~ ! [SY874: $i] :
~ ~ ! [SY875: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY874 @ SV171 )
| ~ ( in @ SY875 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY874 @ SY875 ) ) ) )
| ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2593,plain,
! [SV216: $i,SV174: $i,SV265: $i] :
( ( ( in @ SV265 @ SV174 )
= $false )
| ( ( in @ SV265 @ SV216 )
= $true )
| ( ( subset @ SV174 @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2594,plain,
! [SV174: $i,SV216: $i] :
( ( ( in @ ( sK78_SY726 @ SV216 @ SV174 ) @ SV174 )
= $true )
| ( ( subset @ SV174 @ SV216 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2532]) ).
thf(2595,plain,
! [SV175: $i,SV247: $i] :
( ( ( SV247
!= ( relation_inverse @ SV175 ) )
= $true )
| ( ( ! [SY790: $i,SY791: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 )
| ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 ) ) ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2534]) ).
thf(2596,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ! [SY792: $i,SY793: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 )
| ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 )
| ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 ) ) ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2597,plain,
! [SV217: $i,SV236: $i,SV177: $i] :
( ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2598,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( ~ ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) ) )
= $false )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2599,plain,
! [SV219: $i,SV179: $i] :
( ( ( disjoint @ SV179 @ SV219 )
= $true )
| ( ( ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2538]) ).
thf(2600,plain,
! [SV219: $i,SV179: $i] :
( ( ( ! [SY729: $i] :
~ ~ ( ~ ( in @ SY729 @ SV179 )
| ~ ( in @ SY729 @ SV219 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2601,plain,
! [SV182: $i,SV221: $i] :
( ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) ) )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2543]) ).
thf(2602,plain,
! [SV182: $i,SV221: $i] :
( ( ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) )
= $false )
| ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
= $false )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2603,plain,
! [SV222: $i,SV183: $i,SV238: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ SV268 @ SV238 )
| ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) )
| ( in @ SV268 @ SV238 ) ) )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2604,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
| ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2546]) ).
thf(2605,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2606,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ SV239 )
| ~ ( in @ SV223 @ SV249 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2607,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ( SV256
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
| ! [SY832: $i,SY833: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 )
| ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 ) ) ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2608,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ! [SY834: $i,SY835: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 )
| ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 ) ) )
| ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2550]) ).
thf(2609,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( ! [SY836: $i] :
~ ( ~ ( ~ ( in @ SY836 @ SV257 )
| ~ ! [SY796: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY796 ) @ SV187 )
| ~ ( in @ SY796 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY797: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY836 @ SY797 ) @ SV187 )
| ~ ( in @ SY797 @ SV250 ) )
| ( in @ SY836 @ SV257 ) ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2610,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( ! [SY839: $i] :
~ ( ~ ( ~ ( in @ SY839 @ SV257 )
| ~ ! [SY799: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY799 ) @ SV187 )
| ~ ( in @ SY799 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY800: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY839 @ SY800 ) @ SV187 )
| ~ ( in @ SY800 @ SV250 ) )
| ( in @ SY839 @ SV257 ) ) ) )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2611,plain,
! [SV226: $i,SV189: $i,SV240: $i,SV269: $i] :
( ( ( ~ ( ~ ( in @ SV269 @ SV240 )
| ( SV269 = SV189 )
| ( SV269 = SV226 ) )
| ~ ( ~ ( ( SV269 = SV189 )
| ( SV269 = SV226 ) )
| ( in @ SV269 @ SV240 ) ) )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2612,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( ~ ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ~ ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2554]) ).
thf(2613,plain,
! [SV251: $i,SV190: $i,SV258: $i] :
( ( ( ( SV258
!= ( relation_dom_restriction @ SV190 @ SV251 ) )
| ! [SY842: $i,SY843: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 )
| ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 ) ) ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2555]) ).
thf(2614,plain,
! [SV190: $i,SV251: $i,SV258: $i] :
( ( ( ~ ! [SY844: $i,SY845: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 )
| ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 ) ) )
| ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2615,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( ~ ( ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) )
| ~ ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2616,plain,
! [SV192: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ SV192 ) )
= $true )
| ( ( ~ ! [SY853: $i,SY854: $i] :
( SV261
!= ( ordered_pair @ SY853 @ SY854 ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2617,plain,
! [SV192: $i] :
( ( ( ~ ( in @ ( sK74_SY649 @ SV192 ) @ SV192 ) )
= $false )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2559]) ).
thf(2618,plain,
! [SV192: $i] :
( ( ( ~ ! [SY855: $i,SY856: $i] :
( ( sK74_SY649 @ SV192 )
!= ( ordered_pair @ SY855 @ SY856 ) ) )
= $false )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2559]) ).
thf(2619,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( ! [SY846: $i] :
~ ( ~ ( ~ ( in @ SY846 @ SV259 )
| ~ ! [SY808: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY808 @ SY846 ) @ SV193 )
| ~ ( in @ SY808 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY809: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY809 @ SY846 ) @ SV193 )
| ~ ( in @ SY809 @ SV252 ) )
| ( in @ SY846 @ SV259 ) ) ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2620,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SV259 )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY811 @ SY849 ) @ SV193 )
| ~ ( in @ SY811 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY812 @ SY849 ) @ SV193 )
| ~ ( in @ SY812 @ SV252 ) )
| ( in @ SY849 @ SV259 ) ) ) )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2621,plain,
! [SV194: $i,SV253: $i,SV274: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV274 @ SV253 )
| ~ ! [SY882: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY882 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY883: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY883 ) @ SV194 )
| ( in @ SV274 @ SV253 ) ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(2622,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
| ~ ! [SY884: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY884 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) ) )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2563]) ).
thf(2623,plain,
! [SV195: $i,SV227: $i,SV275: $i] :
( ( ( ! [SY886: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV275 @ SY886 ) @ SV227 )
| ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SY886 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SY886 ) )
| ( in @ ( ordered_pair @ SV275 @ SY886 ) @ SV227 ) ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(2624,plain,
! [SV227: $i,SV195: $i] :
( ( ( ! [SY887: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ SY887 ) @ SV227 )
| ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= SY887 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= SY887 ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ SY887 ) @ SV227 ) ) ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2565]) ).
thf(2625,plain,
! [SV229: $i,SV198: $i,SV241: $i,SV271: $i] :
( ( ( ~ ( ~ ( in @ SV271 @ SV241 )
| ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
| ~ ( ~ ( ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
| ( in @ SV271 @ SV241 ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2626,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ~ ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2627,plain,
! [SV230: $i,SV242: $i,SV200: $i] :
( ( ( in @ SV200 @ ( relation_dom @ SV242 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2568]) ).
thf(2628,plain,
! [SV200: $i,SV242: $i,SV230: $i] :
( ( ( in @ SV230 @ ( relation_rng @ SV242 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV200 @ SV230 ) @ SV242 )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2569]) ).
thf(2629,plain,
! [SV254: $i,SV201: $i] :
( ( ( ~ ( subset @ SV201 @ SV254 ) )
= $true )
| ( ( ! [SY819: $i,SY820: $i] :
( ~ ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV201 )
| ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV254 ) ) )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2570]) ).
thf(2630,plain,
! [SV254: $i,SV201: $i] :
( ( ( ~ ! [SY821: $i,SY822: $i] :
( ~ ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV201 )
| ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV254 ) ) )
= $true )
| ( ( subset @ SV201 @ SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2571]) ).
thf(2631,plain,
! [SV231: $i,SV202: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( ~ ( in @ SV272 @ SV243 )
| ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) )
| ( in @ SV272 @ SV243 ) ) )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2632,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
| ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2573]) ).
thf(2633,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ~ ( ( SV262
!= ( relation_composition @ SV203 @ SV255 ) )
| ! [SY857: $i,SY858: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY858 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY858 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 ) ) ) )
| ~ ( ~ ! [SY861: $i,SY862: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY862 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY862 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 ) ) )
| ( SV262
= ( relation_composition @ SV203 @ SV255 ) ) ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2634,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV233 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2635,plain,
! [SV233: $i,SV159: $i,SV244: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV244 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2636,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV233 ) )
= $true )
| ( ( ~ ( in @ SV206 @ SV244 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2578]) ).
thf(2637,plain,
! [SV208: $i,SV162: $i,SV234: $i] :
( ( ( ! [SY758: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY758 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY758 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY758 @ SV208 ) ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2638,plain,
! [SV208: $i,SV162: $i,SV234: $i] :
( ( ( ! [SY759: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY759 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SY759 @ SV162 ) @ SV234 ) )
| ~ ( in @ SY759 @ SV208 ) ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2580]) ).
thf(2639,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV210 )
| ~ ! [SY865: $i] :
~ ~ ( ~ ( in @ SV263 @ SY865 )
| ~ ( in @ SY865 @ SV165 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2581]) ).
thf(2640,plain,
! [SV210: $i,SV165: $i,SV263: $i] :
( ( ( ~ ~ ! [SY866: $i] :
~ ~ ( ~ ( in @ SV263 @ SY866 )
| ~ ( in @ SY866 @ SV165 ) )
| ( in @ SV263 @ SV210 ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2582]) ).
thf(2641,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
| ~ ! [SY867: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY867 )
| ~ ( in @ SY867 @ SV165 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2642,plain,
! [SV245: $i,SV166: $i] :
( ( ( SV166 = SV245 )
= $false )
| ( ( ! [SY780: $i,SY781: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV245 )
| ( in @ ( ordered_pair @ SY780 @ SY781 ) @ SV166 ) ) ) )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2643,plain,
! [SV245: $i,SV166: $i] :
( ( ( ! [SY782: $i,SY783: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV245 )
| ( in @ ( ordered_pair @ SY782 @ SY783 ) @ SV166 ) ) ) )
= $false )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2644,plain,
! [SV167: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ SV273 @ SV246 )
| ~ ! [SY878: $i] :
~ ( in @ ( ordered_pair @ SY878 @ SV273 ) @ SV167 ) )
| ~ ( ~ ~ ! [SY879: $i] :
~ ( in @ ( ordered_pair @ SY879 @ SV273 ) @ SV167 )
| ( in @ SV273 @ SV246 ) ) )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2645,plain,
! [SV246: $i,SV167: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
| ~ ! [SY880: $i] :
~ ( in @ ( ordered_pair @ SY880 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
| ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2587]) ).
thf(2646,plain,
! [SV170: $i,SV213: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ SV213 )
| ( SV264 = SV170 ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2588]) ).
thf(2647,plain,
! [SV213: $i,SV170: $i,SV264: $i] :
( ( ( ( SV264 != SV170 )
| ( in @ SV264 @ SV213 ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2589]) ).
thf(2648,plain,
! [SV213: $i,SV170: $i] :
( ( ( ~ ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
| ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 ) )
= $false )
| ( ( ~ ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
| ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2649,plain,
! [SV214: $i,SV171: $i,SV235: $i,SV267: $i] :
( ( ( ~ ( ~ ( in @ SV267 @ SV235 )
| ~ ! [SY870: $i] :
~ ~ ! [SY871: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY870 @ SV171 )
| ~ ( in @ SY871 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY870 @ SY871 ) ) ) ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2591]) ).
thf(2650,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i] :
( ( ( ~ ( ~ ~ ! [SY872: $i] :
~ ~ ! [SY873: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY872 @ SV171 )
| ~ ( in @ SY873 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY872 @ SY873 ) ) )
| ( in @ SV267 @ SV235 ) ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2591]) ).
thf(2651,plain,
! [SV235: $i,SV171: $i,SV214: $i] :
( ( ( ~ ( ~ ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
| ~ ! [SY874: $i] :
~ ~ ! [SY875: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY874 @ SV171 )
| ~ ( in @ SY875 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY874 @ SY875 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2652,plain,
! [SV175: $i,SV247: $i] :
( ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( ! [SY790: $i,SY791: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 )
| ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY791 @ SY790 ) @ SV175 )
| ( in @ ( ordered_pair @ SY790 @ SY791 ) @ SV247 ) ) ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2653,plain,
! [SV175: $i,SV247: $i] :
( ( ( ! [SY792: $i,SY793: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 )
| ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY793 @ SY792 ) @ SV175 )
| ( in @ ( ordered_pair @ SY792 @ SY793 ) @ SV247 ) ) ) )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2654,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
= $false )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $false )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2655,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ SV217 )
| ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
= $true )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2598]) ).
thf(2656,plain,
! [SV219: $i,SV179: $i] :
( ( ( ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV179 )
| ~ ( in @ SY728 @ SV219 ) ) )
= $false )
| ( ( disjoint @ SV179 @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2657,plain,
! [SV219: $i,SV179: $i,SV276: $i] :
( ( ( ~ ~ ( ~ ( in @ SV276 @ SV179 )
| ~ ( in @ SV276 @ SV219 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(2658,plain,
! [SV182: $i,SV221: $i] :
( ( ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
| ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 ) )
= $false )
| ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2659,plain,
! [SV182: $i,SV221: $i] :
( ( ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 ) )
= $false )
| ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
= $false )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2602]) ).
thf(2660,plain,
! [SV182: $i,SV221: $i] :
( ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
= $false )
| ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
= $false )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2602]) ).
thf(2661,plain,
! [SV222: $i,SV183: $i,SV238: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ SV268 @ SV238 )
| ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) ) ) )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2603]) ).
thf(2662,plain,
! [SV238: $i,SV222: $i,SV183: $i,SV268: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) )
| ( in @ SV268 @ SV238 ) ) )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2603]) ).
thf(2663,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
| ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2604]) ).
thf(2664,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ SV239 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2605]) ).
thf(2665,plain,
! [SV239: $i,SV184: $i,SV249: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ SV249 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2605]) ).
thf(2666,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ SV239 ) )
= $true )
| ( ( ~ ( in @ SV223 @ SV249 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2667,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( SV256
!= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( ! [SY832: $i,SY833: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 )
| ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 ) ) ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2668,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ! [SY834: $i,SY835: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 )
| ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 ) ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(2669,plain,
! [SV250: $i,SV187: $i,SV257: $i,SV277: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV277 @ SV257 )
| ~ ! [SY888: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY888 ) @ SV187 )
| ~ ( in @ SY888 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY889: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY889 ) @ SV187 )
| ~ ( in @ SY889 @ SV250 ) )
| ( in @ SV277 @ SV257 ) ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(2670,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
| ~ ! [SY890: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY890 ) @ SV187 )
| ~ ( in @ SY890 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) ) )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2610]) ).
thf(2671,plain,
! [SV226: $i,SV189: $i,SV240: $i,SV269: $i] :
( ( ( ~ ( ~ ( in @ SV269 @ SV240 )
| ( SV269 = SV189 )
| ( SV269 = SV226 ) ) )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2611]) ).
thf(2672,plain,
! [SV240: $i,SV226: $i,SV189: $i,SV269: $i] :
( ( ( ~ ( ~ ( ( SV269 = SV189 )
| ( SV269 = SV226 ) )
| ( in @ SV269 @ SV240 ) ) )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2611]) ).
thf(2673,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( ~ ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2674,plain,
! [SV251: $i,SV190: $i,SV258: $i] :
( ( ( SV258
!= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( ! [SY842: $i,SY843: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 )
| ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 ) ) ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2675,plain,
! [SV190: $i,SV251: $i,SV258: $i] :
( ( ( ~ ! [SY844: $i,SY845: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 )
| ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 ) ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2676,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( ~ ( ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2677,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( ~ ( ~ ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) )
| ~ ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2678,plain,
! [SV192: $i,SV261: $i] :
( ( ( in @ SV261 @ SV192 )
= $false )
| ( ( ~ ! [SY853: $i,SY854: $i] :
( SV261
!= ( ordered_pair @ SY853 @ SY854 ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2679,plain,
! [SV192: $i] :
( ( ( in @ ( sK74_SY649 @ SV192 ) @ SV192 )
= $true )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2680,plain,
! [SV192: $i] :
( ( ( ! [SY855: $i,SY856: $i] :
( ( sK74_SY649 @ SV192 )
!= ( ordered_pair @ SY855 @ SY856 ) ) )
= $true )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2618]) ).
thf(2681,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV278: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV278 @ SV259 )
| ~ ! [SY892: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY892 @ SV278 ) @ SV193 )
| ~ ( in @ SY892 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY893 @ SV278 ) @ SV193 )
| ~ ( in @ SY893 @ SV252 ) )
| ( in @ SV278 @ SV259 ) ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2682,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
| ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY894 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY894 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) ) )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2620]) ).
thf(2683,plain,
! [SV194: $i,SV253: $i,SV274: $i] :
( ( ( ~ ( ~ ( in @ SV274 @ SV253 )
| ~ ! [SY882: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY882 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY883: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY883 ) @ SV194 )
| ( in @ SV274 @ SV253 ) ) )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2684,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
| ~ ! [SY884: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY884 ) @ SV194 ) )
| ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2622]) ).
thf(2685,plain,
! [SV195: $i,SV227: $i,SV279: $i,SV275: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
| ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) )
| ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 ) ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(2686,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
| ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2624]) ).
thf(2687,plain,
! [SV229: $i,SV198: $i,SV241: $i,SV271: $i] :
( ( ( ~ ( ~ ( in @ SV271 @ SV241 )
| ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2625]) ).
thf(2688,plain,
! [SV241: $i,SV229: $i,SV198: $i,SV271: $i] :
( ( ( ~ ( ~ ( ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
| ( in @ SV271 @ SV241 ) ) )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2625]) ).
thf(2689,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2626]) ).
thf(2690,plain,
! [SV254: $i,SV201: $i] :
( ( ( subset @ SV201 @ SV254 )
= $false )
| ( ( ! [SY819: $i,SY820: $i] :
( ~ ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV201 )
| ( in @ ( ordered_pair @ SY819 @ SY820 ) @ SV254 ) ) )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2691,plain,
! [SV254: $i,SV201: $i] :
( ( ( ! [SY821: $i,SY822: $i] :
( ~ ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV201 )
| ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SV254 ) ) )
= $false )
| ( ( subset @ SV201 @ SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2692,plain,
! [SV231: $i,SV202: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( ~ ( in @ SV272 @ SV243 )
| ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) ) ) )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2631]) ).
thf(2693,plain,
! [SV243: $i,SV231: $i,SV202: $i,SV272: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) )
| ( in @ SV272 @ SV243 ) ) )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2631]) ).
thf(2694,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
| ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(2695,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ~ ( ( SV262
!= ( relation_composition @ SV203 @ SV255 ) )
| ! [SY857: $i,SY858: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY858 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY858 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 ) ) ) ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2633]) ).
thf(2696,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ~ ( ~ ! [SY861: $i,SY862: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY862 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY862 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 ) ) )
| ( SV262
= ( relation_composition @ SV203 @ SV255 ) ) ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2633]) ).
thf(2697,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ( in @ SV159 @ SV233 )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2634]) ).
thf(2698,plain,
! [SV233: $i,SV159: $i,SV244: $i,SV206: $i] :
( ( ( in @ SV206 @ SV244 )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2635]) ).
thf(2699,plain,
! [SV244: $i,SV206: $i,SV233: $i,SV159: $i] :
( ( ( in @ SV159 @ SV233 )
= $false )
| ( ( ~ ( in @ SV206 @ SV244 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2700,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV162 ) @ SV234 ) )
| ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV208 ) ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2637]) ).
thf(2701,plain,
! [SV208: $i,SV162: $i,SV234: $i,SV280: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV280 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 ) )
| ~ ( in @ SV280 @ SV208 ) ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(2702,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV210 ) )
= $true )
| ( ( ~ ! [SY865: $i] :
~ ~ ( ~ ( in @ SV263 @ SY865 )
| ~ ( in @ SY865 @ SV165 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2703,plain,
! [SV210: $i,SV165: $i,SV263: $i] :
( ( ( ~ ~ ! [SY866: $i] :
~ ~ ( ~ ( in @ SV263 @ SY866 )
| ~ ( in @ SY866 @ SV165 ) ) )
= $true )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2704,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2641]) ).
thf(2705,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ! [SY867: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY867 )
| ~ ( in @ SY867 @ SV165 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2641]) ).
thf(2706,plain,
! [SV245: $i,SV166: $i,SV281: $i] :
( ( ( ! [SY896: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV281 @ SY896 ) @ SV166 )
| ( in @ ( ordered_pair @ SV281 @ SY896 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV281 @ SY896 ) @ SV245 )
| ( in @ ( ordered_pair @ SV281 @ SY896 ) @ SV166 ) ) ) )
= $true )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(2707,plain,
! [SV166: $i,SV245: $i] :
( ( ( ! [SY897: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ SY897 ) @ SV166 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ SY897 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ SY897 ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ SY897 ) @ SV166 ) ) ) )
= $false )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2643]) ).
thf(2708,plain,
! [SV167: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ SV273 @ SV246 )
| ~ ! [SY878: $i] :
~ ( in @ ( ordered_pair @ SY878 @ SV273 ) @ SV167 ) ) )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2709,plain,
! [SV246: $i,SV167: $i,SV273: $i] :
( ( ( ~ ( ~ ~ ! [SY879: $i] :
~ ( in @ ( ordered_pair @ SY879 @ SV273 ) @ SV167 )
| ( in @ SV273 @ SV246 ) ) )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2710,plain,
! [SV246: $i,SV167: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
| ~ ! [SY880: $i] :
~ ( in @ ( ordered_pair @ SY880 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2711,plain,
! [SV170: $i,SV213: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ SV213 ) )
= $true )
| ( ( SV264 = SV170 )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2712,plain,
! [SV213: $i,SV170: $i,SV264: $i] :
( ( ( SV264 != SV170 )
= $true )
| ( ( in @ SV264 @ SV213 )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(2713,plain,
! [SV213: $i,SV170: $i] :
( ( ( ~ ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) )
= $false )
| ( ( ~ ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
| ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2714,plain,
! [SV213: $i,SV170: $i] :
( ( ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 )
= $false )
| ( ( ~ ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
| ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2715,plain,
! [SV214: $i,SV171: $i,SV235: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ SV235 )
| ~ ! [SY870: $i] :
~ ~ ! [SY871: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY870 @ SV171 )
| ~ ( in @ SY871 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY870 @ SY871 ) ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2649]) ).
thf(2716,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i] :
( ( ( ~ ~ ! [SY872: $i] :
~ ~ ! [SY873: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY872 @ SV171 )
| ~ ( in @ SY873 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY872 @ SY873 ) ) )
| ( in @ SV267 @ SV235 ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2650]) ).
thf(2717,plain,
! [SV235: $i,SV171: $i,SV214: $i] :
( ( ( ~ ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
| ~ ! [SY874: $i] :
~ ~ ! [SY875: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY874 @ SV171 )
| ~ ( in @ SY875 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY874 @ SY875 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2718,plain,
! [SV175: $i,SV247: $i,SV282: $i] :
( ( ( ! [SY898: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV282 @ SY898 ) @ SV247 )
| ( in @ ( ordered_pair @ SY898 @ SV282 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY898 @ SV282 ) @ SV175 )
| ( in @ ( ordered_pair @ SV282 @ SY898 ) @ SV247 ) ) ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(2719,plain,
! [SV247: $i,SV175: $i] :
( ( ( ! [SY899: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ SY899 ) @ SV247 )
| ( in @ ( ordered_pair @ SY899 @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY899 @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ SY899 ) @ SV247 ) ) ) )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2653]) ).
thf(2720,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ SV217 ) )
= $false )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $false )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2654]) ).
thf(2721,plain,
! [SV217: $i,SV236: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
= $false )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $false )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2654]) ).
thf(2722,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ SV217 ) )
= $true )
| ( ( ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
= $true )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2723,plain,
! [SV179: $i,SV219: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV179 )
| ~ ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV219 ) ) )
= $false )
| ( ( disjoint @ SV179 @ SV219 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2656]) ).
thf(2724,plain,
! [SV219: $i,SV179: $i,SV276: $i] :
( ( ( ~ ( ~ ( in @ SV276 @ SV179 )
| ~ ( in @ SV276 @ SV219 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2725,plain,
! [SV182: $i,SV221: $i] :
( ( ( ~ ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 ) )
= $false )
| ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2658]) ).
thf(2726,plain,
! [SV182: $i,SV221: $i] :
( ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
= $false )
| ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2658]) ).
thf(2727,plain,
! [SV182: $i,SV221: $i] :
( ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
= $true )
| ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
= $false )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2659]) ).
thf(2728,plain,
! [SV222: $i,SV183: $i,SV238: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV238 )
| ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2661]) ).
thf(2729,plain,
! [SV238: $i,SV222: $i,SV183: $i,SV268: $i] :
( ( ( ~ ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) )
| ( in @ SV268 @ SV238 ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2662]) ).
thf(2730,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
| ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2731,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ( in @ SV184 @ SV239 )
= $true )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2664]) ).
thf(2732,plain,
! [SV239: $i,SV184: $i,SV249: $i,SV223: $i] :
( ( ( in @ SV223 @ SV249 )
= $true )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2665]) ).
thf(2733,plain,
! [SV249: $i,SV223: $i,SV239: $i,SV184: $i] :
( ( ( in @ SV184 @ SV239 )
= $false )
| ( ( ~ ( in @ SV223 @ SV249 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2734,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( ! [SY832: $i,SY833: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 )
| ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY833 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY832 @ SY833 ) @ SV256 ) ) ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2735,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ! [SY834: $i,SY835: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 )
| ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY835 @ SV186 )
| ~ ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SY834 @ SY835 ) @ SV256 ) ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2736,plain,
! [SV250: $i,SV187: $i,SV257: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ SV277 @ SV257 )
| ~ ! [SY888: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY888 ) @ SV187 )
| ~ ( in @ SY888 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY889: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY889 ) @ SV187 )
| ~ ( in @ SY889 @ SV250 ) )
| ( in @ SV277 @ SV257 ) ) )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2737,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( ~ ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
| ~ ! [SY890: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY890 ) @ SV187 )
| ~ ( in @ SY890 @ SV250 ) ) )
| ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2670]) ).
thf(2738,plain,
! [SV226: $i,SV189: $i,SV240: $i,SV269: $i] :
( ( ( ~ ( in @ SV269 @ SV240 )
| ( SV269 = SV189 )
| ( SV269 = SV226 ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2671]) ).
thf(2739,plain,
! [SV240: $i,SV226: $i,SV189: $i,SV269: $i] :
( ( ( ~ ( ( SV269 = SV189 )
| ( SV269 = SV226 ) )
| ( in @ SV269 @ SV240 ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2672]) ).
thf(2740,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2741,plain,
! [SV251: $i,SV190: $i,SV258: $i] :
( ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( ! [SY842: $i,SY843: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 )
| ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY842 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY842 @ SY843 ) @ SV258 ) ) ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2742,plain,
! [SV190: $i,SV251: $i,SV258: $i] :
( ( ( ! [SY844: $i,SY845: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 )
| ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY844 @ SV251 )
| ~ ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SY844 @ SY845 ) @ SV258 ) ) ) )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2743,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2676]) ).
thf(2744,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( ~ ~ ( in @ SV266 @ ( relation_dom @ SV191 ) )
| ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) )
| ~ ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2677]) ).
thf(2745,plain,
! [SV192: $i,SV261: $i] :
( ( ( ! [SY853: $i,SY854: $i] :
( SV261
!= ( ordered_pair @ SY853 @ SY854 ) ) )
= $false )
| ( ( in @ SV261 @ SV192 )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2746,plain,
! [SV283: $i,SV192: $i] :
( ( ( ! [SY900: $i] :
( ( sK74_SY649 @ SV192 )
!= ( ordered_pair @ SV283 @ SY900 ) ) )
= $true )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(2747,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV278: $i] :
( ( ( ~ ( ~ ( in @ SV278 @ SV259 )
| ~ ! [SY892: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY892 @ SV278 ) @ SV193 )
| ~ ( in @ SY892 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY893 @ SV278 ) @ SV193 )
| ~ ( in @ SY893 @ SV252 ) )
| ( in @ SV278 @ SV259 ) ) )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2748,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ( ~ ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
| ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY894 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY894 @ SV252 ) ) )
| ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2682]) ).
thf(2749,plain,
! [SV194: $i,SV253: $i,SV274: $i] :
( ( ( ~ ( ~ ( in @ SV274 @ SV253 )
| ~ ! [SY882: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY882 ) @ SV194 ) ) )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2683]) ).
thf(2750,plain,
! [SV253: $i,SV194: $i,SV274: $i] :
( ( ( ~ ( ~ ~ ! [SY883: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY883 ) @ SV194 )
| ( in @ SV274 @ SV253 ) ) )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2683]) ).
thf(2751,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
| ~ ! [SY884: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY884 ) @ SV194 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2684]) ).
thf(2752,plain,
! [SV195: $i,SV227: $i,SV279: $i,SV275: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
| ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) )
| ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 ) ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2753,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
| ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2686]) ).
thf(2754,plain,
! [SV229: $i,SV198: $i,SV241: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV241 )
| ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2687]) ).
thf(2755,plain,
! [SV241: $i,SV229: $i,SV198: $i,SV271: $i] :
( ( ( ~ ( ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
| ( in @ SV271 @ SV241 ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2688]) ).
thf(2756,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2757,plain,
! [SV254: $i,SV201: $i,SV284: $i] :
( ( ( ! [SY901: $i] :
( ~ ( in @ ( ordered_pair @ SV284 @ SY901 ) @ SV201 )
| ( in @ ( ordered_pair @ SV284 @ SY901 ) @ SV254 ) ) )
= $true )
| ( ( subset @ SV201 @ SV254 )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(2758,plain,
! [SV201: $i,SV254: $i] :
( ( ( ! [SY902: $i] :
( ~ ( in @ ( ordered_pair @ ( sK94_SY821 @ SV254 @ SV201 ) @ SY902 ) @ SV201 )
| ( in @ ( ordered_pair @ ( sK94_SY821 @ SV254 @ SV201 ) @ SY902 ) @ SV254 ) ) )
= $false )
| ( ( subset @ SV201 @ SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2691]) ).
thf(2759,plain,
! [SV231: $i,SV202: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV243 )
| ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2760,plain,
! [SV243: $i,SV231: $i,SV202: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) )
| ( in @ SV272 @ SV243 ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2761,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
| ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2762,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ( SV262
!= ( relation_composition @ SV203 @ SV255 ) )
| ! [SY857: $i,SY858: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY858 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY858 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 ) ) ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2763,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ~ ! [SY861: $i,SY862: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY862 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY862 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 ) ) )
| ( SV262
= ( relation_composition @ SV203 @ SV255 ) ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2696]) ).
thf(2764,plain,
! [SV233: $i,SV159: $i,SV244: $i,SV206: $i] :
( ( ( in @ SV206 @ SV244 )
= $false )
| ( ( in @ SV159 @ SV233 )
= $false )
| ( ( in @ ( ordered_pair @ SV159 @ SV206 ) @ ( cartesian_product2 @ SV233 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2765,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV162 ) @ SV234 ) )
| ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV208 ) ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2700]) ).
thf(2766,plain,
! [SV208: $i,SV162: $i,SV234: $i,SV280: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV280 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 ) )
| ~ ( in @ SV280 @ SV208 ) ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2767,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( in @ SV263 @ SV210 )
= $false )
| ( ( ~ ! [SY865: $i] :
~ ~ ( ~ ( in @ SV263 @ SY865 )
| ~ ( in @ SY865 @ SV165 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2768,plain,
! [SV210: $i,SV165: $i,SV263: $i] :
( ( ( ~ ! [SY866: $i] :
~ ~ ( ~ ( in @ SV263 @ SY866 )
| ~ ( in @ SY866 @ SV165 ) ) )
= $false )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2769,plain,
! [SV210: $i,SV165: $i] :
( ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2704]) ).
thf(2770,plain,
! [SV210: $i,SV165: $i] :
( ( ( ! [SY867: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY867 )
| ~ ( in @ SY867 @ SV165 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2705]) ).
thf(2771,plain,
! [SV245: $i,SV166: $i,SV285: $i,SV281: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 )
| ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 )
| ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 ) ) ) )
= $true )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(2772,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) ) ) )
= $false )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2707]) ).
thf(2773,plain,
! [SV167: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV246 )
| ~ ! [SY878: $i] :
~ ( in @ ( ordered_pair @ SY878 @ SV273 ) @ SV167 ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2708]) ).
thf(2774,plain,
! [SV246: $i,SV167: $i,SV273: $i] :
( ( ( ~ ~ ! [SY879: $i] :
~ ( in @ ( ordered_pair @ SY879 @ SV273 ) @ SV167 )
| ( in @ SV273 @ SV246 ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2709]) ).
thf(2775,plain,
! [SV246: $i,SV167: $i] :
( ( ( ~ ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
| ~ ! [SY880: $i] :
~ ( in @ ( ordered_pair @ SY880 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2776,plain,
! [SV170: $i,SV213: $i,SV264: $i] :
( ( ( in @ SV264 @ SV213 )
= $false )
| ( ( SV264 = SV170 )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2777,plain,
! [SV213: $i,SV170: $i,SV264: $i] :
( ( ( SV264 = SV170 )
= $false )
| ( ( in @ SV264 @ SV213 )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2778,plain,
! [SV213: $i,SV170: $i] :
( ( ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
= $true )
| ( ( ~ ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
| ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) ) )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2713]) ).
thf(2779,plain,
! [SV213: $i,SV170: $i] :
( ( ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
| ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) )
= $false )
| ( ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 )
= $false )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2780,plain,
! [SV214: $i,SV171: $i,SV235: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ SV235 ) )
= $true )
| ( ( ~ ! [SY870: $i] :
~ ~ ! [SY871: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY870 @ SV171 )
| ~ ( in @ SY871 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY870 @ SY871 ) ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(2781,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i] :
( ( ( ~ ~ ! [SY872: $i] :
~ ~ ! [SY873: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY872 @ SV171 )
| ~ ( in @ SY873 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY872 @ SY873 ) ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(2782,plain,
! [SV235: $i,SV171: $i,SV214: $i] :
( ( ( ~ ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2783,plain,
! [SV235: $i,SV214: $i,SV171: $i] :
( ( ( ~ ! [SY874: $i] :
~ ~ ! [SY875: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY874 @ SV171 )
| ~ ( in @ SY875 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY874 @ SY875 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2784,plain,
! [SV175: $i,SV247: $i,SV286: $i,SV282: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 )
| ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 )
| ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 ) ) ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(2785,plain,
! [SV247: $i,SV175: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
| ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) ) ) )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2719]) ).
thf(2786,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( in @ SV177 @ SV217 )
= $true )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $false )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2720]) ).
thf(2787,plain,
! [SV217: $i,SV236: $i,SV177: $i] :
( ( ( in @ SV177 @ ( relation_dom @ SV236 ) )
= $true )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $false )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2721]) ).
thf(2788,plain,
! [SV236: $i,SV217: $i,SV177: $i] :
( ( ( in @ SV177 @ SV217 )
= $false )
| ( ( ~ ( in @ SV177 @ ( relation_dom @ SV236 ) ) )
= $true )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(2789,plain,
! [SV179: $i,SV219: $i] :
( ( ( ~ ( ~ ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV179 )
| ~ ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV219 ) ) )
= $true )
| ( ( disjoint @ SV179 @ SV219 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2723]) ).
thf(2790,plain,
! [SV219: $i,SV179: $i,SV276: $i] :
( ( ( ~ ( in @ SV276 @ SV179 )
| ~ ( in @ SV276 @ SV219 ) )
= $true )
| ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2724]) ).
thf(2791,plain,
! [SV182: $i,SV221: $i] :
( ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV221 )
= $true )
| ( ( in @ ( sK71_SY732 @ SV221 @ SV182 ) @ SV182 )
= $true )
| ( ( SV182 = SV221 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2725]) ).
thf(2792,plain,
! [SV222: $i,SV183: $i,SV238: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV238 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(2793,plain,
! [SV238: $i,SV222: $i,SV183: $i,SV268: $i] :
( ( ( ~ ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) ) )
= $true )
| ( ( in @ SV268 @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(2794,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2730]) ).
thf(2795,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2730]) ).
thf(2796,plain,
! [SV239: $i,SV184: $i,SV249: $i,SV223: $i] :
( ( ( in @ SV223 @ SV249 )
= $false )
| ( ( in @ SV184 @ SV239 )
= $false )
| ( ( in @ ( ordered_pair @ SV184 @ SV223 ) @ ( cartesian_product2 @ SV239 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2797,plain,
! [SV224: $i,SV186: $i,SV256: $i,SV287: $i] :
( ( ( ! [SY903: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV287 @ SY903 ) @ SV256 )
| ~ ( ~ ( in @ SY903 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SY903 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY903 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SY903 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SV287 @ SY903 ) @ SV256 ) ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(2798,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( ! [SY904: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ SY904 ) @ SV256 )
| ~ ( ~ ( in @ SY904 @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ SY904 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY904 @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ SY904 ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ SY904 ) @ SV256 ) ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2735]) ).
thf(2799,plain,
! [SV250: $i,SV187: $i,SV257: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ SV277 @ SV257 )
| ~ ! [SY888: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY888 ) @ SV187 )
| ~ ( in @ SY888 @ SV250 ) ) ) )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2736]) ).
thf(2800,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV277: $i] :
( ( ( ~ ( ~ ~ ! [SY889: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY889 ) @ SV187 )
| ~ ( in @ SY889 @ SV250 ) )
| ( in @ SV277 @ SV257 ) ) )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2736]) ).
thf(2801,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( ~ ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
| ~ ! [SY890: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY890 ) @ SV187 )
| ~ ( in @ SY890 @ SV250 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(2802,plain,
! [SV226: $i,SV189: $i,SV240: $i,SV269: $i] :
( ( ( ~ ( in @ SV269 @ SV240 ) )
= $true )
| ( ( ( SV269 = SV189 )
| ( SV269 = SV226 ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2803,plain,
! [SV240: $i,SV226: $i,SV189: $i,SV269: $i] :
( ( ( ~ ( ( SV269 = SV189 )
| ( SV269 = SV226 ) ) )
= $true )
| ( ( in @ SV269 @ SV240 )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2804,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2740]) ).
thf(2805,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2740]) ).
thf(2806,plain,
! [SV190: $i,SV251: $i,SV258: $i,SV288: $i] :
( ( ( ! [SY905: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV288 @ SY905 ) @ SV258 )
| ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY905 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY905 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SV288 @ SY905 ) @ SV258 ) ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(2807,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ! [SY906: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SY906 ) @ SV258 )
| ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SY906 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SY906 ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SY906 ) @ SV258 ) ) ) )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2742]) ).
thf(2808,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( ~ ( in @ SV266 @ ( relation_dom @ SV191 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2809,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( ~ ~ ( in @ SV266 @ ( relation_dom @ SV191 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) )
| ~ ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2744]) ).
thf(2810,plain,
! [SV192: $i,SV261: $i] :
( ( ( ! [SY907: $i] :
( SV261
!= ( ordered_pair @ ( sK99_SY853 @ SV192 @ SV261 ) @ SY907 ) ) )
= $false )
| ( ( in @ SV261 @ SV192 )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2745]) ).
thf(2811,plain,
! [SV289: $i,SV283: $i,SV192: $i] :
( ( ( ( sK74_SY649 @ SV192 )
!= ( ordered_pair @ SV283 @ SV289 ) )
= $true )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(2812,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV278: $i] :
( ( ( ~ ( ~ ( in @ SV278 @ SV259 )
| ~ ! [SY892: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY892 @ SV278 ) @ SV193 )
| ~ ( in @ SY892 @ SV252 ) ) ) )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2747]) ).
thf(2813,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i] :
( ( ( ~ ( ~ ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY893 @ SV278 ) @ SV193 )
| ~ ( in @ SY893 @ SV252 ) )
| ( in @ SV278 @ SV259 ) ) )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2747]) ).
thf(2814,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ( ~ ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
| ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY894 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY894 @ SV252 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(2815,plain,
! [SV194: $i,SV253: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV253 )
| ~ ! [SY882: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY882 ) @ SV194 ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2749]) ).
thf(2816,plain,
! [SV253: $i,SV194: $i,SV274: $i] :
( ( ( ~ ~ ! [SY883: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY883 ) @ SV194 )
| ( in @ SV274 @ SV253 ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2750]) ).
thf(2817,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
| ~ ! [SY884: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY884 ) @ SV194 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2818,plain,
! [SV195: $i,SV227: $i,SV279: $i,SV275: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
| ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) ) ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2752]) ).
thf(2819,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) )
| ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 ) ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2752]) ).
thf(2820,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
| ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2753]) ).
thf(2821,plain,
! [SV229: $i,SV198: $i,SV241: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV241 ) )
= $true )
| ( ( ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2754]) ).
thf(2822,plain,
! [SV241: $i,SV229: $i,SV198: $i,SV271: $i] :
( ( ( ~ ( ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) ) )
= $true )
| ( ( in @ SV271 @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(2823,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2824,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2825,plain,
! [SV254: $i,SV201: $i,SV290: $i,SV284: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV290 ) @ SV201 )
| ( in @ ( ordered_pair @ SV284 @ SV290 ) @ SV254 ) )
= $true )
| ( ( subset @ SV201 @ SV254 )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(2826,plain,
! [SV201: $i,SV254: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK94_SY821 @ SV254 @ SV201 ) @ ( sK100_SY902 @ SV201 @ SV254 ) ) @ SV201 )
| ( in @ ( ordered_pair @ ( sK94_SY821 @ SV254 @ SV201 ) @ ( sK100_SY902 @ SV201 @ SV254 ) ) @ SV254 ) )
= $false )
| ( ( subset @ SV201 @ SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2758]) ).
thf(2827,plain,
! [SV231: $i,SV202: $i,SV243: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV243 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2759]) ).
thf(2828,plain,
! [SV243: $i,SV231: $i,SV202: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) ) )
= $true )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2760]) ).
thf(2829,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2761]) ).
thf(2830,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2761]) ).
thf(2831,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( SV262
!= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( ! [SY857: $i,SY858: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY858 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY858 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 ) ) ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2762]) ).
thf(2832,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ~ ! [SY861: $i,SY862: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY862 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY862 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 ) ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(2833,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV162 ) @ SV234 ) )
| ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV208 ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2834,plain,
! [SV208: $i,SV162: $i,SV234: $i,SV280: $i] :
( ( ( ~ ~ ( ~ ( in @ SV280 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 ) )
| ~ ( in @ SV280 @ SV208 ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2766]) ).
thf(2835,plain,
! [SV210: $i,SV165: $i,SV263: $i] :
( ( ( ! [SY865: $i] :
~ ~ ( ~ ( in @ SV263 @ SY865 )
| ~ ( in @ SY865 @ SV165 ) ) )
= $false )
| ( ( in @ SV263 @ SV210 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(2836,plain,
! [SV210: $i,SV165: $i,SV263: $i] :
( ( ( ! [SY866: $i] :
~ ~ ( ~ ( in @ SV263 @ SY866 )
| ~ ( in @ SY866 @ SV165 ) ) )
= $true )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2768]) ).
thf(2837,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2838,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
| ~ ( in @ SV291 @ SV165 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(2839,plain,
! [SV245: $i,SV166: $i,SV285: $i,SV281: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 )
| ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 )
| ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 ) ) )
= $false )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2840,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) ) )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2772]) ).
thf(2841,plain,
! [SV167: $i,SV246: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV246 ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ( in @ ( ordered_pair @ SY878 @ SV273 ) @ SV167 ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2842,plain,
! [SV246: $i,SV167: $i,SV273: $i] :
( ( ( ~ ~ ! [SY879: $i] :
~ ( in @ ( ordered_pair @ SY879 @ SV273 ) @ SV167 ) )
= $true )
| ( ( in @ SV273 @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(2843,plain,
! [SV246: $i,SV167: $i] :
( ( ( ~ ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2844,plain,
! [SV246: $i,SV167: $i] :
( ( ( ~ ! [SY880: $i] :
~ ( in @ ( ordered_pair @ SY880 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2845,plain,
! [SV213: $i,SV170: $i] :
( ( ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
| ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 ) )
= $false )
| ( ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2846,plain,
! [SV213: $i,SV170: $i] :
( ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
= $false )
| ( ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 )
= $false )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2779]) ).
thf(2847,plain,
! [SV213: $i,SV170: $i] :
( ( ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
= $false )
| ( ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 )
= $false )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2779]) ).
thf(2848,plain,
! [SV214: $i,SV171: $i,SV235: $i,SV267: $i] :
( ( ( in @ SV267 @ SV235 )
= $false )
| ( ( ~ ! [SY870: $i] :
~ ~ ! [SY871: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY870 @ SV171 )
| ~ ( in @ SY871 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY870 @ SY871 ) ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2849,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i] :
( ( ( ~ ! [SY872: $i] :
~ ~ ! [SY873: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY872 @ SV171 )
| ~ ( in @ SY873 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY872 @ SY873 ) ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2850,plain,
! [SV235: $i,SV171: $i,SV214: $i] :
( ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2782]) ).
thf(2851,plain,
! [SV235: $i,SV214: $i,SV171: $i] :
( ( ( ! [SY874: $i] :
~ ~ ! [SY875: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY874 @ SV171 )
| ~ ( in @ SY875 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY874 @ SY875 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2783]) ).
thf(2852,plain,
! [SV175: $i,SV247: $i,SV286: $i,SV282: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 )
| ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 )
| ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 ) ) )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2853,plain,
! [SV247: $i,SV175: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
| ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(2854,plain,
! [SV217: $i,SV236: $i,SV177: $i] :
( ( ( in @ SV177 @ ( relation_dom @ SV236 ) )
= $false )
| ( ( in @ SV177 @ SV217 )
= $false )
| ( ( in @ SV177 @ ( relation_dom @ ( relation_dom_restriction @ SV236 @ SV217 ) ) )
= $true )
| ( ( relation @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(2855,plain,
! [SV179: $i,SV219: $i] :
( ( ( ~ ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV179 )
| ~ ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV219 ) )
= $false )
| ( ( disjoint @ SV179 @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2856,plain,
! [SV219: $i,SV179: $i,SV276: $i] :
( ( ( ~ ( in @ SV276 @ SV179 ) )
= $true )
| ( ( ~ ( in @ SV276 @ SV219 ) )
= $true )
| ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2790]) ).
thf(2857,plain,
! [SV222: $i,SV183: $i,SV238: $i,SV268: $i] :
( ( ( in @ SV268 @ SV238 )
= $false )
| ( ( ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2858,plain,
! [SV238: $i,SV222: $i,SV183: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) ) )
= $false )
| ( ( in @ SV268 @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(2859,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2794]) ).
thf(2860,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2795]) ).
thf(2861,plain,
! [SV224: $i,SV186: $i,SV256: $i,SV292: $i,SV287: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
| ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 ) ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(2862,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
| ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2798]) ).
thf(2863,plain,
! [SV250: $i,SV187: $i,SV257: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ SV257 )
| ~ ! [SY888: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY888 ) @ SV187 )
| ~ ( in @ SY888 @ SV250 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2799]) ).
thf(2864,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV277: $i] :
( ( ( ~ ~ ! [SY889: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY889 ) @ SV187 )
| ~ ( in @ SY889 @ SV250 ) )
| ( in @ SV277 @ SV257 ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2800]) ).
thf(2865,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
| ~ ! [SY890: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY890 ) @ SV187 )
| ~ ( in @ SY890 @ SV250 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2866,plain,
! [SV226: $i,SV189: $i,SV240: $i,SV269: $i] :
( ( ( in @ SV269 @ SV240 )
= $false )
| ( ( ( SV269 = SV189 )
| ( SV269 = SV226 ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(2867,plain,
! [SV240: $i,SV226: $i,SV189: $i,SV269: $i] :
( ( ( ( SV269 = SV189 )
| ( SV269 = SV226 ) )
= $false )
| ( ( in @ SV269 @ SV240 )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(2868,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
= $true )
| ( ( ~ ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2804]) ).
thf(2869,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
= $false )
| ( ( ~ ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2805]) ).
thf(2870,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 )
= $false )
| ( ( ~ ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) ) )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2805]) ).
thf(2871,plain,
! [SV190: $i,SV251: $i,SV258: $i,SV293: $i,SV288: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
| ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 ) ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(2872,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
| ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) ) )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2807]) ).
thf(2873,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(2874,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( ~ ( in @ SV266 @ ( relation_dom @ SV191 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) )
| ~ ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2875,plain,
! [SV192: $i,SV261: $i] :
( ( ( SV261
!= ( ordered_pair @ ( sK99_SY853 @ SV192 @ SV261 ) @ ( sK103_SY907 @ SV192 @ SV261 ) ) )
= $false )
| ( ( in @ SV261 @ SV192 )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2810]) ).
thf(2876,plain,
! [SV289: $i,SV283: $i,SV192: $i] :
( ( ( ( sK74_SY649 @ SV192 )
= ( ordered_pair @ SV283 @ SV289 ) )
= $false )
| ( ( relation @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(2877,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV278: $i] :
( ( ( ~ ( in @ SV278 @ SV259 )
| ~ ! [SY892: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY892 @ SV278 ) @ SV193 )
| ~ ( in @ SY892 @ SV252 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2812]) ).
thf(2878,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i] :
( ( ( ~ ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY893 @ SV278 ) @ SV193 )
| ~ ( in @ SY893 @ SV252 ) )
| ( in @ SV278 @ SV259 ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2813]) ).
thf(2879,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
| ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY894 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY894 @ SV252 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2880,plain,
! [SV194: $i,SV253: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV253 ) )
= $true )
| ( ( ~ ! [SY882: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY882 ) @ SV194 ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(2881,plain,
! [SV253: $i,SV194: $i,SV274: $i] :
( ( ( ~ ~ ! [SY883: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY883 ) @ SV194 ) )
= $true )
| ( ( in @ SV274 @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(2882,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2817]) ).
thf(2883,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ! [SY884: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY884 ) @ SV194 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2817]) ).
thf(2884,plain,
! [SV195: $i,SV227: $i,SV279: $i,SV275: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
| ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2818]) ).
thf(2885,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( ~ ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) )
| ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2819]) ).
thf(2886,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
| ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(2887,plain,
! [SV229: $i,SV198: $i,SV241: $i,SV271: $i] :
( ( ( in @ SV271 @ SV241 )
= $false )
| ( ( ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(2888,plain,
! [SV241: $i,SV229: $i,SV198: $i,SV271: $i] :
( ( ( ( in @ SV271 @ SV198 )
| ( in @ SV271 @ SV229 ) )
= $false )
| ( ( in @ SV271 @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(2889,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2823]) ).
thf(2890,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2824]) ).
thf(2891,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) ) )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2824]) ).
thf(2892,plain,
! [SV254: $i,SV201: $i,SV290: $i,SV284: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV290 ) @ SV201 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV284 @ SV290 ) @ SV254 )
= $true )
| ( ( subset @ SV201 @ SV254 )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(2893,plain,
! [SV201: $i,SV254: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK94_SY821 @ SV254 @ SV201 ) @ ( sK100_SY902 @ SV201 @ SV254 ) ) @ SV201 ) )
= $false )
| ( ( subset @ SV201 @ SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2826]) ).
thf(2894,plain,
! [SV201: $i,SV254: $i] :
( ( ( in @ ( ordered_pair @ ( sK94_SY821 @ SV254 @ SV201 ) @ ( sK100_SY902 @ SV201 @ SV254 ) ) @ SV254 )
= $false )
| ( ( subset @ SV201 @ SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2826]) ).
thf(2895,plain,
! [SV231: $i,SV202: $i,SV243: $i,SV272: $i] :
( ( ( in @ SV272 @ SV243 )
= $false )
| ( ( ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(2896,plain,
! [SV243: $i,SV231: $i,SV202: $i,SV272: $i] :
( ( ( ~ ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) ) )
= $false )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2897,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2829]) ).
thf(2898,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2830]) ).
thf(2899,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( ! [SY857: $i,SY858: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 )
| ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY826 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY826 @ SY858 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY857 @ SY827 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY827 @ SY858 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV262 ) ) ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(2900,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ! [SY861: $i,SY862: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 )
| ~ ! [SY830: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY830 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY830 @ SY862 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY831: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY861 @ SY831 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY831 @ SY862 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV262 ) ) ) )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(2901,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV162 ) @ SV234 ) ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2833]) ).
thf(2902,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV208 ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2833]) ).
thf(2903,plain,
! [SV208: $i,SV162: $i,SV234: $i,SV280: $i] :
( ( ( ~ ~ ( ~ ( in @ SV280 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 ) ) )
= $true )
| ( ( ~ ( in @ SV280 @ SV208 ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(2904,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( in @ SV263 @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) )
| ~ ( in @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) @ SV165 ) ) )
= $false )
| ( ( in @ SV263 @ SV210 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2835]) ).
thf(2905,plain,
! [SV210: $i,SV165: $i,SV294: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( in @ SV263 @ SV294 )
| ~ ( in @ SV294 @ SV165 ) ) )
= $true )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(2906,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2837]) ).
thf(2907,plain,
! [SV210: $i,SV165: $i] :
( ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2837]) ).
thf(2908,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
| ~ ( in @ SV291 @ SV165 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2909,plain,
! [SV245: $i,SV166: $i,SV285: $i,SV281: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 )
| ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 ) ) )
= $false )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(2910,plain,
! [SV166: $i,SV245: $i,SV285: $i,SV281: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 )
| ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 ) ) )
= $false )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(2911,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) ) )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(2912,plain,
! [SV167: $i,SV246: $i,SV273: $i] :
( ( ( in @ SV273 @ SV246 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ( in @ ( ordered_pair @ SY878 @ SV273 ) @ SV167 ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(2913,plain,
! [SV246: $i,SV167: $i,SV273: $i] :
( ( ( ~ ! [SY879: $i] :
~ ( in @ ( ordered_pair @ SY879 @ SV273 ) @ SV167 ) )
= $false )
| ( ( in @ SV273 @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(2914,plain,
! [SV246: $i,SV167: $i] :
( ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $true )
| ( ( ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2843]) ).
thf(2915,plain,
! [SV246: $i,SV167: $i] :
( ( ( ! [SY880: $i] :
~ ( in @ ( ordered_pair @ SY880 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2844]) ).
thf(2916,plain,
! [SV213: $i,SV170: $i] :
( ( ( ( sK77_SY713 @ SV170 @ SV213 )
!= SV170 )
= $false )
| ( ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2845]) ).
thf(2917,plain,
! [SV213: $i,SV170: $i] :
( ( ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
= $false )
| ( ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2845]) ).
thf(2918,plain,
! [SV213: $i,SV170: $i] :
( ( ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 )
= $true )
| ( ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 )
= $false )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2846]) ).
thf(2919,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i] :
( ( ( ! [SY870: $i] :
~ ~ ! [SY871: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY870 @ SV171 )
| ~ ( in @ SY871 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY870 @ SY871 ) ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2920,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i] :
( ( ( ! [SY872: $i] :
~ ~ ! [SY873: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY872 @ SV171 )
| ~ ( in @ SY873 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SY872 @ SY873 ) ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2849]) ).
thf(2921,plain,
! [SV235: $i,SV214: $i,SV171: $i] :
( ( ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2922,plain,
! [SV235: $i,SV214: $i,SV171: $i,SV295: $i] :
( ( ( ~ ~ ! [SY908: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV295 @ SV171 )
| ~ ( in @ SY908 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SY908 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(2923,plain,
! [SV175: $i,SV247: $i,SV286: $i,SV282: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 )
| ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 ) ) )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2852]) ).
thf(2924,plain,
! [SV247: $i,SV175: $i,SV282: $i,SV286: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 )
| ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 ) ) )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2852]) ).
thf(2925,plain,
! [SV247: $i,SV175: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
| ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(2926,plain,
! [SV179: $i,SV219: $i] :
( ( ( ~ ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV179 ) )
= $false )
| ( ( disjoint @ SV179 @ SV219 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2855]) ).
thf(2927,plain,
! [SV179: $i,SV219: $i] :
( ( ( ~ ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV219 ) )
= $false )
| ( ( disjoint @ SV179 @ SV219 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2855]) ).
thf(2928,plain,
! [SV219: $i,SV179: $i,SV276: $i] :
( ( ( in @ SV276 @ SV179 )
= $false )
| ( ( ~ ( in @ SV276 @ SV219 ) )
= $true )
| ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(2929,plain,
! [SV238: $i,SV222: $i,SV183: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) )
= $false )
| ( ( in @ SV268 @ SV238 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(2930,plain,
! [SV238: $i,SV222: $i,SV183: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV183 )
| ~ ( in @ SV268 @ SV222 ) )
= $true )
| ( ( in @ SV268 @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2858]) ).
thf(2931,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(2932,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 ) )
= $true )
| ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(2933,plain,
! [SV224: $i,SV186: $i,SV256: $i,SV292: $i,SV287: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
| ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(2934,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
| ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2862]) ).
thf(2935,plain,
! [SV250: $i,SV187: $i,SV257: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ SV257 ) )
= $true )
| ( ( ~ ! [SY888: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY888 ) @ SV187 )
| ~ ( in @ SY888 @ SV250 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2863]) ).
thf(2936,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV277: $i] :
( ( ( ~ ~ ! [SY889: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY889 ) @ SV187 )
| ~ ( in @ SY889 @ SV250 ) ) )
= $true )
| ( ( in @ SV277 @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2864]) ).
thf(2937,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(2938,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ! [SY890: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY890 ) @ SV187 )
| ~ ( in @ SY890 @ SV250 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(2939,plain,
! [SV240: $i,SV226: $i,SV189: $i,SV269: $i] :
( ( ( SV269 = SV189 )
= $true )
| ( ( SV269 = SV226 )
= $true )
| ( ( in @ SV269 @ SV240 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(2940,plain,
! [SV226: $i,SV240: $i,SV189: $i,SV269: $i] :
( ( ( SV269 = SV189 )
= $false )
| ( ( in @ SV269 @ SV240 )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2867]) ).
thf(2941,plain,
! [SV189: $i,SV240: $i,SV226: $i,SV269: $i] :
( ( ( SV269 = SV226 )
= $false )
| ( ( in @ SV269 @ SV240 )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2867]) ).
thf(2942,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) )
= $false )
| ( ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(2943,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) )
= $false )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(2944,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
| ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 ) )
= $false )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(2945,plain,
! [SV190: $i,SV251: $i,SV258: $i,SV293: $i,SV288: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
| ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 ) ) )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(2946,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
| ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(2947,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) )
= $false )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(2948,plain,
! [SV270: $i,SV191: $i,SV266: $i] :
( ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( ~ ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) )
| ~ ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2874]) ).
thf(2949,plain,
! [SV192: $i,SV261: $i] :
( ( ( SV261
= ( ordered_pair @ ( sK99_SY853 @ SV192 @ SV261 ) @ ( sK103_SY907 @ SV192 @ SV261 ) ) )
= $true )
| ( ( in @ SV261 @ SV192 )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2875]) ).
thf(2950,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV278: $i] :
( ( ( ~ ( in @ SV278 @ SV259 ) )
= $true )
| ( ( ~ ! [SY892: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY892 @ SV278 ) @ SV193 )
| ~ ( in @ SY892 @ SV252 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2877]) ).
thf(2951,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i] :
( ( ( ~ ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY893 @ SV278 ) @ SV193 )
| ~ ( in @ SY893 @ SV252 ) ) )
= $true )
| ( ( in @ SV278 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(2952,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2879]) ).
thf(2953,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY894 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY894 @ SV252 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2879]) ).
thf(2954,plain,
! [SV194: $i,SV253: $i,SV274: $i] :
( ( ( in @ SV274 @ SV253 )
= $false )
| ( ( ~ ! [SY882: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY882 ) @ SV194 ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(2955,plain,
! [SV253: $i,SV194: $i,SV274: $i] :
( ( ( ~ ! [SY883: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY883 ) @ SV194 ) )
= $false )
| ( ( in @ SV274 @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2881]) ).
thf(2956,plain,
! [SV253: $i,SV194: $i] :
( ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $true )
| ( ( ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2882]) ).
thf(2957,plain,
! [SV253: $i,SV194: $i] :
( ( ( ! [SY884: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY884 ) @ SV194 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2883]) ).
thf(2958,plain,
! [SV195: $i,SV227: $i,SV279: $i,SV275: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2884]) ).
thf(2959,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( ~ ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2885]) ).
thf(2960,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2886]) ).
thf(2961,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2886]) ).
thf(2962,plain,
! [SV241: $i,SV229: $i,SV198: $i,SV271: $i] :
( ( ( in @ SV271 @ SV198 )
= $true )
| ( ( in @ SV271 @ SV229 )
= $true )
| ( ( in @ SV271 @ SV241 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(2963,plain,
! [SV229: $i,SV241: $i,SV198: $i,SV271: $i] :
( ( ( in @ SV271 @ SV198 )
= $false )
| ( ( in @ SV271 @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(2964,plain,
! [SV198: $i,SV241: $i,SV229: $i,SV271: $i] :
( ( ( in @ SV271 @ SV229 )
= $false )
| ( ( in @ SV271 @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(2965,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) )
= $false )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2966,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) )
= $false )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(2967,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 ) )
= $false )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2891]) ).
thf(2968,plain,
! [SV254: $i,SV201: $i,SV290: $i,SV284: $i] :
( ( ( in @ ( ordered_pair @ SV284 @ SV290 ) @ SV201 )
= $false )
| ( ( in @ ( ordered_pair @ SV284 @ SV290 ) @ SV254 )
= $true )
| ( ( subset @ SV201 @ SV254 )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(2969,plain,
! [SV201: $i,SV254: $i] :
( ( ( in @ ( ordered_pair @ ( sK94_SY821 @ SV254 @ SV201 ) @ ( sK100_SY902 @ SV201 @ SV254 ) ) @ SV201 )
= $true )
| ( ( subset @ SV201 @ SV254 )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV201 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2893]) ).
thf(2970,plain,
! [SV243: $i,SV231: $i,SV202: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) )
= $false )
| ( ( in @ SV272 @ SV243 )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(2971,plain,
! [SV243: $i,SV231: $i,SV202: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV202 )
| ~ ~ ( in @ SV272 @ SV231 ) )
= $true )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2896]) ).
thf(2972,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(2973,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2898]) ).
thf(2974,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV296: $i] :
( ( ( ! [SY909: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY909 ) @ SV262 )
| ~ ! [SY910: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY910 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY910 @ SY909 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY911: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY911 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY911 @ SY909 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SV296 @ SY909 ) @ SV262 ) ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(2975,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ! [SY912: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY912 ) @ SV262 )
| ~ ! [SY913: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY913 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY913 @ SY912 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY914: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY914 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY914 @ SY912 ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY912 ) @ SV262 ) ) ) )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2900]) ).
thf(2976,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( ~ ( ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV162 ) @ SV234 ) ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2901]) ).
thf(2977,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV208 )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2902]) ).
thf(2978,plain,
! [SV208: $i,SV162: $i,SV234: $i,SV280: $i] :
( ( ( ~ ( ~ ( in @ SV280 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 ) ) )
= $false )
| ( ( ~ ( in @ SV280 @ SV208 ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(2979,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ SV263 @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) )
| ~ ( in @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) @ SV165 ) ) )
= $true )
| ( ( in @ SV263 @ SV210 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2904]) ).
thf(2980,plain,
! [SV210: $i,SV165: $i,SV294: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ SV263 @ SV294 )
| ~ ( in @ SV294 @ SV165 ) ) )
= $false )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(2981,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) ) )
= $true )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2906]) ).
thf(2982,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
| ~ ( in @ SV291 @ SV165 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2908]) ).
thf(2983,plain,
! [SV245: $i,SV166: $i,SV285: $i,SV281: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 )
| ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 ) )
= $true )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2909]) ).
thf(2984,plain,
! [SV166: $i,SV245: $i,SV285: $i,SV281: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 )
| ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 ) )
= $true )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2910]) ).
thf(2985,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) ) )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(2986,plain,
! [SV246: $i,SV167: $i,SV273: $i] :
( ( ( ! [SY878: $i] :
~ ( in @ ( ordered_pair @ SY878 @ SV273 ) @ SV167 ) )
= $false )
| ( ( in @ SV273 @ SV246 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(2987,plain,
! [SV246: $i,SV167: $i,SV273: $i] :
( ( ( ! [SY879: $i] :
~ ( in @ ( ordered_pair @ SY879 @ SV273 ) @ SV167 ) )
= $true )
| ( ( in @ SV273 @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2913]) ).
thf(2988,plain,
! [SV246: $i,SV167: $i] :
( ( ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) )
= $false )
| ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(2989,plain,
! [SV246: $i,SV167: $i,SV297: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV297 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(2990,plain,
! [SV213: $i,SV170: $i] :
( ( ( ( sK77_SY713 @ SV170 @ SV213 )
= SV170 )
= $true )
| ( ( in @ ( sK77_SY713 @ SV170 @ SV213 ) @ SV213 )
= $true )
| ( ( SV213
= ( singleton @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2916]) ).
thf(2991,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ~ ~ ! [SY915: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ SY915 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SY915 ) ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2919]) ).
thf(2992,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i,SV298: $i] :
( ( ( ~ ~ ! [SY916: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV298 @ SV171 )
| ~ ( in @ SY916 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SV298 @ SY916 ) ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(2993,plain,
! [SV235: $i,SV214: $i,SV171: $i] :
( ( ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2921]) ).
thf(2994,plain,
! [SV235: $i,SV171: $i,SV214: $i] :
( ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2921]) ).
thf(2995,plain,
! [SV235: $i,SV214: $i,SV171: $i,SV295: $i] :
( ( ( ~ ! [SY908: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV295 @ SV171 )
| ~ ( in @ SY908 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SY908 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(2996,plain,
! [SV175: $i,SV247: $i,SV286: $i,SV282: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 )
| ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2923]) ).
thf(2997,plain,
! [SV247: $i,SV175: $i,SV282: $i,SV286: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 )
| ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2924]) ).
thf(2998,plain,
! [SV247: $i,SV175: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
| ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(2999,plain,
! [SV179: $i,SV219: $i] :
( ( ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV179 )
= $true )
| ( ( disjoint @ SV179 @ SV219 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2926]) ).
thf(3000,plain,
! [SV179: $i,SV219: $i] :
( ( ( in @ ( sK93_SY728 @ SV219 @ SV179 ) @ SV219 )
= $true )
| ( ( disjoint @ SV179 @ SV219 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2927]) ).
thf(3001,plain,
! [SV179: $i,SV219: $i,SV276: $i] :
( ( ( in @ SV276 @ SV219 )
= $false )
| ( ( in @ SV276 @ SV179 )
= $false )
| ( ( ~ ( disjoint @ SV179 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(3002,plain,
! [SV222: $i,SV238: $i,SV183: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV183 ) )
= $false )
| ( ( in @ SV268 @ SV238 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2929]) ).
thf(3003,plain,
! [SV183: $i,SV238: $i,SV222: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV222 ) )
= $false )
| ( ( in @ SV268 @ SV238 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2929]) ).
thf(3004,plain,
! [SV238: $i,SV222: $i,SV183: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV183 ) )
= $true )
| ( ( ~ ( in @ SV268 @ SV222 ) )
= $true )
| ( ( in @ SV268 @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2930]) ).
thf(3005,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2931]) ).
thf(3006,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2931]) ).
thf(3007,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(3008,plain,
! [SV224: $i,SV186: $i,SV256: $i,SV292: $i,SV287: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
| ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3009,plain,
! [SV256: $i,SV224: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3010,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
| ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3011,plain,
! [SV250: $i,SV187: $i,SV257: $i,SV277: $i] :
( ( ( in @ SV277 @ SV257 )
= $false )
| ( ( ~ ! [SY888: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY888 ) @ SV187 )
| ~ ( in @ SY888 @ SV250 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2935]) ).
thf(3012,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV277: $i] :
( ( ( ~ ! [SY889: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY889 ) @ SV187 )
| ~ ( in @ SY889 @ SV250 ) ) )
= $false )
| ( ( in @ SV277 @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3013,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2937]) ).
thf(3014,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ! [SY890: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY890 ) @ SV187 )
| ~ ( in @ SY890 @ SV250 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(3015,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) ) )
= $false )
| ( ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2942]) ).
thf(3016,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
= $false )
| ( ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2942]) ).
thf(3017,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) ) )
= $false )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2943]) ).
thf(3018,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
= $false )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2943]) ).
thf(3019,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ~ ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) ) )
= $false )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2944]) ).
thf(3020,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
= $false )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2944]) ).
thf(3021,plain,
! [SV190: $i,SV251: $i,SV258: $i,SV293: $i,SV288: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
| ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) ) ) )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3022,plain,
! [SV258: $i,SV190: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 ) ) )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3023,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
| ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2946]) ).
thf(3024,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) ) )
= $false )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2947]) ).
thf(3025,plain,
! [SV191: $i,SV270: $i,SV266: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) )
= $false )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2947]) ).
thf(3026,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) )
| ~ ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) )
= $false )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3027,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV278: $i] :
( ( ( in @ SV278 @ SV259 )
= $false )
| ( ( ~ ! [SY892: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY892 @ SV278 ) @ SV193 )
| ~ ( in @ SY892 @ SV252 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(3028,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i] :
( ( ( ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY893 @ SV278 ) @ SV193 )
| ~ ( in @ SY893 @ SV252 ) ) )
= $false )
| ( ( in @ SV278 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2951]) ).
thf(3029,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2952]) ).
thf(3030,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ! [SY894: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY894 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY894 @ SV252 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2953]) ).
thf(3031,plain,
! [SV253: $i,SV194: $i,SV274: $i] :
( ( ( ! [SY882: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY882 ) @ SV194 ) )
= $false )
| ( ( in @ SV274 @ SV253 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3032,plain,
! [SV253: $i,SV194: $i,SV274: $i] :
( ( ( ! [SY883: $i] :
~ ( in @ ( ordered_pair @ SV274 @ SY883 ) @ SV194 ) )
= $true )
| ( ( in @ SV274 @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2955]) ).
thf(3033,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) )
= $false )
| ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(3034,plain,
! [SV299: $i,SV253: $i,SV194: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV299 ) @ SV194 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3035,plain,
! [SV195: $i,SV227: $i,SV279: $i,SV275: $i] :
( ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $false )
| ( ( ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3036,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( ~ ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(3037,plain,
! [SV227: $i,SV195: $i] :
( ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2960]) ).
thf(3038,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2961]) ).
thf(3039,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) ) )
= $false )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2965]) ).
thf(3040,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
= $false )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2965]) ).
thf(3041,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) ) )
= $false )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3042,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
= $false )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3043,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) ) )
= $false )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2967]) ).
thf(3044,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
= $false )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2967]) ).
thf(3045,plain,
! [SV231: $i,SV243: $i,SV202: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV202 ) )
= $false )
| ( ( in @ SV272 @ SV243 )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2970]) ).
thf(3046,plain,
! [SV202: $i,SV243: $i,SV231: $i,SV272: $i] :
( ( ( ~ ~ ( in @ SV272 @ SV231 ) )
= $false )
| ( ( in @ SV272 @ SV243 )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2970]) ).
thf(3047,plain,
! [SV243: $i,SV231: $i,SV202: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV202 ) )
= $true )
| ( ( ~ ~ ( in @ SV272 @ SV231 ) )
= $true )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2971]) ).
thf(3048,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2972]) ).
thf(3049,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2972]) ).
thf(3050,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3051,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV300: $i,SV296: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
| ~ ! [SY917: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY917 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY917 @ SV300 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY918: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY918 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY918 @ SV300 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 ) ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3052,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
| ~ ! [SY919: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY919 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY919 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) ) )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2975]) ).
thf(3053,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV162 ) @ SV234 ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3054,plain,
! [SV208: $i,SV162: $i,SV234: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ ( relation_dom @ SV234 ) )
| ~ ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 ) )
= $true )
| ( ( ~ ( in @ SV280 @ SV208 ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2978]) ).
thf(3055,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) )
| ~ ( in @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) @ SV165 ) )
= $false )
| ( ( in @ SV263 @ SV210 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3056,plain,
! [SV210: $i,SV165: $i,SV294: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV294 )
| ~ ( in @ SV294 @ SV165 ) )
= $true )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2980]) ).
thf(3057,plain,
! [SV210: $i,SV165: $i] :
( ( ( ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3058,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 ) )
= $true )
| ( ( ~ ( in @ SV291 @ SV165 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2982]) ).
thf(3059,plain,
! [SV245: $i,SV166: $i,SV285: $i,SV281: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 )
= $true )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3060,plain,
! [SV166: $i,SV245: $i,SV285: $i,SV281: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 )
= $true )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2984]) ).
thf(3061,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) ) )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2985]) ).
thf(3062,plain,
! [SV166: $i,SV245: $i] :
( ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) ) )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2985]) ).
thf(3063,plain,
! [SV273: $i,SV167: $i,SV246: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK108_SY878 @ SV246 @ SV167 @ SV273 ) @ SV273 ) @ SV167 ) )
= $false )
| ( ( in @ SV273 @ SV246 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2986]) ).
thf(3064,plain,
! [SV246: $i,SV167: $i,SV273: $i,SV301: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV301 @ SV273 ) @ SV167 ) )
= $true )
| ( ( in @ SV273 @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3065,plain,
! [SV246: $i,SV167: $i] :
( ( ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $false )
| ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2988]) ).
thf(3066,plain,
! [SV246: $i,SV167: $i] :
( ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $false )
| ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2988]) ).
thf(3067,plain,
! [SV246: $i,SV167: $i,SV297: $i] :
( ( ( in @ ( ordered_pair @ SV297 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $false )
| ( ( ~ ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) ) )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3068,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ~ ! [SY915: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ SY915 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SY915 ) ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2991]) ).
thf(3069,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i,SV298: $i] :
( ( ( ~ ! [SY916: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV298 @ SV171 )
| ~ ( in @ SY916 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SV298 @ SY916 ) ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2992]) ).
thf(3070,plain,
! [SV235: $i,SV214: $i,SV171: $i] :
( ( ( ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) ) )
= $true )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2993]) ).
thf(3071,plain,
! [SV235: $i,SV214: $i,SV171: $i,SV295: $i] :
( ( ( ! [SY908: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV295 @ SV171 )
| ~ ( in @ SY908 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SY908 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2995]) ).
thf(3072,plain,
! [SV175: $i,SV247: $i,SV286: $i,SV282: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2996]) ).
thf(3073,plain,
! [SV247: $i,SV175: $i,SV282: $i,SV286: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3074,plain,
! [SV247: $i,SV175: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3075,plain,
! [SV175: $i,SV247: $i] :
( ( ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3076,plain,
! [SV276: $i,SV219: $i,SV179: $i] :
( ( ( disjoint @ SV179 @ SV219 )
= $false )
| ( ( in @ SV276 @ SV179 )
= $false )
| ( ( in @ SV276 @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3077,plain,
! [SV222: $i,SV238: $i,SV183: $i,SV268: $i] :
( ( ( in @ SV268 @ SV183 )
= $true )
| ( ( in @ SV268 @ SV238 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3002]) ).
thf(3078,plain,
! [SV183: $i,SV238: $i,SV222: $i,SV268: $i] :
( ( ( in @ SV268 @ SV222 )
= $true )
| ( ( in @ SV268 @ SV238 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3003]) ).
thf(3079,plain,
! [SV238: $i,SV222: $i,SV183: $i,SV268: $i] :
( ( ( in @ SV268 @ SV183 )
= $false )
| ( ( ~ ( in @ SV268 @ SV222 ) )
= $true )
| ( ( in @ SV268 @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3080,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) ) )
= $true )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3081,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3082,plain,
! [SV224: $i,SV186: $i,SV256: $i,SV292: $i,SV287: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
| ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3008]) ).
thf(3083,plain,
! [SV256: $i,SV224: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( ~ ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) )
| ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3009]) ).
thf(3084,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
| ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3085,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV277: $i] :
( ( ( ! [SY888: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY888 ) @ SV187 )
| ~ ( in @ SY888 @ SV250 ) ) )
= $false )
| ( ( in @ SV277 @ SV257 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3086,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV277: $i] :
( ( ( ! [SY889: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SY889 ) @ SV187 )
| ~ ( in @ SY889 @ SV250 ) ) )
= $true )
| ( ( in @ SV277 @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3012]) ).
thf(3087,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) )
= $false )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3088,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
| ~ ( in @ SV302 @ SV250 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3089,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
= $true )
| ( ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3015]) ).
thf(3090,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
= $true )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3017]) ).
thf(3091,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
| ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 ) )
= $true )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3019]) ).
thf(3092,plain,
! [SV190: $i,SV251: $i,SV258: $i,SV293: $i,SV288: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
| ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3021]) ).
thf(3093,plain,
! [SV258: $i,SV190: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( ~ ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) )
| ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3022]) ).
thf(3094,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
| ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3095,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3024]) ).
thf(3096,plain,
! [SV191: $i,SV270: $i,SV266: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3025]) ).
thf(3097,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( ~ ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) ) )
= $false )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3098,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( ~ ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) ) )
= $false )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3099,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i] :
( ( ( ! [SY892: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY892 @ SV278 ) @ SV193 )
| ~ ( in @ SY892 @ SV252 ) ) )
= $false )
| ( ( in @ SV278 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3100,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i] :
( ( ( ! [SY893: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY893 @ SV278 ) @ SV193 )
| ~ ( in @ SY893 @ SV252 ) ) )
= $true )
| ( ( in @ SV278 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3028]) ).
thf(3101,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) )
= $false )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3029]) ).
thf(3102,plain,
! [SV259: $i,SV193: $i,SV252: $i,SV303: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SV303 @ SV252 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3103,plain,
! [SV194: $i,SV253: $i,SV274: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV274 @ ( sK109_SY882 @ SV253 @ SV194 @ SV274 ) ) @ SV194 ) )
= $false )
| ( ( in @ SV274 @ SV253 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3031]) ).
thf(3104,plain,
! [SV253: $i,SV194: $i,SV304: $i,SV274: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV274 @ SV304 ) @ SV194 ) )
= $true )
| ( ( in @ SV274 @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3105,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 ) )
= $false )
| ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3033]) ).
thf(3106,plain,
! [SV253: $i,SV194: $i] :
( ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $false )
| ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3033]) ).
thf(3107,plain,
! [SV299: $i,SV253: $i,SV194: $i] :
( ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV299 ) @ SV194 )
= $false )
| ( ( ~ ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) ) )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3108,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3109,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV195 )
| ( SV275 != SV279 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3036]) ).
thf(3110,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3111,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 ) )
= $true )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3038]) ).
thf(3112,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
= $true )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3039]) ).
thf(3113,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
= $true )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3041]) ).
thf(3114,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
| ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 ) )
= $true )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3043]) ).
thf(3115,plain,
! [SV231: $i,SV243: $i,SV202: $i,SV272: $i] :
( ( ( in @ SV272 @ SV202 )
= $true )
| ( ( in @ SV272 @ SV243 )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3045]) ).
thf(3116,plain,
! [SV202: $i,SV243: $i,SV231: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV231 ) )
= $true )
| ( ( in @ SV272 @ SV243 )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3046]) ).
thf(3117,plain,
! [SV243: $i,SV231: $i,SV202: $i,SV272: $i] :
( ( ( in @ SV272 @ SV202 )
= $false )
| ( ( ~ ~ ( in @ SV272 @ SV231 ) )
= $true )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3118,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) ) )
= $true )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3048]) ).
thf(3119,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3120,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV300: $i,SV296: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
| ~ ! [SY917: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY917 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY917 @ SV300 ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY918: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY918 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY918 @ SV300 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3121,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
| ~ ! [SY919: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY919 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY919 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
| ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3052]) ).
thf(3122,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( ~ ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ ( relation_dom @ SV234 ) ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3123,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV162 ) @ SV234 ) )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3124,plain,
! [SV208: $i,SV162: $i,SV234: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ ( relation_dom @ SV234 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 ) )
= $true )
| ( ( ~ ( in @ SV280 @ SV208 ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3054]) ).
thf(3125,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) ) )
= $false )
| ( ( in @ SV263 @ SV210 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3126,plain,
! [SV263: $i,SV165: $i,SV210: $i] :
( ( ( ~ ( in @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) @ SV165 ) )
= $false )
| ( ( in @ SV263 @ SV210 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3127,plain,
! [SV210: $i,SV165: $i,SV294: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV294 ) )
= $true )
| ( ( ~ ( in @ SV294 @ SV165 ) )
= $true )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3056]) ).
thf(3128,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK110_SY868 @ SV210 @ SV165 ) )
| ~ ( in @ ( sK110_SY868 @ SV210 @ SV165 ) @ SV165 ) ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3057]) ).
thf(3129,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( ~ ( in @ SV291 @ SV165 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3130,plain,
! [SV245: $i,SV166: $i,SV285: $i,SV281: $i] :
( ( ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 )
= $false )
| ( ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 )
= $true )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3131,plain,
! [SV166: $i,SV245: $i,SV285: $i,SV281: $i] :
( ( ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV245 )
= $false )
| ( ( in @ ( ordered_pair @ SV281 @ SV285 ) @ SV166 )
= $true )
| ( ( SV166 = SV245 )
= $false )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3132,plain,
! [SV166: $i,SV245: $i] :
( ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) ) )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3061]) ).
thf(3133,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
= $false )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3134,plain,
! [SV273: $i,SV167: $i,SV246: $i] :
( ( ( in @ ( ordered_pair @ ( sK108_SY878 @ SV246 @ SV167 @ SV273 ) @ SV273 ) @ SV167 )
= $true )
| ( ( in @ SV273 @ SV246 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3063]) ).
thf(3135,plain,
! [SV246: $i,SV167: $i,SV273: $i,SV301: $i] :
( ( ( in @ ( ordered_pair @ SV301 @ SV273 ) @ SV167 )
= $false )
| ( ( in @ SV273 @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $false )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3136,plain,
! [SV246: $i,SV167: $i] :
( ( ( ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $true )
| ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3065]) ).
thf(3137,plain,
! [SV297: $i,SV246: $i,SV167: $i] :
( ( ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
| ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV297 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3138,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ! [SY915: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ SY915 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SY915 ) ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3139,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i,SV298: $i] :
( ( ( ! [SY916: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV298 @ SV171 )
| ~ ( in @ SY916 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SV298 @ SY916 ) ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3069]) ).
thf(3140,plain,
! [SV235: $i,SV214: $i,SV171: $i] :
( ( ( ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3141,plain,
! [SV235: $i,SV214: $i,SV305: $i,SV171: $i,SV295: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV295 @ SV171 )
| ~ ( in @ SV305 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SV305 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3142,plain,
! [SV175: $i,SV247: $i,SV286: $i,SV282: $i] :
( ( ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 )
= $false )
| ( ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3143,plain,
! [SV247: $i,SV175: $i,SV282: $i,SV286: $i] :
( ( ( in @ ( ordered_pair @ SV286 @ SV282 ) @ SV175 )
= $false )
| ( ( in @ ( ordered_pair @ SV282 @ SV286 ) @ SV247 )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $false )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3144,plain,
! [SV247: $i,SV175: $i] :
( ( ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) ) )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3145,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3146,plain,
! [SV238: $i,SV183: $i,SV222: $i,SV268: $i] :
( ( ( in @ SV268 @ SV222 )
= $false )
| ( ( in @ SV268 @ SV183 )
= $false )
| ( ( in @ SV268 @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3147,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3080]) ).
thf(3148,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
| ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3149,plain,
! [SV224: $i,SV186: $i,SV256: $i,SV292: $i,SV287: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3082]) ).
thf(3150,plain,
! [SV256: $i,SV224: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( ~ ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3151,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3084]) ).
thf(3152,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3084]) ).
thf(3153,plain,
! [SV187: $i,SV250: $i,SV257: $i,SV277: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) ) @ SV187 )
| ~ ( in @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) @ SV250 ) ) )
= $false )
| ( ( in @ SV277 @ SV257 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3085]) ).
thf(3154,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV306: $i,SV277: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SV306 ) @ SV187 )
| ~ ( in @ SV306 @ SV250 ) ) )
= $true )
| ( ( in @ SV277 @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3155,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) ) )
= $false )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3156,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $false )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3157,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
| ~ ( in @ SV302 @ SV250 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3088]) ).
thf(3158,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
= $true )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 )
= $true )
| ( ( in @ ( sK81_SY775 @ SV226 @ SV189 @ SV240 ) @ SV240 )
= $true )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3089]) ).
thf(3159,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
= $true )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 )
= $true )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3160,plain,
! [SV240: $i,SV189: $i,SV226: $i] :
( ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV189 )
= $true )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 )
= $true )
| ( ( ( sK81_SY775 @ SV226 @ SV189 @ SV240 )
= SV226 )
= $false )
| ( ( SV240
= ( unordered_pair @ SV189 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3161,plain,
! [SV190: $i,SV251: $i,SV258: $i,SV293: $i,SV288: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3162,plain,
! [SV258: $i,SV190: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( ~ ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3093]) ).
thf(3163,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3164,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3165,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3095]) ).
thf(3166,plain,
! [SV191: $i,SV270: $i,SV266: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 ) )
= $true )
| ( ( SV270
= ( apply @ SV191 @ SV266 ) )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3096]) ).
thf(3167,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
| ( SV270 = empty_set ) )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3097]) ).
thf(3168,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( ( SV270 != empty_set )
| ( SV270
= ( apply @ SV191 @ SV266 ) ) )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3098]) ).
thf(3169,plain,
! [SV278: $i,SV193: $i,SV252: $i,SV259: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV278 ) @ SV193 )
| ~ ( in @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV252 ) ) )
= $false )
| ( ( in @ SV278 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3099]) ).
thf(3170,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i,SV307: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV307 @ SV278 ) @ SV193 )
| ~ ( in @ SV307 @ SV252 ) ) )
= $true )
| ( ( in @ SV278 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3171,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) ) )
= $false )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3101]) ).
thf(3172,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $false )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3101]) ).
thf(3173,plain,
! [SV259: $i,SV193: $i,SV252: $i,SV303: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SV303 @ SV252 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3174,plain,
! [SV194: $i,SV253: $i,SV274: $i] :
( ( ( in @ ( ordered_pair @ SV274 @ ( sK109_SY882 @ SV253 @ SV194 @ SV274 ) ) @ SV194 )
= $true )
| ( ( in @ SV274 @ SV253 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3175,plain,
! [SV253: $i,SV194: $i,SV304: $i,SV274: $i] :
( ( ( in @ ( ordered_pair @ SV274 @ SV304 ) @ SV194 )
= $false )
| ( ( in @ SV274 @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3104]) ).
thf(3176,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 ) )
= $true )
| ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3105]) ).
thf(3177,plain,
! [SV299: $i,SV253: $i,SV194: $i] :
( ( ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 )
| ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV299 ) @ SV194 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3107]) ).
thf(3178,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV195 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3179,plain,
! [SV195: $i,SV227: $i,SV279: $i,SV275: $i] :
( ( ( SV275 != SV279 )
= $false )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3180,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV195 ) )
= $true )
| ( ( SV275 != SV279 )
= $true )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3181,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3182,plain,
! [SV227: $i,SV195: $i] :
( ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3183,plain,
! [SV227: $i,SV195: $i] :
( ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3184,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
= $true )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 )
= $true )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV241 )
= $true )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3185,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
= $true )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 )
= $true )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3186,plain,
! [SV241: $i,SV198: $i,SV229: $i] :
( ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV198 )
= $true )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 )
= $true )
| ( ( in @ ( sK82_SY777 @ SV229 @ SV198 @ SV241 ) @ SV229 )
= $false )
| ( ( SV241
= ( set_union2 @ SV198 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3187,plain,
! [SV202: $i,SV243: $i,SV231: $i,SV272: $i] :
( ( ( in @ SV272 @ SV231 )
= $false )
| ( ( in @ SV272 @ SV243 )
= $false )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3188,plain,
! [SV243: $i,SV202: $i,SV231: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV231 ) )
= $false )
| ( ( in @ SV272 @ SV202 )
= $false )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3189,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3190,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) ) )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3119]) ).
thf(3191,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV300: $i,SV296: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
| ~ ! [SY917: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY917 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY917 @ SV300 ) @ SV255 ) ) ) )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3120]) ).
thf(3192,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV296: $i] :
( ( ( ~ ( ~ ~ ! [SY918: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY918 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY918 @ SV300 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3120]) ).
thf(3193,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
| ~ ! [SY919: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY919 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY919 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3121]) ).
thf(3194,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( in @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ ( relation_dom @ SV234 ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3195,plain,
! [SV234: $i,SV162: $i,SV208: $i] :
( ( ( in @ ( ordered_pair @ ( sK90_SY758 @ SV208 @ SV162 @ SV234 ) @ SV162 ) @ SV234 )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $false )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3123]) ).
thf(3196,plain,
! [SV208: $i,SV162: $i,SV234: $i,SV280: $i] :
( ( ( in @ SV280 @ ( relation_dom @ SV234 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 ) )
= $true )
| ( ( ~ ( in @ SV280 @ SV208 ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3124]) ).
thf(3197,plain,
! [SV165: $i,SV210: $i,SV263: $i] :
( ( ( in @ SV263 @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) )
= $true )
| ( ( in @ SV263 @ SV210 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3125]) ).
thf(3198,plain,
! [SV263: $i,SV165: $i,SV210: $i] :
( ( ( in @ ( sK104_SY865 @ SV210 @ SV165 @ SV263 ) @ SV165 )
= $true )
| ( ( in @ SV263 @ SV210 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3126]) ).
thf(3199,plain,
! [SV210: $i,SV165: $i,SV294: $i,SV263: $i] :
( ( ( in @ SV263 @ SV294 )
= $false )
| ( ( ~ ( in @ SV294 @ SV165 ) )
= $true )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3200,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK110_SY868 @ SV210 @ SV165 ) )
| ~ ( in @ ( sK110_SY868 @ SV210 @ SV165 ) @ SV165 ) ) )
= $true )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3201,plain,
! [SV210: $i,SV165: $i,SV291: $i] :
( ( ( in @ SV291 @ SV165 )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( ~ ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) ) )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3129]) ).
thf(3202,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
| ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3132]) ).
thf(3203,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
= $false )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3133]) ).
thf(3204,plain,
! [SV166: $i,SV245: $i] :
( ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
= $false )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3133]) ).
thf(3205,plain,
! [SV246: $i,SV167: $i] :
( ( ( ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $false )
| ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3206,plain,
! [SV297: $i,SV246: $i,SV167: $i] :
( ( ( ~ ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV297 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3137]) ).
thf(3207,plain,
! [SV297: $i,SV246: $i,SV167: $i] :
( ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $false )
| ( ( in @ ( ordered_pair @ SV297 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3137]) ).
thf(3208,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) @ SV214 ) )
| ( SV267
!= ( ordered_pair @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) ) ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3138]) ).
thf(3209,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV308: $i,SV171: $i,SV298: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV298 @ SV171 )
| ~ ( in @ SV308 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SV298 @ SV308 ) ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3210,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ SY921 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SY921 ) ) ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3140]) ).
thf(3211,plain,
! [SV235: $i,SV214: $i,SV305: $i,SV171: $i,SV295: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV295 @ SV171 )
| ~ ( in @ SV305 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SV305 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3212,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3144]) ).
thf(3213,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3145]) ).
thf(3214,plain,
! [SV247: $i,SV175: $i] :
( ( ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3145]) ).
thf(3215,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3147]) ).
thf(3216,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3147]) ).
thf(3217,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3218,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3219,plain,
! [SV224: $i,SV186: $i,SV256: $i,SV292: $i,SV287: $i] :
( ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $false )
| ( ( ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3220,plain,
! [SV256: $i,SV224: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( ~ ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3221,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3151]) ).
thf(3222,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3152]) ).
thf(3223,plain,
! [SV187: $i,SV250: $i,SV257: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV277 @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) ) @ SV187 )
| ~ ( in @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) @ SV250 ) ) )
= $true )
| ( ( in @ SV277 @ SV257 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3153]) ).
thf(3224,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV306: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV277 @ SV306 ) @ SV187 )
| ~ ( in @ SV306 @ SV250 ) ) )
= $false )
| ( ( in @ SV277 @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3154]) ).
thf(3225,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) ) )
= $true )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3155]) ).
thf(3226,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
| ~ ( in @ SV302 @ SV250 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3157]) ).
thf(3227,plain,
! [SV190: $i,SV251: $i,SV258: $i,SV293: $i,SV288: $i] :
( ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $false )
| ( ( ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3228,plain,
! [SV258: $i,SV190: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( ~ ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3229,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3163]) ).
thf(3230,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3164]) ).
thf(3231,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( SV270
= ( apply @ SV191 @ SV266 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3232,plain,
! [SV191: $i,SV270: $i,SV266: $i] :
( ( ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV191 )
= $false )
| ( ( SV270
= ( apply @ SV191 @ SV266 ) )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $false )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3233,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( SV270
!= ( apply @ SV191 @ SV266 ) )
= $true )
| ( ( SV270 = empty_set )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3167]) ).
thf(3234,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( SV270 != empty_set )
= $true )
| ( ( SV270
= ( apply @ SV191 @ SV266 ) )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3235,plain,
! [SV278: $i,SV193: $i,SV252: $i,SV259: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV278 ) @ SV193 )
| ~ ( in @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV252 ) ) )
= $true )
| ( ( in @ SV278 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3169]) ).
thf(3236,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i,SV307: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV307 @ SV278 ) @ SV193 )
| ~ ( in @ SV307 @ SV252 ) ) )
= $false )
| ( ( in @ SV278 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3170]) ).
thf(3237,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) ) )
= $true )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3171]) ).
thf(3238,plain,
! [SV259: $i,SV193: $i,SV252: $i,SV303: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SV303 @ SV252 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3173]) ).
thf(3239,plain,
! [SV253: $i,SV194: $i] :
( ( ( ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 ) )
= $false )
| ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3240,plain,
! [SV299: $i,SV253: $i,SV194: $i] :
( ( ( ~ ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV299 ) @ SV194 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3177]) ).
thf(3241,plain,
! [SV299: $i,SV253: $i,SV194: $i] :
( ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV299 ) @ SV194 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3177]) ).
thf(3242,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( in @ SV275 @ SV195 )
= $true )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3178]) ).
thf(3243,plain,
! [SV195: $i,SV227: $i,SV279: $i,SV275: $i] :
( ( ( SV275 = SV279 )
= $true )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3179]) ).
thf(3244,plain,
! [SV227: $i,SV279: $i,SV195: $i,SV275: $i] :
( ( ( in @ SV275 @ SV195 )
= $false )
| ( ( SV275 != SV279 )
= $true )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3245,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3181]) ).
thf(3246,plain,
! [SV227: $i,SV195: $i] :
( ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) ) )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3247,plain,
! [SV243: $i,SV202: $i,SV231: $i,SV272: $i] :
( ( ( in @ SV272 @ SV231 )
= $true )
| ( ( in @ SV272 @ SV202 )
= $false )
| ( ( in @ SV272 @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3188]) ).
thf(3248,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3189]) ).
thf(3249,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3189]) ).
thf(3250,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
| ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3190]) ).
thf(3251,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV300: $i,SV296: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
| ~ ! [SY917: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY917 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY917 @ SV300 ) @ SV255 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3191]) ).
thf(3252,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV296: $i] :
( ( ( ~ ~ ! [SY918: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY918 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY918 @ SV300 ) @ SV255 ) )
| ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3192]) ).
thf(3253,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
| ~ ! [SY919: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY919 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY919 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3254,plain,
! [SV208: $i,SV234: $i,SV162: $i,SV280: $i] :
( ( ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 )
= $false )
| ( ( in @ SV280 @ ( relation_dom @ SV234 ) )
= $false )
| ( ( ~ ( in @ SV280 @ SV208 ) )
= $true )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3196]) ).
thf(3255,plain,
! [SV210: $i,SV263: $i,SV165: $i,SV294: $i] :
( ( ( in @ SV294 @ SV165 )
= $false )
| ( ( in @ SV263 @ SV294 )
= $false )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3256,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK110_SY868 @ SV210 @ SV165 ) )
| ~ ( in @ ( sK110_SY868 @ SV210 @ SV165 ) @ SV165 ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3257,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) )
| ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3201]) ).
thf(3258,plain,
! [SV166: $i,SV245: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3202]) ).
thf(3259,plain,
! [SV166: $i,SV245: $i] :
( ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3202]) ).
thf(3260,plain,
! [SV166: $i,SV245: $i] :
( ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
= $false )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3203]) ).
thf(3261,plain,
! [SV167: $i,SV246: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK115_SY881 @ SV246 @ SV167 ) @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $false )
| ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3205]) ).
thf(3262,plain,
! [SV297: $i,SV246: $i,SV167: $i] :
( ( ( ~ ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV297 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3206]) ).
thf(3263,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) @ SV214 ) )
| ( SV267
!= ( ordered_pair @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) ) ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3208]) ).
thf(3264,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV308: $i,SV171: $i,SV298: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV298 @ SV171 )
| ~ ( in @ SV308 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SV298 @ SV308 ) ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3209]) ).
thf(3265,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ~ ! [SY921: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ SY921 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SY921 ) ) ) )
= $true )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3266,plain,
! [SV235: $i,SV214: $i,SV305: $i,SV171: $i,SV295: $i] :
( ( ( ~ ~ ( ~ ( in @ SV295 @ SV171 )
| ~ ( in @ SV305 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SV305 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3211]) ).
thf(3267,plain,
! [SV175: $i,SV247: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3212]) ).
thf(3268,plain,
! [SV247: $i,SV175: $i] :
( ( ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3212]) ).
thf(3269,plain,
! [SV175: $i,SV247: $i] :
( ( ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
= $false )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3213]) ).
thf(3270,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $true )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3215]) ).
thf(3271,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $true )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV238 )
= $true )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3216]) ).
thf(3272,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) ) )
= $true )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3217]) ).
thf(3273,plain,
! [SV256: $i,SV224: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3274,plain,
! [SV256: $i,SV224: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV186 )
| ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3220]) ).
thf(3275,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3221]) ).
thf(3276,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3277,plain,
! [SV187: $i,SV250: $i,SV257: $i,SV277: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV277 @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) ) @ SV187 )
| ~ ( in @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) @ SV250 ) )
= $false )
| ( ( in @ SV277 @ SV257 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3223]) ).
thf(3278,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV306: $i,SV277: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV277 @ SV306 ) @ SV187 )
| ~ ( in @ SV306 @ SV250 ) )
= $true )
| ( ( in @ SV277 @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3224]) ).
thf(3279,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) ) )
= $false )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3225]) ).
thf(3280,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 ) )
= $true )
| ( ( ~ ( in @ SV302 @ SV250 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3226]) ).
thf(3281,plain,
! [SV258: $i,SV190: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3282,plain,
! [SV258: $i,SV190: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( ~ ( in @ SV288 @ SV251 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3228]) ).
thf(3283,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3229]) ).
thf(3284,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3285,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( SV270
= ( apply @ SV191 @ SV266 ) )
= $false )
| ( ( SV270 = empty_set )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3286,plain,
! [SV266: $i,SV191: $i,SV270: $i] :
( ( ( SV270 = empty_set )
= $false )
| ( ( SV270
= ( apply @ SV191 @ SV266 ) )
= $true )
| ( ( in @ SV266 @ ( relation_dom @ SV191 ) )
= $true )
| ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3287,plain,
! [SV278: $i,SV193: $i,SV252: $i,SV259: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV278 ) @ SV193 )
| ~ ( in @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV252 ) )
= $false )
| ( ( in @ SV278 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3235]) ).
thf(3288,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i,SV307: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV307 @ SV278 ) @ SV193 )
| ~ ( in @ SV307 @ SV252 ) )
= $true )
| ( ( in @ SV278 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3236]) ).
thf(3289,plain,
! [SV259: $i,SV193: $i,SV252: $i] :
( ( ( ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) ) )
= $false )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3290,plain,
! [SV259: $i,SV193: $i,SV252: $i,SV303: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 ) )
= $true )
| ( ( ~ ( in @ SV303 @ SV252 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3291,plain,
! [SV253: $i,SV194: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ ( sK116_SY885 @ SV253 @ SV194 ) ) @ SV194 ) )
= $false )
| ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3239]) ).
thf(3292,plain,
! [SV299: $i,SV253: $i,SV194: $i] :
( ( ( ~ ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV299 ) @ SV194 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3240]) ).
thf(3293,plain,
! [SV227: $i,SV195: $i,SV279: $i,SV275: $i] :
( ( ( SV275 = SV279 )
= $false )
| ( ( in @ SV275 @ SV195 )
= $false )
| ( ( in @ ( ordered_pair @ SV275 @ SV279 ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $false )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3294,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3245]) ).
thf(3295,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
| ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 ) )
= $false )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3296,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $true )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3248]) ).
thf(3297,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $true )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3249]) ).
thf(3298,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3250]) ).
thf(3299,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3250]) ).
thf(3300,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV300: $i,SV296: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 ) )
= $true )
| ( ( ~ ! [SY917: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY917 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY917 @ SV300 ) @ SV255 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3251]) ).
thf(3301,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV296: $i] :
( ( ( ~ ~ ! [SY918: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY918 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY918 @ SV300 ) @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3252]) ).
thf(3302,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3253]) ).
thf(3303,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ! [SY919: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY919 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY919 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3253]) ).
thf(3304,plain,
! [SV162: $i,SV234: $i,SV208: $i,SV280: $i] :
( ( ( in @ SV280 @ SV208 )
= $false )
| ( ( in @ SV280 @ ( relation_dom @ SV234 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV280 @ SV162 ) @ SV234 )
= $false )
| ( ( in @ SV162 @ ( relation_image @ SV234 @ SV208 ) )
= $true )
| ( ( relation @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3305,plain,
! [SV210: $i,SV165: $i] :
( ( ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK110_SY868 @ SV210 @ SV165 ) ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3256]) ).
thf(3306,plain,
! [SV165: $i,SV210: $i] :
( ( ( ~ ( in @ ( sK110_SY868 @ SV210 @ SV165 ) @ SV165 ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3256]) ).
thf(3307,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3257]) ).
thf(3308,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3257]) ).
thf(3309,plain,
! [SV166: $i,SV245: $i] :
( ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV245 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK91_SY782 @ SV245 @ SV166 ) @ ( sK95_SY897 @ SV166 @ SV245 ) ) @ SV166 )
= $true )
| ( ( SV166 = SV245 )
= $true )
| ( ( relation @ SV245 )
= $false )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3258]) ).
thf(3310,plain,
! [SV167: $i,SV246: $i] :
( ( ( in @ ( ordered_pair @ ( sK115_SY881 @ SV246 @ SV167 ) @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $true )
| ( ( in @ ( sK84_SY787 @ SV167 @ SV246 ) @ SV246 )
= $true )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3261]) ).
thf(3311,plain,
! [SV297: $i,SV246: $i,SV167: $i] :
( ( ( ! [SY881: $i] :
~ ( in @ ( ordered_pair @ SY881 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV297 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3312,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) @ SV214 ) )
| ( SV267
!= ( ordered_pair @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3263]) ).
thf(3313,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV308: $i,SV171: $i,SV298: $i] :
( ( ( ~ ~ ( ~ ( in @ SV298 @ SV171 )
| ~ ( in @ SV308 @ SV214 ) )
| ( SV267
!= ( ordered_pair @ SV298 @ SV308 ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3264]) ).
thf(3314,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ! [SY921: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ SY921 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SY921 ) ) ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3315,plain,
! [SV235: $i,SV214: $i,SV305: $i,SV171: $i,SV295: $i] :
( ( ( ~ ~ ( ~ ( in @ SV295 @ SV171 )
| ~ ( in @ SV305 @ SV214 ) ) )
= $true )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SV305 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3266]) ).
thf(3316,plain,
! [SV175: $i,SV247: $i] :
( ( ( in @ ( ordered_pair @ ( sK96_SY899 @ SV247 @ SV175 ) @ ( sK92_SY792 @ SV175 @ SV247 ) ) @ SV175 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK92_SY792 @ SV175 @ SV247 ) @ ( sK96_SY899 @ SV247 @ SV175 ) ) @ SV247 )
= $true )
| ( ( SV247
= ( relation_inverse @ SV175 ) )
= $true )
| ( ( relation @ SV247 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3267]) ).
thf(3317,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
| ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3272]) ).
thf(3318,plain,
! [SV224: $i,SV256: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV186 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3273]) ).
thf(3319,plain,
! [SV186: $i,SV256: $i,SV224: $i,SV292: $i,SV287: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3273]) ).
thf(3320,plain,
! [SV256: $i,SV224: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV186 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3321,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3275]) ).
thf(3322,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3275]) ).
thf(3323,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3324,plain,
! [SV187: $i,SV250: $i,SV257: $i,SV277: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV277 @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) ) @ SV187 ) )
= $false )
| ( ( in @ SV277 @ SV257 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3277]) ).
thf(3325,plain,
! [SV277: $i,SV187: $i,SV250: $i,SV257: $i] :
( ( ( ~ ( in @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) @ SV250 ) )
= $false )
| ( ( in @ SV277 @ SV257 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3277]) ).
thf(3326,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV306: $i,SV277: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV277 @ SV306 ) @ SV187 ) )
= $true )
| ( ( ~ ( in @ SV306 @ SV250 ) )
= $true )
| ( ( in @ SV277 @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3278]) ).
thf(3327,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) ) @ SV187 )
| ~ ( in @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) @ SV250 ) ) )
= $false )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3279]) ).
thf(3328,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( ~ ( in @ SV302 @ SV250 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3329,plain,
! [SV190: $i,SV258: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( ~ ( in @ SV288 @ SV251 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3330,plain,
! [SV251: $i,SV258: $i,SV190: $i,SV293: $i,SV288: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3331,plain,
! [SV258: $i,SV190: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( ~ ( in @ SV288 @ SV251 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3332,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3283]) ).
thf(3333,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3283]) ).
thf(3334,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3284]) ).
thf(3335,plain,
! [SV278: $i,SV193: $i,SV252: $i,SV259: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV278 ) @ SV193 ) )
= $false )
| ( ( in @ SV278 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3287]) ).
thf(3336,plain,
! [SV278: $i,SV193: $i,SV252: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV252 ) )
= $false )
| ( ( in @ SV278 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3287]) ).
thf(3337,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i,SV307: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV307 @ SV278 ) @ SV193 ) )
= $true )
| ( ( ~ ( in @ SV307 @ SV252 ) )
= $true )
| ( ( in @ SV278 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3288]) ).
thf(3338,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ SV252 ) ) )
= $false )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3289]) ).
thf(3339,plain,
! [SV259: $i,SV193: $i,SV252: $i,SV303: $i] :
( ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( ~ ( in @ SV303 @ SV252 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3290]) ).
thf(3340,plain,
! [SV253: $i,SV194: $i] :
( ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ ( sK116_SY885 @ SV253 @ SV194 ) ) @ SV194 )
= $true )
| ( ( in @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV253 )
= $true )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3291]) ).
thf(3341,plain,
! [SV299: $i,SV253: $i,SV194: $i] :
( ( ( ! [SY885: $i] :
~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SY885 ) @ SV194 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV299 ) @ SV194 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3292]) ).
thf(3342,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3294]) ).
thf(3343,plain,
! [SV227: $i,SV195: $i] :
( ( ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3294]) ).
thf(3344,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) ) )
= $false )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3295]) ).
thf(3345,plain,
! [SV227: $i,SV195: $i] :
( ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $false )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3295]) ).
thf(3346,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV243 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3347,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) ) )
= $true )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3298]) ).
thf(3348,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV300: $i,SV296: $i] :
( ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $false )
| ( ( ~ ! [SY917: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY917 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY917 @ SV300 ) @ SV255 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3300]) ).
thf(3349,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV296: $i] :
( ( ( ~ ! [SY918: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY918 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY918 @ SV300 ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3301]) ).
thf(3350,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3302]) ).
thf(3351,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ! [SY919: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY919 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY919 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3303]) ).
thf(3352,plain,
! [SV210: $i,SV165: $i] :
( ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK110_SY868 @ SV210 @ SV165 ) )
= $true )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3305]) ).
thf(3353,plain,
! [SV165: $i,SV210: $i] :
( ( ( in @ ( sK110_SY868 @ SV210 @ SV165 ) @ SV165 )
= $true )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV210 )
= $true )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3306]) ).
thf(3354,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) ) )
= $true )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3307]) ).
thf(3355,plain,
! [SV167: $i,SV246: $i,SV297: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK119_SY881 @ SV297 @ SV246 @ SV167 ) @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV297 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3311]) ).
thf(3356,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) @ SV214 ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3357,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV267: $i] :
( ( ( SV267
!= ( ordered_pair @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3358,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV308: $i,SV171: $i,SV298: $i] :
( ( ( ~ ~ ( ~ ( in @ SV298 @ SV171 )
| ~ ( in @ SV308 @ SV214 ) ) )
= $true )
| ( ( SV267
!= ( ordered_pair @ SV298 @ SV308 ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3313]) ).
thf(3359,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) ) ) ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3314]) ).
thf(3360,plain,
! [SV235: $i,SV214: $i,SV305: $i,SV171: $i,SV295: $i] :
( ( ( ~ ( ~ ( in @ SV295 @ SV171 )
| ~ ( in @ SV305 @ SV214 ) ) )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SV305 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3315]) ).
thf(3361,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3317]) ).
thf(3362,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( ~ ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 ) )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3317]) ).
thf(3363,plain,
! [SV224: $i,SV256: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( in @ SV292 @ SV186 )
= $true )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3318]) ).
thf(3364,plain,
! [SV186: $i,SV256: $i,SV224: $i,SV292: $i,SV287: $i] :
( ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 )
= $true )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3319]) ).
thf(3365,plain,
! [SV256: $i,SV224: $i,SV287: $i,SV186: $i,SV292: $i] :
( ( ( in @ SV292 @ SV186 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3320]) ).
thf(3366,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3321]) ).
thf(3367,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3368,plain,
! [SV187: $i,SV250: $i,SV257: $i,SV277: $i] :
( ( ( in @ ( ordered_pair @ SV277 @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) ) @ SV187 )
= $true )
| ( ( in @ SV277 @ SV257 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3324]) ).
thf(3369,plain,
! [SV277: $i,SV187: $i,SV250: $i,SV257: $i] :
( ( ( in @ ( sK111_SY888 @ SV257 @ SV250 @ SV187 @ SV277 ) @ SV250 )
= $true )
| ( ( in @ SV277 @ SV257 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3325]) ).
thf(3370,plain,
! [SV257: $i,SV250: $i,SV187: $i,SV306: $i,SV277: $i] :
( ( ( in @ ( ordered_pair @ SV277 @ SV306 ) @ SV187 )
= $false )
| ( ( ~ ( in @ SV306 @ SV250 ) )
= $true )
| ( ( in @ SV277 @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3326]) ).
thf(3371,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) ) @ SV187 )
| ~ ( in @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3327]) ).
thf(3372,plain,
! [SV257: $i,SV187: $i,SV250: $i,SV302: $i] :
( ( ( in @ SV302 @ SV250 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( ~ ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3328]) ).
thf(3373,plain,
! [SV190: $i,SV258: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( in @ SV288 @ SV251 )
= $true )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3329]) ).
thf(3374,plain,
! [SV251: $i,SV258: $i,SV190: $i,SV293: $i,SV288: $i] :
( ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 )
= $true )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3330]) ).
thf(3375,plain,
! [SV258: $i,SV190: $i,SV293: $i,SV251: $i,SV288: $i] :
( ( ( in @ SV288 @ SV251 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3376,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3332]) ).
thf(3377,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) ) )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3378,plain,
! [SV278: $i,SV193: $i,SV252: $i,SV259: $i] :
( ( ( in @ ( ordered_pair @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV278 ) @ SV193 )
= $true )
| ( ( in @ SV278 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3335]) ).
thf(3379,plain,
! [SV278: $i,SV193: $i,SV252: $i,SV259: $i] :
( ( ( in @ ( sK112_SY892 @ SV259 @ SV252 @ SV193 @ SV278 ) @ SV252 )
= $true )
| ( ( in @ SV278 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3336]) ).
thf(3380,plain,
! [SV259: $i,SV252: $i,SV193: $i,SV278: $i,SV307: $i] :
( ( ( in @ ( ordered_pair @ SV307 @ SV278 ) @ SV193 )
= $false )
| ( ( ~ ( in @ SV307 @ SV252 ) )
= $true )
| ( ( in @ SV278 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3381,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ SV252 ) ) )
= $true )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3338]) ).
thf(3382,plain,
! [SV259: $i,SV193: $i,SV252: $i,SV303: $i] :
( ( ( in @ SV303 @ SV252 )
= $false )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( ~ ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3339]) ).
thf(3383,plain,
! [SV299: $i,SV253: $i,SV194: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ ( sK121_SY885 @ SV299 @ SV253 @ SV194 ) ) @ SV194 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV299 ) @ SV194 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3341]) ).
thf(3384,plain,
! [SV227: $i,SV195: $i] :
( ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3342]) ).
thf(3385,plain,
! [SV227: $i,SV195: $i] :
( ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK86_SY748 @ SV195 @ SV227 ) @ ( sK89_SY887 @ SV227 @ SV195 ) ) @ SV227 )
= $true )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3343]) ).
thf(3386,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) ) )
= $true )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3344]) ).
thf(3387,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
| ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3388,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV296: $i] :
( ( ( ! [SY917: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY917 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY917 @ SV300 ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3348]) ).
thf(3389,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV296: $i] :
( ( ( ! [SY918: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SY918 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY918 @ SV300 ) @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3349]) ).
thf(3390,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3350]) ).
thf(3391,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3392,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ! [SY868: $i] :
~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SY868 )
| ~ ( in @ SY868 @ SV165 ) ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3354]) ).
thf(3393,plain,
! [SV167: $i,SV246: $i,SV297: $i] :
( ( ( in @ ( ordered_pair @ ( sK119_SY881 @ SV297 @ SV246 @ SV167 ) @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $true )
| ( ( in @ ( ordered_pair @ SV297 @ ( sK84_SY787 @ SV167 @ SV246 ) ) @ SV167 )
= $false )
| ( ( SV246
= ( relation_rng @ SV167 ) )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3355]) ).
thf(3394,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ~ ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) @ SV214 ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3356]) ).
thf(3395,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV267: $i] :
( ( ( SV267
= ( ordered_pair @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3357]) ).
thf(3396,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV308: $i,SV171: $i,SV298: $i] :
( ( ( ~ ( ~ ( in @ SV298 @ SV171 )
| ~ ( in @ SV308 @ SV214 ) ) )
= $false )
| ( ( SV267
!= ( ordered_pair @ SV298 @ SV308 ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3358]) ).
thf(3397,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) ) ) ) )
= $true )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3359]) ).
thf(3398,plain,
! [SV235: $i,SV214: $i,SV305: $i,SV171: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ SV171 )
| ~ ( in @ SV305 @ SV214 ) )
= $true )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SV305 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3360]) ).
thf(3399,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $true )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3361]) ).
thf(3400,plain,
! [SV238: $i,SV183: $i,SV222: $i] :
( ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $true )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV183 )
= $false )
| ( ( in @ ( sK80_SY772 @ SV222 @ SV183 @ SV238 ) @ SV222 )
= $false )
| ( ( SV238
= ( set_intersection2 @ SV183 @ SV222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3362]) ).
thf(3401,plain,
! [SV256: $i,SV186: $i,SV224: $i,SV292: $i,SV287: $i] :
( ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV224 )
= $false )
| ( ( in @ SV292 @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ SV287 @ SV292 ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $false )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3365]) ).
thf(3402,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3403,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
| ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 ) )
= $false )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3367]) ).
thf(3404,plain,
! [SV257: $i,SV187: $i,SV277: $i,SV250: $i,SV306: $i] :
( ( ( in @ SV306 @ SV250 )
= $false )
| ( ( in @ ( ordered_pair @ SV277 @ SV306 ) @ SV187 )
= $false )
| ( ( in @ SV277 @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3405,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) ) @ SV187 )
| ~ ( in @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) @ SV250 ) )
= $false )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3406,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) )
| ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3372]) ).
thf(3407,plain,
! [SV258: $i,SV251: $i,SV190: $i,SV293: $i,SV288: $i] :
( ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV190 )
= $false )
| ( ( in @ SV288 @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ SV288 @ SV293 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $false )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3375]) ).
thf(3408,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3376]) ).
thf(3409,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
| ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 ) )
= $false )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3410,plain,
! [SV259: $i,SV193: $i,SV278: $i,SV252: $i,SV307: $i] :
( ( ( in @ SV307 @ SV252 )
= $false )
| ( ( in @ ( ordered_pair @ SV307 @ SV278 ) @ SV193 )
= $false )
| ( ( in @ SV278 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3380]) ).
thf(3411,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ SV252 ) )
= $false )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3412,plain,
! [SV303: $i,SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) )
| ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3382]) ).
thf(3413,plain,
! [SV299: $i,SV253: $i,SV194: $i] :
( ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ ( sK121_SY885 @ SV299 @ SV253 @ SV194 ) ) @ SV194 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK85_SY816 @ SV194 @ SV253 ) @ SV299 ) @ SV194 )
= $false )
| ( ( SV253
= ( relation_dom @ SV194 ) )
= $true )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3383]) ).
thf(3414,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
| ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) ) )
= $false )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3415,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3387]) ).
thf(3416,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3387]) ).
thf(3417,plain,
! [SV203: $i,SV300: $i,SV255: $i,SV262: $i,SV296: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) @ SV300 ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3388]) ).
thf(3418,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV310: $i,SV296: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SV310 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SV310 @ SV300 ) @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3419,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3390]) ).
thf(3420,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3390]) ).
thf(3421,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3422,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) )
| ~ ( in @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) @ SV165 ) ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3392]) ).
thf(3423,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) @ SV214 ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3394]) ).
thf(3424,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV308: $i,SV171: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV171 )
| ~ ( in @ SV308 @ SV214 ) )
= $true )
| ( ( SV267
!= ( ordered_pair @ SV298 @ SV308 ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3396]) ).
thf(3425,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) ) ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3426,plain,
! [SV235: $i,SV214: $i,SV305: $i,SV171: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ SV171 ) )
= $true )
| ( ( ~ ( in @ SV305 @ SV214 ) )
= $true )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SV305 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3398]) ).
thf(3427,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3402]) ).
thf(3428,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3402]) ).
thf(3429,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) ) )
= $false )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3403]) ).
thf(3430,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $false )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3403]) ).
thf(3431,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) ) @ SV187 ) )
= $false )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3405]) ).
thf(3432,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( ~ ( in @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) @ SV250 ) )
= $false )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3405]) ).
thf(3433,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3406]) ).
thf(3434,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3406]) ).
thf(3435,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3408]) ).
thf(3436,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3408]) ).
thf(3437,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) ) )
= $false )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3409]) ).
thf(3438,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $false )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3409]) ).
thf(3439,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 ) )
= $false )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3411]) ).
thf(3440,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ SV252 ) )
= $false )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3411]) ).
thf(3441,plain,
! [SV303: $i,SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3412]) ).
thf(3442,plain,
! [SV303: $i,SV259: $i,SV193: $i,SV252: $i] :
( ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $false )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3412]) ).
thf(3443,plain,
! [SV227: $i,SV195: $i] :
( ( ( ~ ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 ) )
= $false )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3414]) ).
thf(3444,plain,
! [SV227: $i,SV195: $i] :
( ( ( ( sK86_SY748 @ SV195 @ SV227 )
!= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3414]) ).
thf(3445,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $true )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3415]) ).
thf(3446,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( ~ ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 ) )
= $true )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3416]) ).
thf(3447,plain,
! [SV203: $i,SV300: $i,SV255: $i,SV262: $i,SV296: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV296 @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) @ SV300 ) @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3417]) ).
thf(3448,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV310: $i,SV296: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV296 @ SV310 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SV310 @ SV300 ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3418]) ).
thf(3449,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3419]) ).
thf(3450,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3421]) ).
thf(3451,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) )
| ~ ( in @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) @ SV165 ) ) )
= $true )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3422]) ).
thf(3452,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3423]) ).
thf(3453,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i] :
( ( ( ~ ( in @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) @ SV214 ) )
= $false )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3423]) ).
thf(3454,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV308: $i,SV171: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV171 ) )
= $true )
| ( ( ~ ( in @ SV308 @ SV214 ) )
= $true )
| ( ( SV267
!= ( ordered_pair @ SV298 @ SV308 ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3424]) ).
thf(3455,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) @ SV214 ) ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3425]) ).
thf(3456,plain,
! [SV235: $i,SV171: $i,SV214: $i] :
( ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3425]) ).
thf(3457,plain,
! [SV235: $i,SV214: $i,SV305: $i,SV171: $i,SV295: $i] :
( ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ~ ( in @ SV305 @ SV214 ) )
= $true )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SV305 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3426]) ).
thf(3458,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3427]) ).
thf(3459,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3428]) ).
thf(3460,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) ) )
= $true )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3429]) ).
thf(3461,plain,
! [SV257: $i,SV187: $i,SV250: $i] :
( ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) ) @ SV187 )
= $true )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3431]) ).
thf(3462,plain,
! [SV250: $i,SV187: $i,SV257: $i] :
( ( ( in @ ( sK117_SY891 @ SV257 @ SV187 @ SV250 ) @ SV250 )
= $true )
| ( ( in @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3432]) ).
thf(3463,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3433]) ).
thf(3464,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3435]) ).
thf(3465,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3436]) ).
thf(3466,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) ) )
= $true )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3437]) ).
thf(3467,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( in @ ( ordered_pair @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $true )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3439]) ).
thf(3468,plain,
! [SV252: $i,SV193: $i,SV259: $i] :
( ( ( in @ ( sK118_SY895 @ SV259 @ SV193 @ SV252 ) @ SV252 )
= $true )
| ( ( in @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3440]) ).
thf(3469,plain,
! [SV303: $i,SV259: $i,SV193: $i,SV252: $i] :
( ( ( ~ ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3441]) ).
thf(3470,plain,
! [SV227: $i,SV195: $i] :
( ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $true )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3443]) ).
thf(3471,plain,
! [SV227: $i,SV195: $i] :
( ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $true )
| ( ( in @ ( sK86_SY748 @ SV195 @ SV227 ) @ SV195 )
= $false )
| ( ( ( sK86_SY748 @ SV195 @ SV227 )
= ( sK89_SY887 @ SV227 @ SV195 ) )
= $false )
| ( ( SV227
= ( identity_relation @ SV195 ) )
= $true )
| ( ( relation @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3444]) ).
thf(3472,plain,
! [SV243: $i,SV202: $i,SV231: $i] :
( ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV202 )
= $false )
| ( ( in @ ( sK83_SY779 @ SV231 @ SV202 @ SV243 ) @ SV231 )
= $true )
| ( ( SV243
= ( set_difference @ SV202 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3473,plain,
! [SV203: $i,SV300: $i,SV255: $i,SV262: $i,SV296: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV296 @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) @ SV300 ) @ SV255 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3474,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV310: $i,SV296: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV296 @ SV310 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SV310 @ SV300 ) @ SV255 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3448]) ).
thf(3475,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3449]) ).
thf(3476,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3450]) ).
thf(3477,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) )
| ~ ( in @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) @ SV165 ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3451]) ).
thf(3478,plain,
! [SV171: $i,SV214: $i,SV267: $i,SV235: $i] :
( ( ( in @ ( sK106_SY870 @ SV235 @ SV267 @ SV214 @ SV171 ) @ SV171 )
= $true )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3452]) ).
thf(3479,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV171: $i] :
( ( ( in @ ( sK113_SY915 @ SV171 @ SV214 @ SV267 @ SV235 ) @ SV214 )
= $true )
| ( ( in @ SV267 @ SV235 )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3453]) ).
thf(3480,plain,
! [SV235: $i,SV267: $i,SV214: $i,SV308: $i,SV171: $i,SV298: $i] :
( ( ( in @ SV298 @ SV171 )
= $false )
| ( ( ~ ( in @ SV308 @ SV214 ) )
= $true )
| ( ( SV267
!= ( ordered_pair @ SV298 @ SV308 ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3481,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ~ ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) @ SV214 ) ) )
= $true )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3455]) ).
thf(3482,plain,
! [SV235: $i,SV171: $i,SV214: $i] :
( ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) ) )
= $true )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3456]) ).
thf(3483,plain,
! [SV235: $i,SV171: $i,SV295: $i,SV214: $i,SV305: $i] :
( ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SV295 @ SV305 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3457]) ).
thf(3484,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
| ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
= $false )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3485,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ! [SY891: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SY891 ) @ SV187 )
| ~ ( in @ SY891 @ SV250 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3486,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
= $false )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3466]) ).
thf(3487,plain,
! [SV303: $i,SV259: $i,SV193: $i,SV252: $i] :
( ( ( ! [SY895: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ SY895 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ SY895 @ SV252 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3469]) ).
thf(3488,plain,
! [SV203: $i,SV300: $i,SV255: $i,SV262: $i,SV296: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV296 @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) ) @ SV203 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3473]) ).
thf(3489,plain,
! [SV296: $i,SV203: $i,SV300: $i,SV255: $i,SV262: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) @ SV300 ) @ SV255 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3473]) ).
thf(3490,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV310: $i,SV296: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV296 @ SV310 ) @ SV203 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV310 @ SV300 ) @ SV255 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3474]) ).
thf(3491,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3475]) ).
thf(3492,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3493,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( ~ ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3477]) ).
thf(3494,plain,
! [SV165: $i,SV210: $i,SV291: $i] :
( ( ( ~ ( in @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) @ SV165 ) )
= $false )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3477]) ).
thf(3495,plain,
! [SV235: $i,SV267: $i,SV171: $i,SV298: $i,SV214: $i,SV308: $i] :
( ( ( in @ SV308 @ SV214 )
= $false )
| ( ( in @ SV298 @ SV171 )
= $false )
| ( ( SV267
!= ( ordered_pair @ SV298 @ SV308 ) )
= $true )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3480]) ).
thf(3496,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) @ SV214 ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3497,plain,
! [SV305: $i,SV295: $i,SV235: $i,SV171: $i,SV214: $i] :
( ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( ~ ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) ) )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3483]) ).
thf(3498,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 ) )
= $false )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3484]) ).
thf(3499,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 ) )
= $false )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3484]) ).
thf(3500,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) ) @ SV187 )
| ~ ( in @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) @ SV250 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3485]) ).
thf(3501,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 ) )
= $false )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3486]) ).
thf(3502,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 ) )
= $false )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3486]) ).
thf(3503,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV303: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ SV252 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3487]) ).
thf(3504,plain,
! [SV203: $i,SV300: $i,SV255: $i,SV262: $i,SV296: $i] :
( ( ( in @ ( ordered_pair @ SV296 @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) ) @ SV203 )
= $true )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3488]) ).
thf(3505,plain,
! [SV296: $i,SV203: $i,SV300: $i,SV255: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK122_SY917 @ SV262 @ SV255 @ SV300 @ SV203 @ SV296 ) @ SV300 ) @ SV255 )
= $true )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3489]) ).
thf(3506,plain,
! [SV262: $i,SV255: $i,SV300: $i,SV203: $i,SV310: $i,SV296: $i] :
( ( ( in @ ( ordered_pair @ SV296 @ SV310 ) @ SV203 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV310 @ SV300 ) @ SV255 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(3507,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3491]) ).
thf(3508,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV309: $i] :
( ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( ~ ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) ) )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3492]) ).
thf(3509,plain,
! [SV291: $i,SV210: $i,SV165: $i] :
( ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) )
= $true )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3493]) ).
thf(3510,plain,
! [SV165: $i,SV210: $i,SV291: $i] :
( ( ( in @ ( sK123_SY868 @ SV291 @ SV210 @ SV165 ) @ SV165 )
= $true )
| ( ( in @ ( sK76_SY709 @ SV165 @ SV210 ) @ SV291 )
= $false )
| ( ( in @ SV291 @ SV165 )
= $false )
| ( ( SV210
= ( union @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3494]) ).
thf(3511,plain,
! [SV235: $i,SV214: $i,SV171: $i,SV308: $i,SV298: $i,SV267: $i] :
( ( ( SV267
= ( ordered_pair @ SV298 @ SV308 ) )
= $false )
| ( ( in @ SV298 @ SV171 )
= $false )
| ( ( in @ SV308 @ SV214 )
= $false )
| ( ( in @ SV267 @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3495]) ).
thf(3512,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3496]) ).
thf(3513,plain,
! [SV235: $i,SV214: $i,SV171: $i] :
( ( ( ~ ( in @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) @ SV214 ) )
= $false )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3496]) ).
thf(3514,plain,
! [SV295: $i,SV305: $i,SV235: $i,SV214: $i,SV171: $i] :
( ( ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) )
| ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3515,plain,
! [SV224: $i,SV186: $i,SV256: $i] :
( ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $true )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3498]) ).
thf(3516,plain,
! [SV256: $i,SV186: $i,SV224: $i] :
( ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $true )
| ( ( in @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_SY834 @ SV224 @ SV186 @ SV256 ) @ ( sK101_SY904 @ SV256 @ SV186 @ SV224 ) ) @ SV224 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV186 @ SV224 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3499]) ).
thf(3517,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) ) @ SV187 )
| ~ ( in @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) @ SV250 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3500]) ).
thf(3518,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $true )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3501]) ).
thf(3519,plain,
! [SV258: $i,SV251: $i,SV190: $i] :
( ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $true )
| ( ( in @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ SV251 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK98_SY844 @ SV190 @ SV251 @ SV258 ) @ ( sK102_SY906 @ SV258 @ SV251 @ SV190 ) ) @ SV190 )
= $false )
| ( ( SV258
= ( relation_dom_restriction @ SV190 @ SV251 ) )
= $true )
| ( ( relation @ SV258 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3502]) ).
thf(3520,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV303: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ SV252 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3503]) ).
thf(3521,plain,
! [SV262: $i,SV203: $i,SV296: $i,SV255: $i,SV300: $i,SV310: $i] :
( ( ( in @ ( ordered_pair @ SV310 @ SV300 ) @ SV255 )
= $false )
| ( ( in @ ( ordered_pair @ SV296 @ SV310 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV296 @ SV300 ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $false )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3522,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(3523,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
| ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3508]) ).
thf(3524,plain,
! [SV171: $i,SV214: $i,SV235: $i] :
( ( ( in @ ( sK114_SY876 @ SV235 @ SV214 @ SV171 ) @ SV171 )
= $true )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3512]) ).
thf(3525,plain,
! [SV235: $i,SV214: $i,SV171: $i] :
( ( ( in @ ( sK120_SY921 @ SV171 @ SV214 @ SV235 ) @ SV214 )
= $true )
| ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $true )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3513]) ).
thf(3526,plain,
! [SV295: $i,SV305: $i,SV235: $i,SV214: $i,SV171: $i] :
( ( ( ~ ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3514]) ).
thf(3527,plain,
! [SV295: $i,SV305: $i,SV235: $i,SV171: $i,SV214: $i] :
( ( ( in @ ( sK79_SY765 @ SV214 @ SV171 @ SV235 ) @ SV235 )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3514]) ).
thf(3528,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) ) @ SV187 )
| ~ ( in @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) @ SV250 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3517]) ).
thf(3529,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV303: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
| ~ ( in @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ SV252 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(3530,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) ) @ SV203 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3522]) ).
thf(3531,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3522]) ).
thf(3532,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3523]) ).
thf(3533,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3523]) ).
thf(3534,plain,
! [SV295: $i,SV305: $i,SV235: $i,SV214: $i,SV171: $i] :
( ( ( ~ ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) ) )
= $true )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3526]) ).
thf(3535,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) ) @ SV187 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3528]) ).
thf(3536,plain,
! [SV250: $i,SV187: $i,SV257: $i,SV302: $i] :
( ( ( ~ ( in @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) @ SV250 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3528]) ).
thf(3537,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV303: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3529]) ).
thf(3538,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV303: $i] :
( ( ( ~ ( in @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ SV252 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3529]) ).
thf(3539,plain,
! [SV262: $i,SV203: $i,SV255: $i] :
( ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) ) @ SV203 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3530]) ).
thf(3540,plain,
! [SV255: $i,SV203: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK124_SY920 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3531]) ).
thf(3541,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3532]) ).
thf(3542,plain,
! [SV295: $i,SV305: $i,SV235: $i,SV214: $i,SV171: $i] :
( ( ( ! [SY876: $i] :
~ ~ ! [SY877: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY876 @ SV171 )
| ~ ( in @ SY877 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ SY876 @ SY877 ) ) ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3543,plain,
! [SV302: $i,SV257: $i,SV187: $i,SV250: $i] :
( ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) ) @ SV187 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3535]) ).
thf(3544,plain,
! [SV250: $i,SV187: $i,SV257: $i,SV302: $i] :
( ( ( in @ ( sK125_SY891 @ SV302 @ SV257 @ SV187 @ SV250 ) @ SV250 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK87_SY839 @ SV250 @ SV187 @ SV257 ) @ SV302 ) @ SV187 )
= $false )
| ( ( in @ SV302 @ SV250 )
= $false )
| ( ( SV257
= ( relation_inverse_image @ SV187 @ SV250 ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3536]) ).
thf(3545,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV303: $i] :
( ( ( in @ ( ordered_pair @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $true )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3537]) ).
thf(3546,plain,
! [SV252: $i,SV193: $i,SV259: $i,SV303: $i] :
( ( ( in @ ( sK126_SY895 @ SV303 @ SV259 @ SV193 @ SV252 ) @ SV252 )
= $true )
| ( ( in @ ( ordered_pair @ SV303 @ ( sK88_SY849 @ SV252 @ SV193 @ SV259 ) ) @ SV193 )
= $false )
| ( ( in @ SV303 @ SV252 )
= $false )
| ( ( SV259
= ( relation_image @ SV193 @ SV252 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3538]) ).
thf(3547,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ! [SY920: $i] :
~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SY920 ) @ SV203 )
| ~ ( in @ ( ordered_pair @ SY920 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3541]) ).
thf(3548,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ~ ~ ! [SY922: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ SY922 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SY922 ) ) ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3542]) ).
thf(3549,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3547]) ).
thf(3550,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ~ ! [SY922: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ SY922 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SY922 ) ) ) )
= $true )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3548]) ).
thf(3551,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3549]) ).
thf(3552,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ! [SY922: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ SY922 @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SY922 ) ) ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3550]) ).
thf(3553,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3551]) ).
thf(3554,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) ) ) ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3552]) ).
thf(3555,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) ) @ SV203 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3553]) ).
thf(3556,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV309: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3553]) ).
thf(3557,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) ) ) ) )
= $true )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3554]) ).
thf(3558,plain,
! [SV309: $i,SV262: $i,SV203: $i,SV255: $i] :
( ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) ) @ SV203 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3555]) ).
thf(3559,plain,
! [SV255: $i,SV203: $i,SV262: $i,SV309: $i] :
( ( ( in @ ( ordered_pair @ ( sK128_SY920 @ SV309 @ SV262 @ SV203 @ SV255 ) @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK105_SY861 @ SV255 @ SV203 @ SV262 ) @ SV309 ) @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV309 @ ( sK107_SY912 @ SV262 @ SV203 @ SV255 ) ) @ SV255 )
= $false )
| ( ( SV262
= ( relation_composition @ SV203 @ SV255 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3556]) ).
thf(3560,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) @ SV214 ) )
| ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) ) ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3557]) ).
thf(3561,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) @ SV214 ) ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3560]) ).
thf(3562,plain,
! [SV305: $i,SV295: $i,SV235: $i,SV171: $i,SV214: $i] :
( ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
!= ( ordered_pair @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3560]) ).
thf(3563,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ~ ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) @ SV214 ) ) )
= $true )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3561]) ).
thf(3564,plain,
! [SV305: $i,SV295: $i,SV235: $i,SV171: $i,SV214: $i] :
( ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) ) )
= $true )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3562]) ).
thf(3565,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
| ~ ( in @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) @ SV214 ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(3566,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3565]) ).
thf(3567,plain,
! [SV295: $i,SV305: $i,SV235: $i,SV214: $i,SV171: $i] :
( ( ( ~ ( in @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) @ SV214 ) )
= $false )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3565]) ).
thf(3568,plain,
! [SV171: $i,SV214: $i,SV235: $i,SV305: $i,SV295: $i] :
( ( ( in @ ( sK127_SY876 @ SV295 @ SV305 @ SV235 @ SV214 @ SV171 ) @ SV171 )
= $true )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3566]) ).
thf(3569,plain,
! [SV295: $i,SV305: $i,SV235: $i,SV214: $i,SV171: $i] :
( ( ( in @ ( sK129_SY922 @ SV171 @ SV214 @ SV235 @ SV305 @ SV295 ) @ SV214 )
= $true )
| ( ( in @ SV305 @ SV214 )
= $false )
| ( ( in @ SV295 @ SV171 )
= $false )
| ( ( ( sK79_SY765 @ SV214 @ SV171 @ SV235 )
= ( ordered_pair @ SV295 @ SV305 ) )
= $false )
| ( ( SV235
= ( cartesian_product2 @ SV171 @ SV214 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3567]) ).
thf(3570,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1968,3569,3568,3564,3559,3558,3546,3545,3544,3543,3540,3539,3533,3527,3525,3524,3521,3519,3518,3516,3515,3511,3510,3509,3505,3504,3482,3479,3478,3472,3471,3470,3468,3467,3465,3464,3462,3461,3459,3458,3445,3442,3438,3434,3430,3420,3413,3410,3407,3404,3401,3400,3399,3395,3393,3385,3384,3379,3378,3374,3373,3369,3368,3364,3363,3353,3352,3346,3345,3340,3333,3322,3316,3310,3309,3308,3304,3299,3296,3293,3286,3285,3271,3270,3269,3268,3260,3259,3255,3247,3243,3242,3241,3232,3231,3218,3214,3207,3204,3198,3197,3195,3194,3187,3186,3185,3184,3182,3175,3174,3172,3160,3159,3158,3156,3146,3143,3142,3135,3134,3131,3130,3115,3106,3078,3077,3076,3066,3049,3044,3042,3040,3020,3018,3016,3006,3000,2999,2994,2990,2977,2969,2968,2964,2963,2962,2949,2941,2940,2939,2918,2917,2907,2894,2876,2854,2847,2796,2791,2787,2786,2777,2776,2764,2732,2731,2727,2726,2698,2697,2679,2660,2628,2627,2594,2593,2576,2575,2542,2541,2540,2533,2508,2505,2469,2460,2459,2458,2419,2411,2385,2384,2383,2382,2381,2380,2368,2367,2356,2347,2346,2295,2252,2235,2224,2211,2186,2181,2171,2164,2125,2058,2005,2004,1990,1989,1984,1983,1981,1980,1979,1978,1977,1976,1975,1974,1973,1972,1971,1970,1969]) ).
thf(3571,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3570,1933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.18 % Computer : n013.cluster.edu
% 0.14/0.18 % Model : x86_64 x86_64
% 0.14/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.18 % Memory : 8046.5625MB
% 0.14/0.18 % OS : Linux 6.8.0-71-generic
% 0.14/0.18 % CPULimit : 300
% 0.14/0.18 % WCLimit : 300
% 0.14/0.18 % DateTime : Tue Oct 6 15:04:51 UTC 2026
% 0.14/0.18 % CPUTime :
% 0.14/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 97.14/16.48 .
% 97.14/16.48
% 97.14/16.48 No.of.Axioms: 70
% 97.14/16.48
% 97.14/16.48 Length.of.Defs: 0
% 97.14/16.48
% 97.14/16.48 Contains.Choice.Funs: false
% 97.14/16.48 .....................................................................................................................................
% 97.14/16.48
% 97.14/16.48 ********************************
% 97.14/16.48 * All subproblems solved! *
% 97.14/16.48 ********************************
% 97.14/16.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:72,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3570,loop_count:0,foatp_calls:1,translation:fof_full)
% 97.14/16.48
% 97.14/16.48 %**** Beginning of derivation protocol ****
% 97.14/16.48 % SZS output start CNFRefutation
% See solution above
% 16.46/16.50
% 16.46/16.50 %**** End of derivation protocol ****
% 16.46/16.50 %**** no. of clauses in derivation: 3427 ****
% 16.46/16.50 %**** clause counter: 3570 ****
% 16.46/16.50
% 16.46/16.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:72,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3570,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------