%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP123^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n009.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 10:24:11 AM UTC 2026
% Result : Theorem 108.60s 18.32s
% Output : CNFRefutation 108.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 186
% Syntax : Number of formulae : 2500 (1072 unt; 0 typ; 0 def)
% Number of atoms : 16955 (6826 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 32412 (5598 ~;4669 |; 84 &;21602 @)
% ( 0 <=>; 459 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 395 ( 395 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 78 usr; 5 con; 0-6 aty)
% Number of variables : 6778 ( 78 ^;6688 !; 12 ?;6778 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_set_a,type,
set_a: $tType ).
thf(tp_abel_semigroup_a,type,
abel_semigroup_a: ( a > a > a ) > $o ).
thf(tp_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(tp_condit1001553558elow_a,type,
condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
thf(tp_condit1627435690bove_a,type,
condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
thf(tp_finite40241356em_a_a,type,
finite40241356em_a_a: ( a > a > a ) > $o ).
thf(tp_greatest_a,type,
greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(tp_inf,type,
inf: a > a > a ).
thf(tp_lattic1885654924_set_a,type,
lattic1885654924_set_a: ( a > a > a ) > $o ).
thf(tp_lattic655834328_set_a,type,
lattic655834328_set_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(tp_lattice_a,type,
lattice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > $o ) > ( a > a > a ) > $o ).
thf(tp_least_a,type,
least_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(tp_less,type,
less: a > a > $o ).
thf(tp_less_eq,type,
less_eq: a > a > $o ).
thf(tp_max_a,type,
max_a: ( a > a > $o ) > a > a > a ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_min_a,type,
min_a: ( a > a > $o ) > a > a > a ).
thf(tp_modula1144073633_aux_a,type,
modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(tp_modula1373251614_aux_a,type,
modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(tp_modula1376131916tice_a,type,
modula1376131916tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(tp_modula1727524044comp_a,type,
modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
thf(tp_modula17988509_aux_a,type,
modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(tp_modula1936294176_aux_a,type,
modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(tp_modula1962211574trib_a,type,
modula1962211574trib_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(tp_modula397570059tice_a,type,
modula397570059tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(tp_modula581031071_aux_a,type,
modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(tp_ordering_a,type,
ordering_a: ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(tp_sK10_SY911,type,
sK10_SY911: a > a > a > a ).
thf(tp_sK11_SY850,type,
sK11_SY850: a > ( a > $o ) > a ).
thf(tp_sK12_SY913,type,
sK12_SY913: a > a > a > a ).
thf(tp_sK13_SY821,type,
sK13_SY821: ( a > $o ) > a > ( a > $o ) > a ).
thf(tp_sK14_SY916,type,
sK14_SY916: a > a > a > a ).
thf(tp_sK15_SY860,type,
sK15_SY860: ( a > $o ) > a > ( a > $o ) > a ).
thf(tp_sK16_SY918,type,
sK16_SY918: a > a > a > a ).
thf(tp_sK17_SY915,type,
sK17_SY915: a > set_a > a ).
thf(tp_sK18_SY917,type,
sK18_SY917: a > set_a > a ).
thf(tp_sK19_SY633,type,
sK19_SY633: set_a > a ).
thf(tp_sK1_SY803,type,
sK1_SY803: a > set_a > a ).
thf(tp_sK20_SY666,type,
sK20_SY666: a > a > ( a > a > a ) > a ).
thf(tp_sK21_SY677,type,
sK21_SY677: a > a > ( a > a > a ) > a ).
thf(tp_sK22_SY720,type,
sK22_SY720: set_a > a ).
thf(tp_sK23_SY920,type,
sK23_SY920: a > a > ( a > a > a ) > a ).
thf(tp_sK24_SY921,type,
sK24_SY921: a > a > ( a > a > a ) > a ).
thf(tp_sK25_SY876,type,
sK25_SY876: a > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK26_SY898,type,
sK26_SY898: a > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK27_SY876,type,
sK27_SY876: a > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK28_SY898,type,
sK28_SY898: a > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK29_SY903,type,
sK29_SY903: a > ( a > $o ) > a ).
thf(tp_sK2_SY819,type,
sK2_SY819: a > set_a > a ).
thf(tp_sK30_SY668,type,
sK30_SY668: a > a > ( a > a > a ) > a ).
thf(tp_sK31_SY679,type,
sK31_SY679: a > a > ( a > a > a ) > a ).
thf(tp_sK32_SY906,type,
sK32_SY906: a > a > ( a > $o ) > a ).
thf(tp_sK33_SY633,type,
sK33_SY633: a > set_a > a ).
thf(tp_sK34_SY927,type,
sK34_SY927: ( a > a > a ) > a > a > a ).
thf(tp_sK35_SY929,type,
sK35_SY929: ( a > a > a ) > a > a > a ).
thf(tp_sK36_SY720,type,
sK36_SY720: a > set_a > a ).
thf(tp_sK37_SY633,type,
sK37_SY633: a > set_a > a ).
thf(tp_sK38_SY932,type,
sK38_SY932: ( a > a > a ) > a > a > a ).
thf(tp_sK39_SY933,type,
sK39_SY933: a > a > ( a > a > a ) > a ).
thf(tp_sK3_SY664,type,
sK3_SY664: a > a > ( a > a > a ) > a ).
thf(tp_sK40_SY720,type,
sK40_SY720: a > set_a > a ).
thf(tp_sK41_SY904,type,
sK41_SY904: a > ( a > $o ) > a ).
thf(tp_sK42_SY904,type,
sK42_SY904: a > ( a > $o ) > a ).
thf(tp_sK43_SY907,type,
sK43_SY907: a > a > ( a > $o ) > a ).
thf(tp_sK44_SY907,type,
sK44_SY907: a > a > ( a > $o ) > a ).
thf(tp_sK4_SY675,type,
sK4_SY675: a > a > ( a > a > a ) > a ).
thf(tp_sK5_SX3,type,
sK5_SX3: a > a > a > a ).
thf(tp_sK6_SX3,type,
sK6_SX3: a > a > a > a ).
thf(tp_sK7_SY804,type,
sK7_SY804: a > ( a > $o ) > a ).
thf(tp_sK8_SY909,type,
sK8_SY909: a > a > ( a > a > a ) > a ).
thf(tp_sK9_SY910,type,
sK9_SY910: ( a > a > a ) > a > a > a ).
thf(tp_semigroup_a,type,
semigroup_a: ( a > a > a ) > $o ).
thf(tp_semilattice_a,type,
semilattice_a: ( a > a > a ) > $o ).
thf(tp_semilattice_order_a,type,
semilattice_order_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(tp_set_gr1491433118Than_a,type,
set_gr1491433118Than_a: ( a > a > $o ) > a > a > set_a ).
thf(tp_sup,type,
sup: a > a > a ).
thf(tp_x,type,
x: a ).
thf(tp_y,type,
y: a ).
thf(tp_z,type,
z: a ).
thf(1,axiom,
! [A: a,B: a] : ( condit1001553558elow_a @ less_eq @ ( set_gr1491433118Than_a @ less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_local_Obdd__below__Ioo) ).
thf(2,axiom,
! [A3: set_a,M4: a] :
( ! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( less_eq @ X3 @ M4 ) )
=> ( condit1627435690bove_a @ less_eq @ A3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_local_Obdd__aboveI) ).
thf(3,axiom,
! [A3: set_a,M3: a] :
( ! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( less_eq @ M3 @ X3 ) )
=> ( condit1001553558elow_a @ less_eq @ A3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_local_Obdd__belowI) ).
thf(4,axiom,
! [A3: set_a] :
( ( condit1627435690bove_a @ less_eq @ A3 )
= ( ? [M2: a] :
! [X2: a] :
( ( member_a @ X2 @ A3 )
=> ( less_eq @ X2 @ M2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_local_Obdd__above__def) ).
thf(5,axiom,
! [A3: set_a] :
( ( condit1001553558elow_a @ less_eq @ A3 )
= ( ? [M: a] :
! [X2: a] :
( ( member_a @ X2 @ A3 )
=> ( less_eq @ M @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_local_Obdd__below__def) ).
thf(35,axiom,
lattic1885654924_set_a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_local_OInf__fin_Osemilattice__set__axioms) ).
thf(36,axiom,
lattic1885654924_set_a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_local_OSup__fin_Osemilattice__set__axioms) ).
thf(45,axiom,
abel_semigroup_a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_local_Oinf_Oabel__semigroup__axioms) ).
thf(46,axiom,
abel_semigroup_a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_local_Osup_Oabel__semigroup__axioms) ).
thf(47,axiom,
semilattice_a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_local_Oinf_Osemilattice__axioms) ).
thf(48,axiom,
semilattice_a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_local_Osup_Osemilattice__axioms) ).
thf(49,axiom,
semigroup_a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_local_Oinf_Osemigroup__axioms) ).
thf(50,axiom,
semigroup_a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_local_Osup_Osemigroup__axioms) ).
thf(54,axiom,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_local_Oc__a) ).
thf(55,axiom,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_local_Ob__a) ).
thf(56,axiom,
finite40241356em_a_a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_local_Ocomp__fun__idem__inf) ).
thf(57,axiom,
finite40241356em_a_a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_local_Ocomp__fun__idem__sup) ).
thf(58,axiom,
ordering_a @ less_eq @ less,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_local_Oorder_Oordering__axioms) ).
thf(59,axiom,
semilattice_order_a @ inf @ less_eq @ less,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_local_Oinf_Osemilattice__order__axioms) ).
thf(66,axiom,
! [A: a,B: a,C: a] :
( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_local_Oa__aux__def) ).
thf(67,axiom,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_local_Ob__aux__def) ).
thf(68,axiom,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_local_Oc__aux__def) ).
thf(69,axiom,
! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
=> ( modula1727524044comp_a @ less_eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_local_OM5__lattice__incomp) ).
thf(70,axiom,
lattic655834328_set_a @ inf @ less_eq @ less,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_local_OInf__fin_Osemilattice__order__set__axioms) ).
thf(71,axiom,
! [C: a,A: a,B: a] :
( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
= ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_local_Oe__c__a__b) ).
thf(72,axiom,
! [B: a,C: a,A: a] :
( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
= ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_local_Oe__b__c__a) ).
thf(73,axiom,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_local_Oe__aux__def) ).
thf(74,axiom,
! [C: a,A: a,B: a] :
( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ C @ ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_local_Oc__meet__e) ).
thf(75,axiom,
! [B: a,A: a,C: a] :
( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ B @ ( sup @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_local_Ob__meet__e) ).
thf(76,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_local_Oa__meet__e) ).
thf(77,axiom,
! [C: a,A: a,B: a] :
( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
= ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_local_Od__c__a__b) ).
thf(78,axiom,
! [B: a,C: a,A: a] :
( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
= ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_local_Od__b__c__a) ).
thf(79,axiom,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_local_Od__aux__def) ).
thf(80,axiom,
! [B: a,A: a,C: a] :
( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ B @ ( inf @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_local_Ob__join__d) ).
thf(81,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_local_Oa__join__d) ).
thf(82,axiom,
! [P: a > $o,X: a] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X @ Y4 ) )
=> ( ( least_a @ less_eq @ P )
= X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_local_OLeast__equality) ).
thf(83,axiom,
! [P: a > $o,X: a,Q: a > $o] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X @ Y4 ) )
=> ( ! [X3: a] :
( ( P @ X3 )
=> ( ! [Y5: a] :
( ( P @ Y5 )
=> ( less_eq @ X3 @ Y5 ) )
=> ( Q @ X3 ) ) )
=> ( Q @ ( least_a @ less_eq @ P ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_local_OLeastI2__order) ).
thf(84,axiom,
! [P: a > $o,Z2: a] :
( ? [X4: a] :
( ( P @ X4 )
& ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X4 @ Y4 ) )
& ! [Y4: a] :
( ( ( P @ Y4 )
& ! [Ya: a] :
( ( P @ Ya )
=> ( less_eq @ Y4 @ Ya ) ) )
=> ( Y4 = X4 ) ) )
=> ( ( P @ Z2 )
=> ( less_eq @ ( least_a @ less_eq @ P ) @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_local_OLeast1__le) ).
thf(85,axiom,
! [P: a > $o] :
( ? [X4: a] :
( ( P @ X4 )
& ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X4 @ Y4 ) )
& ! [Y4: a] :
( ( ( P @ Y4 )
& ! [Ya: a] :
( ( P @ Ya )
=> ( less_eq @ Y4 @ Ya ) ) )
=> ( Y4 = X4 ) ) )
=> ( P @ ( least_a @ less_eq @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_local_OLeast1I) ).
thf(86,axiom,
! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ B )
= ( inf @ B @ C ) )
& ( ( inf @ C @ A )
= ( inf @ B @ C ) )
& ( ( sup @ A @ B )
= ( sup @ B @ C ) )
& ( ( sup @ C @ A )
= ( sup @ B @ C ) )
& ( less @ ( inf @ A @ B ) @ ( sup @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_local_OM5__lattice__def) ).
thf(87,axiom,
! [X: a,Y: a] :
( ( sup @ X @ ( inf @ X @ Y ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_local_Osup__inf__absorb) ).
thf(88,axiom,
! [X: a,Y: a] :
( ( inf @ X @ ( sup @ X @ Y ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_local_Oinf__sup__absorb) ).
thf(89,axiom,
! [B: a,C: a,A: a] :
( ( less_eq @ ( sup @ B @ C ) @ A )
= ( ( less_eq @ B @ A )
& ( less_eq @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_local_Osup_Obounded__iff) ).
thf(90,axiom,
! [X: a,Y: a,Z2: a] :
( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
= ( ( less_eq @ X @ Z2 )
& ( less_eq @ Y @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_local_Ole__sup__iff) ).
thf(91,axiom,
! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
= ( ( less_eq @ X @ Y )
& ( less_eq @ X @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_local_Ole__inf__iff) ).
thf(92,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_local_Oinf_Obounded__iff) ).
thf(93,axiom,
! [A: a,B: a,C: a] :
( ( modula1962211574trib_a @ inf @ less @ sup @ A @ B @ C )
= ( less @ ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_local_Ono__distrib__def) ).
thf(94,axiom,
! [A: a,B: a,C: a] :
( ( modula397570059tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ C )
= ( inf @ B @ C ) )
& ( less @ A @ B )
& ( ( sup @ A @ C )
= ( sup @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_local_ON5__lattice__def) ).
thf(95,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min_a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min_a @ less_eq @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_local_Omin__def) ).
thf(96,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_local_Omax__def) ).
thf(97,axiom,
! [P: a > $o,X: a] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ Y4 @ X ) )
=> ( ( greatest_a @ less_eq @ P )
= X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_local_OGreatest__equality) ).
thf(98,axiom,
! [P: a > $o,X: a,Q: a > $o] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ Y4 @ X ) )
=> ( ! [X3: a] :
( ( P @ X3 )
=> ( ! [Y5: a] :
( ( P @ Y5 )
=> ( less_eq @ Y5 @ X3 ) )
=> ( Q @ X3 ) ) )
=> ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_local_OGreatestI2__order) ).
thf(99,axiom,
! [X: a,Y: a] :
( ( sup @ X @ ( sup @ X @ Y ) )
= ( sup @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_local_Osup__left__idem) ).
thf(100,axiom,
! [X: a] :
( ( sup @ X @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_local_Osup__idem) ).
thf(101,axiom,
! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_local_Osup_Oright__idem) ).
thf(102,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_local_Osup_Oleft__idem) ).
thf(103,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_local_Osup_Oidem) ).
thf(104,axiom,
! [X: a,Y: a] :
( ( inf @ ( inf @ X @ Y ) @ Y )
= ( inf @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_local_Oinf__right__idem) ).
thf(105,axiom,
! [X: a,Y: a] :
( ( inf @ X @ ( inf @ X @ Y ) )
= ( inf @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_local_Oinf__left__idem) ).
thf(106,axiom,
! [X: a] :
( ( inf @ X @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_local_Oinf__idem) ).
thf(107,axiom,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_local_Oinf_Oright__idem) ).
thf(108,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_local_Oinf_Oleft__idem) ).
thf(109,axiom,
! [A: a] :
( ( inf @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_local_Oinf_Oidem) ).
thf(110,axiom,
! [X: a] : ( less_eq @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_local_Oorder__refl) ).
thf(111,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_local_Oorder_Orefl) ).
thf(112,axiom,
! [X: a,Y: a] :
( ( modula1727524044comp_a @ less_eq @ X @ Y )
= ( ~ ( less_eq @ X @ Y )
& ~ ( less_eq @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_local_Oincomp__def) ).
thf(113,axiom,
! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_local_Odistrib__sup__le) ).
thf(114,axiom,
! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_local_Odistrib__inf__le) ).
thf(115,axiom,
! [X: a,Y: a,Z2: a] :
( ! [X3: a,Y4: a,Z3: a] :
( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
= ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
=> ( ( inf @ X @ ( sup @ Y @ Z2 ) )
= ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_local_Odistrib__imp2) ).
thf(116,axiom,
! [X: a,Y: a,Z2: a] :
( ! [X3: a,Y4: a,Z3: a] :
( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
= ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
=> ( ( sup @ X @ ( inf @ Y @ Z2 ) )
= ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_local_Odistrib__imp1) ).
thf(117,axiom,
! [B: a,A: a] :
( ( less @ B @ A )
= ( ( A
= ( sup @ A @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_local_Osup_Ostrict__order__iff) ).
thf(118,axiom,
! [C: a,B: a,A: a] :
( ( less @ C @ B )
=> ( less @ C @ ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_local_Osup_Ostrict__coboundedI2) ).
thf(119,axiom,
! [C: a,A: a,B: a] :
( ( less @ C @ A )
=> ( less @ C @ ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_local_Osup_Ostrict__coboundedI1) ).
thf(120,axiom,
! [B: a,C: a,A: a] :
( ( less @ ( sup @ B @ C ) @ A )
=> ~ ( ( less @ B @ A )
=> ~ ( less @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_local_Osup_Ostrict__boundedE) ).
thf(121,axiom,
! [X: a,B: a,A: a] :
( ( less @ X @ B )
=> ( less @ X @ ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_local_Oless__supI2) ).
thf(122,axiom,
! [X: a,A: a,B: a] :
( ( less @ X @ A )
=> ( less @ X @ ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_local_Oless__supI1) ).
thf(123,axiom,
! [B: a,X: a,A: a] :
( ( less @ B @ X )
=> ( less @ ( inf @ A @ B ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_local_Oless__infI2) ).
thf(124,axiom,
! [A: a,X: a,B: a] :
( ( less @ A @ X )
=> ( less @ ( inf @ A @ B ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_local_Oless__infI1) ).
thf(125,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( A
= ( inf @ A @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_local_Oinf_Ostrict__order__iff) ).
thf(126,axiom,
! [B: a,C: a,A: a] :
( ( less @ B @ C )
=> ( less @ ( inf @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_local_Oinf_Ostrict__coboundedI2) ).
thf(127,axiom,
! [A: a,C: a,B: a] :
( ( less @ A @ C )
=> ( less @ ( inf @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_local_Oinf_Ostrict__coboundedI1) ).
thf(128,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ ( inf @ B @ C ) )
=> ~ ( ( less @ A @ B )
=> ~ ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_local_Oinf_Ostrict__boundedE) ).
thf(129,axiom,
! [F: a > a > a,X: a,Y: a] :
( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
=> ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
=> ( ! [X3: a,Y4: a,Z3: a] :
( ( less_eq @ Y4 @ X3 )
=> ( ( less_eq @ Z3 @ X3 )
=> ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
=> ( ( sup @ X @ Y )
= ( F @ X @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_local_Osup__unique) ).
thf(130,axiom,
! [A: a,C: a,B: a,D: a] :
( ( less_eq @ A @ C )
=> ( ( less_eq @ B @ D )
=> ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_local_Osup__mono) ).
thf(131,axiom,
! [Y: a,X: a,Z2: a] :
( ( less_eq @ Y @ X )
=> ( ( less_eq @ Z2 @ X )
=> ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_local_Osup__least) ).
thf(132,axiom,
! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_local_Osup__ge2) ).
thf(133,axiom,
! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_local_Osup__ge1) ).
thf(134,axiom,
! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( sup @ X @ Y )
= Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_local_Osup__absorb2) ).
thf(135,axiom,
! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ( ( sup @ X @ Y )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_local_Osup__absorb1) ).
thf(136,axiom,
! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( A
= ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_local_Osup_Oorder__iff) ).
thf(137,axiom,
! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_local_Osup_OorderI) ).
thf(138,axiom,
! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( A
= ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_local_Osup_OorderE) ).
thf(139,axiom,
! [C: a,A: a,D: a,B: a] :
( ( less_eq @ C @ A )
=> ( ( less_eq @ D @ B )
=> ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_local_Osup_Omono) ).
thf(140,axiom,
! [C: a,B: a,A: a] :
( ( less_eq @ C @ B )
=> ( less_eq @ C @ ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_local_Osup_OcoboundedI2) ).
thf(141,axiom,
! [C: a,A: a,B: a] :
( ( less_eq @ C @ A )
=> ( less_eq @ C @ ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_local_Osup_OcoboundedI1) ).
thf(142,axiom,
! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_local_Osup_Ocobounded2) ).
thf(143,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_local_Osup_Ocobounded1) ).
thf(144,axiom,
! [B: a,A: a,C: a] :
( ( less_eq @ B @ A )
=> ( ( less_eq @ C @ A )
=> ( less_eq @ ( sup @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_local_Osup_OboundedI) ).
thf(145,axiom,
! [B: a,C: a,A: a] :
( ( less_eq @ ( sup @ B @ C ) @ A )
=> ~ ( ( less_eq @ B @ A )
=> ~ ( less_eq @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_local_Osup_OboundedE) ).
thf(146,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_local_Osup_Oabsorb__iff2) ).
thf(147,axiom,
! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( ( sup @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_local_Osup_Oabsorb__iff1) ).
thf(148,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_local_Osup_Oabsorb2) ).
thf(149,axiom,
! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( ( sup @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_local_Osup_Oabsorb1) ).
thf(150,axiom,
! [X: a,B: a,A: a] :
( ( less_eq @ X @ B )
=> ( less_eq @ X @ ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_local_Ole__supI2) ).
thf(151,axiom,
! [X: a,A: a,B: a] :
( ( less_eq @ X @ A )
=> ( less_eq @ X @ ( sup @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_local_Ole__supI1) ).
thf(152,axiom,
! [A: a,X: a,B: a] :
( ( less_eq @ A @ X )
=> ( ( less_eq @ B @ X )
=> ( less_eq @ ( sup @ A @ B ) @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_local_Ole__supI) ).
thf(153,axiom,
! [A: a,B: a,X: a] :
( ( less_eq @ ( sup @ A @ B ) @ X )
=> ~ ( ( less_eq @ A @ X )
=> ~ ( less_eq @ B @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_local_Ole__supE) ).
thf(154,axiom,
! [X: a,Y: a] :
( ( less_eq @ X @ Y )
= ( ( sup @ X @ Y )
= Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_local_Ole__iff__sup) ).
thf(155,axiom,
! [B: a,X: a,A: a] :
( ( less_eq @ B @ X )
=> ( less_eq @ ( inf @ A @ B ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_local_Ole__infI2) ).
thf(156,axiom,
! [A: a,X: a,B: a] :
( ( less_eq @ A @ X )
=> ( less_eq @ ( inf @ A @ B ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_local_Ole__infI1) ).
thf(157,axiom,
! [X: a,A: a,B: a] :
( ( less_eq @ X @ A )
=> ( ( less_eq @ X @ B )
=> ( less_eq @ X @ ( inf @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_local_Ole__infI) ).
thf(158,axiom,
! [X: a,A: a,B: a] :
( ( less_eq @ X @ ( inf @ A @ B ) )
=> ~ ( ( less_eq @ X @ A )
=> ~ ( less_eq @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_local_Ole__infE) ).
thf(159,axiom,
! [X: a,Y: a] :
( ( less_eq @ X @ Y )
= ( ( inf @ X @ Y )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_local_Ole__iff__inf) ).
thf(160,axiom,
! [F: a > a > a,X: a,Y: a] :
( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
=> ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
=> ( ! [X3: a,Y4: a,Z3: a] :
( ( less_eq @ X3 @ Y4 )
=> ( ( less_eq @ X3 @ Z3 )
=> ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
=> ( ( inf @ X @ Y )
= ( F @ X @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_local_Oinf__unique) ).
thf(161,axiom,
! [A: a,C: a,B: a,D: a] :
( ( less_eq @ A @ C )
=> ( ( less_eq @ B @ D )
=> ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_local_Oinf__mono) ).
thf(162,axiom,
! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_local_Oinf__le2) ).
thf(163,axiom,
! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_local_Oinf__le1) ).
thf(164,axiom,
! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ Y )
=> ( ( less_eq @ X @ Z2 )
=> ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_local_Oinf__greatest) ).
thf(165,axiom,
! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ( ( inf @ X @ Y )
= Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_local_Oinf__absorb2) ).
thf(166,axiom,
! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( inf @ X @ Y )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_local_Oinf__absorb1) ).
thf(167,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_local_Oinf_Oorder__iff) ).
thf(168,axiom,
! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_local_Oinf_OorderI) ).
thf(169,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_local_Oinf_OorderE) ).
thf(170,axiom,
! [B: a,C: a,A: a] :
( ( less_eq @ B @ C )
=> ( less_eq @ ( inf @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_local_Oinf_OcoboundedI2) ).
thf(171,axiom,
! [A: a,C: a,B: a] :
( ( less_eq @ A @ C )
=> ( less_eq @ ( inf @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_local_Oinf_OcoboundedI1) ).
thf(172,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_local_Oinf_Ocobounded2) ).
thf(173,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_local_Oinf_Ocobounded1) ).
thf(174,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_local_Oinf_OboundedI) ).
thf(175,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_local_Oinf_OboundedE) ).
thf(176,axiom,
! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( ( inf @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_local_Oinf_Oabsorb__iff2) ).
thf(177,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_local_Oinf_Oabsorb__iff1) ).
thf(178,axiom,
! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( ( inf @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_local_Oinf_Oabsorb2) ).
thf(179,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_local_Oinf_Oabsorb1) ).
thf(180,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_local_Oorder_Ostrict__trans2) ).
thf(181,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_local_Oorder_Ostrict__trans1) ).
thf(182,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_local_Oorder_Ostrict__implies__order) ).
thf(183,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_local_Oorder_Ostrict__iff__order) ).
thf(184,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_local_Oorder_Oorder__iff__strict) ).
thf(185,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ A @ B )
=> ( less @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_local_Oorder_Onot__eq__order__implies__strict) ).
thf(186,axiom,
! [X: a,Y: a,Z2: a] :
( ( less @ X @ Y )
=> ( ( less_eq @ Y @ Z2 )
=> ( less @ X @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_local_Oless__le__trans) ).
thf(187,axiom,
! [X: a,Y: a] :
( ( less @ X @ Y )
= ( ( less_eq @ X @ Y )
& ~ ( less_eq @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_local_Oless__le__not__le) ).
thf(188,axiom,
! [X: a,Y: a] :
( ( less @ X @ Y )
= ( ( less_eq @ X @ Y )
& ( X != Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_local_Oless__le) ).
thf(189,axiom,
! [X: a,Y: a] :
( ( less @ X @ Y )
=> ( less_eq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_local_Oless__imp__le) ).
thf(190,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( A != B )
=> ( less @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_local_Ole__neq__trans) ).
thf(191,axiom,
! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ Y )
=> ( ( less @ Y @ Z2 )
=> ( less @ X @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_local_Ole__less__trans) ).
thf(192,axiom,
! [X: a,Y: a] :
( ( less_eq @ X @ Y )
= ( ( less @ X @ Y )
| ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_local_Ole__less) ).
thf(193,axiom,
! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( less @ X @ Y )
| ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_local_Ole__imp__less__or__eq) ).
thf(194,axiom,
! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ~ ( less @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_local_OleD) ).
thf(195,axiom,
! [B: a,A: a,C: a] :
( ( less @ B @ A )
=> ( ( less_eq @ C @ B )
=> ( less @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_local_Odual__order_Ostrict__trans2) ).
thf(196,axiom,
! [B: a,A: a,C: a] :
( ( less_eq @ B @ A )
=> ( ( less @ C @ B )
=> ( less @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_local_Odual__order_Ostrict__trans1) ).
thf(197,axiom,
! [B: a,A: a] :
( ( less @ B @ A )
=> ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_local_Odual__order_Ostrict__implies__order) ).
thf(198,axiom,
! [B: a,A: a] :
( ( less @ B @ A )
= ( ( less_eq @ B @ A )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_local_Odual__order_Ostrict__iff__order) ).
thf(199,axiom,
! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( ( less @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_local_Odual__order_Oorder__iff__strict) ).
thf(200,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ B @ A )
=> ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_local_Odual__order_Onot__eq__order__implies__strict) ).
thf(201,axiom,
! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( ~ ( less @ X @ Y ) )
= ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_local_Oantisym__conv2) ).
thf(205,axiom,
! [X: a,Y: a] :
( ~ ( less @ X @ Y )
=> ( ( less_eq @ X @ Y )
= ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_local_Oantisym__conv1) ).
thf(206,axiom,
! [X: a,Y: a,Z2: a] :
( ( sup @ X @ ( sup @ Y @ Z2 ) )
= ( sup @ Y @ ( sup @ X @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_local_Osup__left__commute) ).
thf(207,axiom,
! [X: a,Y: a] :
( ( sup @ X @ Y )
= ( sup @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_local_Osup__commute) ).
thf(208,axiom,
! [X: a,Y: a,Z2: a] :
( ( sup @ ( sup @ X @ Y ) @ Z2 )
= ( sup @ X @ ( sup @ Y @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_local_Osup__assoc) ).
thf(209,axiom,
! [B: a,A: a,C: a] :
( ( sup @ B @ ( sup @ A @ C ) )
= ( sup @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_local_Osup_Oleft__commute) ).
thf(210,axiom,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_local_Osup_Ocommute) ).
thf(211,axiom,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_local_Osup_Oassoc) ).
thf(212,axiom,
! [X: a,Y: a,Z2: a] :
( ( inf @ X @ ( inf @ Y @ Z2 ) )
= ( inf @ Y @ ( inf @ X @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_local_Oinf__left__commute) ).
thf(213,axiom,
! [X: a,Y: a] :
( ( inf @ X @ Y )
= ( inf @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_local_Oinf__commute) ).
thf(214,axiom,
! [X: a,Y: a,Z2: a] :
( ( inf @ ( inf @ X @ Y ) @ Z2 )
= ( inf @ X @ ( inf @ Y @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_local_Oinf__assoc) ).
thf(215,axiom,
! [B: a,A: a,C: a] :
( ( inf @ B @ ( inf @ A @ C ) )
= ( inf @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_local_Oinf_Oleft__commute) ).
thf(216,axiom,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_local_Oinf_Ocommute) ).
thf(217,axiom,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_local_Oinf_Oassoc) ).
thf(237,axiom,
! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ Y )
=> ( ( less_eq @ Y @ Z2 )
=> ( less_eq @ X @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_local_Oorder__trans) ).
thf(238,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_local_Oorder_Otrans) ).
thf(239,axiom,
( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
= ( ^ [A2: a,B2: a] :
( ( less_eq @ A2 @ B2 )
& ( less_eq @ B2 @ A2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_local_Oorder_Oeq__iff) ).
thf(240,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_local_Oorder_Oantisym) ).
thf(241,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_local_Oord__le__eq__trans) ).
thf(242,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_local_Oord__eq__le__trans) ).
thf(243,axiom,
! [X: a,Y: a] :
( ( X = Y )
=> ( less_eq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_local_Oeq__refl) ).
thf(244,axiom,
( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
= ( ^ [X2: a,Y3: a] :
( ( less_eq @ X2 @ Y3 )
& ( less_eq @ Y3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_local_Oeq__iff) ).
thf(245,axiom,
! [B: a,A: a,C: a] :
( ( less_eq @ B @ A )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_local_Odual__order_Otrans) ).
thf(246,axiom,
( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
= ( ^ [A2: a,B2: a] :
( ( less_eq @ B2 @ A2 )
& ( less_eq @ A2 @ B2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_local_Odual__order_Oeq__iff) ).
thf(247,axiom,
! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( ( less_eq @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_local_Odual__order_Oantisym) ).
thf(248,axiom,
! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ( ( less_eq @ X @ Y )
= ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_local_Oantisym__conv) ).
thf(249,axiom,
! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( less_eq @ Y @ X )
=> ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_local_Oantisym) ).
thf(250,axiom,
less @ ( sup @ x @ ( inf @ y @ z ) ) @ ( inf @ y @ ( sup @ x @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(251,axiom,
( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(252,axiom,
less_eq @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(253,axiom,
lattice_a @ inf @ less_eq @ less @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(254,conjecture,
less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(255,negated_conjecture,
( ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) )
= $false ),
inference(negate_conjecture,[status(cth)],[254]) ).
thf(256,plain,
( ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) )
= $false ),
inference(unfold_def,[status(thm)],[255]) ).
thf(257,plain,
( ( ! [A: a,B: a] : ( condit1001553558elow_a @ less_eq @ ( set_gr1491433118Than_a @ less @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(258,plain,
( ( ! [A3: set_a,M4: a] :
( ! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( less_eq @ X3 @ M4 ) )
=> ( condit1627435690bove_a @ less_eq @ A3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(259,plain,
( ( ! [A3: set_a,M3: a] :
( ! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( less_eq @ M3 @ X3 ) )
=> ( condit1001553558elow_a @ less_eq @ A3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(260,plain,
( ( ! [A3: set_a] :
( ( condit1627435690bove_a @ less_eq @ A3 )
= ( ? [M2: a] :
! [X2: a] :
( ( member_a @ X2 @ A3 )
=> ( less_eq @ X2 @ M2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(261,plain,
( ( ! [A3: set_a] :
( ( condit1001553558elow_a @ less_eq @ A3 )
= ( ? [M: a] :
! [X2: a] :
( ( member_a @ X2 @ A3 )
=> ( less_eq @ M @ X2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(262,plain,
( ( lattic1885654924_set_a @ inf )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(263,plain,
( ( lattic1885654924_set_a @ sup )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(264,plain,
( ( abel_semigroup_a @ inf )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(265,plain,
( ( abel_semigroup_a @ sup )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(266,plain,
( ( semilattice_a @ inf )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(267,plain,
( ( semilattice_a @ sup )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(268,plain,
( ( semigroup_a @ inf )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(269,plain,
( ( semigroup_a @ sup )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(270,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(271,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(272,plain,
( ( finite40241356em_a_a @ inf )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(273,plain,
( ( finite40241356em_a_a @ sup )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(274,plain,
( ( ordering_a @ less_eq @ less )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(275,plain,
( ( semilattice_order_a @ inf @ less_eq @ less )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(276,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(277,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(278,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(279,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
=> ( modula1727524044comp_a @ less_eq @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(280,plain,
( ( lattic655834328_set_a @ inf @ less_eq @ less )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(281,plain,
( ( ! [C: a,A: a,B: a] :
( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
= ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(282,plain,
( ( ! [B: a,C: a,A: a] :
( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
= ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(283,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(284,plain,
( ( ! [C: a,A: a,B: a] :
( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(285,plain,
( ( ! [B: a,A: a,C: a] :
( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ B @ ( sup @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(286,plain,
( ( ! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ A @ ( sup @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(287,plain,
( ( ! [C: a,A: a,B: a] :
( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
= ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(288,plain,
( ( ! [B: a,C: a,A: a] :
( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
= ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(289,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(290,plain,
( ( ! [B: a,A: a,C: a] :
( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ B @ ( inf @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(291,plain,
( ( ! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ A @ ( inf @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(292,plain,
( ( ! [P: a > $o,X: a] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X @ Y4 ) )
=> ( ( least_a @ less_eq @ P )
= X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(293,plain,
( ( ! [P: a > $o,X: a,Q: a > $o] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X @ Y4 ) )
=> ( ! [X3: a] :
( ( P @ X3 )
=> ( ! [Y5: a] :
( ( P @ Y5 )
=> ( less_eq @ X3 @ Y5 ) )
=> ( Q @ X3 ) ) )
=> ( Q @ ( least_a @ less_eq @ P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(294,plain,
( ( ! [P: a > $o,Z2: a] :
( ? [X4: a] :
( ( P @ X4 )
& ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X4 @ Y4 ) )
& ! [Y4: a] :
( ( ( P @ Y4 )
& ! [Ya: a] :
( ( P @ Ya )
=> ( less_eq @ Y4 @ Ya ) ) )
=> ( Y4 = X4 ) ) )
=> ( ( P @ Z2 )
=> ( less_eq @ ( least_a @ less_eq @ P ) @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(295,plain,
( ( ! [P: a > $o] :
( ? [X4: a] :
( ( P @ X4 )
& ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X4 @ Y4 ) )
& ! [Y4: a] :
( ( ( P @ Y4 )
& ! [Ya: a] :
( ( P @ Ya )
=> ( less_eq @ Y4 @ Ya ) ) )
=> ( Y4 = X4 ) ) )
=> ( P @ ( least_a @ less_eq @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(296,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ B )
= ( inf @ B @ C ) )
& ( ( inf @ C @ A )
= ( inf @ B @ C ) )
& ( ( sup @ A @ B )
= ( sup @ B @ C ) )
& ( ( sup @ C @ A )
= ( sup @ B @ C ) )
& ( less @ ( inf @ A @ B ) @ ( sup @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(297,plain,
( ( ! [X: a,Y: a] :
( ( sup @ X @ ( inf @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(298,plain,
( ( ! [X: a,Y: a] :
( ( inf @ X @ ( sup @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(299,plain,
( ( ! [B: a,C: a,A: a] :
( ( less_eq @ ( sup @ B @ C ) @ A )
= ( ( less_eq @ B @ A )
& ( less_eq @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(300,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
= ( ( less_eq @ X @ Z2 )
& ( less_eq @ Y @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(301,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
= ( ( less_eq @ X @ Y )
& ( less_eq @ X @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(302,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(303,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1962211574trib_a @ inf @ less @ sup @ A @ B @ C )
= ( less @ ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(304,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula397570059tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ C )
= ( inf @ B @ C ) )
& ( less @ A @ B )
& ( ( sup @ A @ C )
= ( sup @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(305,plain,
( ( ! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min_a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min_a @ less_eq @ A @ B )
= B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(306,plain,
( ( ! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(307,plain,
( ( ! [P: a > $o,X: a] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ Y4 @ X ) )
=> ( ( greatest_a @ less_eq @ P )
= X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(308,plain,
( ( ! [P: a > $o,X: a,Q: a > $o] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ Y4 @ X ) )
=> ( ! [X3: a] :
( ( P @ X3 )
=> ( ! [Y5: a] :
( ( P @ Y5 )
=> ( less_eq @ Y5 @ X3 ) )
=> ( Q @ X3 ) ) )
=> ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(309,plain,
( ( ! [X: a,Y: a] :
( ( sup @ X @ ( sup @ X @ Y ) )
= ( sup @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(310,plain,
( ( ! [X: a] :
( ( sup @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(311,plain,
( ( ! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(312,plain,
( ( ! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(313,plain,
( ( ! [A: a] :
( ( sup @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(314,plain,
( ( ! [X: a,Y: a] :
( ( inf @ ( inf @ X @ Y ) @ Y )
= ( inf @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(315,plain,
( ( ! [X: a,Y: a] :
( ( inf @ X @ ( inf @ X @ Y ) )
= ( inf @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(316,plain,
( ( ! [X: a] :
( ( inf @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(317,plain,
( ( ! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(318,plain,
( ( ! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(319,plain,
( ( ! [A: a] :
( ( inf @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(320,plain,
( ( ! [X: a] : ( less_eq @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(321,plain,
( ( ! [A: a] : ( less_eq @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(322,plain,
( ( ! [X: a,Y: a] :
( ( modula1727524044comp_a @ less_eq @ X @ Y )
= ( ~ ( less_eq @ X @ Y )
& ~ ( less_eq @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(323,plain,
( ( ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(324,plain,
( ( ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(325,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ! [X3: a,Y4: a,Z3: a] :
( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
= ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
=> ( ( inf @ X @ ( sup @ Y @ Z2 ) )
= ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(326,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ! [X3: a,Y4: a,Z3: a] :
( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
= ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
=> ( ( sup @ X @ ( inf @ Y @ Z2 ) )
= ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(327,plain,
( ( ! [B: a,A: a] :
( ( less @ B @ A )
= ( ( A
= ( sup @ A @ B ) )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(328,plain,
( ( ! [C: a,B: a,A: a] :
( ( less @ C @ B )
=> ( less @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(329,plain,
( ( ! [C: a,A: a,B: a] :
( ( less @ C @ A )
=> ( less @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(330,plain,
( ( ! [B: a,C: a,A: a] :
( ( less @ ( sup @ B @ C ) @ A )
=> ~ ( ( less @ B @ A )
=> ~ ( less @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(331,plain,
( ( ! [X: a,B: a,A: a] :
( ( less @ X @ B )
=> ( less @ X @ ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(332,plain,
( ( ! [X: a,A: a,B: a] :
( ( less @ X @ A )
=> ( less @ X @ ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(333,plain,
( ( ! [B: a,X: a,A: a] :
( ( less @ B @ X )
=> ( less @ ( inf @ A @ B ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(334,plain,
( ( ! [A: a,X: a,B: a] :
( ( less @ A @ X )
=> ( less @ ( inf @ A @ B ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(335,plain,
( ( ! [A: a,B: a] :
( ( less @ A @ B )
= ( ( A
= ( inf @ A @ B ) )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(336,plain,
( ( ! [B: a,C: a,A: a] :
( ( less @ B @ C )
=> ( less @ ( inf @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(337,plain,
( ( ! [A: a,C: a,B: a] :
( ( less @ A @ C )
=> ( less @ ( inf @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(338,plain,
( ( ! [A: a,B: a,C: a] :
( ( less @ A @ ( inf @ B @ C ) )
=> ~ ( ( less @ A @ B )
=> ~ ( less @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(339,plain,
( ( ! [F: a > a > a,X: a,Y: a] :
( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
=> ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
=> ( ! [X3: a,Y4: a,Z3: a] :
( ( less_eq @ Y4 @ X3 )
=> ( ( less_eq @ Z3 @ X3 )
=> ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
=> ( ( sup @ X @ Y )
= ( F @ X @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(340,plain,
( ( ! [A: a,C: a,B: a,D: a] :
( ( less_eq @ A @ C )
=> ( ( less_eq @ B @ D )
=> ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(341,plain,
( ( ! [Y: a,X: a,Z2: a] :
( ( less_eq @ Y @ X )
=> ( ( less_eq @ Z2 @ X )
=> ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(342,plain,
( ( ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(343,plain,
( ( ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(344,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( sup @ X @ Y )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(345,plain,
( ( ! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ( ( sup @ X @ Y )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(346,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( A
= ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(347,plain,
( ( ! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(348,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( A
= ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(349,plain,
( ( ! [C: a,A: a,D: a,B: a] :
( ( less_eq @ C @ A )
=> ( ( less_eq @ D @ B )
=> ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(350,plain,
( ( ! [C: a,B: a,A: a] :
( ( less_eq @ C @ B )
=> ( less_eq @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(351,plain,
( ( ! [C: a,A: a,B: a] :
( ( less_eq @ C @ A )
=> ( less_eq @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(352,plain,
( ( ! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(353,plain,
( ( ! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(354,plain,
( ( ! [B: a,A: a,C: a] :
( ( less_eq @ B @ A )
=> ( ( less_eq @ C @ A )
=> ( less_eq @ ( sup @ B @ C ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(355,plain,
( ( ! [B: a,C: a,A: a] :
( ( less_eq @ ( sup @ B @ C ) @ A )
=> ~ ( ( less_eq @ B @ A )
=> ~ ( less_eq @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(356,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(357,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( ( sup @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(358,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(359,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( ( sup @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(360,plain,
( ( ! [X: a,B: a,A: a] :
( ( less_eq @ X @ B )
=> ( less_eq @ X @ ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(361,plain,
( ( ! [X: a,A: a,B: a] :
( ( less_eq @ X @ A )
=> ( less_eq @ X @ ( sup @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(362,plain,
( ( ! [A: a,X: a,B: a] :
( ( less_eq @ A @ X )
=> ( ( less_eq @ B @ X )
=> ( less_eq @ ( sup @ A @ B ) @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(363,plain,
( ( ! [A: a,B: a,X: a] :
( ( less_eq @ ( sup @ A @ B ) @ X )
=> ~ ( ( less_eq @ A @ X )
=> ~ ( less_eq @ B @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(364,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
= ( ( sup @ X @ Y )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(365,plain,
( ( ! [B: a,X: a,A: a] :
( ( less_eq @ B @ X )
=> ( less_eq @ ( inf @ A @ B ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(366,plain,
( ( ! [A: a,X: a,B: a] :
( ( less_eq @ A @ X )
=> ( less_eq @ ( inf @ A @ B ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(367,plain,
( ( ! [X: a,A: a,B: a] :
( ( less_eq @ X @ A )
=> ( ( less_eq @ X @ B )
=> ( less_eq @ X @ ( inf @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(368,plain,
( ( ! [X: a,A: a,B: a] :
( ( less_eq @ X @ ( inf @ A @ B ) )
=> ~ ( ( less_eq @ X @ A )
=> ~ ( less_eq @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(369,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
= ( ( inf @ X @ Y )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(370,plain,
( ( ! [F: a > a > a,X: a,Y: a] :
( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
=> ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
=> ( ! [X3: a,Y4: a,Z3: a] :
( ( less_eq @ X3 @ Y4 )
=> ( ( less_eq @ X3 @ Z3 )
=> ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
=> ( ( inf @ X @ Y )
= ( F @ X @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(371,plain,
( ( ! [A: a,C: a,B: a,D: a] :
( ( less_eq @ A @ C )
=> ( ( less_eq @ B @ D )
=> ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(372,plain,
( ( ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(373,plain,
( ( ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(374,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ Y )
=> ( ( less_eq @ X @ Z2 )
=> ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(375,plain,
( ( ! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ( ( inf @ X @ Y )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(376,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( inf @ X @ Y )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(377,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(378,plain,
( ( ! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(379,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(380,plain,
( ( ! [B: a,C: a,A: a] :
( ( less_eq @ B @ C )
=> ( less_eq @ ( inf @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(381,plain,
( ( ! [A: a,C: a,B: a] :
( ( less_eq @ A @ C )
=> ( less_eq @ ( inf @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(382,plain,
( ( ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(383,plain,
( ( ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(384,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(385,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(386,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( ( inf @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(387,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(388,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( ( inf @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(389,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(390,plain,
( ( ! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(391,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(392,plain,
( ( ! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(393,plain,
( ( ! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(394,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(395,plain,
( ( ! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ A @ B )
=> ( less @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(396,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less @ X @ Y )
=> ( ( less_eq @ Y @ Z2 )
=> ( less @ X @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(397,plain,
( ( ! [X: a,Y: a] :
( ( less @ X @ Y )
= ( ( less_eq @ X @ Y )
& ~ ( less_eq @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(398,plain,
( ( ! [X: a,Y: a] :
( ( less @ X @ Y )
= ( ( less_eq @ X @ Y )
& ( X != Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(399,plain,
( ( ! [X: a,Y: a] :
( ( less @ X @ Y )
=> ( less_eq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(400,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( A != B )
=> ( less @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(401,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ Y )
=> ( ( less @ Y @ Z2 )
=> ( less @ X @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(402,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
= ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(403,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(404,plain,
( ( ! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ~ ( less @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(405,plain,
( ( ! [B: a,A: a,C: a] :
( ( less @ B @ A )
=> ( ( less_eq @ C @ B )
=> ( less @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(406,plain,
( ( ! [B: a,A: a,C: a] :
( ( less_eq @ B @ A )
=> ( ( less @ C @ B )
=> ( less @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(407,plain,
( ( ! [B: a,A: a] :
( ( less @ B @ A )
=> ( less_eq @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(408,plain,
( ( ! [B: a,A: a] :
( ( less @ B @ A )
= ( ( less_eq @ B @ A )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(409,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( ( less @ B @ A )
| ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(410,plain,
( ( ! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ B @ A )
=> ( less @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(411,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( ~ ( less @ X @ Y ) )
= ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(412,plain,
( ( ! [X: a,Y: a] :
( ~ ( less @ X @ Y )
=> ( ( less_eq @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(413,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( sup @ X @ ( sup @ Y @ Z2 ) )
= ( sup @ Y @ ( sup @ X @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(414,plain,
( ( ! [X: a,Y: a] :
( ( sup @ X @ Y )
= ( sup @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(415,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( sup @ ( sup @ X @ Y ) @ Z2 )
= ( sup @ X @ ( sup @ Y @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(416,plain,
( ( ! [B: a,A: a,C: a] :
( ( sup @ B @ ( sup @ A @ C ) )
= ( sup @ A @ ( sup @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(417,plain,
( ( ! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(418,plain,
( ( ! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(419,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( inf @ X @ ( inf @ Y @ Z2 ) )
= ( inf @ Y @ ( inf @ X @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(420,plain,
( ( ! [X: a,Y: a] :
( ( inf @ X @ Y )
= ( inf @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(421,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( inf @ ( inf @ X @ Y ) @ Z2 )
= ( inf @ X @ ( inf @ Y @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(422,plain,
( ( ! [B: a,A: a,C: a] :
( ( inf @ B @ ( inf @ A @ C ) )
= ( inf @ A @ ( inf @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(423,plain,
( ( ! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(424,plain,
( ( ! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(425,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ Y )
=> ( ( less_eq @ Y @ Z2 )
=> ( less_eq @ X @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(426,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(427,plain,
( ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
= ( ^ [A2: a,B2: a] :
( ( less_eq @ A2 @ B2 )
& ( less_eq @ B2 @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(428,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(429,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(430,plain,
( ( ! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(431,plain,
( ( ! [X: a,Y: a] :
( ( X = Y )
=> ( less_eq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(432,plain,
( ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
= ( ^ [X2: a,Y3: a] :
( ( less_eq @ X2 @ Y3 )
& ( less_eq @ Y3 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(433,plain,
( ( ! [B: a,A: a,C: a] :
( ( less_eq @ B @ A )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(434,plain,
( ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
= ( ^ [A2: a,B2: a] :
( ( less_eq @ B2 @ A2 )
& ( less_eq @ A2 @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(435,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( ( less_eq @ A @ B )
=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(436,plain,
( ( ! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ( ( less_eq @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(437,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( less_eq @ Y @ X )
=> ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(438,plain,
( ( less @ ( sup @ x @ ( inf @ y @ z ) ) @ ( inf @ y @ ( sup @ x @ z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(439,plain,
( ( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(440,plain,
( ( less_eq @ x @ y )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(441,plain,
( ( lattice_a @ inf @ less_eq @ less @ sup )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(442,plain,
( ( ~ ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[256]) ).
thf(443,plain,
( ( lattice_a @ inf @ less_eq @ less @ sup )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(444,plain,
( ( less_eq @ x @ y )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(445,plain,
( ( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(446,plain,
( ( less @ ( sup @ x @ ( inf @ y @ z ) ) @ ( inf @ y @ ( sup @ x @ z ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(447,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( less_eq @ Y @ X )
=> ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(448,plain,
( ( ! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ( ( less_eq @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(449,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( ( less_eq @ A @ B )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(450,plain,
( ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
= ( ^ [A2: a,B2: a] :
( ( less_eq @ B2 @ A2 )
& ( less_eq @ A2 @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(451,plain,
( ( ! [B: a,A: a,C: a] :
( ( less_eq @ B @ A )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(452,plain,
( ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
= ( ^ [X2: a,Y3: a] :
( ( less_eq @ X2 @ Y3 )
& ( less_eq @ Y3 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(453,plain,
( ( ! [X: a,Y: a] :
( ( X = Y )
=> ( less_eq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(454,plain,
( ( ! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(455,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(456,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(457,plain,
( ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
= ( ^ [A2: a,B2: a] :
( ( less_eq @ A2 @ B2 )
& ( less_eq @ B2 @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(458,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(459,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ Y )
=> ( ( less_eq @ Y @ Z2 )
=> ( less_eq @ X @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(460,plain,
( ( ! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(461,plain,
( ( ! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(462,plain,
( ( ! [B: a,A: a,C: a] :
( ( inf @ B @ ( inf @ A @ C ) )
= ( inf @ A @ ( inf @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(463,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( inf @ ( inf @ X @ Y ) @ Z2 )
= ( inf @ X @ ( inf @ Y @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(464,plain,
( ( ! [X: a,Y: a] :
( ( inf @ X @ Y )
= ( inf @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(465,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( inf @ X @ ( inf @ Y @ Z2 ) )
= ( inf @ Y @ ( inf @ X @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(466,plain,
( ( ! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(467,plain,
( ( ! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(468,plain,
( ( ! [B: a,A: a,C: a] :
( ( sup @ B @ ( sup @ A @ C ) )
= ( sup @ A @ ( sup @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(469,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( sup @ ( sup @ X @ Y ) @ Z2 )
= ( sup @ X @ ( sup @ Y @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(470,plain,
( ( ! [X: a,Y: a] :
( ( sup @ X @ Y )
= ( sup @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(471,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( sup @ X @ ( sup @ Y @ Z2 ) )
= ( sup @ Y @ ( sup @ X @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(472,plain,
( ( ! [X: a,Y: a] :
( ~ ( less @ X @ Y )
=> ( ( less_eq @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(473,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( ~ ( less @ X @ Y ) )
= ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(474,plain,
( ( ! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ B @ A )
=> ( less @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(475,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( ( less @ B @ A )
| ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(476,plain,
( ( ! [B: a,A: a] :
( ( less @ B @ A )
= ( ( less_eq @ B @ A )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(477,plain,
( ( ! [B: a,A: a] :
( ( less @ B @ A )
=> ( less_eq @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(478,plain,
( ( ! [B: a,A: a,C: a] :
( ( less_eq @ B @ A )
=> ( ( less @ C @ B )
=> ( less @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(479,plain,
( ( ! [B: a,A: a,C: a] :
( ( less @ B @ A )
=> ( ( less_eq @ C @ B )
=> ( less @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(480,plain,
( ( ! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ~ ( less @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(481,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(482,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
= ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(483,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ Y )
=> ( ( less @ Y @ Z2 )
=> ( less @ X @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(484,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( A != B )
=> ( less @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(485,plain,
( ( ! [X: a,Y: a] :
( ( less @ X @ Y )
=> ( less_eq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(486,plain,
( ( ! [X: a,Y: a] :
( ( less @ X @ Y )
= ( ( less_eq @ X @ Y )
& ( X != Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(487,plain,
( ( ! [X: a,Y: a] :
( ( less @ X @ Y )
= ( ( less_eq @ X @ Y )
& ~ ( less_eq @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(488,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less @ X @ Y )
=> ( ( less_eq @ Y @ Z2 )
=> ( less @ X @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(489,plain,
( ( ! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ A @ B )
=> ( less @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(490,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(491,plain,
( ( ! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(492,plain,
( ( ! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(493,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(494,plain,
( ( ! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(495,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(496,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( ( inf @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(497,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(498,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( ( inf @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(499,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(500,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(501,plain,
( ( ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(502,plain,
( ( ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(503,plain,
( ( ! [A: a,C: a,B: a] :
( ( less_eq @ A @ C )
=> ( less_eq @ ( inf @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(504,plain,
( ( ! [B: a,C: a,A: a] :
( ( less_eq @ B @ C )
=> ( less_eq @ ( inf @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(505,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(506,plain,
( ( ! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(507,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(508,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( inf @ X @ Y )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(509,plain,
( ( ! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ( ( inf @ X @ Y )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(510,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ Y )
=> ( ( less_eq @ X @ Z2 )
=> ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(511,plain,
( ( ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(512,plain,
( ( ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(513,plain,
( ( ! [A: a,C: a,B: a,D: a] :
( ( less_eq @ A @ C )
=> ( ( less_eq @ B @ D )
=> ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(514,plain,
( ( ! [F: a > a > a,X: a,Y: a] :
( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
=> ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
=> ( ! [X3: a,Y4: a,Z3: a] :
( ( less_eq @ X3 @ Y4 )
=> ( ( less_eq @ X3 @ Z3 )
=> ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
=> ( ( inf @ X @ Y )
= ( F @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(515,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
= ( ( inf @ X @ Y )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(516,plain,
( ( ! [X: a,A: a,B: a] :
( ( less_eq @ X @ ( inf @ A @ B ) )
=> ~ ( ( less_eq @ X @ A )
=> ~ ( less_eq @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(517,plain,
( ( ! [X: a,A: a,B: a] :
( ( less_eq @ X @ A )
=> ( ( less_eq @ X @ B )
=> ( less_eq @ X @ ( inf @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(518,plain,
( ( ! [A: a,X: a,B: a] :
( ( less_eq @ A @ X )
=> ( less_eq @ ( inf @ A @ B ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(519,plain,
( ( ! [B: a,X: a,A: a] :
( ( less_eq @ B @ X )
=> ( less_eq @ ( inf @ A @ B ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(520,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
= ( ( sup @ X @ Y )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(521,plain,
( ( ! [A: a,B: a,X: a] :
( ( less_eq @ ( sup @ A @ B ) @ X )
=> ~ ( ( less_eq @ A @ X )
=> ~ ( less_eq @ B @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(522,plain,
( ( ! [A: a,X: a,B: a] :
( ( less_eq @ A @ X )
=> ( ( less_eq @ B @ X )
=> ( less_eq @ ( sup @ A @ B ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(523,plain,
( ( ! [X: a,A: a,B: a] :
( ( less_eq @ X @ A )
=> ( less_eq @ X @ ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(524,plain,
( ( ! [X: a,B: a,A: a] :
( ( less_eq @ X @ B )
=> ( less_eq @ X @ ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(525,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( ( sup @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(526,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(527,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( ( sup @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(528,plain,
( ( ! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(529,plain,
( ( ! [B: a,C: a,A: a] :
( ( less_eq @ ( sup @ B @ C ) @ A )
=> ~ ( ( less_eq @ B @ A )
=> ~ ( less_eq @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(530,plain,
( ( ! [B: a,A: a,C: a] :
( ( less_eq @ B @ A )
=> ( ( less_eq @ C @ A )
=> ( less_eq @ ( sup @ B @ C ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(531,plain,
( ( ! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(532,plain,
( ( ! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(533,plain,
( ( ! [C: a,A: a,B: a] :
( ( less_eq @ C @ A )
=> ( less_eq @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(534,plain,
( ( ! [C: a,B: a,A: a] :
( ( less_eq @ C @ B )
=> ( less_eq @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(535,plain,
( ( ! [C: a,A: a,D: a,B: a] :
( ( less_eq @ C @ A )
=> ( ( less_eq @ D @ B )
=> ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(536,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
=> ( A
= ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(537,plain,
( ( ! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(538,plain,
( ( ! [B: a,A: a] :
( ( less_eq @ B @ A )
= ( A
= ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(539,plain,
( ( ! [Y: a,X: a] :
( ( less_eq @ Y @ X )
=> ( ( sup @ X @ Y )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(540,plain,
( ( ! [X: a,Y: a] :
( ( less_eq @ X @ Y )
=> ( ( sup @ X @ Y )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(541,plain,
( ( ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(542,plain,
( ( ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(543,plain,
( ( ! [Y: a,X: a,Z2: a] :
( ( less_eq @ Y @ X )
=> ( ( less_eq @ Z2 @ X )
=> ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(544,plain,
( ( ! [A: a,C: a,B: a,D: a] :
( ( less_eq @ A @ C )
=> ( ( less_eq @ B @ D )
=> ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(545,plain,
( ( ! [F: a > a > a,X: a,Y: a] :
( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
=> ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
=> ( ! [X3: a,Y4: a,Z3: a] :
( ( less_eq @ Y4 @ X3 )
=> ( ( less_eq @ Z3 @ X3 )
=> ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
=> ( ( sup @ X @ Y )
= ( F @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(546,plain,
( ( ! [A: a,B: a,C: a] :
( ( less @ A @ ( inf @ B @ C ) )
=> ~ ( ( less @ A @ B )
=> ~ ( less @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(547,plain,
( ( ! [A: a,C: a,B: a] :
( ( less @ A @ C )
=> ( less @ ( inf @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(548,plain,
( ( ! [B: a,C: a,A: a] :
( ( less @ B @ C )
=> ( less @ ( inf @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(549,plain,
( ( ! [A: a,B: a] :
( ( less @ A @ B )
= ( ( A
= ( inf @ A @ B ) )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(550,plain,
( ( ! [A: a,X: a,B: a] :
( ( less @ A @ X )
=> ( less @ ( inf @ A @ B ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(551,plain,
( ( ! [B: a,X: a,A: a] :
( ( less @ B @ X )
=> ( less @ ( inf @ A @ B ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(552,plain,
( ( ! [X: a,A: a,B: a] :
( ( less @ X @ A )
=> ( less @ X @ ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(553,plain,
( ( ! [X: a,B: a,A: a] :
( ( less @ X @ B )
=> ( less @ X @ ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(554,plain,
( ( ! [B: a,C: a,A: a] :
( ( less @ ( sup @ B @ C ) @ A )
=> ~ ( ( less @ B @ A )
=> ~ ( less @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(555,plain,
( ( ! [C: a,A: a,B: a] :
( ( less @ C @ A )
=> ( less @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(556,plain,
( ( ! [C: a,B: a,A: a] :
( ( less @ C @ B )
=> ( less @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(557,plain,
( ( ! [B: a,A: a] :
( ( less @ B @ A )
= ( ( A
= ( sup @ A @ B ) )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(558,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ! [X3: a,Y4: a,Z3: a] :
( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
= ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
=> ( ( sup @ X @ ( inf @ Y @ Z2 ) )
= ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(559,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ! [X3: a,Y4: a,Z3: a] :
( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
= ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
=> ( ( inf @ X @ ( sup @ Y @ Z2 ) )
= ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(560,plain,
( ( ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(561,plain,
( ( ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(562,plain,
( ( ! [X: a,Y: a] :
( ( modula1727524044comp_a @ less_eq @ X @ Y )
= ( ~ ( less_eq @ X @ Y )
& ~ ( less_eq @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(563,plain,
( ( ! [A: a] : ( less_eq @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(564,plain,
( ( ! [X: a] : ( less_eq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(565,plain,
( ( ! [A: a] :
( ( inf @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(566,plain,
( ( ! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(567,plain,
( ( ! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(568,plain,
( ( ! [X: a] :
( ( inf @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(569,plain,
( ( ! [X: a,Y: a] :
( ( inf @ X @ ( inf @ X @ Y ) )
= ( inf @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(570,plain,
( ( ! [X: a,Y: a] :
( ( inf @ ( inf @ X @ Y ) @ Y )
= ( inf @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(571,plain,
( ( ! [A: a] :
( ( sup @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(572,plain,
( ( ! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(573,plain,
( ( ! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(574,plain,
( ( ! [X: a] :
( ( sup @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(575,plain,
( ( ! [X: a,Y: a] :
( ( sup @ X @ ( sup @ X @ Y ) )
= ( sup @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(576,plain,
( ( ! [P: a > $o,X: a,Q: a > $o] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ Y4 @ X ) )
=> ( ! [X3: a] :
( ( P @ X3 )
=> ( ! [Y5: a] :
( ( P @ Y5 )
=> ( less_eq @ Y5 @ X3 ) )
=> ( Q @ X3 ) ) )
=> ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(577,plain,
( ( ! [P: a > $o,X: a] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ Y4 @ X ) )
=> ( ( greatest_a @ less_eq @ P )
= X ) ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(578,plain,
( ( ! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= A ) ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(579,plain,
( ( ! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min_a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min_a @ less_eq @ A @ B )
= B ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(580,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula397570059tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ C )
= ( inf @ B @ C ) )
& ( less @ A @ B )
& ( ( sup @ A @ C )
= ( sup @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(581,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1962211574trib_a @ inf @ less @ sup @ A @ B @ C )
= ( less @ ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(582,plain,
( ( ! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(583,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
= ( ( less_eq @ X @ Y )
& ( less_eq @ X @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(584,plain,
( ( ! [X: a,Y: a,Z2: a] :
( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
= ( ( less_eq @ X @ Z2 )
& ( less_eq @ Y @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(585,plain,
( ( ! [B: a,C: a,A: a] :
( ( less_eq @ ( sup @ B @ C ) @ A )
= ( ( less_eq @ B @ A )
& ( less_eq @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(586,plain,
( ( ! [X: a,Y: a] :
( ( inf @ X @ ( sup @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(587,plain,
( ( ! [X: a,Y: a] :
( ( sup @ X @ ( inf @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(588,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ B )
= ( inf @ B @ C ) )
& ( ( inf @ C @ A )
= ( inf @ B @ C ) )
& ( ( sup @ A @ B )
= ( sup @ B @ C ) )
& ( ( sup @ C @ A )
= ( sup @ B @ C ) )
& ( less @ ( inf @ A @ B ) @ ( sup @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(589,plain,
( ( ! [P: a > $o] :
( ? [X4: a] :
( ( P @ X4 )
& ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X4 @ Y4 ) )
& ! [Y4: a] :
( ( ( P @ Y4 )
& ! [Ya: a] :
( ( P @ Ya )
=> ( less_eq @ Y4 @ Ya ) ) )
=> ( Y4 = X4 ) ) )
=> ( P @ ( least_a @ less_eq @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(590,plain,
( ( ! [P: a > $o,Z2: a] :
( ? [X4: a] :
( ( P @ X4 )
& ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X4 @ Y4 ) )
& ! [Y4: a] :
( ( ( P @ Y4 )
& ! [Ya: a] :
( ( P @ Ya )
=> ( less_eq @ Y4 @ Ya ) ) )
=> ( Y4 = X4 ) ) )
=> ( ( P @ Z2 )
=> ( less_eq @ ( least_a @ less_eq @ P ) @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(591,plain,
( ( ! [P: a > $o,X: a,Q: a > $o] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X @ Y4 ) )
=> ( ! [X3: a] :
( ( P @ X3 )
=> ( ! [Y5: a] :
( ( P @ Y5 )
=> ( less_eq @ X3 @ Y5 ) )
=> ( Q @ X3 ) ) )
=> ( Q @ ( least_a @ less_eq @ P ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(592,plain,
( ( ! [P: a > $o,X: a] :
( ( P @ X )
=> ( ! [Y4: a] :
( ( P @ Y4 )
=> ( less_eq @ X @ Y4 ) )
=> ( ( least_a @ less_eq @ P )
= X ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(593,plain,
( ( ! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ A @ ( inf @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(594,plain,
( ( ! [B: a,A: a,C: a] :
( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ B @ ( inf @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(595,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(596,plain,
( ( ! [B: a,C: a,A: a] :
( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
= ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(597,plain,
( ( ! [C: a,A: a,B: a] :
( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
= ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(598,plain,
( ( ! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ A @ ( sup @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(599,plain,
( ( ! [B: a,A: a,C: a] :
( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ B @ ( sup @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(600,plain,
( ( ! [C: a,A: a,B: a] :
( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ C @ ( sup @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(601,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(602,plain,
( ( ! [B: a,C: a,A: a] :
( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
= ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(603,plain,
( ( ! [C: a,A: a,B: a] :
( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
= ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(604,plain,
( ( lattic655834328_set_a @ inf @ less_eq @ less )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(605,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
=> ( modula1727524044comp_a @ less_eq @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(606,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(607,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(608,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(609,plain,
( ( semilattice_order_a @ inf @ less_eq @ less )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(610,plain,
( ( ordering_a @ less_eq @ less )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(611,plain,
( ( finite40241356em_a_a @ sup )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(612,plain,
( ( finite40241356em_a_a @ inf )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(613,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(614,plain,
( ( ! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(615,plain,
( ( semigroup_a @ sup )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(616,plain,
( ( semigroup_a @ inf )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(617,plain,
( ( semilattice_a @ sup )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(618,plain,
( ( semilattice_a @ inf )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(619,plain,
( ( abel_semigroup_a @ sup )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(620,plain,
( ( abel_semigroup_a @ inf )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(621,plain,
( ( lattic1885654924_set_a @ sup )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(622,plain,
( ( lattic1885654924_set_a @ inf )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(623,plain,
( ( ! [A3: set_a] :
( ( condit1001553558elow_a @ less_eq @ A3 )
= ( ? [M: a] :
! [X2: a] :
( ( member_a @ X2 @ A3 )
=> ( less_eq @ M @ X2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(624,plain,
( ( ! [A3: set_a] :
( ( condit1627435690bove_a @ less_eq @ A3 )
= ( ? [M2: a] :
! [X2: a] :
( ( member_a @ X2 @ A3 )
=> ( less_eq @ X2 @ M2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(625,plain,
( ( ! [A3: set_a,M3: a] :
( ! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( less_eq @ M3 @ X3 ) )
=> ( condit1001553558elow_a @ less_eq @ A3 ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(626,plain,
( ( ! [A3: set_a,M4: a] :
( ! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( less_eq @ X3 @ M4 ) )
=> ( condit1627435690bove_a @ less_eq @ A3 ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(627,plain,
( ( ! [A: a,B: a] : ( condit1001553558elow_a @ less_eq @ ( set_gr1491433118Than_a @ less @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(628,plain,
( ( ~ ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(629,plain,
( ( ! [SX0: a,SX1: a] :
( ( less @ SX0 @ SX1 )
= ( ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(630,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX0 @ SX2 )
| ( less_eq @ SX0 @ ( inf @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(631,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( SX1 != SX2 )
| ( less_eq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(632,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( less_eq @ SX0 @ ( sup @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(633,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX2 )
| ( less @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(634,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ~ ( less @ SX0 @ SX1 )
| ( ( less_eq @ SX0 @ SX1 )
= ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(635,plain,
( ( ! [SX0: a,SX1: a] :
( ( less @ SX0 @ SX1 )
= ( ~ ( ( SX0
!= ( inf @ SX0 @ SX1 ) )
| ~ ( ( SX0 != SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(636,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( ~ ( less @ SX0 @ SX1 ) )
= ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(637,plain,
( ( ( ^ [SX0: a,SX1: a] : ( SX0 = SX1 ) )
= ( ^ [SX0: a,SX1: a] :
~ ( ~ ( less_eq @ SX1 @ SX0 )
| ~ ( less_eq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(638,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ ( inf @ SX1 @ SX2 ) )
| ~ ( ~ ( less @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(639,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( sup @ SX1 @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(640,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( SX0 != SX1 )
| ~ ( less_eq @ SX1 @ SX2 )
| ( less_eq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(641,plain,
( ( ! [SX0: a,SX1: a] :
( ( SX0
!= ( inf @ SX0 @ SX1 ) )
| ( less_eq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(642,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( less_eq @ SX1 @ SX0 )
= ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(643,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( less_eq @ ( inf @ SX2 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(644,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( less_eq @ SX0 @ SX1 )
| ( less @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(645,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less @ SX2 @ SX0 )
| ( less @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(646,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less_eq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(647,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX2 @ SX3 )
| ( less_eq @ ( sup @ SX0 @ SX2 ) @ ( sup @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(648,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( inf @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(649,plain,
( ( ! [SX0: a,SX1: a] :
( ( SX0
!= ( sup @ SX0 @ SX1 ) )
| ( less_eq @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(650,plain,
( ( ( ^ [SX0: a,SX1: a] : ( SX0 = SX1 ) )
= ( ^ [SX0: a,SX1: a] :
~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(651,plain,
( ( ! [SX0: a > $o] :
( ~ ~ ! [SX1: a] :
~ ~ ( ~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( less_eq @ SX1 @ SX2 ) ) )
| ~ ! [SX2: a] :
( ~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: a] :
( ~ ( SX0 @ SX3 )
| ( less_eq @ SX2 @ SX3 ) ) )
| ( SX2 = SX1 ) ) )
| ( SX0 @ ( least_a @ less_eq @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(652,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(653,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( less_eq @ SX0 @ ( sup @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(654,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ ( inf @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(655,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( SX0
= ( inf @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(656,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( inf @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(657,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX2 @ SX1 )
| ( less_eq @ ( sup @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(658,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less @ SX1 @ SX2 )
| ( less @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(659,plain,
( ( ( ^ [SX0: a,SX1: a] : ( SX0 = SX1 ) )
= ( ^ [SX0: a,SX1: a] :
~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(660,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX0 @ SX2 )
| ( less_eq @ SX0 @ ( inf @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(661,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( less_eq @ ( inf @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(662,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ SX0 @ ( sup @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(663,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( inf @ SX1 @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(664,plain,
( ( ! [SX0: a,SX1: a] :
( ( less @ SX0 @ SX1 )
= ( ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( ( SX1 != SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(665,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ~ ! [SX2: a] :
~ ~ ( ~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: a] :
( ~ ( SX0 @ SX3 )
| ( less_eq @ SX2 @ SX3 ) ) )
| ~ ! [SX3: a] :
( ~ ~ ( ~ ( SX0 @ SX3 )
| ~ ! [SX4: a] :
( ~ ( SX0 @ SX4 )
| ( less_eq @ SX3 @ SX4 ) ) )
| ( SX3 = SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ( less_eq @ ( least_a @ less_eq @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(666,plain,
( ( ! [SX0: set_a,SX1: a] :
( ~ ! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( less_eq @ SX2 @ SX1 ) )
| ( condit1627435690bove_a @ less_eq @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(667,plain,
( ( ! [SX0: a,SX1: a] :
( ( less @ SX0 @ SX1 )
= ( ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(668,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( less_eq @ SX2 @ SX1 ) )
| ( ( greatest_a @ less_eq @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(669,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( less_eq @ SX0 @ ( inf @ SX1 @ SX2 ) )
= ( ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(670,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( sup @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(671,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( sup @ SX1 @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(672,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX2 )
| ( less_eq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(673,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(674,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ ( inf @ SX1 @ SX2 ) )
| ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(675,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ SX0 @ ( sup @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(676,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( less_eq @ ( inf @ SX2 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(677,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX0 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(678,plain,
( ( ! [SX0: a,SX1: a] :
~ ( ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ( ( min_a @ less_eq @ SX0 @ SX1 )
= SX0 ) )
| ~ ( ~ ~ ( less_eq @ SX0 @ SX1 )
| ( ( min_a @ less_eq @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(679,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ ( inf @ SX2 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(680,plain,
( ( ! [SX0: set_a] :
( ( condit1627435690bove_a @ less_eq @ SX0 )
= ( ~ ! [SX1: a] :
~ ! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( less_eq @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(681,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX2 )
| ( less_eq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(682,plain,
( ( ! [SX0: a,SX1: a] :
( ( less @ SX0 @ SX1 )
= ( ~ ( ( SX1
!= ( sup @ SX1 @ SX0 ) )
| ~ ( ( SX1 != SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(683,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX2 @ SX0 )
| ( less_eq @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(684,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ ( inf @ SX1 @ SX2 ) )
| ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(685,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( SX1
= ( sup @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(686,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( less_eq @ ( sup @ SX0 @ SX1 ) @ SX2 )
= ( ~ ( ~ ( less_eq @ SX0 @ SX2 )
| ~ ( less_eq @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(687,plain,
( ( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(688,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( less_eq @ SX0 @ ( inf @ SX1 @ SX2 ) )
= ( ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(689,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX0 @ SX2 )
| ( less_eq @ SX0 @ ( inf @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(690,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( sup @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(691,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less @ SX1 @ SX2 )
| ( less @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(692,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ~ ( less_eq @ SX2 @ SX0 )
| ( less @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(693,plain,
( ( ! [SX0: set_a,SX1: a] :
( ~ ! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( less_eq @ SX1 @ SX2 ) )
| ( condit1001553558elow_a @ less_eq @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(694,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(695,plain,
( ( ! [SX0: a > $o,SX1: a,SX2: a > $o] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX3: a] :
( ~ ( SX0 @ SX3 )
| ( less_eq @ SX3 @ SX1 ) )
| ~ ! [SX3: a] :
( ~ ( SX0 @ SX3 )
| ~ ! [SX4: a] :
( ~ ( SX0 @ SX4 )
| ( less_eq @ SX4 @ SX3 ) )
| ( SX2 @ SX3 ) )
| ( SX2 @ ( greatest_a @ less_eq @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(696,plain,
( ( ! [SX0: a > a > a,SX1: a,SX2: a] :
( ~ ! [SX3: a,SX4: a] : ( less_eq @ ( SX0 @ SX3 @ SX4 ) @ SX3 )
| ~ ! [SX3: a,SX4: a] : ( less_eq @ ( SX0 @ SX3 @ SX4 ) @ SX4 )
| ~ ! [SX3: a,SX4: a,SX5: a] :
( ~ ( less_eq @ SX3 @ SX4 )
| ~ ( less_eq @ SX3 @ SX5 )
| ( less_eq @ SX3 @ ( SX0 @ SX4 @ SX5 ) ) )
| ( ( inf @ SX1 @ SX2 )
= ( SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(697,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( less_eq @ ( inf @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(698,plain,
( ( ! [SX0: a > a > a,SX1: a,SX2: a] :
( ~ ! [SX3: a,SX4: a] : ( less_eq @ SX3 @ ( SX0 @ SX3 @ SX4 ) )
| ~ ! [SX3: a,SX4: a] : ( less_eq @ SX4 @ ( SX0 @ SX3 @ SX4 ) )
| ~ ! [SX3: a,SX4: a,SX5: a] :
( ~ ( less_eq @ SX4 @ SX3 )
| ~ ( less_eq @ SX5 @ SX3 )
| ( less_eq @ ( SX0 @ SX4 @ SX5 ) @ SX3 ) )
| ( ( sup @ SX1 @ SX2 )
= ( SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(699,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX2 @ SX3 )
| ( less_eq @ ( inf @ SX0 @ SX2 ) @ ( inf @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(700,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( less_eq @ SX1 @ SX0 )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(701,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ SX0 @ ( sup @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(702,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( less @ SX0 @ SX1 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(703,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( less_eq @ SX0 @ ( sup @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(704,plain,
( ( ! [SX0: a,SX1: a] :
( ( SX0 != SX1 )
| ( less_eq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(705,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( ( inf @ SX1 @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(706,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( inf @ SX3 @ ( sup @ SX4 @ SX5 ) )
= ( sup @ ( inf @ SX3 @ SX4 ) @ ( inf @ SX3 @ SX5 ) ) )
| ( ( sup @ SX0 @ ( inf @ SX1 @ SX2 ) )
= ( inf @ ( sup @ SX0 @ SX1 ) @ ( sup @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(707,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX2 @ SX1 )
| ( less_eq @ ( sup @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(708,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( less_eq @ SX1 @ SX2 ) )
| ( ( least_a @ less_eq @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(709,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX2 @ SX3 )
| ( less_eq @ ( sup @ SX0 @ SX2 ) @ ( sup @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(710,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less_eq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(711,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ ( sup @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( less_eq @ SX0 @ SX2 )
| ~ ( less_eq @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(712,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX2 @ SX1 )
| ( less_eq @ ( sup @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(713,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ SX0 @ ( sup @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(714,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ ( sup @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( less @ SX0 @ SX2 )
| ~ ( less @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(715,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ( less_eq @ SX0 @ ( sup @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(716,plain,
( ( ! [SX0: a,SX1: a] :
~ ( ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ( ( max_a @ less_eq @ SX0 @ SX1 )
= SX1 ) )
| ~ ( ~ ~ ( less_eq @ SX0 @ SX1 )
| ( ( max_a @ less_eq @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(717,plain,
( ( ! [SX0: a,SX1: a] :
( ( less @ SX0 @ SX1 )
= ( ~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ~ ( less_eq @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(718,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ ( inf @ SX2 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(719,plain,
( ( ! [SX0: set_a] :
( ( condit1001553558elow_a @ less_eq @ SX0 )
= ( ~ ! [SX1: a] :
~ ! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( less_eq @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(720,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less_eq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(721,plain,
( ( ! [SX0: a > $o,SX1: a,SX2: a > $o] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX3: a] :
( ~ ( SX0 @ SX3 )
| ( less_eq @ SX1 @ SX3 ) )
| ~ ! [SX3: a] :
( ~ ( SX0 @ SX3 )
| ~ ! [SX4: a] :
( ~ ( SX0 @ SX4 )
| ( less_eq @ SX3 @ SX4 ) )
| ( SX2 @ SX3 ) )
| ( SX2 @ ( least_a @ less_eq @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(722,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SX0 @ SX1 @ SX2 )
| ( modula1727524044comp_a @ less_eq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(723,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( modula397570059tice_a @ inf @ less @ sup @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ~ ( ( ( inf @ SX0 @ SX2 )
!= ( inf @ SX1 @ SX2 ) )
| ~ ( less @ SX0 @ SX1 ) )
| ( ( sup @ SX0 @ SX2 )
!= ( sup @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(724,plain,
( ( ! [SX0: a,SX1: a] :
( ( modula1727524044comp_a @ less_eq @ SX0 @ SX1 )
= ( ~ ( ~ ~ ( less_eq @ SX0 @ SX1 )
| ~ ~ ( less_eq @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(725,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ( less @ ( inf @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(726,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less_eq @ ( sup @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( less_eq @ SX0 @ SX2 )
| ~ ( less_eq @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(727,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) )
| ( less @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(728,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( less_eq @ ( sup @ SX0 @ SX1 ) @ SX2 )
= ( ~ ( ~ ( less_eq @ SX0 @ SX2 )
| ~ ( less_eq @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(729,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( sup @ SX3 @ ( inf @ SX4 @ SX5 ) )
= ( inf @ ( sup @ SX3 @ SX4 ) @ ( sup @ SX3 @ SX5 ) ) )
| ( ( inf @ SX0 @ ( sup @ SX1 @ SX2 ) )
= ( sup @ ( inf @ SX0 @ SX1 ) @ ( inf @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(730,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( less @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX2 )
| ( less @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(731,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SX0 @ SX1 )
!= ( inf @ SX1 @ SX2 ) )
| ( ( inf @ SX2 @ SX0 )
!= ( inf @ SX1 @ SX2 ) ) )
| ( ( sup @ SX0 @ SX1 )
!= ( sup @ SX1 @ SX2 ) ) )
| ( ( sup @ SX2 @ SX0 )
!= ( sup @ SX1 @ SX2 ) ) )
| ~ ( less @ ( inf @ SX0 @ SX1 ) @ ( sup @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(732,plain,
! [SV1: a] :
( ( ! [SY460: a,SY461: a] :
( ( inf @ ( inf @ SV1 @ SY460 ) @ SY461 )
= ( inf @ SV1 @ ( inf @ SY460 @ SY461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(733,plain,
! [SV2: a] :
( ( ! [SY462: a] :
( ( inf @ SV2 @ SY462 )
= ( inf @ SY462 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(734,plain,
! [SV3: a] :
( ( ! [SY463: a,SY464: a] :
( ( inf @ SV3 @ ( inf @ SY463 @ SY464 ) )
= ( inf @ SY463 @ ( inf @ SV3 @ SY464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(735,plain,
! [SV4: a] :
( ( ! [SY465: a,SY466: a] :
( ( inf @ ( inf @ SV4 @ SY465 ) @ SY466 )
= ( inf @ SV4 @ ( inf @ SY465 @ SY466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(736,plain,
! [SV5: a] :
( ( ! [SY467: a] :
( ( inf @ SV5 @ SY467 )
= ( inf @ SY467 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(737,plain,
! [SV6: a] :
( ( ! [SY468: a,SY469: a] :
( ( inf @ SV6 @ ( inf @ SY468 @ SY469 ) )
= ( inf @ SY468 @ ( inf @ SV6 @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(738,plain,
! [SV7: a] :
( ( ! [SY470: a,SY471: a] :
( ( sup @ ( sup @ SV7 @ SY470 ) @ SY471 )
= ( sup @ SV7 @ ( sup @ SY470 @ SY471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(739,plain,
! [SV8: a] :
( ( ! [SY472: a] :
( ( sup @ SV8 @ SY472 )
= ( sup @ SY472 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(740,plain,
! [SV9: a] :
( ( ! [SY473: a,SY474: a] :
( ( sup @ SV9 @ ( sup @ SY473 @ SY474 ) )
= ( sup @ SY473 @ ( sup @ SV9 @ SY474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(741,plain,
! [SV10: a] :
( ( ! [SY475: a,SY476: a] :
( ( sup @ ( sup @ SV10 @ SY475 ) @ SY476 )
= ( sup @ SV10 @ ( sup @ SY475 @ SY476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(742,plain,
! [SV11: a] :
( ( ! [SY477: a] :
( ( sup @ SV11 @ SY477 )
= ( sup @ SY477 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(743,plain,
! [SV12: a] :
( ( ! [SY478: a,SY479: a] :
( ( sup @ SV12 @ ( sup @ SY478 @ SY479 ) )
= ( sup @ SY478 @ ( sup @ SV12 @ SY479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(744,plain,
! [SV13: a] :
( ( ! [SY480: a] :
( ( less_eq @ SV13 @ SY480 )
= ( ( less @ SV13 @ SY480 )
| ( SY480 = SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(745,plain,
! [SV14: a] :
( ( ! [SY481: a] :
( ( less_eq @ SV14 @ SY481 )
= ( ( less @ SV14 @ SY481 )
| ( SV14 = SY481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(746,plain,
! [SV15: a] :
( ( ! [SY482: a] :
( ( less_eq @ SV15 @ SY482 )
= ( ( less @ SV15 @ SY482 )
| ( SV15 = SY482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(747,plain,
! [SV16: a] :
( ( ! [SY483: a] :
( ( less_eq @ SV16 @ SY483 )
= ( ( inf @ SV16 @ SY483 )
= SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(748,plain,
! [SV17: a] :
( ( ! [SY484: a] :
( ( less_eq @ SV17 @ SY484 )
= ( ( inf @ SY484 @ SV17 )
= SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(749,plain,
! [SV18: a] :
( ( ! [SY485: a] : ( less_eq @ ( inf @ SV18 @ SY485 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(750,plain,
! [SV19: a] :
( ( ! [SY486: a] : ( less_eq @ ( inf @ SV19 @ SY486 ) @ SY486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(751,plain,
! [SV20: a] :
( ( ! [SY487: a] :
( ( less_eq @ SV20 @ SY487 )
= ( SV20
= ( inf @ SV20 @ SY487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(752,plain,
! [SV21: a] :
( ( ! [SY488: a] : ( less_eq @ ( inf @ SV21 @ SY488 ) @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(753,plain,
! [SV22: a] :
( ( ! [SY489: a] : ( less_eq @ ( inf @ SV22 @ SY489 ) @ SY489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(754,plain,
! [SV23: a] :
( ( ! [SY490: a] :
( ( less_eq @ SV23 @ SY490 )
= ( ( inf @ SV23 @ SY490 )
= SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(755,plain,
! [SV24: a] :
( ( ! [SY491: a] :
( ( less_eq @ SV24 @ SY491 )
= ( ( sup @ SV24 @ SY491 )
= SY491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(756,plain,
! [SV25: a] :
( ( ! [SY492: a] :
( ( less_eq @ SV25 @ SY492 )
= ( ( sup @ SY492 @ SV25 )
= SY492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(757,plain,
! [SV26: a] :
( ( ! [SY493: a] :
( ( less_eq @ SV26 @ SY493 )
= ( ( sup @ SV26 @ SY493 )
= SY493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(758,plain,
! [SV27: a] :
( ( ! [SY494: a] : ( less_eq @ SV27 @ ( sup @ SV27 @ SY494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(759,plain,
! [SV28: a] :
( ( ! [SY495: a] : ( less_eq @ SV28 @ ( sup @ SY495 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(760,plain,
! [SV29: a] :
( ( ! [SY496: a] :
( ( less_eq @ SV29 @ SY496 )
= ( SY496
= ( sup @ SY496 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(761,plain,
! [SV30: a] :
( ( ! [SY497: a] : ( less_eq @ SV30 @ ( sup @ SV30 @ SY497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(762,plain,
! [SV31: a] :
( ( ! [SY498: a] : ( less_eq @ SV31 @ ( sup @ SY498 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(763,plain,
! [SV32: a] :
( ( ! [SY499: a,SY500: a] : ( less_eq @ ( sup @ ( inf @ SV32 @ SY499 ) @ ( inf @ SV32 @ SY500 ) ) @ ( inf @ SV32 @ ( sup @ SY499 @ SY500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(764,plain,
! [SV33: a] :
( ( ! [SY501: a,SY502: a] : ( less_eq @ ( sup @ SV33 @ ( inf @ SY501 @ SY502 ) ) @ ( inf @ ( sup @ SV33 @ SY501 ) @ ( sup @ SV33 @ SY502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(765,plain,
! [SV34: a] :
( ( less_eq @ SV34 @ SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(766,plain,
! [SV35: a] :
( ( less_eq @ SV35 @ SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(767,plain,
! [SV36: a] :
( ( ( inf @ SV36 @ SV36 )
= SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(768,plain,
! [SV37: a] :
( ( ! [SY503: a] :
( ( inf @ SV37 @ ( inf @ SV37 @ SY503 ) )
= ( inf @ SV37 @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(769,plain,
! [SV38: a] :
( ( ! [SY504: a] :
( ( inf @ ( inf @ SV38 @ SY504 ) @ SY504 )
= ( inf @ SV38 @ SY504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(770,plain,
! [SV39: a] :
( ( ( inf @ SV39 @ SV39 )
= SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(771,plain,
! [SV40: a] :
( ( ! [SY505: a] :
( ( inf @ SV40 @ ( inf @ SV40 @ SY505 ) )
= ( inf @ SV40 @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(772,plain,
! [SV41: a] :
( ( ! [SY506: a] :
( ( inf @ ( inf @ SV41 @ SY506 ) @ SY506 )
= ( inf @ SV41 @ SY506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(773,plain,
! [SV42: a] :
( ( ( sup @ SV42 @ SV42 )
= SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(774,plain,
! [SV43: a] :
( ( ! [SY507: a] :
( ( sup @ SV43 @ ( sup @ SV43 @ SY507 ) )
= ( sup @ SV43 @ SY507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(775,plain,
! [SV44: a] :
( ( ! [SY508: a] :
( ( sup @ ( sup @ SV44 @ SY508 ) @ SY508 )
= ( sup @ SV44 @ SY508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(776,plain,
! [SV45: a] :
( ( ( sup @ SV45 @ SV45 )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(777,plain,
! [SV46: a] :
( ( ! [SY509: a] :
( ( sup @ SV46 @ ( sup @ SV46 @ SY509 ) )
= ( sup @ SV46 @ SY509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(778,plain,
! [SV47: a] :
( ( ! [SY510: a,SY511: a] :
( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SY510 @ SY511 )
= ( less @ ( sup @ ( inf @ SV47 @ SY510 ) @ ( inf @ SY511 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SY510 @ SY511 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(779,plain,
! [SV48: a] :
( ( ! [SY512: a] :
( ( inf @ SV48 @ ( sup @ SV48 @ SY512 ) )
= SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(780,plain,
! [SV49: a] :
( ( ! [SY513: a] :
( ( sup @ SV49 @ ( inf @ SV49 @ SY513 ) )
= SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(781,plain,
! [SV50: a] :
( ( ! [SY514: a,SY515: a] :
( ( sup @ SV50 @ ( modula1936294176_aux_a @ inf @ sup @ SV50 @ SY514 @ SY515 ) )
= ( sup @ SV50 @ ( inf @ SY514 @ SY515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(782,plain,
! [SV51: a] :
( ( ! [SY516: a,SY517: a] :
( ( sup @ SV51 @ ( modula1936294176_aux_a @ inf @ sup @ SY516 @ SV51 @ SY517 ) )
= ( sup @ SV51 @ ( inf @ SY517 @ SY516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(783,plain,
! [SV52: a] :
( ( ! [SY518: a,SY519: a] :
( ( modula1936294176_aux_a @ inf @ sup @ SV52 @ SY518 @ SY519 )
= ( sup @ ( sup @ ( inf @ SV52 @ SY518 ) @ ( inf @ SY518 @ SY519 ) ) @ ( inf @ SY519 @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(784,plain,
! [SV53: a] :
( ( ! [SY520: a,SY521: a] :
( ( modula1936294176_aux_a @ inf @ sup @ SV53 @ SY520 @ SY521 )
= ( modula1936294176_aux_a @ inf @ sup @ SY521 @ SV53 @ SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(785,plain,
! [SV54: a] :
( ( ! [SY522: a,SY523: a] :
( ( modula1936294176_aux_a @ inf @ sup @ SV54 @ SY522 @ SY523 )
= ( modula1936294176_aux_a @ inf @ sup @ SY522 @ SY523 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(786,plain,
! [SV55: a] :
( ( ! [SY524: a,SY525: a] :
( ( inf @ SV55 @ ( modula1144073633_aux_a @ inf @ sup @ SV55 @ SY524 @ SY525 ) )
= ( inf @ SV55 @ ( sup @ SY524 @ SY525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(787,plain,
! [SV56: a] :
( ( ! [SY526: a,SY527: a] :
( ( inf @ SV56 @ ( modula1144073633_aux_a @ inf @ sup @ SY526 @ SV56 @ SY527 ) )
= ( inf @ SV56 @ ( sup @ SY527 @ SY526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(788,plain,
! [SV57: a] :
( ( ! [SY528: a,SY529: a] :
( ( inf @ SV57 @ ( modula1144073633_aux_a @ inf @ sup @ SY528 @ SY529 @ SV57 ) )
= ( inf @ SV57 @ ( sup @ SY528 @ SY529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(789,plain,
! [SV58: a] :
( ( ! [SY530: a,SY531: a] :
( ( modula1144073633_aux_a @ inf @ sup @ SV58 @ SY530 @ SY531 )
= ( inf @ ( inf @ ( sup @ SV58 @ SY530 ) @ ( sup @ SY530 @ SY531 ) ) @ ( sup @ SY531 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(790,plain,
! [SV59: a] :
( ( ! [SY532: a,SY533: a] :
( ( modula1144073633_aux_a @ inf @ sup @ SV59 @ SY532 @ SY533 )
= ( modula1144073633_aux_a @ inf @ sup @ SY533 @ SV59 @ SY532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(791,plain,
! [SV60: a] :
( ( ! [SY534: a,SY535: a] :
( ( modula1144073633_aux_a @ inf @ sup @ SV60 @ SY534 @ SY535 )
= ( modula1144073633_aux_a @ inf @ sup @ SY534 @ SY535 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(792,plain,
! [SV61: a] :
( ( ! [SY536: a,SY537: a] :
( ( modula581031071_aux_a @ inf @ sup @ SV61 @ SY536 @ SY537 )
= ( sup @ ( inf @ SY537 @ ( modula1144073633_aux_a @ inf @ sup @ SV61 @ SY536 @ SY537 ) ) @ ( modula1936294176_aux_a @ inf @ sup @ SV61 @ SY536 @ SY537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(793,plain,
! [SV62: a] :
( ( ! [SY538: a,SY539: a] :
( ( modula1373251614_aux_a @ inf @ sup @ SV62 @ SY538 @ SY539 )
= ( sup @ ( inf @ SY538 @ ( modula1144073633_aux_a @ inf @ sup @ SV62 @ SY538 @ SY539 ) ) @ ( modula1936294176_aux_a @ inf @ sup @ SV62 @ SY538 @ SY539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(794,plain,
! [SV63: a] :
( ( ! [SY540: a,SY541: a] :
( ( modula17988509_aux_a @ inf @ sup @ SV63 @ SY540 @ SY541 )
= ( sup @ ( inf @ SV63 @ ( modula1144073633_aux_a @ inf @ sup @ SV63 @ SY540 @ SY541 ) ) @ ( modula1936294176_aux_a @ inf @ sup @ SV63 @ SY540 @ SY541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(795,plain,
! [SV64: a] :
( ( ! [SY542: a,SY543: a] :
( ( modula1373251614_aux_a @ inf @ sup @ SV64 @ SY542 @ SY543 )
= ( modula17988509_aux_a @ inf @ sup @ SY542 @ SY543 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(796,plain,
! [SV65: a] :
( ( ! [SY544: a,SY545: a] :
( ( modula581031071_aux_a @ inf @ sup @ SV65 @ SY544 @ SY545 )
= ( modula17988509_aux_a @ inf @ sup @ SY545 @ SV65 @ SY544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(797,plain,
! [SV66: a] :
( ( ! [SY546: a] : ( condit1001553558elow_a @ less_eq @ ( set_gr1491433118Than_a @ less @ SV66 @ SY546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(798,plain,
( ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(799,plain,
! [SV67: a] :
( ( ! [SY547: a] :
( ( less @ SV67 @ SY547 )
= ( ~ ( ~ ( less_eq @ SV67 @ SY547 )
| ~ ( ( SV67 != SY547 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(800,plain,
! [SV68: a] :
( ( ! [SY548: a,SY549: a] :
( ~ ( less_eq @ SV68 @ SY548 )
| ~ ( less_eq @ SV68 @ SY549 )
| ( less_eq @ SV68 @ ( inf @ SY548 @ SY549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(801,plain,
! [SV69: a] :
( ( ! [SY550: a,SY551: a] :
( ~ ( less_eq @ SV69 @ SY550 )
| ( SY550 != SY551 )
| ( less_eq @ SV69 @ SY551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(802,plain,
! [SV70: a] :
( ( ! [SY552: a,SY553: a] :
( ~ ( less_eq @ SV70 @ SY552 )
| ( less_eq @ SV70 @ ( sup @ SY553 @ SY552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(803,plain,
! [SV71: a] :
( ( ! [SY554: a,SY555: a] :
( ~ ( less @ SV71 @ SY554 )
| ~ ( less_eq @ SY554 @ SY555 )
| ( less @ SV71 @ SY555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(804,plain,
! [SV72: a] :
( ( ! [SY556: a] :
( ~ ~ ( less @ SV72 @ SY556 )
| ( ( less_eq @ SV72 @ SY556 )
= ( SV72 = SY556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(805,plain,
! [SV73: a] :
( ( ! [SY557: a] :
( ( less @ SV73 @ SY557 )
= ( ~ ( ( SV73
!= ( inf @ SV73 @ SY557 ) )
| ~ ( ( SV73 != SY557 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(806,plain,
! [SV74: a] :
( ( ! [SY558: a] :
( ~ ( less_eq @ SV74 @ SY558 )
| ( ( ~ ( less @ SV74 @ SY558 ) )
= ( SV74 = SY558 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(807,plain,
( ( ! [SV75: a] :
( ( ^ [SY559: a] : ( SV75 = SY559 ) )
= ( ^ [SY560: a] :
~ ( ~ ( less_eq @ SY560 @ SV75 )
| ~ ( less_eq @ SV75 @ SY560 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[637]) ).
thf(808,plain,
( ( ( ^ [SX0: a,SX1: a] : ( SX0 = SX1 ) )
= ( ^ [SX0: a,SX1: a] :
~ ( ~ ( less_eq @ SX1 @ SX0 )
| ~ ( less_eq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[637]) ).
thf(809,plain,
! [SV76: a] :
( ( ! [SY561: a,SY562: a] :
( ~ ( less @ SV76 @ ( inf @ SY561 @ SY562 ) )
| ~ ( ~ ( less @ SV76 @ SY561 )
| ~ ( less @ SV76 @ SY562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(810,plain,
! [SV77: a] :
( ( ! [SY563: a] :
( ~ ( less_eq @ SV77 @ SY563 )
| ( ( sup @ SY563 @ SV77 )
= SY563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(811,plain,
! [SV78: a] :
( ( ! [SY564: a,SY565: a] :
( ( SV78 != SY564 )
| ~ ( less_eq @ SY564 @ SY565 )
| ( less_eq @ SV78 @ SY565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(812,plain,
! [SV79: a] :
( ( ! [SY566: a] :
( ( SV79
!= ( inf @ SV79 @ SY566 ) )
| ( less_eq @ SV79 @ SY566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(813,plain,
! [SV80: a] :
( ( ! [SY567: a] :
( ~ ( less_eq @ SV80 @ SY567 )
| ( ( less_eq @ SY567 @ SV80 )
= ( SY567 = SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(814,plain,
! [SV81: a] :
( ( ! [SY568: a,SY569: a] :
( ~ ( less_eq @ SV81 @ SY568 )
| ( less_eq @ ( inf @ SY569 @ SV81 ) @ SY568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(815,plain,
! [SV82: a] :
( ( ! [SY570: a] :
( ~ ( ( SV82 != SY570 ) )
| ~ ( less_eq @ SV82 @ SY570 )
| ( less @ SV82 @ SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(816,plain,
! [SV83: a] :
( ( ! [SY571: a,SY572: a] :
( ~ ( less_eq @ SV83 @ SY571 )
| ~ ( less @ SY572 @ SV83 )
| ( less @ SY572 @ SY571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(817,plain,
! [SV84: a] :
( ( ! [SY573: a] :
( ~ ( less @ SV84 @ SY573 )
| ( less_eq @ SV84 @ SY573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(818,plain,
! [SV85: a] :
( ( ! [SY574: a,SY575: a,SY576: a] :
( ~ ( less_eq @ SV85 @ SY574 )
| ~ ( less_eq @ SY575 @ SY576 )
| ( less_eq @ ( sup @ SV85 @ SY575 ) @ ( sup @ SY574 @ SY576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(819,plain,
! [SV86: a] :
( ( ! [SY577: a] :
( ~ ( less_eq @ SV86 @ SY577 )
| ( ( inf @ SV86 @ SY577 )
= SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(820,plain,
! [SV87: a] :
( ( ! [SY578: a] :
( ( SV87
!= ( sup @ SV87 @ SY578 ) )
| ( less_eq @ SY578 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(821,plain,
( ( ! [SV88: a] :
( ( ^ [SY579: a] : ( SV88 = SY579 ) )
= ( ^ [SY580: a] :
~ ( ~ ( less_eq @ SV88 @ SY580 )
| ~ ( less_eq @ SY580 @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[650]) ).
thf(822,plain,
( ( ( ^ [SX0: a,SX1: a] : ( SX0 = SX1 ) )
= ( ^ [SX0: a,SX1: a] :
~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[650]) ).
thf(823,plain,
! [SV89: a > $o] :
( ( ~ ~ ! [SY581: a] :
~ ~ ( ~ ~ ( ~ ( SV89 @ SY581 )
| ~ ! [SY582: a] :
( ~ ( SV89 @ SY582 )
| ( less_eq @ SY581 @ SY582 ) ) )
| ~ ! [SY583: a] :
( ~ ~ ( ~ ( SV89 @ SY583 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY583 @ SY584 ) ) )
| ( SY583 = SY581 ) ) )
| ( SV89 @ ( least_a @ less_eq @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(824,plain,
! [SV90: a] :
( ( ! [SY585: a] :
( ~ ( less_eq @ SV90 @ SY585 )
| ~ ( less_eq @ SY585 @ SV90 )
| ( SV90 = SY585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(825,plain,
! [SV91: a] :
( ( ! [SY586: a,SY587: a] :
( ~ ( less_eq @ SV91 @ SY586 )
| ( less_eq @ SV91 @ ( sup @ SY586 @ SY587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(826,plain,
! [SV92: a] :
( ( ! [SY588: a,SY589: a] :
( ~ ( less @ SV92 @ SY588 )
| ( less @ ( inf @ SV92 @ SY589 ) @ SY588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(827,plain,
! [SV93: a] :
( ( ! [SY590: a] :
( ~ ( less_eq @ SV93 @ SY590 )
| ( SV93
= ( inf @ SV93 @ SY590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(828,plain,
! [SV94: a] :
( ( ! [SY591: a] :
( ~ ( less_eq @ SV94 @ SY591 )
| ( ( inf @ SV94 @ SY591 )
= SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(829,plain,
! [SV95: a] :
( ( ! [SY592: a,SY593: a] :
( ~ ( less_eq @ SV95 @ SY592 )
| ~ ( less_eq @ SY593 @ SY592 )
| ( less_eq @ ( sup @ SV95 @ SY593 ) @ SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(830,plain,
! [SV96: a] :
( ( ! [SY594: a,SY595: a] :
( ~ ( less_eq @ SV96 @ SY594 )
| ~ ( less @ SY594 @ SY595 )
| ( less @ SV96 @ SY595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(831,plain,
( ( ! [SV97: a] :
( ( ^ [SY596: a] : ( SV97 = SY596 ) )
= ( ^ [SY597: a] :
~ ( ~ ( less_eq @ SV97 @ SY597 )
| ~ ( less_eq @ SY597 @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[659]) ).
thf(832,plain,
( ( ( ^ [SX0: a,SX1: a] : ( SX0 = SX1 ) )
= ( ^ [SX0: a,SX1: a] :
~ ( ~ ( less_eq @ SX0 @ SX1 )
| ~ ( less_eq @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[659]) ).
thf(833,plain,
! [SV98: a] :
( ( ! [SY598: a,SY599: a] :
( ~ ( less_eq @ SV98 @ SY598 )
| ~ ( less_eq @ SV98 @ SY599 )
| ( less_eq @ SV98 @ ( inf @ SY598 @ SY599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(834,plain,
! [SV99: a] :
( ( ! [SY600: a,SY601: a] :
( ~ ( less_eq @ SV99 @ SY600 )
| ( less_eq @ ( inf @ SV99 @ SY601 ) @ SY600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(835,plain,
! [SV100: a] :
( ( ! [SY602: a,SY603: a] :
( ~ ( less @ SV100 @ SY602 )
| ( less @ SV100 @ ( sup @ SY602 @ SY603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(836,plain,
! [SV101: a] :
( ( ! [SY604: a] :
( ~ ( less_eq @ SV101 @ SY604 )
| ( ( inf @ SY604 @ SV101 )
= SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(837,plain,
! [SV102: a] :
( ( ! [SY605: a] :
( ( less @ SV102 @ SY605 )
= ( ~ ( ~ ( less_eq @ SV102 @ SY605 )
| ~ ( ( SY605 != SV102 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(838,plain,
! [SV103: a > $o] :
( ( ! [SY606: a] :
( ~ ~ ! [SY607: a] :
~ ~ ( ~ ~ ( ~ ( SV103 @ SY607 )
| ~ ! [SY608: a] :
( ~ ( SV103 @ SY608 )
| ( less_eq @ SY607 @ SY608 ) ) )
| ~ ! [SY609: a] :
( ~ ~ ( ~ ( SV103 @ SY609 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY609 @ SY610 ) ) )
| ( SY609 = SY607 ) ) )
| ~ ( SV103 @ SY606 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SY606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(839,plain,
! [SV104: set_a] :
( ( ! [SY611: a] :
( ~ ! [SY612: a] :
( ~ ( member_a @ SY612 @ SV104 )
| ( less_eq @ SY612 @ SY611 ) )
| ( condit1627435690bove_a @ less_eq @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(840,plain,
! [SV105: a] :
( ( ! [SY613: a] :
( ( less @ SV105 @ SY613 )
= ( ~ ( ~ ( less_eq @ SV105 @ SY613 )
| ~ ( ( SV105 != SY613 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(841,plain,
! [SV106: a > $o] :
( ( ! [SY614: a] :
( ~ ( SV106 @ SY614 )
| ~ ! [SY615: a] :
( ~ ( SV106 @ SY615 )
| ( less_eq @ SY615 @ SY614 ) )
| ( ( greatest_a @ less_eq @ SV106 )
= SY614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(842,plain,
! [SV107: a] :
( ( ! [SY616: a,SY617: a] :
( ( less_eq @ SV107 @ ( inf @ SY616 @ SY617 ) )
= ( ~ ( ~ ( less_eq @ SV107 @ SY616 )
| ~ ( less_eq @ SV107 @ SY617 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(843,plain,
! [SV108: a] :
( ( ! [SY618: a] :
( ~ ( less_eq @ SV108 @ SY618 )
| ( ( sup @ SV108 @ SY618 )
= SY618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(844,plain,
! [SV109: a] :
( ( ! [SY619: a] :
( ~ ( less_eq @ SV109 @ SY619 )
| ( ( sup @ SY619 @ SV109 )
= SY619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(845,plain,
! [SV110: a] :
( ( ! [SY620: a,SY621: a] :
( ~ ( less_eq @ SV110 @ SY620 )
| ~ ( less_eq @ SY620 @ SY621 )
| ( less_eq @ SV110 @ SY621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(846,plain,
! [SV111: a] :
( ( ! [SY622: a] :
( ~ ( less_eq @ SV111 @ SY622 )
| ~ ( less @ SY622 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(847,plain,
! [SV112: a] :
( ( ! [SY623: a,SY624: a] :
( ~ ( less_eq @ SV112 @ ( inf @ SY623 @ SY624 ) )
| ~ ( ~ ( less_eq @ SV112 @ SY623 )
| ~ ( less_eq @ SV112 @ SY624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(848,plain,
! [SV113: a] :
( ( ! [SY625: a,SY626: a] :
( ~ ( less @ SV113 @ SY625 )
| ( less @ SV113 @ ( sup @ SY625 @ SY626 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(849,plain,
! [SV114: a] :
( ( ! [SY627: a,SY628: a] :
( ~ ( less_eq @ SV114 @ SY627 )
| ( less_eq @ ( inf @ SY628 @ SV114 ) @ SY627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(850,plain,
! [SV115: a] :
( ( ! [SY629: a] :
( ~ ( less_eq @ SV115 @ SY629 )
| ~ ( less_eq @ SY629 @ SV115 )
| ( SY629 = SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(851,plain,
! [SV116: a] :
( ( ! [SY630: a] :
~ ( ~ ( ~ ( less_eq @ SV116 @ SY630 )
| ( ( min_a @ less_eq @ SV116 @ SY630 )
= SV116 ) )
| ~ ( ~ ~ ( less_eq @ SV116 @ SY630 )
| ( ( min_a @ less_eq @ SV116 @ SY630 )
= SY630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(852,plain,
! [SV117: a] :
( ( ! [SY631: a,SY632: a] :
( ~ ( less @ SV117 @ SY631 )
| ( less @ ( inf @ SY632 @ SV117 ) @ SY631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(853,plain,
! [SV118: set_a] :
( ( ( condit1627435690bove_a @ less_eq @ SV118 )
= ( ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(854,plain,
! [SV119: a] :
( ( ! [SY635: a,SY636: a] :
( ~ ( less_eq @ SV119 @ SY635 )
| ~ ( less_eq @ SY635 @ SY636 )
| ( less_eq @ SV119 @ SY636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(855,plain,
! [SV120: a] :
( ( ! [SY637: a] :
( ( less @ SV120 @ SY637 )
= ( ~ ( ( SY637
!= ( sup @ SY637 @ SV120 ) )
| ~ ( ( SY637 != SV120 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(856,plain,
! [SV121: a] :
( ( ! [SY638: a,SY639: a] :
( ~ ( less_eq @ SV121 @ SY638 )
| ~ ( less_eq @ SY639 @ SV121 )
| ( less_eq @ SY639 @ SY638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(857,plain,
! [SV122: a] :
( ( ! [SY640: a,SY641: a] :
( ~ ( less_eq @ SV122 @ ( inf @ SY640 @ SY641 ) )
| ~ ( ~ ( less_eq @ SV122 @ SY640 )
| ~ ( less_eq @ SV122 @ SY641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(858,plain,
! [SV123: a] :
( ( ! [SY642: a] :
( ~ ( less_eq @ SV123 @ SY642 )
| ( SY642
= ( sup @ SY642 @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(859,plain,
! [SV124: a] :
( ( ! [SY643: a,SY644: a] :
( ( less_eq @ ( sup @ SV124 @ SY643 ) @ SY644 )
= ( ~ ( ~ ( less_eq @ SV124 @ SY644 )
| ~ ( less_eq @ SY643 @ SY644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(860,plain,
( ( ( sup @ x @ ( inf @ y @ z ) )
= ( inf @ y @ ( sup @ x @ z ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(861,plain,
! [SV125: a] :
( ( ! [SY645: a,SY646: a] :
( ( less_eq @ SV125 @ ( inf @ SY645 @ SY646 ) )
= ( ~ ( ~ ( less_eq @ SV125 @ SY645 )
| ~ ( less_eq @ SV125 @ SY646 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(862,plain,
! [SV126: a] :
( ( ! [SY647: a,SY648: a] :
( ~ ( less_eq @ SV126 @ SY647 )
| ~ ( less_eq @ SV126 @ SY648 )
| ( less_eq @ SV126 @ ( inf @ SY647 @ SY648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(863,plain,
! [SV127: a] :
( ( ! [SY649: a] :
( ~ ( less_eq @ SV127 @ SY649 )
| ( ( sup @ SV127 @ SY649 )
= SY649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(864,plain,
! [SV128: a] :
( ( ! [SY650: a,SY651: a] :
( ~ ( less_eq @ SV128 @ SY650 )
| ~ ( less @ SY650 @ SY651 )
| ( less @ SV128 @ SY651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(865,plain,
! [SV129: a] :
( ( ! [SY652: a,SY653: a] :
( ~ ( less @ SV129 @ SY652 )
| ~ ( less_eq @ SY653 @ SV129 )
| ( less @ SY653 @ SY652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(866,plain,
! [SV130: set_a] :
( ( ! [SY654: a] :
( ~ ! [SY655: a] :
( ~ ( member_a @ SY655 @ SV130 )
| ( less_eq @ SY654 @ SY655 ) )
| ( condit1001553558elow_a @ less_eq @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(867,plain,
! [SV131: a] :
( ( ! [SY656: a] :
( ~ ( less_eq @ SV131 @ SY656 )
| ~ ( less_eq @ SY656 @ SV131 )
| ( SV131 = SY656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(868,plain,
! [SV132: a > $o] :
( ( ! [SY657: a,SY658: a > $o] :
( ~ ( SV132 @ SY657 )
| ~ ! [SY659: a] :
( ~ ( SV132 @ SY659 )
| ( less_eq @ SY659 @ SY657 ) )
| ~ ! [SY660: a] :
( ~ ( SV132 @ SY660 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY660 ) )
| ( SY658 @ SY660 ) )
| ( SY658 @ ( greatest_a @ less_eq @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(869,plain,
! [SV133: a > a > a] :
( ( ! [SY662: a,SY663: a] :
( ~ ! [SY664: a,SY665: a] : ( less_eq @ ( SV133 @ SY664 @ SY665 ) @ SY664 )
| ~ ! [SY666: a,SY667: a] : ( less_eq @ ( SV133 @ SY666 @ SY667 ) @ SY667 )
| ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SY662 @ SY663 )
= ( SV133 @ SY662 @ SY663 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(870,plain,
! [SV134: a] :
( ( ! [SY671: a,SY672: a] :
( ~ ( less_eq @ SV134 @ SY671 )
| ( less_eq @ ( inf @ SV134 @ SY672 ) @ SY671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(871,plain,
! [SV135: a > a > a] :
( ( ! [SY673: a,SY674: a] :
( ~ ! [SY675: a,SY676: a] : ( less_eq @ SY675 @ ( SV135 @ SY675 @ SY676 ) )
| ~ ! [SY677: a,SY678: a] : ( less_eq @ SY678 @ ( SV135 @ SY677 @ SY678 ) )
| ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SY673 @ SY674 )
= ( SV135 @ SY673 @ SY674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(872,plain,
! [SV136: a] :
( ( ! [SY682: a,SY683: a,SY684: a] :
( ~ ( less_eq @ SV136 @ SY682 )
| ~ ( less_eq @ SY683 @ SY684 )
| ( less_eq @ ( inf @ SV136 @ SY683 ) @ ( inf @ SY682 @ SY684 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(873,plain,
! [SV137: a] :
( ( ! [SY685: a] :
( ~ ( ( SV137 != SY685 ) )
| ~ ( less_eq @ SY685 @ SV137 )
| ( less @ SY685 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(874,plain,
! [SV138: a] :
( ( ! [SY686: a,SY687: a] :
( ~ ( less @ SV138 @ SY686 )
| ( less @ SV138 @ ( sup @ SY687 @ SY686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(875,plain,
! [SV139: a] :
( ( ! [SY688: a] :
( ~ ( less_eq @ SV139 @ SY688 )
| ( less @ SV139 @ SY688 )
| ( SV139 = SY688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(876,plain,
! [SV140: a] :
( ( ! [SY689: a,SY690: a] :
( ~ ( less_eq @ SV140 @ SY689 )
| ( less_eq @ SV140 @ ( sup @ SY689 @ SY690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(877,plain,
! [SV141: a] :
( ( ! [SY691: a] :
( ( SV141 != SY691 )
| ( less_eq @ SV141 @ SY691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(878,plain,
! [SV142: a] :
( ( ! [SY692: a] :
( ~ ( less_eq @ SV142 @ SY692 )
| ( ( inf @ SY692 @ SV142 )
= SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(879,plain,
! [SV143: a] :
( ( ! [SY693: a,SY694: a] :
( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( inf @ SX3 @ ( sup @ SX4 @ SX5 ) )
= ( sup @ ( inf @ SX3 @ SX4 ) @ ( inf @ SX3 @ SX5 ) ) )
| ( ( sup @ SV143 @ ( inf @ SY693 @ SY694 ) )
= ( inf @ ( sup @ SV143 @ SY693 ) @ ( sup @ SV143 @ SY694 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(880,plain,
! [SV144: a] :
( ( ! [SY698: a,SY699: a] :
( ~ ( less_eq @ SV144 @ SY698 )
| ~ ( less_eq @ SY699 @ SY698 )
| ( less_eq @ ( sup @ SV144 @ SY699 ) @ SY698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(881,plain,
! [SV145: a > $o] :
( ( ! [SY700: a] :
( ~ ( SV145 @ SY700 )
| ~ ! [SY701: a] :
( ~ ( SV145 @ SY701 )
| ( less_eq @ SY700 @ SY701 ) )
| ( ( least_a @ less_eq @ SV145 )
= SY700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(882,plain,
! [SV146: a] :
( ( ! [SY702: a,SY703: a,SY704: a] :
( ~ ( less_eq @ SV146 @ SY702 )
| ~ ( less_eq @ SY703 @ SY704 )
| ( less_eq @ ( sup @ SV146 @ SY703 ) @ ( sup @ SY702 @ SY704 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(883,plain,
! [SV147: a] :
( ( ! [SY705: a] :
( ~ ( less @ SV147 @ SY705 )
| ( less_eq @ SV147 @ SY705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(884,plain,
! [SV148: a] :
( ( ! [SY706: a,SY707: a] :
( ~ ( less_eq @ ( sup @ SV148 @ SY706 ) @ SY707 )
| ~ ( ~ ( less_eq @ SV148 @ SY707 )
| ~ ( less_eq @ SY706 @ SY707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(885,plain,
! [SV149: a] :
( ( ! [SY708: a,SY709: a] :
( ~ ( less_eq @ SV149 @ SY708 )
| ~ ( less_eq @ SY709 @ SY708 )
| ( less_eq @ ( sup @ SV149 @ SY709 ) @ SY708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(886,plain,
! [SV150: a] :
( ( ! [SY710: a,SY711: a] :
( ~ ( less @ SV150 @ SY710 )
| ( less @ SV150 @ ( sup @ SY711 @ SY710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(887,plain,
! [SV151: a] :
( ( ! [SY712: a,SY713: a] :
( ~ ( less @ ( sup @ SV151 @ SY712 ) @ SY713 )
| ~ ( ~ ( less @ SV151 @ SY713 )
| ~ ( less @ SY712 @ SY713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(888,plain,
! [SV152: a] :
( ( ! [SY714: a,SY715: a] :
( ~ ( less_eq @ SV152 @ SY714 )
| ( less_eq @ SV152 @ ( sup @ SY715 @ SY714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(889,plain,
! [SV153: a] :
( ( ! [SY716: a] :
~ ( ~ ( ~ ( less_eq @ SV153 @ SY716 )
| ( ( max_a @ less_eq @ SV153 @ SY716 )
= SY716 ) )
| ~ ( ~ ~ ( less_eq @ SV153 @ SY716 )
| ( ( max_a @ less_eq @ SV153 @ SY716 )
= SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(890,plain,
! [SV154: a] :
( ( ! [SY717: a] :
( ( less @ SV154 @ SY717 )
= ( ~ ( ~ ( less_eq @ SV154 @ SY717 )
| ~ ~ ( less_eq @ SY717 @ SV154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(891,plain,
! [SV155: a] :
( ( ! [SY718: a,SY719: a] :
( ~ ( less @ SV155 @ SY718 )
| ( less @ ( inf @ SY719 @ SV155 ) @ SY718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(892,plain,
! [SV156: set_a] :
( ( ( condit1001553558elow_a @ less_eq @ SV156 )
= ( ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(893,plain,
! [SV157: a] :
( ( ! [SY722: a] :
( ~ ( less @ SV157 @ SY722 )
| ( less_eq @ SV157 @ SY722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(894,plain,
! [SV158: a > $o] :
( ( ! [SY723: a,SY724: a > $o] :
( ~ ( SV158 @ SY723 )
| ~ ! [SY725: a] :
( ~ ( SV158 @ SY725 )
| ( less_eq @ SY723 @ SY725 ) )
| ~ ! [SY726: a] :
( ~ ( SV158 @ SY726 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY726 @ SY727 ) )
| ( SY724 @ SY726 ) )
| ( SY724 @ ( least_a @ less_eq @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(895,plain,
! [SV159: a] :
( ( ! [SY728: a,SY729: a] :
( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV159 @ SY728 @ SY729 )
| ( modula1727524044comp_a @ less_eq @ SV159 @ SY728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(896,plain,
! [SV160: a] :
( ( ! [SY730: a,SY731: a] :
( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SY730 @ SY731 )
= ( ~ ( ~ ~ ( ( ( inf @ SV160 @ SY731 )
!= ( inf @ SY730 @ SY731 ) )
| ~ ( less @ SV160 @ SY730 ) )
| ( ( sup @ SV160 @ SY731 )
!= ( sup @ SY730 @ SY731 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(897,plain,
! [SV161: a] :
( ( ! [SY732: a] :
( ( modula1727524044comp_a @ less_eq @ SV161 @ SY732 )
= ( ~ ( ~ ~ ( less_eq @ SV161 @ SY732 )
| ~ ~ ( less_eq @ SY732 @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(898,plain,
! [SV162: a] :
( ( ! [SY733: a,SY734: a] :
( ~ ( less @ SV162 @ SY733 )
| ( less @ ( inf @ SV162 @ SY734 ) @ SY733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(899,plain,
! [SV163: a] :
( ( ! [SY735: a,SY736: a] :
( ~ ( less_eq @ ( sup @ SV163 @ SY735 ) @ SY736 )
| ~ ( ~ ( less_eq @ SV163 @ SY736 )
| ~ ( less_eq @ SY735 @ SY736 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(900,plain,
! [SV164: a] :
( ( ! [SY737: a] :
( ~ ( less_eq @ SV164 @ SY737 )
| ~ ( ( SV164 != SY737 ) )
| ( less @ SV164 @ SY737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(901,plain,
! [SV165: a] :
( ( ! [SY738: a,SY739: a] :
( ( less_eq @ ( sup @ SV165 @ SY738 ) @ SY739 )
= ( ~ ( ~ ( less_eq @ SV165 @ SY739 )
| ~ ( less_eq @ SY738 @ SY739 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(902,plain,
! [SV166: a] :
( ( ! [SY740: a,SY741: a] :
( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( sup @ SX3 @ ( inf @ SX4 @ SX5 ) )
= ( inf @ ( sup @ SX3 @ SX4 ) @ ( sup @ SX3 @ SX5 ) ) )
| ( ( inf @ SV166 @ ( sup @ SY740 @ SY741 ) )
= ( sup @ ( inf @ SV166 @ SY740 ) @ ( inf @ SV166 @ SY741 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(903,plain,
! [SV167: a] :
( ( ! [SY745: a,SY746: a] :
( ~ ( less @ SV167 @ SY745 )
| ~ ( less_eq @ SY745 @ SY746 )
| ( less @ SV167 @ SY746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(904,plain,
! [SV168: a] :
( ( ! [SY747: a,SY748: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SY747 @ SY748 )
= ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SY747 )
!= ( inf @ SY747 @ SY748 ) )
| ( ( inf @ SY748 @ SV168 )
!= ( inf @ SY747 @ SY748 ) ) )
| ( ( sup @ SV168 @ SY747 )
!= ( sup @ SY747 @ SY748 ) ) )
| ( ( sup @ SY748 @ SV168 )
!= ( sup @ SY747 @ SY748 ) ) )
| ~ ( less @ ( inf @ SV168 @ SY747 ) @ ( sup @ SV168 @ SY747 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(905,plain,
! [SV169: a,SV1: a] :
( ( ! [SY749: a] :
( ( inf @ ( inf @ SV1 @ SV169 ) @ SY749 )
= ( inf @ SV1 @ ( inf @ SV169 @ SY749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(906,plain,
! [SV170: a,SV2: a] :
( ( ( inf @ SV2 @ SV170 )
= ( inf @ SV170 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(907,plain,
! [SV171: a,SV3: a] :
( ( ! [SY750: a] :
( ( inf @ SV3 @ ( inf @ SV171 @ SY750 ) )
= ( inf @ SV171 @ ( inf @ SV3 @ SY750 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(908,plain,
! [SV172: a,SV4: a] :
( ( ! [SY751: a] :
( ( inf @ ( inf @ SV4 @ SV172 ) @ SY751 )
= ( inf @ SV4 @ ( inf @ SV172 @ SY751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(909,plain,
! [SV173: a,SV5: a] :
( ( ( inf @ SV5 @ SV173 )
= ( inf @ SV173 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(910,plain,
! [SV174: a,SV6: a] :
( ( ! [SY752: a] :
( ( inf @ SV6 @ ( inf @ SV174 @ SY752 ) )
= ( inf @ SV174 @ ( inf @ SV6 @ SY752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(911,plain,
! [SV175: a,SV7: a] :
( ( ! [SY753: a] :
( ( sup @ ( sup @ SV7 @ SV175 ) @ SY753 )
= ( sup @ SV7 @ ( sup @ SV175 @ SY753 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(912,plain,
! [SV176: a,SV8: a] :
( ( ( sup @ SV8 @ SV176 )
= ( sup @ SV176 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(913,plain,
! [SV177: a,SV9: a] :
( ( ! [SY754: a] :
( ( sup @ SV9 @ ( sup @ SV177 @ SY754 ) )
= ( sup @ SV177 @ ( sup @ SV9 @ SY754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(914,plain,
! [SV178: a,SV10: a] :
( ( ! [SY755: a] :
( ( sup @ ( sup @ SV10 @ SV178 ) @ SY755 )
= ( sup @ SV10 @ ( sup @ SV178 @ SY755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(915,plain,
! [SV179: a,SV11: a] :
( ( ( sup @ SV11 @ SV179 )
= ( sup @ SV179 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(916,plain,
! [SV180: a,SV12: a] :
( ( ! [SY756: a] :
( ( sup @ SV12 @ ( sup @ SV180 @ SY756 ) )
= ( sup @ SV180 @ ( sup @ SV12 @ SY756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(917,plain,
! [SV181: a,SV13: a] :
( ( ( less_eq @ SV13 @ SV181 )
= ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(918,plain,
! [SV182: a,SV14: a] :
( ( ( less_eq @ SV14 @ SV182 )
= ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(919,plain,
! [SV183: a,SV15: a] :
( ( ( less_eq @ SV15 @ SV183 )
= ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(920,plain,
! [SV184: a,SV16: a] :
( ( ( less_eq @ SV16 @ SV184 )
= ( ( inf @ SV16 @ SV184 )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(921,plain,
! [SV185: a,SV17: a] :
( ( ( less_eq @ SV17 @ SV185 )
= ( ( inf @ SV185 @ SV17 )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(922,plain,
! [SV186: a,SV18: a] :
( ( less_eq @ ( inf @ SV18 @ SV186 ) @ SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(923,plain,
! [SV187: a,SV19: a] :
( ( less_eq @ ( inf @ SV19 @ SV187 ) @ SV187 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(924,plain,
! [SV188: a,SV20: a] :
( ( ( less_eq @ SV20 @ SV188 )
= ( SV20
= ( inf @ SV20 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(925,plain,
! [SV189: a,SV21: a] :
( ( less_eq @ ( inf @ SV21 @ SV189 ) @ SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(926,plain,
! [SV190: a,SV22: a] :
( ( less_eq @ ( inf @ SV22 @ SV190 ) @ SV190 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(927,plain,
! [SV191: a,SV23: a] :
( ( ( less_eq @ SV23 @ SV191 )
= ( ( inf @ SV23 @ SV191 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(928,plain,
! [SV192: a,SV24: a] :
( ( ( less_eq @ SV24 @ SV192 )
= ( ( sup @ SV24 @ SV192 )
= SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(929,plain,
! [SV193: a,SV25: a] :
( ( ( less_eq @ SV25 @ SV193 )
= ( ( sup @ SV193 @ SV25 )
= SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(930,plain,
! [SV194: a,SV26: a] :
( ( ( less_eq @ SV26 @ SV194 )
= ( ( sup @ SV26 @ SV194 )
= SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(931,plain,
! [SV195: a,SV27: a] :
( ( less_eq @ SV27 @ ( sup @ SV27 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(932,plain,
! [SV196: a,SV28: a] :
( ( less_eq @ SV28 @ ( sup @ SV196 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(933,plain,
! [SV197: a,SV29: a] :
( ( ( less_eq @ SV29 @ SV197 )
= ( SV197
= ( sup @ SV197 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(934,plain,
! [SV198: a,SV30: a] :
( ( less_eq @ SV30 @ ( sup @ SV30 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(935,plain,
! [SV199: a,SV31: a] :
( ( less_eq @ SV31 @ ( sup @ SV199 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(936,plain,
! [SV200: a,SV32: a] :
( ( ! [SY757: a] : ( less_eq @ ( sup @ ( inf @ SV32 @ SV200 ) @ ( inf @ SV32 @ SY757 ) ) @ ( inf @ SV32 @ ( sup @ SV200 @ SY757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(937,plain,
! [SV201: a,SV33: a] :
( ( ! [SY758: a] : ( less_eq @ ( sup @ SV33 @ ( inf @ SV201 @ SY758 ) ) @ ( inf @ ( sup @ SV33 @ SV201 ) @ ( sup @ SV33 @ SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(938,plain,
! [SV202: a,SV37: a] :
( ( ( inf @ SV37 @ ( inf @ SV37 @ SV202 ) )
= ( inf @ SV37 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(939,plain,
! [SV203: a,SV38: a] :
( ( ( inf @ ( inf @ SV38 @ SV203 ) @ SV203 )
= ( inf @ SV38 @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(940,plain,
! [SV204: a,SV40: a] :
( ( ( inf @ SV40 @ ( inf @ SV40 @ SV204 ) )
= ( inf @ SV40 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(941,plain,
! [SV205: a,SV41: a] :
( ( ( inf @ ( inf @ SV41 @ SV205 ) @ SV205 )
= ( inf @ SV41 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(942,plain,
! [SV206: a,SV43: a] :
( ( ( sup @ SV43 @ ( sup @ SV43 @ SV206 ) )
= ( sup @ SV43 @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(943,plain,
! [SV207: a,SV44: a] :
( ( ( sup @ ( sup @ SV44 @ SV207 ) @ SV207 )
= ( sup @ SV44 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(944,plain,
! [SV208: a,SV46: a] :
( ( ( sup @ SV46 @ ( sup @ SV46 @ SV208 ) )
= ( sup @ SV46 @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(945,plain,
! [SV209: a,SV47: a] :
( ( ! [SY759: a] :
( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SY759 )
= ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SY759 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SY759 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(946,plain,
! [SV210: a,SV48: a] :
( ( ( inf @ SV48 @ ( sup @ SV48 @ SV210 ) )
= SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(947,plain,
! [SV211: a,SV49: a] :
( ( ( sup @ SV49 @ ( inf @ SV49 @ SV211 ) )
= SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(948,plain,
! [SV212: a,SV50: a] :
( ( ! [SY760: a] :
( ( sup @ SV50 @ ( modula1936294176_aux_a @ inf @ sup @ SV50 @ SV212 @ SY760 ) )
= ( sup @ SV50 @ ( inf @ SV212 @ SY760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(949,plain,
! [SV213: a,SV51: a] :
( ( ! [SY761: a] :
( ( sup @ SV51 @ ( modula1936294176_aux_a @ inf @ sup @ SV213 @ SV51 @ SY761 ) )
= ( sup @ SV51 @ ( inf @ SY761 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(950,plain,
! [SV214: a,SV52: a] :
( ( ! [SY762: a] :
( ( modula1936294176_aux_a @ inf @ sup @ SV52 @ SV214 @ SY762 )
= ( sup @ ( sup @ ( inf @ SV52 @ SV214 ) @ ( inf @ SV214 @ SY762 ) ) @ ( inf @ SY762 @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(951,plain,
! [SV215: a,SV53: a] :
( ( ! [SY763: a] :
( ( modula1936294176_aux_a @ inf @ sup @ SV53 @ SV215 @ SY763 )
= ( modula1936294176_aux_a @ inf @ sup @ SY763 @ SV53 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(952,plain,
! [SV216: a,SV54: a] :
( ( ! [SY764: a] :
( ( modula1936294176_aux_a @ inf @ sup @ SV54 @ SV216 @ SY764 )
= ( modula1936294176_aux_a @ inf @ sup @ SV216 @ SY764 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(953,plain,
! [SV217: a,SV55: a] :
( ( ! [SY765: a] :
( ( inf @ SV55 @ ( modula1144073633_aux_a @ inf @ sup @ SV55 @ SV217 @ SY765 ) )
= ( inf @ SV55 @ ( sup @ SV217 @ SY765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(954,plain,
! [SV218: a,SV56: a] :
( ( ! [SY766: a] :
( ( inf @ SV56 @ ( modula1144073633_aux_a @ inf @ sup @ SV218 @ SV56 @ SY766 ) )
= ( inf @ SV56 @ ( sup @ SY766 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(955,plain,
! [SV219: a,SV57: a] :
( ( ! [SY767: a] :
( ( inf @ SV57 @ ( modula1144073633_aux_a @ inf @ sup @ SV219 @ SY767 @ SV57 ) )
= ( inf @ SV57 @ ( sup @ SV219 @ SY767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(956,plain,
! [SV220: a,SV58: a] :
( ( ! [SY768: a] :
( ( modula1144073633_aux_a @ inf @ sup @ SV58 @ SV220 @ SY768 )
= ( inf @ ( inf @ ( sup @ SV58 @ SV220 ) @ ( sup @ SV220 @ SY768 ) ) @ ( sup @ SY768 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(957,plain,
! [SV221: a,SV59: a] :
( ( ! [SY769: a] :
( ( modula1144073633_aux_a @ inf @ sup @ SV59 @ SV221 @ SY769 )
= ( modula1144073633_aux_a @ inf @ sup @ SY769 @ SV59 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(958,plain,
! [SV222: a,SV60: a] :
( ( ! [SY770: a] :
( ( modula1144073633_aux_a @ inf @ sup @ SV60 @ SV222 @ SY770 )
= ( modula1144073633_aux_a @ inf @ sup @ SV222 @ SY770 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(959,plain,
! [SV223: a,SV61: a] :
( ( ! [SY771: a] :
( ( modula581031071_aux_a @ inf @ sup @ SV61 @ SV223 @ SY771 )
= ( sup @ ( inf @ SY771 @ ( modula1144073633_aux_a @ inf @ sup @ SV61 @ SV223 @ SY771 ) ) @ ( modula1936294176_aux_a @ inf @ sup @ SV61 @ SV223 @ SY771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(960,plain,
! [SV224: a,SV62: a] :
( ( ! [SY772: a] :
( ( modula1373251614_aux_a @ inf @ sup @ SV62 @ SV224 @ SY772 )
= ( sup @ ( inf @ SV224 @ ( modula1144073633_aux_a @ inf @ sup @ SV62 @ SV224 @ SY772 ) ) @ ( modula1936294176_aux_a @ inf @ sup @ SV62 @ SV224 @ SY772 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(961,plain,
! [SV225: a,SV63: a] :
( ( ! [SY773: a] :
( ( modula17988509_aux_a @ inf @ sup @ SV63 @ SV225 @ SY773 )
= ( sup @ ( inf @ SV63 @ ( modula1144073633_aux_a @ inf @ sup @ SV63 @ SV225 @ SY773 ) ) @ ( modula1936294176_aux_a @ inf @ sup @ SV63 @ SV225 @ SY773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(962,plain,
! [SV226: a,SV64: a] :
( ( ! [SY774: a] :
( ( modula1373251614_aux_a @ inf @ sup @ SV64 @ SV226 @ SY774 )
= ( modula17988509_aux_a @ inf @ sup @ SV226 @ SY774 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(963,plain,
! [SV227: a,SV65: a] :
( ( ! [SY775: a] :
( ( modula581031071_aux_a @ inf @ sup @ SV65 @ SV227 @ SY775 )
= ( modula17988509_aux_a @ inf @ sup @ SY775 @ SV65 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(964,plain,
! [SV228: a,SV66: a] :
( ( condit1001553558elow_a @ less_eq @ ( set_gr1491433118Than_a @ less @ SV66 @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(965,plain,
! [SV229: a,SV67: a] :
( ( ( less @ SV67 @ SV229 )
= ( ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(966,plain,
! [SV230: a,SV68: a] :
( ( ! [SY776: a] :
( ~ ( less_eq @ SV68 @ SV230 )
| ~ ( less_eq @ SV68 @ SY776 )
| ( less_eq @ SV68 @ ( inf @ SV230 @ SY776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(967,plain,
! [SV231: a,SV69: a] :
( ( ! [SY777: a] :
( ~ ( less_eq @ SV69 @ SV231 )
| ( SV231 != SY777 )
| ( less_eq @ SV69 @ SY777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(968,plain,
! [SV232: a,SV70: a] :
( ( ! [SY778: a] :
( ~ ( less_eq @ SV70 @ SV232 )
| ( less_eq @ SV70 @ ( sup @ SY778 @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(969,plain,
! [SV233: a,SV71: a] :
( ( ! [SY779: a] :
( ~ ( less @ SV71 @ SV233 )
| ~ ( less_eq @ SV233 @ SY779 )
| ( less @ SV71 @ SY779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(970,plain,
! [SV234: a,SV72: a] :
( ( ~ ~ ( less @ SV72 @ SV234 )
| ( ( less_eq @ SV72 @ SV234 )
= ( SV72 = SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(971,plain,
! [SV235: a,SV73: a] :
( ( ( less @ SV73 @ SV235 )
= ( ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(972,plain,
! [SV236: a,SV74: a] :
( ( ~ ( less_eq @ SV74 @ SV236 )
| ( ( ~ ( less @ SV74 @ SV236 ) )
= ( SV74 = SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(973,plain,
! [SV237: a] :
( ( ( ^ [SY780: a] : ( SV237 = SY780 ) )
= ( ^ [SY781: a] :
~ ( ~ ( less_eq @ SY781 @ SV237 )
| ~ ( less_eq @ SV237 @ SY781 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(974,plain,
! [SV238: a,SV76: a] :
( ( ! [SY782: a] :
( ~ ( less @ SV76 @ ( inf @ SV238 @ SY782 ) )
| ~ ( ~ ( less @ SV76 @ SV238 )
| ~ ( less @ SV76 @ SY782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(975,plain,
! [SV239: a,SV77: a] :
( ( ~ ( less_eq @ SV77 @ SV239 )
| ( ( sup @ SV239 @ SV77 )
= SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(976,plain,
! [SV240: a,SV78: a] :
( ( ! [SY783: a] :
( ( SV78 != SV240 )
| ~ ( less_eq @ SV240 @ SY783 )
| ( less_eq @ SV78 @ SY783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(977,plain,
! [SV241: a,SV79: a] :
( ( ( SV79
!= ( inf @ SV79 @ SV241 ) )
| ( less_eq @ SV79 @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(978,plain,
! [SV242: a,SV80: a] :
( ( ~ ( less_eq @ SV80 @ SV242 )
| ( ( less_eq @ SV242 @ SV80 )
= ( SV242 = SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(979,plain,
! [SV243: a,SV81: a] :
( ( ! [SY784: a] :
( ~ ( less_eq @ SV81 @ SV243 )
| ( less_eq @ ( inf @ SY784 @ SV81 ) @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(980,plain,
! [SV244: a,SV82: a] :
( ( ~ ( ( SV82 != SV244 ) )
| ~ ( less_eq @ SV82 @ SV244 )
| ( less @ SV82 @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(981,plain,
! [SV245: a,SV83: a] :
( ( ! [SY785: a] :
( ~ ( less_eq @ SV83 @ SV245 )
| ~ ( less @ SY785 @ SV83 )
| ( less @ SY785 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(982,plain,
! [SV246: a,SV84: a] :
( ( ~ ( less @ SV84 @ SV246 )
| ( less_eq @ SV84 @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(983,plain,
! [SV247: a,SV85: a] :
( ( ! [SY786: a,SY787: a] :
( ~ ( less_eq @ SV85 @ SV247 )
| ~ ( less_eq @ SY786 @ SY787 )
| ( less_eq @ ( sup @ SV85 @ SY786 ) @ ( sup @ SV247 @ SY787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(984,plain,
! [SV248: a,SV86: a] :
( ( ~ ( less_eq @ SV86 @ SV248 )
| ( ( inf @ SV86 @ SV248 )
= SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(985,plain,
! [SV249: a,SV87: a] :
( ( ( SV87
!= ( sup @ SV87 @ SV249 ) )
| ( less_eq @ SV249 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(986,plain,
! [SV250: a] :
( ( ( ^ [SY788: a] : ( SV250 = SY788 ) )
= ( ^ [SY789: a] :
~ ( ~ ( less_eq @ SV250 @ SY789 )
| ~ ( less_eq @ SY789 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(987,plain,
! [SV89: a > $o] :
( ( ( ~ ~ ! [SY581: a] :
~ ~ ( ~ ~ ( ~ ( SV89 @ SY581 )
| ~ ! [SY582: a] :
( ~ ( SV89 @ SY582 )
| ( less_eq @ SY581 @ SY582 ) ) )
| ~ ! [SY583: a] :
( ~ ~ ( ~ ( SV89 @ SY583 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY583 @ SY584 ) ) )
| ( SY583 = SY581 ) ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(988,plain,
! [SV251: a,SV90: a] :
( ( ~ ( less_eq @ SV90 @ SV251 )
| ~ ( less_eq @ SV251 @ SV90 )
| ( SV90 = SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(989,plain,
! [SV252: a,SV91: a] :
( ( ! [SY790: a] :
( ~ ( less_eq @ SV91 @ SV252 )
| ( less_eq @ SV91 @ ( sup @ SV252 @ SY790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(990,plain,
! [SV253: a,SV92: a] :
( ( ! [SY791: a] :
( ~ ( less @ SV92 @ SV253 )
| ( less @ ( inf @ SV92 @ SY791 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(991,plain,
! [SV254: a,SV93: a] :
( ( ~ ( less_eq @ SV93 @ SV254 )
| ( SV93
= ( inf @ SV93 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(992,plain,
! [SV255: a,SV94: a] :
( ( ~ ( less_eq @ SV94 @ SV255 )
| ( ( inf @ SV94 @ SV255 )
= SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(993,plain,
! [SV256: a,SV95: a] :
( ( ! [SY792: a] :
( ~ ( less_eq @ SV95 @ SV256 )
| ~ ( less_eq @ SY792 @ SV256 )
| ( less_eq @ ( sup @ SV95 @ SY792 ) @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(994,plain,
! [SV257: a,SV96: a] :
( ( ! [SY793: a] :
( ~ ( less_eq @ SV96 @ SV257 )
| ~ ( less @ SV257 @ SY793 )
| ( less @ SV96 @ SY793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(995,plain,
! [SV258: a] :
( ( ( ^ [SY794: a] : ( SV258 = SY794 ) )
= ( ^ [SY795: a] :
~ ( ~ ( less_eq @ SV258 @ SY795 )
| ~ ( less_eq @ SY795 @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(996,plain,
! [SV259: a,SV98: a] :
( ( ! [SY796: a] :
( ~ ( less_eq @ SV98 @ SV259 )
| ~ ( less_eq @ SV98 @ SY796 )
| ( less_eq @ SV98 @ ( inf @ SV259 @ SY796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(997,plain,
! [SV260: a,SV99: a] :
( ( ! [SY797: a] :
( ~ ( less_eq @ SV99 @ SV260 )
| ( less_eq @ ( inf @ SV99 @ SY797 ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(998,plain,
! [SV261: a,SV100: a] :
( ( ! [SY798: a] :
( ~ ( less @ SV100 @ SV261 )
| ( less @ SV100 @ ( sup @ SV261 @ SY798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(999,plain,
! [SV262: a,SV101: a] :
( ( ~ ( less_eq @ SV101 @ SV262 )
| ( ( inf @ SV262 @ SV101 )
= SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1000,plain,
! [SV263: a,SV102: a] :
( ( ( less @ SV102 @ SV263 )
= ( ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1001,plain,
! [SV264: a,SV103: a > $o] :
( ( ~ ~ ! [SY607: a] :
~ ~ ( ~ ~ ( ~ ( SV103 @ SY607 )
| ~ ! [SY608: a] :
( ~ ( SV103 @ SY608 )
| ( less_eq @ SY607 @ SY608 ) ) )
| ~ ! [SY609: a] :
( ~ ~ ( ~ ( SV103 @ SY609 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY609 @ SY610 ) ) )
| ( SY609 = SY607 ) ) )
| ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1002,plain,
! [SV265: a,SV104: set_a] :
( ( ~ ! [SY803: a] :
( ~ ( member_a @ SY803 @ SV104 )
| ( less_eq @ SY803 @ SV265 ) )
| ( condit1627435690bove_a @ less_eq @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1003,plain,
! [SV266: a,SV105: a] :
( ( ( less @ SV105 @ SV266 )
= ( ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1004,plain,
! [SV267: a,SV106: a > $o] :
( ( ~ ( SV106 @ SV267 )
| ~ ! [SY804: a] :
( ~ ( SV106 @ SY804 )
| ( less_eq @ SY804 @ SV267 ) )
| ( ( greatest_a @ less_eq @ SV106 )
= SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1005,plain,
! [SV268: a,SV107: a] :
( ( ! [SY805: a] :
( ( less_eq @ SV107 @ ( inf @ SV268 @ SY805 ) )
= ( ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SY805 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1006,plain,
! [SV269: a,SV108: a] :
( ( ~ ( less_eq @ SV108 @ SV269 )
| ( ( sup @ SV108 @ SV269 )
= SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1007,plain,
! [SV270: a,SV109: a] :
( ( ~ ( less_eq @ SV109 @ SV270 )
| ( ( sup @ SV270 @ SV109 )
= SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1008,plain,
! [SV271: a,SV110: a] :
( ( ! [SY806: a] :
( ~ ( less_eq @ SV110 @ SV271 )
| ~ ( less_eq @ SV271 @ SY806 )
| ( less_eq @ SV110 @ SY806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1009,plain,
! [SV272: a,SV111: a] :
( ( ~ ( less_eq @ SV111 @ SV272 )
| ~ ( less @ SV272 @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1010,plain,
! [SV273: a,SV112: a] :
( ( ! [SY807: a] :
( ~ ( less_eq @ SV112 @ ( inf @ SV273 @ SY807 ) )
| ~ ( ~ ( less_eq @ SV112 @ SV273 )
| ~ ( less_eq @ SV112 @ SY807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1011,plain,
! [SV274: a,SV113: a] :
( ( ! [SY808: a] :
( ~ ( less @ SV113 @ SV274 )
| ( less @ SV113 @ ( sup @ SV274 @ SY808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1012,plain,
! [SV275: a,SV114: a] :
( ( ! [SY809: a] :
( ~ ( less_eq @ SV114 @ SV275 )
| ( less_eq @ ( inf @ SY809 @ SV114 ) @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1013,plain,
! [SV276: a,SV115: a] :
( ( ~ ( less_eq @ SV115 @ SV276 )
| ~ ( less_eq @ SV276 @ SV115 )
| ( SV276 = SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1014,plain,
! [SV277: a,SV116: a] :
( ( ~ ( ~ ( ~ ( less_eq @ SV116 @ SV277 )
| ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV116 ) )
| ~ ( ~ ~ ( less_eq @ SV116 @ SV277 )
| ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1015,plain,
! [SV278: a,SV117: a] :
( ( ! [SY810: a] :
( ~ ( less @ SV117 @ SV278 )
| ( less @ ( inf @ SY810 @ SV117 ) @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1016,plain,
! [SV118: set_a] :
( ( ~ ( ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
| ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[853]) ).
thf(1017,plain,
! [SV118: set_a] :
( ( ( condit1627435690bove_a @ less_eq @ SV118 )
= ( ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[853]) ).
thf(1018,plain,
! [SV279: a,SV119: a] :
( ( ! [SY811: a] :
( ~ ( less_eq @ SV119 @ SV279 )
| ~ ( less_eq @ SV279 @ SY811 )
| ( less_eq @ SV119 @ SY811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1019,plain,
! [SV280: a,SV120: a] :
( ( ( less @ SV120 @ SV280 )
= ( ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1020,plain,
! [SV281: a,SV121: a] :
( ( ! [SY812: a] :
( ~ ( less_eq @ SV121 @ SV281 )
| ~ ( less_eq @ SY812 @ SV121 )
| ( less_eq @ SY812 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1021,plain,
! [SV282: a,SV122: a] :
( ( ! [SY813: a] :
( ~ ( less_eq @ SV122 @ ( inf @ SV282 @ SY813 ) )
| ~ ( ~ ( less_eq @ SV122 @ SV282 )
| ~ ( less_eq @ SV122 @ SY813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1022,plain,
! [SV283: a,SV123: a] :
( ( ~ ( less_eq @ SV123 @ SV283 )
| ( SV283
= ( sup @ SV283 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1023,plain,
! [SV284: a,SV124: a] :
( ( ! [SY814: a] :
( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SY814 )
= ( ~ ( ~ ( less_eq @ SV124 @ SY814 )
| ~ ( less_eq @ SV284 @ SY814 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1024,plain,
! [SV285: a,SV125: a] :
( ( ! [SY815: a] :
( ( less_eq @ SV125 @ ( inf @ SV285 @ SY815 ) )
= ( ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SY815 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1025,plain,
! [SV286: a,SV126: a] :
( ( ! [SY816: a] :
( ~ ( less_eq @ SV126 @ SV286 )
| ~ ( less_eq @ SV126 @ SY816 )
| ( less_eq @ SV126 @ ( inf @ SV286 @ SY816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1026,plain,
! [SV287: a,SV127: a] :
( ( ~ ( less_eq @ SV127 @ SV287 )
| ( ( sup @ SV127 @ SV287 )
= SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1027,plain,
! [SV288: a,SV128: a] :
( ( ! [SY817: a] :
( ~ ( less_eq @ SV128 @ SV288 )
| ~ ( less @ SV288 @ SY817 )
| ( less @ SV128 @ SY817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1028,plain,
! [SV289: a,SV129: a] :
( ( ! [SY818: a] :
( ~ ( less @ SV129 @ SV289 )
| ~ ( less_eq @ SY818 @ SV129 )
| ( less @ SY818 @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1029,plain,
! [SV290: a,SV130: set_a] :
( ( ~ ! [SY819: a] :
( ~ ( member_a @ SY819 @ SV130 )
| ( less_eq @ SV290 @ SY819 ) )
| ( condit1001553558elow_a @ less_eq @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1030,plain,
! [SV291: a,SV131: a] :
( ( ~ ( less_eq @ SV131 @ SV291 )
| ~ ( less_eq @ SV291 @ SV131 )
| ( SV131 = SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1031,plain,
! [SV292: a,SV132: a > $o] :
( ( ! [SY820: a > $o] :
( ~ ( SV132 @ SV292 )
| ~ ! [SY821: a] :
( ~ ( SV132 @ SY821 )
| ( less_eq @ SY821 @ SV292 ) )
| ~ ! [SY660: a] :
( ~ ( SV132 @ SY660 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY660 ) )
| ( SY820 @ SY660 ) )
| ( SY820 @ ( greatest_a @ less_eq @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1032,plain,
! [SV293: a,SV133: a > a > a] :
( ( ! [SY824: a] :
( ~ ! [SY664: a,SY665: a] : ( less_eq @ ( SV133 @ SY664 @ SY665 ) @ SY664 )
| ~ ! [SY666: a,SY667: a] : ( less_eq @ ( SV133 @ SY666 @ SY667 ) @ SY667 )
| ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SY824 )
= ( SV133 @ SV293 @ SY824 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1033,plain,
! [SV294: a,SV134: a] :
( ( ! [SY832: a] :
( ~ ( less_eq @ SV134 @ SV294 )
| ( less_eq @ ( inf @ SV134 @ SY832 ) @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1034,plain,
! [SV295: a,SV135: a > a > a] :
( ( ! [SY833: a] :
( ~ ! [SY675: a,SY676: a] : ( less_eq @ SY675 @ ( SV135 @ SY675 @ SY676 ) )
| ~ ! [SY677: a,SY678: a] : ( less_eq @ SY678 @ ( SV135 @ SY677 @ SY678 ) )
| ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SY833 )
= ( SV135 @ SV295 @ SY833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1035,plain,
! [SV296: a,SV136: a] :
( ( ! [SY841: a,SY842: a] :
( ~ ( less_eq @ SV136 @ SV296 )
| ~ ( less_eq @ SY841 @ SY842 )
| ( less_eq @ ( inf @ SV136 @ SY841 ) @ ( inf @ SV296 @ SY842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1036,plain,
! [SV297: a,SV137: a] :
( ( ~ ( ( SV137 != SV297 ) )
| ~ ( less_eq @ SV297 @ SV137 )
| ( less @ SV297 @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1037,plain,
! [SV298: a,SV138: a] :
( ( ! [SY843: a] :
( ~ ( less @ SV138 @ SV298 )
| ( less @ SV138 @ ( sup @ SY843 @ SV298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1038,plain,
! [SV299: a,SV139: a] :
( ( ~ ( less_eq @ SV139 @ SV299 )
| ( less @ SV139 @ SV299 )
| ( SV139 = SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1039,plain,
! [SV300: a,SV140: a] :
( ( ! [SY844: a] :
( ~ ( less_eq @ SV140 @ SV300 )
| ( less_eq @ SV140 @ ( sup @ SV300 @ SY844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1040,plain,
! [SV301: a,SV141: a] :
( ( ( SV141 != SV301 )
| ( less_eq @ SV141 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1041,plain,
! [SV302: a,SV142: a] :
( ( ~ ( less_eq @ SV142 @ SV302 )
| ( ( inf @ SV302 @ SV142 )
= SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1042,plain,
! [SV303: a,SV143: a] :
( ( ! [SY845: a] :
( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( inf @ SX3 @ ( sup @ SX4 @ SX5 ) )
= ( sup @ ( inf @ SX3 @ SX4 ) @ ( inf @ SX3 @ SX5 ) ) )
| ( ( sup @ SV143 @ ( inf @ SV303 @ SY845 ) )
= ( inf @ ( sup @ SV143 @ SV303 ) @ ( sup @ SV143 @ SY845 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1043,plain,
! [SV304: a,SV144: a] :
( ( ! [SY849: a] :
( ~ ( less_eq @ SV144 @ SV304 )
| ~ ( less_eq @ SY849 @ SV304 )
| ( less_eq @ ( sup @ SV144 @ SY849 ) @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1044,plain,
! [SV305: a,SV145: a > $o] :
( ( ~ ( SV145 @ SV305 )
| ~ ! [SY850: a] :
( ~ ( SV145 @ SY850 )
| ( less_eq @ SV305 @ SY850 ) )
| ( ( least_a @ less_eq @ SV145 )
= SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1045,plain,
! [SV306: a,SV146: a] :
( ( ! [SY851: a,SY852: a] :
( ~ ( less_eq @ SV146 @ SV306 )
| ~ ( less_eq @ SY851 @ SY852 )
| ( less_eq @ ( sup @ SV146 @ SY851 ) @ ( sup @ SV306 @ SY852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1046,plain,
! [SV307: a,SV147: a] :
( ( ~ ( less @ SV147 @ SV307 )
| ( less_eq @ SV147 @ SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1047,plain,
! [SV308: a,SV148: a] :
( ( ! [SY853: a] :
( ~ ( less_eq @ ( sup @ SV148 @ SV308 ) @ SY853 )
| ~ ( ~ ( less_eq @ SV148 @ SY853 )
| ~ ( less_eq @ SV308 @ SY853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1048,plain,
! [SV309: a,SV149: a] :
( ( ! [SY854: a] :
( ~ ( less_eq @ SV149 @ SV309 )
| ~ ( less_eq @ SY854 @ SV309 )
| ( less_eq @ ( sup @ SV149 @ SY854 ) @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1049,plain,
! [SV310: a,SV150: a] :
( ( ! [SY855: a] :
( ~ ( less @ SV150 @ SV310 )
| ( less @ SV150 @ ( sup @ SY855 @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1050,plain,
! [SV311: a,SV151: a] :
( ( ! [SY856: a] :
( ~ ( less @ ( sup @ SV151 @ SV311 ) @ SY856 )
| ~ ( ~ ( less @ SV151 @ SY856 )
| ~ ( less @ SV311 @ SY856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1051,plain,
! [SV312: a,SV152: a] :
( ( ! [SY857: a] :
( ~ ( less_eq @ SV152 @ SV312 )
| ( less_eq @ SV152 @ ( sup @ SY857 @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1052,plain,
! [SV313: a,SV153: a] :
( ( ~ ( ~ ( ~ ( less_eq @ SV153 @ SV313 )
| ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV313 ) )
| ~ ( ~ ~ ( less_eq @ SV153 @ SV313 )
| ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1053,plain,
! [SV314: a,SV154: a] :
( ( ( less @ SV154 @ SV314 )
= ( ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1054,plain,
! [SV315: a,SV155: a] :
( ( ! [SY858: a] :
( ~ ( less @ SV155 @ SV315 )
| ( less @ ( inf @ SY858 @ SV155 ) @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1055,plain,
! [SV156: set_a] :
( ( ~ ( ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
| ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[892]) ).
thf(1056,plain,
! [SV156: set_a] :
( ( ( condit1001553558elow_a @ less_eq @ SV156 )
= ( ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[892]) ).
thf(1057,plain,
! [SV316: a,SV157: a] :
( ( ~ ( less @ SV157 @ SV316 )
| ( less_eq @ SV157 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1058,plain,
! [SV317: a,SV158: a > $o] :
( ( ! [SY859: a > $o] :
( ~ ( SV158 @ SV317 )
| ~ ! [SY860: a] :
( ~ ( SV158 @ SY860 )
| ( less_eq @ SV317 @ SY860 ) )
| ~ ! [SY726: a] :
( ~ ( SV158 @ SY726 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY726 @ SY727 ) )
| ( SY859 @ SY726 ) )
| ( SY859 @ ( least_a @ less_eq @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1059,plain,
! [SV318: a,SV159: a] :
( ( ! [SY863: a] :
( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV159 @ SV318 @ SY863 )
| ( modula1727524044comp_a @ less_eq @ SV159 @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1060,plain,
! [SV319: a,SV160: a] :
( ( ! [SY864: a] :
( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SY864 )
= ( ~ ( ~ ~ ( ( ( inf @ SV160 @ SY864 )
!= ( inf @ SV319 @ SY864 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SY864 )
!= ( sup @ SV319 @ SY864 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1061,plain,
! [SV320: a,SV161: a] :
( ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= ( ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1062,plain,
! [SV321: a,SV162: a] :
( ( ! [SY865: a] :
( ~ ( less @ SV162 @ SV321 )
| ( less @ ( inf @ SV162 @ SY865 ) @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1063,plain,
! [SV322: a,SV163: a] :
( ( ! [SY866: a] :
( ~ ( less_eq @ ( sup @ SV163 @ SV322 ) @ SY866 )
| ~ ( ~ ( less_eq @ SV163 @ SY866 )
| ~ ( less_eq @ SV322 @ SY866 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1064,plain,
! [SV323: a,SV164: a] :
( ( ~ ( less_eq @ SV164 @ SV323 )
| ~ ( ( SV164 != SV323 ) )
| ( less @ SV164 @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1065,plain,
! [SV324: a,SV165: a] :
( ( ! [SY867: a] :
( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SY867 )
= ( ~ ( ~ ( less_eq @ SV165 @ SY867 )
| ~ ( less_eq @ SV324 @ SY867 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1066,plain,
! [SV325: a,SV166: a] :
( ( ! [SY868: a] :
( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( sup @ SX3 @ ( inf @ SX4 @ SX5 ) )
= ( inf @ ( sup @ SX3 @ SX4 ) @ ( sup @ SX3 @ SX5 ) ) )
| ( ( inf @ SV166 @ ( sup @ SV325 @ SY868 ) )
= ( sup @ ( inf @ SV166 @ SV325 ) @ ( inf @ SV166 @ SY868 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1067,plain,
! [SV326: a,SV167: a] :
( ( ! [SY872: a] :
( ~ ( less @ SV167 @ SV326 )
| ~ ( less_eq @ SV326 @ SY872 )
| ( less @ SV167 @ SY872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1068,plain,
! [SV327: a,SV168: a] :
( ( ! [SY873: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SY873 )
= ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SY873 ) )
| ( ( inf @ SY873 @ SV168 )
!= ( inf @ SV327 @ SY873 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SY873 ) ) )
| ( ( sup @ SY873 @ SV168 )
!= ( sup @ SV327 @ SY873 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1069,plain,
! [SV328: a,SV169: a,SV1: a] :
( ( ( inf @ ( inf @ SV1 @ SV169 ) @ SV328 )
= ( inf @ SV1 @ ( inf @ SV169 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1070,plain,
! [SV329: a,SV171: a,SV3: a] :
( ( ( inf @ SV3 @ ( inf @ SV171 @ SV329 ) )
= ( inf @ SV171 @ ( inf @ SV3 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1071,plain,
! [SV330: a,SV172: a,SV4: a] :
( ( ( inf @ ( inf @ SV4 @ SV172 ) @ SV330 )
= ( inf @ SV4 @ ( inf @ SV172 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1072,plain,
! [SV331: a,SV174: a,SV6: a] :
( ( ( inf @ SV6 @ ( inf @ SV174 @ SV331 ) )
= ( inf @ SV174 @ ( inf @ SV6 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1073,plain,
! [SV332: a,SV175: a,SV7: a] :
( ( ( sup @ ( sup @ SV7 @ SV175 ) @ SV332 )
= ( sup @ SV7 @ ( sup @ SV175 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1074,plain,
! [SV333: a,SV177: a,SV9: a] :
( ( ( sup @ SV9 @ ( sup @ SV177 @ SV333 ) )
= ( sup @ SV177 @ ( sup @ SV9 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1075,plain,
! [SV334: a,SV178: a,SV10: a] :
( ( ( sup @ ( sup @ SV10 @ SV178 ) @ SV334 )
= ( sup @ SV10 @ ( sup @ SV178 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1076,plain,
! [SV335: a,SV180: a,SV12: a] :
( ( ( sup @ SV12 @ ( sup @ SV180 @ SV335 ) )
= ( sup @ SV180 @ ( sup @ SV12 @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1077,plain,
! [SV181: a,SV13: a] :
( ( ~ ( ( less_eq @ SV13 @ SV181 )
| ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) )
| ~ ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[917]) ).
thf(1078,plain,
! [SV181: a,SV13: a] :
( ( ( less_eq @ SV13 @ SV181 )
= ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[917]) ).
thf(1079,plain,
! [SV182: a,SV14: a] :
( ( ~ ( ( less_eq @ SV14 @ SV182 )
| ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) )
| ~ ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[918]) ).
thf(1080,plain,
! [SV182: a,SV14: a] :
( ( ( less_eq @ SV14 @ SV182 )
= ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[918]) ).
thf(1081,plain,
! [SV183: a,SV15: a] :
( ( ~ ( ( less_eq @ SV15 @ SV183 )
| ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) )
| ~ ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[919]) ).
thf(1082,plain,
! [SV183: a,SV15: a] :
( ( ( less_eq @ SV15 @ SV183 )
= ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[919]) ).
thf(1083,plain,
! [SV184: a,SV16: a] :
( ( ~ ( ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
= SV16 ) )
| ~ ( ~ ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
!= SV16 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[920]) ).
thf(1084,plain,
! [SV184: a,SV16: a] :
( ( ( less_eq @ SV16 @ SV184 )
= ( ( inf @ SV16 @ SV184 )
= SV16 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[920]) ).
thf(1085,plain,
! [SV185: a,SV17: a] :
( ( ~ ( ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
= SV17 ) )
| ~ ( ~ ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
!= SV17 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[921]) ).
thf(1086,plain,
! [SV185: a,SV17: a] :
( ( ( less_eq @ SV17 @ SV185 )
= ( ( inf @ SV185 @ SV17 )
= SV17 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[921]) ).
thf(1087,plain,
! [SV188: a,SV20: a] :
( ( ~ ( ( less_eq @ SV20 @ SV188 )
| ( SV20
= ( inf @ SV20 @ SV188 ) ) )
| ~ ( ~ ( less_eq @ SV20 @ SV188 )
| ( SV20
!= ( inf @ SV20 @ SV188 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[924]) ).
thf(1088,plain,
! [SV188: a,SV20: a] :
( ( ( less_eq @ SV20 @ SV188 )
= ( SV20
= ( inf @ SV20 @ SV188 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[924]) ).
thf(1089,plain,
! [SV191: a,SV23: a] :
( ( ~ ( ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
= SV23 ) )
| ~ ( ~ ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
!= SV23 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[927]) ).
thf(1090,plain,
! [SV191: a,SV23: a] :
( ( ( less_eq @ SV23 @ SV191 )
= ( ( inf @ SV23 @ SV191 )
= SV23 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[927]) ).
thf(1091,plain,
! [SV192: a,SV24: a] :
( ( ~ ( ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
= SV192 ) )
| ~ ( ~ ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
!= SV192 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[928]) ).
thf(1092,plain,
! [SV192: a,SV24: a] :
( ( ( less_eq @ SV24 @ SV192 )
= ( ( sup @ SV24 @ SV192 )
= SV192 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[928]) ).
thf(1093,plain,
! [SV193: a,SV25: a] :
( ( ~ ( ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
= SV193 ) )
| ~ ( ~ ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
!= SV193 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[929]) ).
thf(1094,plain,
! [SV193: a,SV25: a] :
( ( ( less_eq @ SV25 @ SV193 )
= ( ( sup @ SV193 @ SV25 )
= SV193 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[929]) ).
thf(1095,plain,
! [SV194: a,SV26: a] :
( ( ~ ( ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
= SV194 ) )
| ~ ( ~ ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
!= SV194 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[930]) ).
thf(1096,plain,
! [SV194: a,SV26: a] :
( ( ( less_eq @ SV26 @ SV194 )
= ( ( sup @ SV26 @ SV194 )
= SV194 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[930]) ).
thf(1097,plain,
! [SV197: a,SV29: a] :
( ( ~ ( ( less_eq @ SV29 @ SV197 )
| ( SV197
= ( sup @ SV197 @ SV29 ) ) )
| ~ ( ~ ( less_eq @ SV29 @ SV197 )
| ( SV197
!= ( sup @ SV197 @ SV29 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[933]) ).
thf(1098,plain,
! [SV197: a,SV29: a] :
( ( ( less_eq @ SV29 @ SV197 )
= ( SV197
= ( sup @ SV197 @ SV29 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[933]) ).
thf(1099,plain,
! [SV336: a,SV200: a,SV32: a] :
( ( less_eq @ ( sup @ ( inf @ SV32 @ SV200 ) @ ( inf @ SV32 @ SV336 ) ) @ ( inf @ SV32 @ ( sup @ SV200 @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1100,plain,
! [SV337: a,SV201: a,SV33: a] :
( ( less_eq @ ( sup @ SV33 @ ( inf @ SV201 @ SV337 ) ) @ ( inf @ ( sup @ SV33 @ SV201 ) @ ( sup @ SV33 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1101,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1102,plain,
! [SV339: a,SV212: a,SV50: a] :
( ( ( sup @ SV50 @ ( modula1936294176_aux_a @ inf @ sup @ SV50 @ SV212 @ SV339 ) )
= ( sup @ SV50 @ ( inf @ SV212 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1103,plain,
! [SV340: a,SV213: a,SV51: a] :
( ( ( sup @ SV51 @ ( modula1936294176_aux_a @ inf @ sup @ SV213 @ SV51 @ SV340 ) )
= ( sup @ SV51 @ ( inf @ SV340 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1104,plain,
! [SV341: a,SV214: a,SV52: a] :
( ( ( modula1936294176_aux_a @ inf @ sup @ SV52 @ SV214 @ SV341 )
= ( sup @ ( sup @ ( inf @ SV52 @ SV214 ) @ ( inf @ SV214 @ SV341 ) ) @ ( inf @ SV341 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1105,plain,
! [SV342: a,SV215: a,SV53: a] :
( ( ( modula1936294176_aux_a @ inf @ sup @ SV53 @ SV215 @ SV342 )
= ( modula1936294176_aux_a @ inf @ sup @ SV342 @ SV53 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1106,plain,
! [SV343: a,SV216: a,SV54: a] :
( ( ( modula1936294176_aux_a @ inf @ sup @ SV54 @ SV216 @ SV343 )
= ( modula1936294176_aux_a @ inf @ sup @ SV216 @ SV343 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1107,plain,
! [SV344: a,SV217: a,SV55: a] :
( ( ( inf @ SV55 @ ( modula1144073633_aux_a @ inf @ sup @ SV55 @ SV217 @ SV344 ) )
= ( inf @ SV55 @ ( sup @ SV217 @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1108,plain,
! [SV345: a,SV218: a,SV56: a] :
( ( ( inf @ SV56 @ ( modula1144073633_aux_a @ inf @ sup @ SV218 @ SV56 @ SV345 ) )
= ( inf @ SV56 @ ( sup @ SV345 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1109,plain,
! [SV346: a,SV219: a,SV57: a] :
( ( ( inf @ SV57 @ ( modula1144073633_aux_a @ inf @ sup @ SV219 @ SV346 @ SV57 ) )
= ( inf @ SV57 @ ( sup @ SV219 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1110,plain,
! [SV347: a,SV220: a,SV58: a] :
( ( ( modula1144073633_aux_a @ inf @ sup @ SV58 @ SV220 @ SV347 )
= ( inf @ ( inf @ ( sup @ SV58 @ SV220 ) @ ( sup @ SV220 @ SV347 ) ) @ ( sup @ SV347 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1111,plain,
! [SV348: a,SV221: a,SV59: a] :
( ( ( modula1144073633_aux_a @ inf @ sup @ SV59 @ SV221 @ SV348 )
= ( modula1144073633_aux_a @ inf @ sup @ SV348 @ SV59 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1112,plain,
! [SV349: a,SV222: a,SV60: a] :
( ( ( modula1144073633_aux_a @ inf @ sup @ SV60 @ SV222 @ SV349 )
= ( modula1144073633_aux_a @ inf @ sup @ SV222 @ SV349 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1113,plain,
! [SV350: a,SV223: a,SV61: a] :
( ( ( modula581031071_aux_a @ inf @ sup @ SV61 @ SV223 @ SV350 )
= ( sup @ ( inf @ SV350 @ ( modula1144073633_aux_a @ inf @ sup @ SV61 @ SV223 @ SV350 ) ) @ ( modula1936294176_aux_a @ inf @ sup @ SV61 @ SV223 @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1114,plain,
! [SV351: a,SV224: a,SV62: a] :
( ( ( modula1373251614_aux_a @ inf @ sup @ SV62 @ SV224 @ SV351 )
= ( sup @ ( inf @ SV224 @ ( modula1144073633_aux_a @ inf @ sup @ SV62 @ SV224 @ SV351 ) ) @ ( modula1936294176_aux_a @ inf @ sup @ SV62 @ SV224 @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1115,plain,
! [SV352: a,SV225: a,SV63: a] :
( ( ( modula17988509_aux_a @ inf @ sup @ SV63 @ SV225 @ SV352 )
= ( sup @ ( inf @ SV63 @ ( modula1144073633_aux_a @ inf @ sup @ SV63 @ SV225 @ SV352 ) ) @ ( modula1936294176_aux_a @ inf @ sup @ SV63 @ SV225 @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1116,plain,
! [SV353: a,SV226: a,SV64: a] :
( ( ( modula1373251614_aux_a @ inf @ sup @ SV64 @ SV226 @ SV353 )
= ( modula17988509_aux_a @ inf @ sup @ SV226 @ SV353 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1117,plain,
! [SV354: a,SV227: a,SV65: a] :
( ( ( modula581031071_aux_a @ inf @ sup @ SV65 @ SV227 @ SV354 )
= ( modula17988509_aux_a @ inf @ sup @ SV354 @ SV65 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1118,plain,
! [SV229: a,SV67: a] :
( ( ~ ( ( less @ SV67 @ SV229 )
| ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) )
| ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[965]) ).
thf(1119,plain,
! [SV229: a,SV67: a] :
( ( ( less @ SV67 @ SV229 )
= ( ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[965]) ).
thf(1120,plain,
! [SV355: a,SV230: a,SV68: a] :
( ( ~ ( less_eq @ SV68 @ SV230 )
| ~ ( less_eq @ SV68 @ SV355 )
| ( less_eq @ SV68 @ ( inf @ SV230 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1121,plain,
! [SV356: a,SV231: a,SV69: a] :
( ( ~ ( less_eq @ SV69 @ SV231 )
| ( SV231 != SV356 )
| ( less_eq @ SV69 @ SV356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1122,plain,
! [SV357: a,SV232: a,SV70: a] :
( ( ~ ( less_eq @ SV70 @ SV232 )
| ( less_eq @ SV70 @ ( sup @ SV357 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1123,plain,
! [SV358: a,SV233: a,SV71: a] :
( ( ~ ( less @ SV71 @ SV233 )
| ~ ( less_eq @ SV233 @ SV358 )
| ( less @ SV71 @ SV358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1124,plain,
! [SV234: a,SV72: a] :
( ( ( ~ ~ ( less @ SV72 @ SV234 ) )
= $true )
| ( ( ( less_eq @ SV72 @ SV234 )
= ( SV72 = SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1125,plain,
! [SV235: a,SV73: a] :
( ( ~ ( ( less @ SV73 @ SV235 )
| ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) )
| ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[971]) ).
thf(1126,plain,
! [SV235: a,SV73: a] :
( ( ( less @ SV73 @ SV235 )
= ( ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[971]) ).
thf(1127,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ( less_eq @ SV74 @ SV236 ) )
= $true )
| ( ( ( ~ ( less @ SV74 @ SV236 ) )
= ( SV74 = SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1128,plain,
! [SV237: a] :
( ( ! [SV359: a] :
( ( SV237 = SV359 )
= ( ~ ( ~ ( less_eq @ SV359 @ SV237 )
| ~ ( less_eq @ SV237 @ SV359 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[973]) ).
thf(1129,plain,
! [SV237: a] :
( ( ( ^ [SY780: a] : ( SV237 = SY780 ) )
= ( ^ [SY781: a] :
~ ( ~ ( less_eq @ SY781 @ SV237 )
| ~ ( less_eq @ SV237 @ SY781 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[973]) ).
thf(1130,plain,
! [SV360: a,SV238: a,SV76: a] :
( ( ~ ( less @ SV76 @ ( inf @ SV238 @ SV360 ) )
| ~ ( ~ ( less @ SV76 @ SV238 )
| ~ ( less @ SV76 @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1131,plain,
! [SV239: a,SV77: a] :
( ( ( ~ ( less_eq @ SV77 @ SV239 ) )
= $true )
| ( ( ( sup @ SV239 @ SV77 )
= SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1132,plain,
! [SV361: a,SV240: a,SV78: a] :
( ( ( SV78 != SV240 )
| ~ ( less_eq @ SV240 @ SV361 )
| ( less_eq @ SV78 @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1133,plain,
! [SV241: a,SV79: a] :
( ( ( SV79
!= ( inf @ SV79 @ SV241 ) )
= $true )
| ( ( less_eq @ SV79 @ SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1134,plain,
! [SV242: a,SV80: a] :
( ( ( ~ ( less_eq @ SV80 @ SV242 ) )
= $true )
| ( ( ( less_eq @ SV242 @ SV80 )
= ( SV242 = SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1135,plain,
! [SV362: a,SV243: a,SV81: a] :
( ( ~ ( less_eq @ SV81 @ SV243 )
| ( less_eq @ ( inf @ SV362 @ SV81 ) @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1136,plain,
! [SV244: a,SV82: a] :
( ( ( ~ ( ( SV82 != SV244 ) ) )
= $true )
| ( ( ~ ( less_eq @ SV82 @ SV244 )
| ( less @ SV82 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1137,plain,
! [SV363: a,SV245: a,SV83: a] :
( ( ~ ( less_eq @ SV83 @ SV245 )
| ~ ( less @ SV363 @ SV83 )
| ( less @ SV363 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1138,plain,
! [SV246: a,SV84: a] :
( ( ( ~ ( less @ SV84 @ SV246 ) )
= $true )
| ( ( less_eq @ SV84 @ SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1139,plain,
! [SV364: a,SV247: a,SV85: a] :
( ( ! [SY874: a] :
( ~ ( less_eq @ SV85 @ SV247 )
| ~ ( less_eq @ SV364 @ SY874 )
| ( less_eq @ ( sup @ SV85 @ SV364 ) @ ( sup @ SV247 @ SY874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1140,plain,
! [SV248: a,SV86: a] :
( ( ( ~ ( less_eq @ SV86 @ SV248 ) )
= $true )
| ( ( ( inf @ SV86 @ SV248 )
= SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1141,plain,
! [SV249: a,SV87: a] :
( ( ( SV87
!= ( sup @ SV87 @ SV249 ) )
= $true )
| ( ( less_eq @ SV249 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1142,plain,
! [SV250: a] :
( ( ! [SV365: a] :
( ( SV250 = SV365 )
= ( ~ ( ~ ( less_eq @ SV250 @ SV365 )
| ~ ( less_eq @ SV365 @ SV250 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[986]) ).
thf(1143,plain,
! [SV250: a] :
( ( ( ^ [SY788: a] : ( SV250 = SY788 ) )
= ( ^ [SY789: a] :
~ ( ~ ( less_eq @ SV250 @ SY789 )
| ~ ( less_eq @ SY789 @ SV250 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[986]) ).
thf(1144,plain,
! [SV89: a > $o] :
( ( ( ~ ! [SY581: a] :
~ ~ ( ~ ~ ( ~ ( SV89 @ SY581 )
| ~ ! [SY582: a] :
( ~ ( SV89 @ SY582 )
| ( less_eq @ SY581 @ SY582 ) ) )
| ~ ! [SY583: a] :
( ~ ~ ( ~ ( SV89 @ SY583 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY583 @ SY584 ) ) )
| ( SY583 = SY581 ) ) ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1145,plain,
! [SV251: a,SV90: a] :
( ( ( ~ ( less_eq @ SV90 @ SV251 ) )
= $true )
| ( ( ~ ( less_eq @ SV251 @ SV90 )
| ( SV90 = SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1146,plain,
! [SV366: a,SV252: a,SV91: a] :
( ( ~ ( less_eq @ SV91 @ SV252 )
| ( less_eq @ SV91 @ ( sup @ SV252 @ SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1147,plain,
! [SV367: a,SV253: a,SV92: a] :
( ( ~ ( less @ SV92 @ SV253 )
| ( less @ ( inf @ SV92 @ SV367 ) @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1148,plain,
! [SV254: a,SV93: a] :
( ( ( ~ ( less_eq @ SV93 @ SV254 ) )
= $true )
| ( ( SV93
= ( inf @ SV93 @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1149,plain,
! [SV255: a,SV94: a] :
( ( ( ~ ( less_eq @ SV94 @ SV255 ) )
= $true )
| ( ( ( inf @ SV94 @ SV255 )
= SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1150,plain,
! [SV368: a,SV256: a,SV95: a] :
( ( ~ ( less_eq @ SV95 @ SV256 )
| ~ ( less_eq @ SV368 @ SV256 )
| ( less_eq @ ( sup @ SV95 @ SV368 ) @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1151,plain,
! [SV369: a,SV257: a,SV96: a] :
( ( ~ ( less_eq @ SV96 @ SV257 )
| ~ ( less @ SV257 @ SV369 )
| ( less @ SV96 @ SV369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1152,plain,
! [SV258: a] :
( ( ! [SV370: a] :
( ( SV258 = SV370 )
= ( ~ ( ~ ( less_eq @ SV258 @ SV370 )
| ~ ( less_eq @ SV370 @ SV258 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[995]) ).
thf(1153,plain,
! [SV258: a] :
( ( ( ^ [SY794: a] : ( SV258 = SY794 ) )
= ( ^ [SY795: a] :
~ ( ~ ( less_eq @ SV258 @ SY795 )
| ~ ( less_eq @ SY795 @ SV258 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[995]) ).
thf(1154,plain,
! [SV371: a,SV259: a,SV98: a] :
( ( ~ ( less_eq @ SV98 @ SV259 )
| ~ ( less_eq @ SV98 @ SV371 )
| ( less_eq @ SV98 @ ( inf @ SV259 @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1155,plain,
! [SV372: a,SV260: a,SV99: a] :
( ( ~ ( less_eq @ SV99 @ SV260 )
| ( less_eq @ ( inf @ SV99 @ SV372 ) @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1156,plain,
! [SV373: a,SV261: a,SV100: a] :
( ( ~ ( less @ SV100 @ SV261 )
| ( less @ SV100 @ ( sup @ SV261 @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1157,plain,
! [SV262: a,SV101: a] :
( ( ( ~ ( less_eq @ SV101 @ SV262 ) )
= $true )
| ( ( ( inf @ SV262 @ SV101 )
= SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1158,plain,
! [SV263: a,SV102: a] :
( ( ~ ( ( less @ SV102 @ SV263 )
| ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) )
| ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1000]) ).
thf(1159,plain,
! [SV263: a,SV102: a] :
( ( ( less @ SV102 @ SV263 )
= ( ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1000]) ).
thf(1160,plain,
! [SV264: a,SV103: a > $o] :
( ( ( ~ ~ ! [SY607: a] :
~ ~ ( ~ ~ ( ~ ( SV103 @ SY607 )
| ~ ! [SY608: a] :
( ~ ( SV103 @ SY608 )
| ( less_eq @ SY607 @ SY608 ) ) )
| ~ ! [SY609: a] :
( ~ ~ ( ~ ( SV103 @ SY609 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY609 @ SY610 ) ) )
| ( SY609 = SY607 ) ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1161,plain,
! [SV265: a,SV104: set_a] :
( ( ( ~ ! [SY803: a] :
( ~ ( member_a @ SY803 @ SV104 )
| ( less_eq @ SY803 @ SV265 ) ) )
= $true )
| ( ( condit1627435690bove_a @ less_eq @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1162,plain,
! [SV266: a,SV105: a] :
( ( ~ ( ( less @ SV105 @ SV266 )
| ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) )
| ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1003]) ).
thf(1163,plain,
! [SV266: a,SV105: a] :
( ( ( less @ SV105 @ SV266 )
= ( ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1003]) ).
thf(1164,plain,
! [SV267: a,SV106: a > $o] :
( ( ( ~ ( SV106 @ SV267 ) )
= $true )
| ( ( ~ ! [SY804: a] :
( ~ ( SV106 @ SY804 )
| ( less_eq @ SY804 @ SV267 ) )
| ( ( greatest_a @ less_eq @ SV106 )
= SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1165,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= ( ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1166,plain,
! [SV269: a,SV108: a] :
( ( ( ~ ( less_eq @ SV108 @ SV269 ) )
= $true )
| ( ( ( sup @ SV108 @ SV269 )
= SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1167,plain,
! [SV270: a,SV109: a] :
( ( ( ~ ( less_eq @ SV109 @ SV270 ) )
= $true )
| ( ( ( sup @ SV270 @ SV109 )
= SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1168,plain,
! [SV375: a,SV271: a,SV110: a] :
( ( ~ ( less_eq @ SV110 @ SV271 )
| ~ ( less_eq @ SV271 @ SV375 )
| ( less_eq @ SV110 @ SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1169,plain,
! [SV272: a,SV111: a] :
( ( ( ~ ( less_eq @ SV111 @ SV272 ) )
= $true )
| ( ( ~ ( less @ SV272 @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1170,plain,
! [SV376: a,SV273: a,SV112: a] :
( ( ~ ( less_eq @ SV112 @ ( inf @ SV273 @ SV376 ) )
| ~ ( ~ ( less_eq @ SV112 @ SV273 )
| ~ ( less_eq @ SV112 @ SV376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1171,plain,
! [SV377: a,SV274: a,SV113: a] :
( ( ~ ( less @ SV113 @ SV274 )
| ( less @ SV113 @ ( sup @ SV274 @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1172,plain,
! [SV378: a,SV275: a,SV114: a] :
( ( ~ ( less_eq @ SV114 @ SV275 )
| ( less_eq @ ( inf @ SV378 @ SV114 ) @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1173,plain,
! [SV276: a,SV115: a] :
( ( ( ~ ( less_eq @ SV115 @ SV276 ) )
= $true )
| ( ( ~ ( less_eq @ SV276 @ SV115 )
| ( SV276 = SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1174,plain,
! [SV277: a,SV116: a] :
( ( ~ ( ~ ( less_eq @ SV116 @ SV277 )
| ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV116 ) )
| ~ ( ~ ~ ( less_eq @ SV116 @ SV277 )
| ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV277 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1175,plain,
! [SV379: a,SV278: a,SV117: a] :
( ( ~ ( less @ SV117 @ SV278 )
| ( less @ ( inf @ SV379 @ SV117 ) @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1176,plain,
! [SV118: set_a] :
( ( ( ~ ( ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1177,plain,
! [SV380: a,SV279: a,SV119: a] :
( ( ~ ( less_eq @ SV119 @ SV279 )
| ~ ( less_eq @ SV279 @ SV380 )
| ( less_eq @ SV119 @ SV380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1178,plain,
! [SV280: a,SV120: a] :
( ( ~ ( ( less @ SV120 @ SV280 )
| ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) )
| ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1019]) ).
thf(1179,plain,
! [SV280: a,SV120: a] :
( ( ( less @ SV120 @ SV280 )
= ( ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1019]) ).
thf(1180,plain,
! [SV381: a,SV281: a,SV121: a] :
( ( ~ ( less_eq @ SV121 @ SV281 )
| ~ ( less_eq @ SV381 @ SV121 )
| ( less_eq @ SV381 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1181,plain,
! [SV382: a,SV282: a,SV122: a] :
( ( ~ ( less_eq @ SV122 @ ( inf @ SV282 @ SV382 ) )
| ~ ( ~ ( less_eq @ SV122 @ SV282 )
| ~ ( less_eq @ SV122 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1182,plain,
! [SV283: a,SV123: a] :
( ( ( ~ ( less_eq @ SV123 @ SV283 ) )
= $true )
| ( ( SV283
= ( sup @ SV283 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1183,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= ( ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1184,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= ( ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1185,plain,
! [SV385: a,SV286: a,SV126: a] :
( ( ~ ( less_eq @ SV126 @ SV286 )
| ~ ( less_eq @ SV126 @ SV385 )
| ( less_eq @ SV126 @ ( inf @ SV286 @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1186,plain,
! [SV287: a,SV127: a] :
( ( ( ~ ( less_eq @ SV127 @ SV287 ) )
= $true )
| ( ( ( sup @ SV127 @ SV287 )
= SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1187,plain,
! [SV386: a,SV288: a,SV128: a] :
( ( ~ ( less_eq @ SV128 @ SV288 )
| ~ ( less @ SV288 @ SV386 )
| ( less @ SV128 @ SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1188,plain,
! [SV387: a,SV289: a,SV129: a] :
( ( ~ ( less @ SV129 @ SV289 )
| ~ ( less_eq @ SV387 @ SV129 )
| ( less @ SV387 @ SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1189,plain,
! [SV290: a,SV130: set_a] :
( ( ( ~ ! [SY819: a] :
( ~ ( member_a @ SY819 @ SV130 )
| ( less_eq @ SV290 @ SY819 ) ) )
= $true )
| ( ( condit1001553558elow_a @ less_eq @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1190,plain,
! [SV291: a,SV131: a] :
( ( ( ~ ( less_eq @ SV131 @ SV291 ) )
= $true )
| ( ( ~ ( less_eq @ SV291 @ SV131 )
| ( SV131 = SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1191,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ~ ( SV132 @ SV292 )
| ~ ! [SY821: a] :
( ~ ( SV132 @ SY821 )
| ( less_eq @ SY821 @ SV292 ) )
| ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) )
| ( SV388 @ ( greatest_a @ less_eq @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1192,plain,
! [SV389: a,SV293: a,SV133: a > a > a] :
( ( ~ ! [SY664: a,SY665: a] : ( less_eq @ ( SV133 @ SY664 @ SY665 ) @ SY664 )
| ~ ! [SY666: a,SY667: a] : ( less_eq @ ( SV133 @ SY666 @ SY667 ) @ SY667 )
| ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1193,plain,
! [SV390: a,SV294: a,SV134: a] :
( ( ~ ( less_eq @ SV134 @ SV294 )
| ( less_eq @ ( inf @ SV134 @ SV390 ) @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1194,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ~ ! [SY675: a,SY676: a] : ( less_eq @ SY675 @ ( SV135 @ SY675 @ SY676 ) )
| ~ ! [SY677: a,SY678: a] : ( less_eq @ SY678 @ ( SV135 @ SY677 @ SY678 ) )
| ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1195,plain,
! [SV392: a,SV296: a,SV136: a] :
( ( ! [SY892: a] :
( ~ ( less_eq @ SV136 @ SV296 )
| ~ ( less_eq @ SV392 @ SY892 )
| ( less_eq @ ( inf @ SV136 @ SV392 ) @ ( inf @ SV296 @ SY892 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1196,plain,
! [SV297: a,SV137: a] :
( ( ( ~ ( ( SV137 != SV297 ) ) )
= $true )
| ( ( ~ ( less_eq @ SV297 @ SV137 )
| ( less @ SV297 @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1197,plain,
! [SV393: a,SV298: a,SV138: a] :
( ( ~ ( less @ SV138 @ SV298 )
| ( less @ SV138 @ ( sup @ SV393 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1198,plain,
! [SV299: a,SV139: a] :
( ( ( ~ ( less_eq @ SV139 @ SV299 ) )
= $true )
| ( ( ( less @ SV139 @ SV299 )
| ( SV139 = SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1199,plain,
! [SV394: a,SV300: a,SV140: a] :
( ( ~ ( less_eq @ SV140 @ SV300 )
| ( less_eq @ SV140 @ ( sup @ SV300 @ SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1200,plain,
! [SV301: a,SV141: a] :
( ( ( SV141 != SV301 )
= $true )
| ( ( less_eq @ SV141 @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1201,plain,
! [SV302: a,SV142: a] :
( ( ( ~ ( less_eq @ SV142 @ SV302 ) )
= $true )
| ( ( ( inf @ SV302 @ SV142 )
= SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1202,plain,
! [SV395: a,SV303: a,SV143: a] :
( ( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( inf @ SX3 @ ( sup @ SX4 @ SX5 ) )
= ( sup @ ( inf @ SX3 @ SX4 ) @ ( inf @ SX3 @ SX5 ) ) )
| ( ( sup @ SV143 @ ( inf @ SV303 @ SV395 ) )
= ( inf @ ( sup @ SV143 @ SV303 ) @ ( sup @ SV143 @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1203,plain,
! [SV396: a,SV304: a,SV144: a] :
( ( ~ ( less_eq @ SV144 @ SV304 )
| ~ ( less_eq @ SV396 @ SV304 )
| ( less_eq @ ( sup @ SV144 @ SV396 ) @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1204,plain,
! [SV305: a,SV145: a > $o] :
( ( ( ~ ( SV145 @ SV305 ) )
= $true )
| ( ( ~ ! [SY850: a] :
( ~ ( SV145 @ SY850 )
| ( less_eq @ SV305 @ SY850 ) )
| ( ( least_a @ less_eq @ SV145 )
= SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1205,plain,
! [SV397: a,SV306: a,SV146: a] :
( ( ! [SY896: a] :
( ~ ( less_eq @ SV146 @ SV306 )
| ~ ( less_eq @ SV397 @ SY896 )
| ( less_eq @ ( sup @ SV146 @ SV397 ) @ ( sup @ SV306 @ SY896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1206,plain,
! [SV307: a,SV147: a] :
( ( ( ~ ( less @ SV147 @ SV307 ) )
= $true )
| ( ( less_eq @ SV147 @ SV307 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1207,plain,
! [SV398: a,SV308: a,SV148: a] :
( ( ~ ( less_eq @ ( sup @ SV148 @ SV308 ) @ SV398 )
| ~ ( ~ ( less_eq @ SV148 @ SV398 )
| ~ ( less_eq @ SV308 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1208,plain,
! [SV399: a,SV309: a,SV149: a] :
( ( ~ ( less_eq @ SV149 @ SV309 )
| ~ ( less_eq @ SV399 @ SV309 )
| ( less_eq @ ( sup @ SV149 @ SV399 ) @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1209,plain,
! [SV400: a,SV310: a,SV150: a] :
( ( ~ ( less @ SV150 @ SV310 )
| ( less @ SV150 @ ( sup @ SV400 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1210,plain,
! [SV401: a,SV311: a,SV151: a] :
( ( ~ ( less @ ( sup @ SV151 @ SV311 ) @ SV401 )
| ~ ( ~ ( less @ SV151 @ SV401 )
| ~ ( less @ SV311 @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1211,plain,
! [SV402: a,SV312: a,SV152: a] :
( ( ~ ( less_eq @ SV152 @ SV312 )
| ( less_eq @ SV152 @ ( sup @ SV402 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1212,plain,
! [SV313: a,SV153: a] :
( ( ~ ( ~ ( less_eq @ SV153 @ SV313 )
| ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV313 ) )
| ~ ( ~ ~ ( less_eq @ SV153 @ SV313 )
| ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV153 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1213,plain,
! [SV314: a,SV154: a] :
( ( ~ ( ( less @ SV154 @ SV314 )
| ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) )
| ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1053]) ).
thf(1214,plain,
! [SV314: a,SV154: a] :
( ( ( less @ SV154 @ SV314 )
= ( ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1053]) ).
thf(1215,plain,
! [SV403: a,SV315: a,SV155: a] :
( ( ~ ( less @ SV155 @ SV315 )
| ( less @ ( inf @ SV403 @ SV155 ) @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1216,plain,
! [SV156: set_a] :
( ( ( ~ ( ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1217,plain,
! [SV316: a,SV157: a] :
( ( ( ~ ( less @ SV157 @ SV316 ) )
= $true )
| ( ( less_eq @ SV157 @ SV316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1218,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ~ ( SV158 @ SV317 )
| ~ ! [SY860: a] :
( ~ ( SV158 @ SY860 )
| ( less_eq @ SV317 @ SY860 ) )
| ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) )
| ( SV404 @ ( least_a @ less_eq @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1219,plain,
! [SV405: a,SV318: a,SV159: a] :
( ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV159 @ SV318 @ SV405 )
| ( modula1727524044comp_a @ less_eq @ SV159 @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1220,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= ( ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1221,plain,
! [SV320: a,SV161: a] :
( ( ~ ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) )
| ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1061]) ).
thf(1222,plain,
! [SV320: a,SV161: a] :
( ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= ( ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1061]) ).
thf(1223,plain,
! [SV407: a,SV321: a,SV162: a] :
( ( ~ ( less @ SV162 @ SV321 )
| ( less @ ( inf @ SV162 @ SV407 ) @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1224,plain,
! [SV408: a,SV322: a,SV163: a] :
( ( ~ ( less_eq @ ( sup @ SV163 @ SV322 ) @ SV408 )
| ~ ( ~ ( less_eq @ SV163 @ SV408 )
| ~ ( less_eq @ SV322 @ SV408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1225,plain,
! [SV323: a,SV164: a] :
( ( ( ~ ( less_eq @ SV164 @ SV323 ) )
= $true )
| ( ( ~ ( ( SV164 != SV323 ) )
| ( less @ SV164 @ SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1226,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= ( ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1227,plain,
! [SV410: a,SV325: a,SV166: a] :
( ( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( sup @ SX3 @ ( inf @ SX4 @ SX5 ) )
= ( inf @ ( sup @ SX3 @ SX4 ) @ ( sup @ SX3 @ SX5 ) ) )
| ( ( inf @ SV166 @ ( sup @ SV325 @ SV410 ) )
= ( sup @ ( inf @ SV166 @ SV325 ) @ ( inf @ SV166 @ SV410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1228,plain,
! [SV411: a,SV326: a,SV167: a] :
( ( ~ ( less @ SV167 @ SV326 )
| ~ ( less_eq @ SV326 @ SV411 )
| ( less @ SV167 @ SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1229,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1230,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( ( less_eq @ SV13 @ SV181 )
| ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1231,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( ( less_eq @ SV14 @ SV182 )
| ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1232,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( ( less_eq @ SV15 @ SV183 )
| ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1233,plain,
! [SV184: a,SV16: a] :
( ( ( ~ ( ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
= SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
!= SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1234,plain,
! [SV185: a,SV17: a] :
( ( ( ~ ( ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
= SV17 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
!= SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1235,plain,
! [SV188: a,SV20: a] :
( ( ( ~ ( ( less_eq @ SV20 @ SV188 )
| ( SV20
= ( inf @ SV20 @ SV188 ) ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV20 @ SV188 )
| ( SV20
!= ( inf @ SV20 @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1236,plain,
! [SV191: a,SV23: a] :
( ( ( ~ ( ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
= SV23 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
!= SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1237,plain,
! [SV192: a,SV24: a] :
( ( ( ~ ( ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
= SV192 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
!= SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1238,plain,
! [SV193: a,SV25: a] :
( ( ( ~ ( ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
= SV193 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
!= SV193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1239,plain,
! [SV194: a,SV26: a] :
( ( ( ~ ( ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
= SV194 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
!= SV194 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1240,plain,
! [SV197: a,SV29: a] :
( ( ( ~ ( ( less_eq @ SV29 @ SV197 )
| ( SV197
= ( sup @ SV197 @ SV29 ) ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV29 @ SV197 )
| ( SV197
!= ( sup @ SV197 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1241,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ~ ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) )
| ~ ( ~ ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ~ ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1101]) ).
thf(1242,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1101]) ).
thf(1243,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( ( less @ SV67 @ SV229 )
| ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1244,plain,
! [SV355: a,SV230: a,SV68: a] :
( ( ( ~ ( less_eq @ SV68 @ SV230 ) )
= $true )
| ( ( ~ ( less_eq @ SV68 @ SV355 )
| ( less_eq @ SV68 @ ( inf @ SV230 @ SV355 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1245,plain,
! [SV356: a,SV231: a,SV69: a] :
( ( ( ~ ( less_eq @ SV69 @ SV231 ) )
= $true )
| ( ( ( SV231 != SV356 )
| ( less_eq @ SV69 @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1246,plain,
! [SV357: a,SV232: a,SV70: a] :
( ( ( ~ ( less_eq @ SV70 @ SV232 ) )
= $true )
| ( ( less_eq @ SV70 @ ( sup @ SV357 @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1247,plain,
! [SV358: a,SV233: a,SV71: a] :
( ( ( ~ ( less @ SV71 @ SV233 ) )
= $true )
| ( ( ~ ( less_eq @ SV233 @ SV358 )
| ( less @ SV71 @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1248,plain,
! [SV234: a,SV72: a] :
( ( ( ~ ( less @ SV72 @ SV234 ) )
= $false )
| ( ( ( less_eq @ SV72 @ SV234 )
= ( SV72 = SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1249,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( ( less @ SV73 @ SV235 )
| ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1250,plain,
! [SV236: a,SV74: a] :
( ( ( less_eq @ SV74 @ SV236 )
= $false )
| ( ( ( ~ ( less @ SV74 @ SV236 ) )
= ( SV74 = SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1251,plain,
! [SV413: a,SV237: a] :
( ( ( SV237 = SV413 )
= ( ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1252,plain,
! [SV360: a,SV238: a,SV76: a] :
( ( ( ~ ( less @ SV76 @ ( inf @ SV238 @ SV360 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV76 @ SV238 )
| ~ ( less @ SV76 @ SV360 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1253,plain,
! [SV239: a,SV77: a] :
( ( ( less_eq @ SV77 @ SV239 )
= $false )
| ( ( ( sup @ SV239 @ SV77 )
= SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1254,plain,
! [SV361: a,SV240: a,SV78: a] :
( ( ( SV78 != SV240 )
= $true )
| ( ( ~ ( less_eq @ SV240 @ SV361 )
| ( less_eq @ SV78 @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1255,plain,
! [SV241: a,SV79: a] :
( ( ( SV79
= ( inf @ SV79 @ SV241 ) )
= $false )
| ( ( less_eq @ SV79 @ SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1256,plain,
! [SV242: a,SV80: a] :
( ( ( less_eq @ SV80 @ SV242 )
= $false )
| ( ( ( less_eq @ SV242 @ SV80 )
= ( SV242 = SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1257,plain,
! [SV362: a,SV243: a,SV81: a] :
( ( ( ~ ( less_eq @ SV81 @ SV243 ) )
= $true )
| ( ( less_eq @ ( inf @ SV362 @ SV81 ) @ SV243 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1258,plain,
! [SV244: a,SV82: a] :
( ( ( SV82 != SV244 )
= $false )
| ( ( ~ ( less_eq @ SV82 @ SV244 )
| ( less @ SV82 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1259,plain,
! [SV363: a,SV245: a,SV83: a] :
( ( ( ~ ( less_eq @ SV83 @ SV245 ) )
= $true )
| ( ( ~ ( less @ SV363 @ SV83 )
| ( less @ SV363 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1260,plain,
! [SV246: a,SV84: a] :
( ( ( less @ SV84 @ SV246 )
= $false )
| ( ( less_eq @ SV84 @ SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1261,plain,
! [SV414: a,SV364: a,SV247: a,SV85: a] :
( ( ~ ( less_eq @ SV85 @ SV247 )
| ~ ( less_eq @ SV364 @ SV414 )
| ( less_eq @ ( sup @ SV85 @ SV364 ) @ ( sup @ SV247 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1262,plain,
! [SV248: a,SV86: a] :
( ( ( less_eq @ SV86 @ SV248 )
= $false )
| ( ( ( inf @ SV86 @ SV248 )
= SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1263,plain,
! [SV249: a,SV87: a] :
( ( ( SV87
= ( sup @ SV87 @ SV249 ) )
= $false )
| ( ( less_eq @ SV249 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1264,plain,
! [SV415: a,SV250: a] :
( ( ( SV250 = SV415 )
= ( ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1265,plain,
! [SV89: a > $o] :
( ( ( ! [SY581: a] :
~ ~ ( ~ ~ ( ~ ( SV89 @ SY581 )
| ~ ! [SY582: a] :
( ~ ( SV89 @ SY582 )
| ( less_eq @ SY581 @ SY582 ) ) )
| ~ ! [SY583: a] :
( ~ ~ ( ~ ( SV89 @ SY583 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY583 @ SY584 ) ) )
| ( SY583 = SY581 ) ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1266,plain,
! [SV251: a,SV90: a] :
( ( ( less_eq @ SV90 @ SV251 )
= $false )
| ( ( ~ ( less_eq @ SV251 @ SV90 )
| ( SV90 = SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1267,plain,
! [SV366: a,SV252: a,SV91: a] :
( ( ( ~ ( less_eq @ SV91 @ SV252 ) )
= $true )
| ( ( less_eq @ SV91 @ ( sup @ SV252 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1268,plain,
! [SV367: a,SV253: a,SV92: a] :
( ( ( ~ ( less @ SV92 @ SV253 ) )
= $true )
| ( ( less @ ( inf @ SV92 @ SV367 ) @ SV253 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1269,plain,
! [SV254: a,SV93: a] :
( ( ( less_eq @ SV93 @ SV254 )
= $false )
| ( ( SV93
= ( inf @ SV93 @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1270,plain,
! [SV255: a,SV94: a] :
( ( ( less_eq @ SV94 @ SV255 )
= $false )
| ( ( ( inf @ SV94 @ SV255 )
= SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1271,plain,
! [SV368: a,SV256: a,SV95: a] :
( ( ( ~ ( less_eq @ SV95 @ SV256 ) )
= $true )
| ( ( ~ ( less_eq @ SV368 @ SV256 )
| ( less_eq @ ( sup @ SV95 @ SV368 ) @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1272,plain,
! [SV369: a,SV257: a,SV96: a] :
( ( ( ~ ( less_eq @ SV96 @ SV257 ) )
= $true )
| ( ( ~ ( less @ SV257 @ SV369 )
| ( less @ SV96 @ SV369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1273,plain,
! [SV416: a,SV258: a] :
( ( ( SV258 = SV416 )
= ( ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1274,plain,
! [SV371: a,SV259: a,SV98: a] :
( ( ( ~ ( less_eq @ SV98 @ SV259 ) )
= $true )
| ( ( ~ ( less_eq @ SV98 @ SV371 )
| ( less_eq @ SV98 @ ( inf @ SV259 @ SV371 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1275,plain,
! [SV372: a,SV260: a,SV99: a] :
( ( ( ~ ( less_eq @ SV99 @ SV260 ) )
= $true )
| ( ( less_eq @ ( inf @ SV99 @ SV372 ) @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1276,plain,
! [SV373: a,SV261: a,SV100: a] :
( ( ( ~ ( less @ SV100 @ SV261 ) )
= $true )
| ( ( less @ SV100 @ ( sup @ SV261 @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1277,plain,
! [SV262: a,SV101: a] :
( ( ( less_eq @ SV101 @ SV262 )
= $false )
| ( ( ( inf @ SV262 @ SV101 )
= SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1278,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( ( less @ SV102 @ SV263 )
| ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1279,plain,
! [SV264: a,SV103: a > $o] :
( ( ( ~ ! [SY607: a] :
~ ~ ( ~ ~ ( ~ ( SV103 @ SY607 )
| ~ ! [SY608: a] :
( ~ ( SV103 @ SY608 )
| ( less_eq @ SY607 @ SY608 ) ) )
| ~ ! [SY609: a] :
( ~ ~ ( ~ ( SV103 @ SY609 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY609 @ SY610 ) ) )
| ( SY609 = SY607 ) ) ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1280,plain,
! [SV265: a,SV104: set_a] :
( ( ( ! [SY803: a] :
( ~ ( member_a @ SY803 @ SV104 )
| ( less_eq @ SY803 @ SV265 ) ) )
= $false )
| ( ( condit1627435690bove_a @ less_eq @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1281,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( ( less @ SV105 @ SV266 )
| ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1282,plain,
! [SV267: a,SV106: a > $o] :
( ( ( SV106 @ SV267 )
= $false )
| ( ( ~ ! [SY804: a] :
( ~ ( SV106 @ SY804 )
| ( less_eq @ SY804 @ SV267 ) )
| ( ( greatest_a @ less_eq @ SV106 )
= SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1283,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ~ ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) )
| ~ ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1165]) ).
thf(1284,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= ( ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1165]) ).
thf(1285,plain,
! [SV269: a,SV108: a] :
( ( ( less_eq @ SV108 @ SV269 )
= $false )
| ( ( ( sup @ SV108 @ SV269 )
= SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1286,plain,
! [SV270: a,SV109: a] :
( ( ( less_eq @ SV109 @ SV270 )
= $false )
| ( ( ( sup @ SV270 @ SV109 )
= SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1287,plain,
! [SV375: a,SV271: a,SV110: a] :
( ( ( ~ ( less_eq @ SV110 @ SV271 ) )
= $true )
| ( ( ~ ( less_eq @ SV271 @ SV375 )
| ( less_eq @ SV110 @ SV375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1288,plain,
! [SV272: a,SV111: a] :
( ( ( less_eq @ SV111 @ SV272 )
= $false )
| ( ( ~ ( less @ SV272 @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1289,plain,
! [SV376: a,SV273: a,SV112: a] :
( ( ( ~ ( less_eq @ SV112 @ ( inf @ SV273 @ SV376 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV112 @ SV273 )
| ~ ( less_eq @ SV112 @ SV376 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1290,plain,
! [SV377: a,SV274: a,SV113: a] :
( ( ( ~ ( less @ SV113 @ SV274 ) )
= $true )
| ( ( less @ SV113 @ ( sup @ SV274 @ SV377 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1291,plain,
! [SV378: a,SV275: a,SV114: a] :
( ( ( ~ ( less_eq @ SV114 @ SV275 ) )
= $true )
| ( ( less_eq @ ( inf @ SV378 @ SV114 ) @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1292,plain,
! [SV276: a,SV115: a] :
( ( ( less_eq @ SV115 @ SV276 )
= $false )
| ( ( ~ ( less_eq @ SV276 @ SV115 )
| ( SV276 = SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1293,plain,
! [SV277: a,SV116: a] :
( ( ~ ( ~ ( less_eq @ SV116 @ SV277 )
| ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV116 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1294,plain,
! [SV277: a,SV116: a] :
( ( ~ ( ~ ~ ( less_eq @ SV116 @ SV277 )
| ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV277 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1295,plain,
! [SV379: a,SV278: a,SV117: a] :
( ( ( ~ ( less @ SV117 @ SV278 ) )
= $true )
| ( ( less @ ( inf @ SV379 @ SV117 ) @ SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1175]) ).
thf(1296,plain,
! [SV118: set_a] :
( ( ( ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1297,plain,
! [SV380: a,SV279: a,SV119: a] :
( ( ( ~ ( less_eq @ SV119 @ SV279 ) )
= $true )
| ( ( ~ ( less_eq @ SV279 @ SV380 )
| ( less_eq @ SV119 @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1298,plain,
! [SV280: a,SV120: a] :
( ( ( ~ ( ( less @ SV120 @ SV280 )
| ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1299,plain,
! [SV381: a,SV281: a,SV121: a] :
( ( ( ~ ( less_eq @ SV121 @ SV281 ) )
= $true )
| ( ( ~ ( less_eq @ SV381 @ SV121 )
| ( less_eq @ SV381 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1300,plain,
! [SV382: a,SV282: a,SV122: a] :
( ( ( ~ ( less_eq @ SV122 @ ( inf @ SV282 @ SV382 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV122 @ SV282 )
| ~ ( less_eq @ SV122 @ SV382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1301,plain,
! [SV283: a,SV123: a] :
( ( ( less_eq @ SV123 @ SV283 )
= $false )
| ( ( SV283
= ( sup @ SV283 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1302,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ~ ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) )
| ~ ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1183]) ).
thf(1303,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= ( ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1183]) ).
thf(1304,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ~ ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) )
| ~ ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1184]) ).
thf(1305,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= ( ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1184]) ).
thf(1306,plain,
! [SV385: a,SV286: a,SV126: a] :
( ( ( ~ ( less_eq @ SV126 @ SV286 ) )
= $true )
| ( ( ~ ( less_eq @ SV126 @ SV385 )
| ( less_eq @ SV126 @ ( inf @ SV286 @ SV385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1307,plain,
! [SV287: a,SV127: a] :
( ( ( less_eq @ SV127 @ SV287 )
= $false )
| ( ( ( sup @ SV127 @ SV287 )
= SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1308,plain,
! [SV386: a,SV288: a,SV128: a] :
( ( ( ~ ( less_eq @ SV128 @ SV288 ) )
= $true )
| ( ( ~ ( less @ SV288 @ SV386 )
| ( less @ SV128 @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1309,plain,
! [SV387: a,SV289: a,SV129: a] :
( ( ( ~ ( less @ SV129 @ SV289 ) )
= $true )
| ( ( ~ ( less_eq @ SV387 @ SV129 )
| ( less @ SV387 @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1310,plain,
! [SV290: a,SV130: set_a] :
( ( ( ! [SY819: a] :
( ~ ( member_a @ SY819 @ SV130 )
| ( less_eq @ SV290 @ SY819 ) ) )
= $false )
| ( ( condit1001553558elow_a @ less_eq @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1311,plain,
! [SV291: a,SV131: a] :
( ( ( less_eq @ SV131 @ SV291 )
= $false )
| ( ( ~ ( less_eq @ SV291 @ SV131 )
| ( SV131 = SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1312,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ( SV132 @ SV292 ) )
= $true )
| ( ( ~ ! [SY821: a] :
( ~ ( SV132 @ SY821 )
| ( less_eq @ SY821 @ SV292 ) )
| ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) )
| ( SV388 @ ( greatest_a @ less_eq @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1313,plain,
! [SV389: a,SV293: a,SV133: a > a > a] :
( ( ( ~ ! [SY664: a,SY665: a] : ( less_eq @ ( SV133 @ SY664 @ SY665 ) @ SY664 ) )
= $true )
| ( ( ~ ! [SY666: a,SY667: a] : ( less_eq @ ( SV133 @ SY666 @ SY667 ) @ SY667 )
| ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1314,plain,
! [SV390: a,SV294: a,SV134: a] :
( ( ( ~ ( less_eq @ SV134 @ SV294 ) )
= $true )
| ( ( less_eq @ ( inf @ SV134 @ SV390 ) @ SV294 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1315,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( ~ ! [SY675: a,SY676: a] : ( less_eq @ SY675 @ ( SV135 @ SY675 @ SY676 ) ) )
= $true )
| ( ( ~ ! [SY677: a,SY678: a] : ( less_eq @ SY678 @ ( SV135 @ SY677 @ SY678 ) )
| ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1316,plain,
! [SV417: a,SV392: a,SV296: a,SV136: a] :
( ( ~ ( less_eq @ SV136 @ SV296 )
| ~ ( less_eq @ SV392 @ SV417 )
| ( less_eq @ ( inf @ SV136 @ SV392 ) @ ( inf @ SV296 @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1317,plain,
! [SV297: a,SV137: a] :
( ( ( SV137 != SV297 )
= $false )
| ( ( ~ ( less_eq @ SV297 @ SV137 )
| ( less @ SV297 @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1318,plain,
! [SV393: a,SV298: a,SV138: a] :
( ( ( ~ ( less @ SV138 @ SV298 ) )
= $true )
| ( ( less @ SV138 @ ( sup @ SV393 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1319,plain,
! [SV299: a,SV139: a] :
( ( ( less_eq @ SV139 @ SV299 )
= $false )
| ( ( ( less @ SV139 @ SV299 )
| ( SV139 = SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1320,plain,
! [SV394: a,SV300: a,SV140: a] :
( ( ( ~ ( less_eq @ SV140 @ SV300 ) )
= $true )
| ( ( less_eq @ SV140 @ ( sup @ SV300 @ SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1321,plain,
! [SV301: a,SV141: a] :
( ( ( SV141 = SV301 )
= $false )
| ( ( less_eq @ SV141 @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1322,plain,
! [SV302: a,SV142: a] :
( ( ( less_eq @ SV142 @ SV302 )
= $false )
| ( ( ( inf @ SV302 @ SV142 )
= SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1323,plain,
! [SV395: a,SV303: a,SV143: a] :
( ( ( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( inf @ SX3 @ ( sup @ SX4 @ SX5 ) )
= ( sup @ ( inf @ SX3 @ SX4 ) @ ( inf @ SX3 @ SX5 ) ) ) )
= $true )
| ( ( ( sup @ SV143 @ ( inf @ SV303 @ SV395 ) )
= ( inf @ ( sup @ SV143 @ SV303 ) @ ( sup @ SV143 @ SV395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1324,plain,
! [SV396: a,SV304: a,SV144: a] :
( ( ( ~ ( less_eq @ SV144 @ SV304 ) )
= $true )
| ( ( ~ ( less_eq @ SV396 @ SV304 )
| ( less_eq @ ( sup @ SV144 @ SV396 ) @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1325,plain,
! [SV305: a,SV145: a > $o] :
( ( ( SV145 @ SV305 )
= $false )
| ( ( ~ ! [SY850: a] :
( ~ ( SV145 @ SY850 )
| ( less_eq @ SV305 @ SY850 ) )
| ( ( least_a @ less_eq @ SV145 )
= SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1326,plain,
! [SV418: a,SV397: a,SV306: a,SV146: a] :
( ( ~ ( less_eq @ SV146 @ SV306 )
| ~ ( less_eq @ SV397 @ SV418 )
| ( less_eq @ ( sup @ SV146 @ SV397 ) @ ( sup @ SV306 @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1327,plain,
! [SV307: a,SV147: a] :
( ( ( less @ SV147 @ SV307 )
= $false )
| ( ( less_eq @ SV147 @ SV307 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1328,plain,
! [SV398: a,SV308: a,SV148: a] :
( ( ( ~ ( less_eq @ ( sup @ SV148 @ SV308 ) @ SV398 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV148 @ SV398 )
| ~ ( less_eq @ SV308 @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1329,plain,
! [SV399: a,SV309: a,SV149: a] :
( ( ( ~ ( less_eq @ SV149 @ SV309 ) )
= $true )
| ( ( ~ ( less_eq @ SV399 @ SV309 )
| ( less_eq @ ( sup @ SV149 @ SV399 ) @ SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1330,plain,
! [SV400: a,SV310: a,SV150: a] :
( ( ( ~ ( less @ SV150 @ SV310 ) )
= $true )
| ( ( less @ SV150 @ ( sup @ SV400 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1331,plain,
! [SV401: a,SV311: a,SV151: a] :
( ( ( ~ ( less @ ( sup @ SV151 @ SV311 ) @ SV401 ) )
= $true )
| ( ( ~ ( ~ ( less @ SV151 @ SV401 )
| ~ ( less @ SV311 @ SV401 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1332,plain,
! [SV402: a,SV312: a,SV152: a] :
( ( ( ~ ( less_eq @ SV152 @ SV312 ) )
= $true )
| ( ( less_eq @ SV152 @ ( sup @ SV402 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1333,plain,
! [SV313: a,SV153: a] :
( ( ~ ( ~ ( less_eq @ SV153 @ SV313 )
| ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV313 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1334,plain,
! [SV313: a,SV153: a] :
( ( ~ ( ~ ~ ( less_eq @ SV153 @ SV313 )
| ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV153 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1335,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( ( less @ SV154 @ SV314 )
| ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1336,plain,
! [SV403: a,SV315: a,SV155: a] :
( ( ( ~ ( less @ SV155 @ SV315 ) )
= $true )
| ( ( less @ ( inf @ SV403 @ SV155 ) @ SV315 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1337,plain,
! [SV156: set_a] :
( ( ( ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1338,plain,
! [SV316: a,SV157: a] :
( ( ( less @ SV157 @ SV316 )
= $false )
| ( ( less_eq @ SV157 @ SV316 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1339,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ( SV158 @ SV317 ) )
= $true )
| ( ( ~ ! [SY860: a] :
( ~ ( SV158 @ SY860 )
| ( less_eq @ SV317 @ SY860 ) )
| ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) )
| ( SV404 @ ( least_a @ less_eq @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1340,plain,
! [SV405: a,SV318: a,SV159: a] :
( ( ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV159 @ SV318 @ SV405 ) )
= $true )
| ( ( modula1727524044comp_a @ less_eq @ SV159 @ SV318 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1341,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ~ ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) )
| ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1220]) ).
thf(1342,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= ( ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1220]) ).
thf(1343,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1344,plain,
! [SV407: a,SV321: a,SV162: a] :
( ( ( ~ ( less @ SV162 @ SV321 ) )
= $true )
| ( ( less @ ( inf @ SV162 @ SV407 ) @ SV321 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1345,plain,
! [SV408: a,SV322: a,SV163: a] :
( ( ( ~ ( less_eq @ ( sup @ SV163 @ SV322 ) @ SV408 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV163 @ SV408 )
| ~ ( less_eq @ SV322 @ SV408 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1346,plain,
! [SV323: a,SV164: a] :
( ( ( less_eq @ SV164 @ SV323 )
= $false )
| ( ( ~ ( ( SV164 != SV323 ) )
| ( less @ SV164 @ SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1347,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ~ ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) )
| ~ ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1226]) ).
thf(1348,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= ( ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1226]) ).
thf(1349,plain,
! [SV410: a,SV325: a,SV166: a] :
( ( ( ~ ! [SX3: a,SX4: a,SX5: a] :
( ( sup @ SX3 @ ( inf @ SX4 @ SX5 ) )
= ( inf @ ( sup @ SX3 @ SX4 ) @ ( sup @ SX3 @ SX5 ) ) ) )
= $true )
| ( ( ( inf @ SV166 @ ( sup @ SV325 @ SV410 ) )
= ( sup @ ( inf @ SV166 @ SV325 ) @ ( inf @ SV166 @ SV410 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1350,plain,
! [SV411: a,SV326: a,SV167: a] :
( ( ( ~ ( less @ SV167 @ SV326 ) )
= $true )
| ( ( ~ ( less_eq @ SV326 @ SV411 )
| ( less @ SV167 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1351,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ~ ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) )
| ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1229]) ).
thf(1352,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1229]) ).
thf(1353,plain,
! [SV181: a,SV13: a] :
( ( ( ( less_eq @ SV13 @ SV181 )
| ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1354,plain,
! [SV182: a,SV14: a] :
( ( ( ( less_eq @ SV14 @ SV182 )
| ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1355,plain,
! [SV183: a,SV15: a] :
( ( ( ( less_eq @ SV15 @ SV183 )
| ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1356,plain,
! [SV184: a,SV16: a] :
( ( ( ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
= SV16 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
!= SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1357,plain,
! [SV185: a,SV17: a] :
( ( ( ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
= SV17 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
!= SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1358,plain,
! [SV188: a,SV20: a] :
( ( ( ( less_eq @ SV20 @ SV188 )
| ( SV20
= ( inf @ SV20 @ SV188 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV20 @ SV188 )
| ( SV20
!= ( inf @ SV20 @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1359,plain,
! [SV191: a,SV23: a] :
( ( ( ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
= SV23 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
!= SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1360,plain,
! [SV192: a,SV24: a] :
( ( ( ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
= SV192 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
!= SV192 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1361,plain,
! [SV193: a,SV25: a] :
( ( ( ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
= SV193 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
!= SV193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1362,plain,
! [SV194: a,SV26: a] :
( ( ( ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
= SV194 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
!= SV194 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1363,plain,
! [SV197: a,SV29: a] :
( ( ( ( less_eq @ SV29 @ SV197 )
| ( SV197
= ( sup @ SV197 @ SV29 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV29 @ SV197 )
| ( SV197
!= ( sup @ SV197 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1364,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( ~ ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ~ ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1365,plain,
! [SV229: a,SV67: a] :
( ( ( ( less @ SV67 @ SV229 )
| ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1366,plain,
! [SV355: a,SV230: a,SV68: a] :
( ( ( less_eq @ SV68 @ SV230 )
= $false )
| ( ( ~ ( less_eq @ SV68 @ SV355 )
| ( less_eq @ SV68 @ ( inf @ SV230 @ SV355 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1367,plain,
! [SV356: a,SV231: a,SV69: a] :
( ( ( less_eq @ SV69 @ SV231 )
= $false )
| ( ( ( SV231 != SV356 )
| ( less_eq @ SV69 @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1368,plain,
! [SV357: a,SV232: a,SV70: a] :
( ( ( less_eq @ SV70 @ SV232 )
= $false )
| ( ( less_eq @ SV70 @ ( sup @ SV357 @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1369,plain,
! [SV358: a,SV233: a,SV71: a] :
( ( ( less @ SV71 @ SV233 )
= $false )
| ( ( ~ ( less_eq @ SV233 @ SV358 )
| ( less @ SV71 @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1370,plain,
! [SV234: a,SV72: a] :
( ( ( less @ SV72 @ SV234 )
= $true )
| ( ( ( less_eq @ SV72 @ SV234 )
= ( SV72 = SV234 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1371,plain,
! [SV235: a,SV73: a] :
( ( ( ( less @ SV73 @ SV235 )
| ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1372,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ( ~ ( less @ SV74 @ SV236 )
| ( SV74 = SV236 ) )
| ~ ( ~ ~ ( less @ SV74 @ SV236 )
| ( SV74 != SV236 ) ) )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1250]) ).
thf(1373,plain,
! [SV236: a,SV74: a] :
( ( ( ( ~ ( less @ SV74 @ SV236 ) )
= ( SV74 = SV236 ) )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1250]) ).
thf(1374,plain,
! [SV413: a,SV237: a] :
( ( ~ ( ( SV237 = SV413 )
| ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) )
| ~ ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1251]) ).
thf(1375,plain,
! [SV413: a,SV237: a] :
( ( ( SV237 = SV413 )
= ( ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1251]) ).
thf(1376,plain,
! [SV360: a,SV238: a,SV76: a] :
( ( ( less @ SV76 @ ( inf @ SV238 @ SV360 ) )
= $false )
| ( ( ~ ( ~ ( less @ SV76 @ SV238 )
| ~ ( less @ SV76 @ SV360 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1377,plain,
! [SV361: a,SV240: a,SV78: a] :
( ( ( SV78 = SV240 )
= $false )
| ( ( ~ ( less_eq @ SV240 @ SV361 )
| ( less_eq @ SV78 @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1378,plain,
! [SV80: a,SV242: a] :
( ( ( ~ ( ( less_eq @ SV242 @ SV80 )
| ( SV242 = SV80 ) )
| ~ ( ~ ( less_eq @ SV242 @ SV80 )
| ( SV242 != SV80 ) ) )
= $true )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1256]) ).
thf(1379,plain,
! [SV80: a,SV242: a] :
( ( ( ( less_eq @ SV242 @ SV80 )
= ( SV242 = SV80 ) )
= $true )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1256]) ).
thf(1380,plain,
! [SV362: a,SV243: a,SV81: a] :
( ( ( less_eq @ SV81 @ SV243 )
= $false )
| ( ( less_eq @ ( inf @ SV362 @ SV81 ) @ SV243 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1381,plain,
! [SV244: a,SV82: a] :
( ( ( SV82 = SV244 )
= $true )
| ( ( ~ ( less_eq @ SV82 @ SV244 )
| ( less @ SV82 @ SV244 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1382,plain,
! [SV363: a,SV245: a,SV83: a] :
( ( ( less_eq @ SV83 @ SV245 )
= $false )
| ( ( ~ ( less @ SV363 @ SV83 )
| ( less @ SV363 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1383,plain,
! [SV414: a,SV364: a,SV247: a,SV85: a] :
( ( ( ~ ( less_eq @ SV85 @ SV247 ) )
= $true )
| ( ( ~ ( less_eq @ SV364 @ SV414 )
| ( less_eq @ ( sup @ SV85 @ SV364 ) @ ( sup @ SV247 @ SV414 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1384,plain,
! [SV415: a,SV250: a] :
( ( ~ ( ( SV250 = SV415 )
| ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) )
| ~ ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1264]) ).
thf(1385,plain,
! [SV415: a,SV250: a] :
( ( ( SV250 = SV415 )
= ( ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1264]) ).
thf(1386,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( SV89 @ SV419 )
| ~ ! [SY903: a] :
( ~ ( SV89 @ SY903 )
| ( less_eq @ SV419 @ SY903 ) ) )
| ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1387,plain,
! [SV90: a,SV251: a] :
( ( ( ~ ( less_eq @ SV251 @ SV90 ) )
= $true )
| ( ( SV90 = SV251 )
= $true )
| ( ( less_eq @ SV90 @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1388,plain,
! [SV366: a,SV252: a,SV91: a] :
( ( ( less_eq @ SV91 @ SV252 )
= $false )
| ( ( less_eq @ SV91 @ ( sup @ SV252 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1389,plain,
! [SV367: a,SV253: a,SV92: a] :
( ( ( less @ SV92 @ SV253 )
= $false )
| ( ( less @ ( inf @ SV92 @ SV367 ) @ SV253 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1390,plain,
! [SV368: a,SV256: a,SV95: a] :
( ( ( less_eq @ SV95 @ SV256 )
= $false )
| ( ( ~ ( less_eq @ SV368 @ SV256 )
| ( less_eq @ ( sup @ SV95 @ SV368 ) @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1391,plain,
! [SV369: a,SV257: a,SV96: a] :
( ( ( less_eq @ SV96 @ SV257 )
= $false )
| ( ( ~ ( less @ SV257 @ SV369 )
| ( less @ SV96 @ SV369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1392,plain,
! [SV416: a,SV258: a] :
( ( ~ ( ( SV258 = SV416 )
| ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) )
| ~ ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1273]) ).
thf(1393,plain,
! [SV416: a,SV258: a] :
( ( ( SV258 = SV416 )
= ( ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1273]) ).
thf(1394,plain,
! [SV371: a,SV259: a,SV98: a] :
( ( ( less_eq @ SV98 @ SV259 )
= $false )
| ( ( ~ ( less_eq @ SV98 @ SV371 )
| ( less_eq @ SV98 @ ( inf @ SV259 @ SV371 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1395,plain,
! [SV372: a,SV260: a,SV99: a] :
( ( ( less_eq @ SV99 @ SV260 )
= $false )
| ( ( less_eq @ ( inf @ SV99 @ SV372 ) @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1396,plain,
! [SV373: a,SV261: a,SV100: a] :
( ( ( less @ SV100 @ SV261 )
= $false )
| ( ( less @ SV100 @ ( sup @ SV261 @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1397,plain,
! [SV263: a,SV102: a] :
( ( ( ( less @ SV102 @ SV263 )
| ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1398,plain,
! [SV264: a,SV103: a > $o] :
( ( ( ! [SY607: a] :
~ ~ ( ~ ~ ( ~ ( SV103 @ SY607 )
| ~ ! [SY608: a] :
( ~ ( SV103 @ SY608 )
| ( less_eq @ SY607 @ SY608 ) ) )
| ~ ! [SY609: a] :
( ~ ~ ( ~ ( SV103 @ SY609 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY609 @ SY610 ) ) )
| ( SY609 = SY607 ) ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1399,plain,
! [SV104: set_a,SV265: a] :
( ( ( ~ ( member_a @ ( sK1_SY803 @ SV265 @ SV104 ) @ SV104 )
| ( less_eq @ ( sK1_SY803 @ SV265 @ SV104 ) @ SV265 ) )
= $false )
| ( ( condit1627435690bove_a @ less_eq @ SV104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1280]) ).
thf(1400,plain,
! [SV266: a,SV105: a] :
( ( ( ( less @ SV105 @ SV266 )
| ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1401,plain,
! [SV267: a,SV106: a > $o] :
( ( ( ~ ! [SY804: a] :
( ~ ( SV106 @ SY804 )
| ( less_eq @ SY804 @ SV267 ) ) )
= $true )
| ( ( ( greatest_a @ less_eq @ SV106 )
= SV267 )
= $true )
| ( ( SV106 @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1402,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1403,plain,
! [SV375: a,SV271: a,SV110: a] :
( ( ( less_eq @ SV110 @ SV271 )
= $false )
| ( ( ~ ( less_eq @ SV271 @ SV375 )
| ( less_eq @ SV110 @ SV375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1404,plain,
! [SV111: a,SV272: a] :
( ( ( less @ SV272 @ SV111 )
= $false )
| ( ( less_eq @ SV111 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1405,plain,
! [SV376: a,SV273: a,SV112: a] :
( ( ( less_eq @ SV112 @ ( inf @ SV273 @ SV376 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV112 @ SV273 )
| ~ ( less_eq @ SV112 @ SV376 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1406,plain,
! [SV377: a,SV274: a,SV113: a] :
( ( ( less @ SV113 @ SV274 )
= $false )
| ( ( less @ SV113 @ ( sup @ SV274 @ SV377 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1407,plain,
! [SV378: a,SV275: a,SV114: a] :
( ( ( less_eq @ SV114 @ SV275 )
= $false )
| ( ( less_eq @ ( inf @ SV378 @ SV114 ) @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1408,plain,
! [SV115: a,SV276: a] :
( ( ( ~ ( less_eq @ SV276 @ SV115 ) )
= $true )
| ( ( SV276 = SV115 )
= $true )
| ( ( less_eq @ SV115 @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1409,plain,
! [SV277: a,SV116: a] :
( ( ~ ( less_eq @ SV116 @ SV277 )
| ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV116 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1293]) ).
thf(1410,plain,
! [SV277: a,SV116: a] :
( ( ~ ~ ( less_eq @ SV116 @ SV277 )
| ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV277 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1411,plain,
! [SV379: a,SV278: a,SV117: a] :
( ( ( less @ SV117 @ SV278 )
= $false )
| ( ( less @ ( inf @ SV379 @ SV117 ) @ SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1412,plain,
! [SV118: set_a] :
( ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1413,plain,
! [SV118: set_a] :
( ( ( ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1414,plain,
! [SV380: a,SV279: a,SV119: a] :
( ( ( less_eq @ SV119 @ SV279 )
= $false )
| ( ( ~ ( less_eq @ SV279 @ SV380 )
| ( less_eq @ SV119 @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1415,plain,
! [SV280: a,SV120: a] :
( ( ( ( less @ SV120 @ SV280 )
| ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1416,plain,
! [SV381: a,SV281: a,SV121: a] :
( ( ( less_eq @ SV121 @ SV281 )
= $false )
| ( ( ~ ( less_eq @ SV381 @ SV121 )
| ( less_eq @ SV381 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1417,plain,
! [SV382: a,SV282: a,SV122: a] :
( ( ( less_eq @ SV122 @ ( inf @ SV282 @ SV382 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV122 @ SV282 )
| ~ ( less_eq @ SV122 @ SV382 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1418,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( ~ ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1419,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1420,plain,
! [SV385: a,SV286: a,SV126: a] :
( ( ( less_eq @ SV126 @ SV286 )
= $false )
| ( ( ~ ( less_eq @ SV126 @ SV385 )
| ( less_eq @ SV126 @ ( inf @ SV286 @ SV385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1421,plain,
! [SV386: a,SV288: a,SV128: a] :
( ( ( less_eq @ SV128 @ SV288 )
= $false )
| ( ( ~ ( less @ SV288 @ SV386 )
| ( less @ SV128 @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1422,plain,
! [SV387: a,SV289: a,SV129: a] :
( ( ( less @ SV129 @ SV289 )
= $false )
| ( ( ~ ( less_eq @ SV387 @ SV129 )
| ( less @ SV387 @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1423,plain,
! [SV130: set_a,SV290: a] :
( ( ( ~ ( member_a @ ( sK2_SY819 @ SV290 @ SV130 ) @ SV130 )
| ( less_eq @ SV290 @ ( sK2_SY819 @ SV290 @ SV130 ) ) )
= $false )
| ( ( condit1001553558elow_a @ less_eq @ SV130 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1310]) ).
thf(1424,plain,
! [SV131: a,SV291: a] :
( ( ( ~ ( less_eq @ SV291 @ SV131 ) )
= $true )
| ( ( SV131 = SV291 )
= $true )
| ( ( less_eq @ SV131 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1425,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( SV132 @ SV292 )
= $false )
| ( ( ~ ! [SY821: a] :
( ~ ( SV132 @ SY821 )
| ( less_eq @ SY821 @ SV292 ) )
| ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) )
| ( SV388 @ ( greatest_a @ less_eq @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1426,plain,
! [SV389: a,SV293: a,SV133: a > a > a] :
( ( ( ! [SY664: a,SY665: a] : ( less_eq @ ( SV133 @ SY664 @ SY665 ) @ SY664 ) )
= $false )
| ( ( ~ ! [SY666: a,SY667: a] : ( less_eq @ ( SV133 @ SY666 @ SY667 ) @ SY667 )
| ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1427,plain,
! [SV390: a,SV294: a,SV134: a] :
( ( ( less_eq @ SV134 @ SV294 )
= $false )
| ( ( less_eq @ ( inf @ SV134 @ SV390 ) @ SV294 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1428,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( ! [SY675: a,SY676: a] : ( less_eq @ SY675 @ ( SV135 @ SY675 @ SY676 ) ) )
= $false )
| ( ( ~ ! [SY677: a,SY678: a] : ( less_eq @ SY678 @ ( SV135 @ SY677 @ SY678 ) )
| ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1429,plain,
! [SV417: a,SV392: a,SV296: a,SV136: a] :
( ( ( ~ ( less_eq @ SV136 @ SV296 ) )
= $true )
| ( ( ~ ( less_eq @ SV392 @ SV417 )
| ( less_eq @ ( inf @ SV136 @ SV392 ) @ ( inf @ SV296 @ SV417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1430,plain,
! [SV297: a,SV137: a] :
( ( ( SV137 = SV297 )
= $true )
| ( ( ~ ( less_eq @ SV297 @ SV137 )
| ( less @ SV297 @ SV137 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1317]) ).
thf(1431,plain,
! [SV393: a,SV298: a,SV138: a] :
( ( ( less @ SV138 @ SV298 )
= $false )
| ( ( less @ SV138 @ ( sup @ SV393 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1432,plain,
! [SV299: a,SV139: a] :
( ( ( less @ SV139 @ SV299 )
= $true )
| ( ( SV139 = SV299 )
= $true )
| ( ( less_eq @ SV139 @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1433,plain,
! [SV394: a,SV300: a,SV140: a] :
( ( ( less_eq @ SV140 @ SV300 )
= $false )
| ( ( less_eq @ SV140 @ ( sup @ SV300 @ SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1434,plain,
! [SV395: a,SV303: a,SV143: a] :
( ( ( ! [SX3: a,SX4: a,SX5: a] :
( ( inf @ SX3 @ ( sup @ SX4 @ SX5 ) )
= ( sup @ ( inf @ SX3 @ SX4 ) @ ( inf @ SX3 @ SX5 ) ) ) )
= $false )
| ( ( ( sup @ SV143 @ ( inf @ SV303 @ SV395 ) )
= ( inf @ ( sup @ SV143 @ SV303 ) @ ( sup @ SV143 @ SV395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1435,plain,
! [SV396: a,SV304: a,SV144: a] :
( ( ( less_eq @ SV144 @ SV304 )
= $false )
| ( ( ~ ( less_eq @ SV396 @ SV304 )
| ( less_eq @ ( sup @ SV144 @ SV396 ) @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1436,plain,
! [SV305: a,SV145: a > $o] :
( ( ( ~ ! [SY850: a] :
( ~ ( SV145 @ SY850 )
| ( less_eq @ SV305 @ SY850 ) ) )
= $true )
| ( ( ( least_a @ less_eq @ SV145 )
= SV305 )
= $true )
| ( ( SV145 @ SV305 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1437,plain,
! [SV418: a,SV397: a,SV306: a,SV146: a] :
( ( ( ~ ( less_eq @ SV146 @ SV306 ) )
= $true )
| ( ( ~ ( less_eq @ SV397 @ SV418 )
| ( less_eq @ ( sup @ SV146 @ SV397 ) @ ( sup @ SV306 @ SV418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1438,plain,
! [SV398: a,SV308: a,SV148: a] :
( ( ( less_eq @ ( sup @ SV148 @ SV308 ) @ SV398 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV148 @ SV398 )
| ~ ( less_eq @ SV308 @ SV398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1439,plain,
! [SV399: a,SV309: a,SV149: a] :
( ( ( less_eq @ SV149 @ SV309 )
= $false )
| ( ( ~ ( less_eq @ SV399 @ SV309 )
| ( less_eq @ ( sup @ SV149 @ SV399 ) @ SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1440,plain,
! [SV400: a,SV310: a,SV150: a] :
( ( ( less @ SV150 @ SV310 )
= $false )
| ( ( less @ SV150 @ ( sup @ SV400 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1441,plain,
! [SV401: a,SV311: a,SV151: a] :
( ( ( less @ ( sup @ SV151 @ SV311 ) @ SV401 )
= $false )
| ( ( ~ ( ~ ( less @ SV151 @ SV401 )
| ~ ( less @ SV311 @ SV401 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1442,plain,
! [SV402: a,SV312: a,SV152: a] :
( ( ( less_eq @ SV152 @ SV312 )
= $false )
| ( ( less_eq @ SV152 @ ( sup @ SV402 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1443,plain,
! [SV313: a,SV153: a] :
( ( ~ ( less_eq @ SV153 @ SV313 )
| ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV313 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1444,plain,
! [SV313: a,SV153: a] :
( ( ~ ~ ( less_eq @ SV153 @ SV313 )
| ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV153 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1445,plain,
! [SV314: a,SV154: a] :
( ( ( ( less @ SV154 @ SV314 )
| ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1446,plain,
! [SV403: a,SV315: a,SV155: a] :
( ( ( less @ SV155 @ SV315 )
= $false )
| ( ( less @ ( inf @ SV403 @ SV155 ) @ SV315 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1447,plain,
! [SV156: set_a] :
( ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1448,plain,
! [SV156: set_a] :
( ( ( ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1449,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( SV158 @ SV317 )
= $false )
| ( ( ~ ! [SY860: a] :
( ~ ( SV158 @ SY860 )
| ( less_eq @ SV317 @ SY860 ) )
| ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) )
| ( SV404 @ ( least_a @ less_eq @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1450,plain,
! [SV405: a,SV318: a,SV159: a] :
( ( ( modula1376131916tice_a @ inf @ less @ sup @ SV159 @ SV318 @ SV405 )
= $false )
| ( ( modula1727524044comp_a @ less_eq @ SV159 @ SV318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1451,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( ~ ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1452,plain,
! [SV320: a,SV161: a] :
( ( ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) )
= $false )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1453,plain,
! [SV407: a,SV321: a,SV162: a] :
( ( ( less @ SV162 @ SV321 )
= $false )
| ( ( less @ ( inf @ SV162 @ SV407 ) @ SV321 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1454,plain,
! [SV408: a,SV322: a,SV163: a] :
( ( ( less_eq @ ( sup @ SV163 @ SV322 ) @ SV408 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV163 @ SV408 )
| ~ ( less_eq @ SV322 @ SV408 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1455,plain,
! [SV323: a,SV164: a] :
( ( ( ~ ( ( SV164 != SV323 ) ) )
= $true )
| ( ( less @ SV164 @ SV323 )
= $true )
| ( ( less_eq @ SV164 @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1456,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( ~ ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1457,plain,
! [SV410: a,SV325: a,SV166: a] :
( ( ( ! [SX3: a,SX4: a,SX5: a] :
( ( sup @ SX3 @ ( inf @ SX4 @ SX5 ) )
= ( inf @ ( sup @ SX3 @ SX4 ) @ ( sup @ SX3 @ SX5 ) ) ) )
= $false )
| ( ( ( inf @ SV166 @ ( sup @ SV325 @ SV410 ) )
= ( sup @ ( inf @ SV166 @ SV325 ) @ ( inf @ SV166 @ SV410 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1458,plain,
! [SV411: a,SV326: a,SV167: a] :
( ( ( less @ SV167 @ SV326 )
= $false )
| ( ( ~ ( less_eq @ SV326 @ SV411 )
| ( less @ SV167 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1459,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1460,plain,
! [SV181: a,SV13: a] :
( ( ( less_eq @ SV13 @ SV181 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1461,plain,
! [SV181: a,SV13: a] :
( ( ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1462,plain,
! [SV182: a,SV14: a] :
( ( ( less_eq @ SV14 @ SV182 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1463,plain,
! [SV182: a,SV14: a] :
( ( ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1464,plain,
! [SV183: a,SV15: a] :
( ( ( less_eq @ SV15 @ SV183 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1465,plain,
! [SV183: a,SV15: a] :
( ( ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1466,plain,
! [SV184: a,SV16: a] :
( ( ( less_eq @ SV16 @ SV184 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
!= SV16 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1467,plain,
! [SV184: a,SV16: a] :
( ( ( ( inf @ SV16 @ SV184 )
= SV16 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
!= SV16 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1468,plain,
! [SV185: a,SV17: a] :
( ( ( less_eq @ SV17 @ SV185 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
!= SV17 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1469,plain,
! [SV17: a,SV185: a] :
( ( ( ( inf @ SV185 @ SV17 )
= SV17 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
!= SV17 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1470,plain,
! [SV188: a,SV20: a] :
( ( ( less_eq @ SV20 @ SV188 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV20 @ SV188 )
| ( SV20
!= ( inf @ SV20 @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1471,plain,
! [SV188: a,SV20: a] :
( ( ( SV20
= ( inf @ SV20 @ SV188 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV20 @ SV188 )
| ( SV20
!= ( inf @ SV20 @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1472,plain,
! [SV191: a,SV23: a] :
( ( ( less_eq @ SV23 @ SV191 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
!= SV23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1473,plain,
! [SV191: a,SV23: a] :
( ( ( ( inf @ SV23 @ SV191 )
= SV23 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
!= SV23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1474,plain,
! [SV192: a,SV24: a] :
( ( ( less_eq @ SV24 @ SV192 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
!= SV192 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1475,plain,
! [SV192: a,SV24: a] :
( ( ( ( sup @ SV24 @ SV192 )
= SV192 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
!= SV192 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1476,plain,
! [SV193: a,SV25: a] :
( ( ( less_eq @ SV25 @ SV193 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
!= SV193 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1477,plain,
! [SV25: a,SV193: a] :
( ( ( ( sup @ SV193 @ SV25 )
= SV193 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
!= SV193 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1478,plain,
! [SV194: a,SV26: a] :
( ( ( less_eq @ SV26 @ SV194 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
!= SV194 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1479,plain,
! [SV194: a,SV26: a] :
( ( ( ( sup @ SV26 @ SV194 )
= SV194 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
!= SV194 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1480,plain,
! [SV197: a,SV29: a] :
( ( ( less_eq @ SV29 @ SV197 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV29 @ SV197 )
| ( SV197
!= ( sup @ SV197 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1481,plain,
! [SV29: a,SV197: a] :
( ( ( SV197
= ( sup @ SV197 @ SV29 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV29 @ SV197 )
| ( SV197
!= ( sup @ SV197 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1482,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) )
= $false )
| ( ( ~ ( ~ ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ~ ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1483,plain,
! [SV229: a,SV67: a] :
( ( ( less @ SV67 @ SV229 )
= $false )
| ( ( ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1484,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1485,plain,
! [SV230: a,SV355: a,SV68: a] :
( ( ( ~ ( less_eq @ SV68 @ SV355 ) )
= $true )
| ( ( less_eq @ SV68 @ ( inf @ SV230 @ SV355 ) )
= $true )
| ( ( less_eq @ SV68 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1486,plain,
! [SV69: a,SV356: a,SV231: a] :
( ( ( SV231 != SV356 )
= $true )
| ( ( less_eq @ SV69 @ SV356 )
= $true )
| ( ( less_eq @ SV69 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1487,plain,
! [SV71: a,SV358: a,SV233: a] :
( ( ( ~ ( less_eq @ SV233 @ SV358 ) )
= $true )
| ( ( less @ SV71 @ SV358 )
= $true )
| ( ( less @ SV71 @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1488,plain,
! [SV234: a,SV72: a] :
( ( ( ~ ( ( less_eq @ SV72 @ SV234 )
| ( SV72 = SV234 ) )
| ~ ( ~ ( less_eq @ SV72 @ SV234 )
| ( SV72 != SV234 ) ) )
= $true )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1370]) ).
thf(1489,plain,
! [SV234: a,SV72: a] :
( ( ( ( less_eq @ SV72 @ SV234 )
= ( SV72 = SV234 ) )
= $true )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1370]) ).
thf(1490,plain,
! [SV235: a,SV73: a] :
( ( ( less @ SV73 @ SV235 )
= $false )
| ( ( ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1491,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1492,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ( ~ ( less @ SV74 @ SV236 )
| ( SV74 = SV236 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( less @ SV74 @ SV236 )
| ( SV74 != SV236 ) ) )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1493,plain,
! [SV413: a,SV237: a] :
( ( ( ~ ( ( SV237 = SV413 )
| ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true )
| ( ( ~ ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1494,plain,
! [SV360: a,SV238: a,SV76: a] :
( ( ( ~ ( less @ SV76 @ SV238 )
| ~ ( less @ SV76 @ SV360 ) )
= $false )
| ( ( less @ SV76 @ ( inf @ SV238 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1495,plain,
! [SV78: a,SV361: a,SV240: a] :
( ( ( ~ ( less_eq @ SV240 @ SV361 ) )
= $true )
| ( ( less_eq @ SV78 @ SV361 )
= $true )
| ( ( SV78 = SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1496,plain,
! [SV80: a,SV242: a] :
( ( ( ~ ( ( less_eq @ SV242 @ SV80 )
| ( SV242 = SV80 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV242 @ SV80 )
| ( SV242 != SV80 ) ) )
= $true )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1497,plain,
! [SV244: a,SV82: a] :
( ( ( ~ ( less_eq @ SV82 @ SV244 ) )
= $true )
| ( ( less @ SV82 @ SV244 )
= $true )
| ( ( SV82 = SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1498,plain,
! [SV245: a,SV83: a,SV363: a] :
( ( ( ~ ( less @ SV363 @ SV83 ) )
= $true )
| ( ( less @ SV363 @ SV245 )
= $true )
| ( ( less_eq @ SV83 @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1499,plain,
! [SV414: a,SV364: a,SV247: a,SV85: a] :
( ( ( less_eq @ SV85 @ SV247 )
= $false )
| ( ( ~ ( less_eq @ SV364 @ SV414 )
| ( less_eq @ ( sup @ SV85 @ SV364 ) @ ( sup @ SV247 @ SV414 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1500,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( ( SV250 = SV415 )
| ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true )
| ( ( ~ ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1501,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( ~ ~ ( ~ ( SV89 @ SV419 )
| ~ ! [SY903: a] :
( ~ ( SV89 @ SY903 )
| ( less_eq @ SV419 @ SY903 ) ) )
| ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1502,plain,
! [SV90: a,SV251: a] :
( ( ( less_eq @ SV251 @ SV90 )
= $false )
| ( ( SV90 = SV251 )
= $true )
| ( ( less_eq @ SV90 @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1503,plain,
! [SV95: a,SV256: a,SV368: a] :
( ( ( ~ ( less_eq @ SV368 @ SV256 ) )
= $true )
| ( ( less_eq @ ( sup @ SV95 @ SV368 ) @ SV256 )
= $true )
| ( ( less_eq @ SV95 @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1504,plain,
! [SV96: a,SV369: a,SV257: a] :
( ( ( ~ ( less @ SV257 @ SV369 ) )
= $true )
| ( ( less @ SV96 @ SV369 )
= $true )
| ( ( less_eq @ SV96 @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1505,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( ( SV258 = SV416 )
| ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true )
| ( ( ~ ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1506,plain,
! [SV259: a,SV371: a,SV98: a] :
( ( ( ~ ( less_eq @ SV98 @ SV371 ) )
= $true )
| ( ( less_eq @ SV98 @ ( inf @ SV259 @ SV371 ) )
= $true )
| ( ( less_eq @ SV98 @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1394]) ).
thf(1507,plain,
! [SV263: a,SV102: a] :
( ( ( less @ SV102 @ SV263 )
= $false )
| ( ( ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1508,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1509,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( SV103 @ SV420 )
| ~ ! [SY906: a] :
( ~ ( SV103 @ SY906 )
| ( less_eq @ SV420 @ SY906 ) ) )
| ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1510,plain,
! [SV104: set_a,SV265: a] :
( ( ( ~ ( member_a @ ( sK1_SY803 @ SV265 @ SV104 ) @ SV104 ) )
= $false )
| ( ( condit1627435690bove_a @ less_eq @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1511,plain,
! [SV104: set_a,SV265: a] :
( ( ( less_eq @ ( sK1_SY803 @ SV265 @ SV104 ) @ SV265 )
= $false )
| ( ( condit1627435690bove_a @ less_eq @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1512,plain,
! [SV266: a,SV105: a] :
( ( ( less @ SV105 @ SV266 )
= $false )
| ( ( ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1513,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1514,plain,
! [SV267: a,SV106: a > $o] :
( ( ( ! [SY804: a] :
( ~ ( SV106 @ SY804 )
| ( less_eq @ SY804 @ SV267 ) ) )
= $false )
| ( ( ( greatest_a @ less_eq @ SV106 )
= SV267 )
= $true )
| ( ( SV106 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1515,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1516,plain,
! [SV110: a,SV375: a,SV271: a] :
( ( ( ~ ( less_eq @ SV271 @ SV375 ) )
= $true )
| ( ( less_eq @ SV110 @ SV375 )
= $true )
| ( ( less_eq @ SV110 @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1517,plain,
! [SV376: a,SV273: a,SV112: a] :
( ( ( ~ ( less_eq @ SV112 @ SV273 )
| ~ ( less_eq @ SV112 @ SV376 ) )
= $false )
| ( ( less_eq @ SV112 @ ( inf @ SV273 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1518,plain,
! [SV115: a,SV276: a] :
( ( ( less_eq @ SV276 @ SV115 )
= $false )
| ( ( SV276 = SV115 )
= $true )
| ( ( less_eq @ SV115 @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1519,plain,
! [SV277: a,SV116: a] :
( ( ( ~ ( less_eq @ SV116 @ SV277 ) )
= $true )
| ( ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1520,plain,
! [SV277: a,SV116: a] :
( ( ( ~ ~ ( less_eq @ SV116 @ SV277 ) )
= $true )
| ( ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1521,plain,
! [SV118: set_a] :
( ( ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1522,plain,
! [SV118: set_a] :
( ( ( ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $true )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1523,plain,
! [SV119: a,SV380: a,SV279: a] :
( ( ( ~ ( less_eq @ SV279 @ SV380 ) )
= $true )
| ( ( less_eq @ SV119 @ SV380 )
= $true )
| ( ( less_eq @ SV119 @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1524,plain,
! [SV280: a,SV120: a] :
( ( ( less @ SV120 @ SV280 )
= $false )
| ( ( ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1525,plain,
! [SV120: a,SV280: a] :
( ( ( ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1526,plain,
! [SV281: a,SV121: a,SV381: a] :
( ( ( ~ ( less_eq @ SV381 @ SV121 ) )
= $true )
| ( ( less_eq @ SV381 @ SV281 )
= $true )
| ( ( less_eq @ SV121 @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1527,plain,
! [SV382: a,SV282: a,SV122: a] :
( ( ( ~ ( less_eq @ SV122 @ SV282 )
| ~ ( less_eq @ SV122 @ SV382 ) )
= $false )
| ( ( less_eq @ SV122 @ ( inf @ SV282 @ SV382 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1528,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1529,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1530,plain,
! [SV286: a,SV385: a,SV126: a] :
( ( ( ~ ( less_eq @ SV126 @ SV385 ) )
= $true )
| ( ( less_eq @ SV126 @ ( inf @ SV286 @ SV385 ) )
= $true )
| ( ( less_eq @ SV126 @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1531,plain,
! [SV128: a,SV386: a,SV288: a] :
( ( ( ~ ( less @ SV288 @ SV386 ) )
= $true )
| ( ( less @ SV128 @ SV386 )
= $true )
| ( ( less_eq @ SV128 @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1532,plain,
! [SV289: a,SV129: a,SV387: a] :
( ( ( ~ ( less_eq @ SV387 @ SV129 ) )
= $true )
| ( ( less @ SV387 @ SV289 )
= $true )
| ( ( less @ SV129 @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1533,plain,
! [SV130: set_a,SV290: a] :
( ( ( ~ ( member_a @ ( sK2_SY819 @ SV290 @ SV130 ) @ SV130 ) )
= $false )
| ( ( condit1001553558elow_a @ less_eq @ SV130 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1534,plain,
! [SV130: set_a,SV290: a] :
( ( ( less_eq @ SV290 @ ( sK2_SY819 @ SV290 @ SV130 ) )
= $false )
| ( ( condit1001553558elow_a @ less_eq @ SV130 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1535,plain,
! [SV131: a,SV291: a] :
( ( ( less_eq @ SV291 @ SV131 )
= $false )
| ( ( SV131 = SV291 )
= $true )
| ( ( less_eq @ SV131 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1536,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ! [SY821: a] :
( ~ ( SV132 @ SY821 )
| ( less_eq @ SY821 @ SV292 ) ) )
= $true )
| ( ( ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) )
| ( SV388 @ ( greatest_a @ less_eq @ SV132 ) ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1537,plain,
! [SV293: a,SV389: a,SV133: a > a > a] :
( ( ( ! [SY909: a] : ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ SY909 ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) ) )
= $false )
| ( ( ~ ! [SY666: a,SY667: a] : ( less_eq @ ( SV133 @ SY666 @ SY667 ) @ SY667 )
| ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1426]) ).
thf(1538,plain,
! [SV135: a > a > a,SV295: a,SV391: a] :
( ( ( ! [SY910: a] : ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ SY910 ) ) )
= $false )
| ( ( ~ ! [SY677: a,SY678: a] : ( less_eq @ SY678 @ ( SV135 @ SY677 @ SY678 ) )
| ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1428]) ).
thf(1539,plain,
! [SV417: a,SV392: a,SV296: a,SV136: a] :
( ( ( less_eq @ SV136 @ SV296 )
= $false )
| ( ( ~ ( less_eq @ SV392 @ SV417 )
| ( less_eq @ ( inf @ SV136 @ SV392 ) @ ( inf @ SV296 @ SV417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1540,plain,
! [SV137: a,SV297: a] :
( ( ( ~ ( less_eq @ SV297 @ SV137 ) )
= $true )
| ( ( less @ SV297 @ SV137 )
= $true )
| ( ( SV137 = SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1541,plain,
! [SV143: a,SV303: a,SV395: a] :
( ( ( ! [SY911: a,SY912: a] :
( ( inf @ ( sK5_SX3 @ SV395 @ SV303 @ SV143 ) @ ( sup @ SY911 @ SY912 ) )
= ( sup @ ( inf @ ( sK5_SX3 @ SV395 @ SV303 @ SV143 ) @ SY911 ) @ ( inf @ ( sK5_SX3 @ SV395 @ SV303 @ SV143 ) @ SY912 ) ) ) )
= $false )
| ( ( ( sup @ SV143 @ ( inf @ SV303 @ SV395 ) )
= ( inf @ ( sup @ SV143 @ SV303 ) @ ( sup @ SV143 @ SV395 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1434]) ).
thf(1542,plain,
! [SV144: a,SV304: a,SV396: a] :
( ( ( ~ ( less_eq @ SV396 @ SV304 ) )
= $true )
| ( ( less_eq @ ( sup @ SV144 @ SV396 ) @ SV304 )
= $true )
| ( ( less_eq @ SV144 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1543,plain,
! [SV305: a,SV145: a > $o] :
( ( ( ! [SY850: a] :
( ~ ( SV145 @ SY850 )
| ( less_eq @ SV305 @ SY850 ) ) )
= $false )
| ( ( ( least_a @ less_eq @ SV145 )
= SV305 )
= $true )
| ( ( SV145 @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1544,plain,
! [SV418: a,SV397: a,SV306: a,SV146: a] :
( ( ( less_eq @ SV146 @ SV306 )
= $false )
| ( ( ~ ( less_eq @ SV397 @ SV418 )
| ( less_eq @ ( sup @ SV146 @ SV397 ) @ ( sup @ SV306 @ SV418 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1545,plain,
! [SV308: a,SV398: a,SV148: a] :
( ( ( ~ ( less_eq @ SV148 @ SV398 )
| ~ ( less_eq @ SV308 @ SV398 ) )
= $false )
| ( ( less_eq @ ( sup @ SV148 @ SV308 ) @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1546,plain,
! [SV149: a,SV309: a,SV399: a] :
( ( ( ~ ( less_eq @ SV399 @ SV309 ) )
= $true )
| ( ( less_eq @ ( sup @ SV149 @ SV399 ) @ SV309 )
= $true )
| ( ( less_eq @ SV149 @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1547,plain,
! [SV311: a,SV401: a,SV151: a] :
( ( ( ~ ( less @ SV151 @ SV401 )
| ~ ( less @ SV311 @ SV401 ) )
= $false )
| ( ( less @ ( sup @ SV151 @ SV311 ) @ SV401 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1548,plain,
! [SV313: a,SV153: a] :
( ( ( ~ ( less_eq @ SV153 @ SV313 ) )
= $true )
| ( ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV313 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1549,plain,
! [SV313: a,SV153: a] :
( ( ( ~ ~ ( less_eq @ SV153 @ SV313 ) )
= $true )
| ( ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1550,plain,
! [SV314: a,SV154: a] :
( ( ( less @ SV154 @ SV314 )
= $false )
| ( ( ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1551,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) )
= $false )
| ( ( ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1552,plain,
! [SV156: set_a] :
( ( ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1553,plain,
! [SV156: set_a] :
( ( ( ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $true )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1554,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ! [SY860: a] :
( ~ ( SV158 @ SY860 )
| ( less_eq @ SV317 @ SY860 ) ) )
= $true )
| ( ( ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) )
| ( SV404 @ ( least_a @ less_eq @ SV158 ) ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1555,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) )
= $false )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1556,plain,
! [SV320: a,SV161: a] :
( ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1557,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) )
= $false )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1558,plain,
! [SV322: a,SV408: a,SV163: a] :
( ( ( ~ ( less_eq @ SV163 @ SV408 )
| ~ ( less_eq @ SV322 @ SV408 ) )
= $false )
| ( ( less_eq @ ( sup @ SV163 @ SV322 ) @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1559,plain,
! [SV323: a,SV164: a] :
( ( ( SV164 != SV323 )
= $false )
| ( ( less @ SV164 @ SV323 )
= $true )
| ( ( less_eq @ SV164 @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1560,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1561,plain,
! [SV166: a,SV325: a,SV410: a] :
( ( ( ! [SY913: a,SY914: a] :
( ( sup @ ( sK6_SX3 @ SV410 @ SV325 @ SV166 ) @ ( inf @ SY913 @ SY914 ) )
= ( inf @ ( sup @ ( sK6_SX3 @ SV410 @ SV325 @ SV166 ) @ SY913 ) @ ( sup @ ( sK6_SX3 @ SV410 @ SV325 @ SV166 ) @ SY914 ) ) ) )
= $false )
| ( ( ( inf @ SV166 @ ( sup @ SV325 @ SV410 ) )
= ( sup @ ( inf @ SV166 @ SV325 ) @ ( inf @ SV166 @ SV410 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1457]) ).
thf(1562,plain,
! [SV167: a,SV411: a,SV326: a] :
( ( ( ~ ( less_eq @ SV326 @ SV411 ) )
= $true )
| ( ( less @ SV167 @ SV411 )
= $true )
| ( ( less @ SV167 @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1563,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) )
= $false )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1564,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) )
= $false )
| ( ( less_eq @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1565,plain,
! [SV181: a,SV13: a] :
( ( ( less @ SV13 @ SV181 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1566,plain,
! [SV13: a,SV181: a] :
( ( ( SV181 = SV13 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1567,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) )
= $false )
| ( ( less_eq @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1568,plain,
! [SV182: a,SV14: a] :
( ( ( less @ SV14 @ SV182 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1569,plain,
! [SV182: a,SV14: a] :
( ( ( SV14 = SV182 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1570,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) )
= $false )
| ( ( less_eq @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1571,plain,
! [SV183: a,SV15: a] :
( ( ( less @ SV15 @ SV183 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1572,plain,
! [SV183: a,SV15: a] :
( ( ( SV15 = SV183 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1573,plain,
! [SV184: a,SV16: a] :
( ( ( ~ ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
!= SV16 ) )
= $false )
| ( ( less_eq @ SV16 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1574,plain,
! [SV184: a,SV16: a] :
( ( ( ~ ( less_eq @ SV16 @ SV184 )
| ( ( inf @ SV16 @ SV184 )
!= SV16 ) )
= $false )
| ( ( ( inf @ SV16 @ SV184 )
= SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1575,plain,
! [SV185: a,SV17: a] :
( ( ( ~ ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
!= SV17 ) )
= $false )
| ( ( less_eq @ SV17 @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1576,plain,
! [SV185: a,SV17: a] :
( ( ( ~ ( less_eq @ SV17 @ SV185 )
| ( ( inf @ SV185 @ SV17 )
!= SV17 ) )
= $false )
| ( ( ( inf @ SV185 @ SV17 )
= SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1577,plain,
! [SV188: a,SV20: a] :
( ( ( ~ ( less_eq @ SV20 @ SV188 )
| ( SV20
!= ( inf @ SV20 @ SV188 ) ) )
= $false )
| ( ( less_eq @ SV20 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1578,plain,
! [SV188: a,SV20: a] :
( ( ( ~ ( less_eq @ SV20 @ SV188 )
| ( SV20
!= ( inf @ SV20 @ SV188 ) ) )
= $false )
| ( ( SV20
= ( inf @ SV20 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1579,plain,
! [SV191: a,SV23: a] :
( ( ( ~ ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
!= SV23 ) )
= $false )
| ( ( less_eq @ SV23 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1580,plain,
! [SV191: a,SV23: a] :
( ( ( ~ ( less_eq @ SV23 @ SV191 )
| ( ( inf @ SV23 @ SV191 )
!= SV23 ) )
= $false )
| ( ( ( inf @ SV23 @ SV191 )
= SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1581,plain,
! [SV192: a,SV24: a] :
( ( ( ~ ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
!= SV192 ) )
= $false )
| ( ( less_eq @ SV24 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1582,plain,
! [SV192: a,SV24: a] :
( ( ( ~ ( less_eq @ SV24 @ SV192 )
| ( ( sup @ SV24 @ SV192 )
!= SV192 ) )
= $false )
| ( ( ( sup @ SV24 @ SV192 )
= SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1583,plain,
! [SV193: a,SV25: a] :
( ( ( ~ ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
!= SV193 ) )
= $false )
| ( ( less_eq @ SV25 @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1584,plain,
! [SV193: a,SV25: a] :
( ( ( ~ ( less_eq @ SV25 @ SV193 )
| ( ( sup @ SV193 @ SV25 )
!= SV193 ) )
= $false )
| ( ( ( sup @ SV193 @ SV25 )
= SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1585,plain,
! [SV194: a,SV26: a] :
( ( ( ~ ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
!= SV194 ) )
= $false )
| ( ( less_eq @ SV26 @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1586,plain,
! [SV194: a,SV26: a] :
( ( ( ~ ( less_eq @ SV26 @ SV194 )
| ( ( sup @ SV26 @ SV194 )
!= SV194 ) )
= $false )
| ( ( ( sup @ SV26 @ SV194 )
= SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1587,plain,
! [SV197: a,SV29: a] :
( ( ( ~ ( less_eq @ SV29 @ SV197 )
| ( SV197
!= ( sup @ SV197 @ SV29 ) ) )
= $false )
| ( ( less_eq @ SV29 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1588,plain,
! [SV197: a,SV29: a] :
( ( ( ~ ( less_eq @ SV29 @ SV197 )
| ( SV197
!= ( sup @ SV197 @ SV29 ) ) )
= $false )
| ( ( SV197
= ( sup @ SV197 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1589,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= $false )
| ( ( ~ ( ~ ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ~ ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1590,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) )
= $false )
| ( ( ~ ( ~ ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ~ ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1591,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) )
= $false )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1592,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1593,plain,
! [SV230: a,SV355: a,SV68: a] :
( ( ( less_eq @ SV68 @ SV355 )
= $false )
| ( ( less_eq @ SV68 @ ( inf @ SV230 @ SV355 ) )
= $true )
| ( ( less_eq @ SV68 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1594,plain,
! [SV69: a,SV356: a,SV231: a] :
( ( ( SV231 = SV356 )
= $false )
| ( ( less_eq @ SV69 @ SV356 )
= $true )
| ( ( less_eq @ SV69 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1595,plain,
! [SV71: a,SV358: a,SV233: a] :
( ( ( less_eq @ SV233 @ SV358 )
= $false )
| ( ( less @ SV71 @ SV358 )
= $true )
| ( ( less @ SV71 @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1596,plain,
! [SV234: a,SV72: a] :
( ( ( ~ ( ( less_eq @ SV72 @ SV234 )
| ( SV72 = SV234 ) ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV72 @ SV234 )
| ( SV72 != SV234 ) ) )
= $true )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1597,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) )
= $false )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1598,plain,
! [SV235: a,SV73: a] :
( ( ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1599,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ( less @ SV74 @ SV236 )
| ( SV74 = SV236 ) )
= $false )
| ( ( ~ ( ~ ~ ( less @ SV74 @ SV236 )
| ( SV74 != SV236 ) ) )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1600,plain,
! [SV413: a,SV237: a] :
( ( ( ( SV237 = SV413 )
| ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) )
= $false )
| ( ( ~ ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1601,plain,
! [SV360: a,SV238: a,SV76: a] :
( ( ( ~ ( less @ SV76 @ SV238 ) )
= $false )
| ( ( less @ SV76 @ ( inf @ SV238 @ SV360 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1602,plain,
! [SV238: a,SV360: a,SV76: a] :
( ( ( ~ ( less @ SV76 @ SV360 ) )
= $false )
| ( ( less @ SV76 @ ( inf @ SV238 @ SV360 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1603,plain,
! [SV78: a,SV361: a,SV240: a] :
( ( ( less_eq @ SV240 @ SV361 )
= $false )
| ( ( less_eq @ SV78 @ SV361 )
= $true )
| ( ( SV78 = SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1604,plain,
! [SV80: a,SV242: a] :
( ( ( ( less_eq @ SV242 @ SV80 )
| ( SV242 = SV80 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV242 @ SV80 )
| ( SV242 != SV80 ) ) )
= $true )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1605,plain,
! [SV244: a,SV82: a] :
( ( ( less_eq @ SV82 @ SV244 )
= $false )
| ( ( less @ SV82 @ SV244 )
= $true )
| ( ( SV82 = SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1606,plain,
! [SV245: a,SV83: a,SV363: a] :
( ( ( less @ SV363 @ SV83 )
= $false )
| ( ( less @ SV363 @ SV245 )
= $true )
| ( ( less_eq @ SV83 @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1607,plain,
! [SV247: a,SV85: a,SV414: a,SV364: a] :
( ( ( ~ ( less_eq @ SV364 @ SV414 ) )
= $true )
| ( ( less_eq @ ( sup @ SV85 @ SV364 ) @ ( sup @ SV247 @ SV414 ) )
= $true )
| ( ( less_eq @ SV85 @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1608,plain,
! [SV415: a,SV250: a] :
( ( ( ( SV250 = SV415 )
| ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) )
= $false )
| ( ( ~ ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1609,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ~ ( ~ ( SV89 @ SV419 )
| ~ ! [SY903: a] :
( ~ ( SV89 @ SY903 )
| ( less_eq @ SV419 @ SY903 ) ) )
| ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1501]) ).
thf(1610,plain,
! [SV95: a,SV256: a,SV368: a] :
( ( ( less_eq @ SV368 @ SV256 )
= $false )
| ( ( less_eq @ ( sup @ SV95 @ SV368 ) @ SV256 )
= $true )
| ( ( less_eq @ SV95 @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1611,plain,
! [SV96: a,SV369: a,SV257: a] :
( ( ( less @ SV257 @ SV369 )
= $false )
| ( ( less @ SV96 @ SV369 )
= $true )
| ( ( less_eq @ SV96 @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1612,plain,
! [SV416: a,SV258: a] :
( ( ( ( SV258 = SV416 )
| ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) )
= $false )
| ( ( ~ ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1613,plain,
! [SV259: a,SV371: a,SV98: a] :
( ( ( less_eq @ SV98 @ SV371 )
= $false )
| ( ( less_eq @ SV98 @ ( inf @ SV259 @ SV371 ) )
= $true )
| ( ( less_eq @ SV98 @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1614,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) )
= $false )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1615,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1616,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ~ ( ~ ~ ( ~ ( SV103 @ SV420 )
| ~ ! [SY906: a] :
( ~ ( SV103 @ SY906 )
| ( less_eq @ SV420 @ SY906 ) ) )
| ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1617,plain,
! [SV104: set_a,SV265: a] :
( ( ( member_a @ ( sK1_SY803 @ SV265 @ SV104 ) @ SV104 )
= $true )
| ( ( condit1627435690bove_a @ less_eq @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1618,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) )
= $false )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1619,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1620,plain,
! [SV267: a,SV106: a > $o] :
( ( ( ~ ( SV106 @ ( sK7_SY804 @ SV267 @ SV106 ) )
| ( less_eq @ ( sK7_SY804 @ SV267 @ SV106 ) @ SV267 ) )
= $false )
| ( ( ( greatest_a @ less_eq @ SV106 )
= SV267 )
= $true )
| ( ( SV106 @ SV267 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1514]) ).
thf(1621,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1515]) ).
thf(1622,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1515]) ).
thf(1623,plain,
! [SV110: a,SV375: a,SV271: a] :
( ( ( less_eq @ SV271 @ SV375 )
= $false )
| ( ( less_eq @ SV110 @ SV375 )
= $true )
| ( ( less_eq @ SV110 @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1624,plain,
! [SV376: a,SV273: a,SV112: a] :
( ( ( ~ ( less_eq @ SV112 @ SV273 ) )
= $false )
| ( ( less_eq @ SV112 @ ( inf @ SV273 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1517]) ).
thf(1625,plain,
! [SV273: a,SV376: a,SV112: a] :
( ( ( ~ ( less_eq @ SV112 @ SV376 ) )
= $false )
| ( ( less_eq @ SV112 @ ( inf @ SV273 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1517]) ).
thf(1626,plain,
! [SV277: a,SV116: a] :
( ( ( less_eq @ SV116 @ SV277 )
= $false )
| ( ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1627,plain,
! [SV277: a,SV116: a] :
( ( ( ~ ( less_eq @ SV116 @ SV277 ) )
= $false )
| ( ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1628,plain,
! [SV118: set_a] :
( ( ( ~ ( condit1627435690bove_a @ less_eq @ SV118 ) )
= $false )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1521]) ).
thf(1629,plain,
! [SV118: set_a] :
( ( ( ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1521]) ).
thf(1630,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ! [SY915: a] :
( ~ ( member_a @ SY915 @ SV118 )
| ( less_eq @ SY915 @ SV421 ) ) )
= $true )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1631,plain,
! [SV119: a,SV380: a,SV279: a] :
( ( ( less_eq @ SV279 @ SV380 )
= $false )
| ( ( less_eq @ SV119 @ SV380 )
= $true )
| ( ( less_eq @ SV119 @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1632,plain,
! [SV280: a,SV120: a] :
( ( ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) )
= $false )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1633,plain,
! [SV120: a,SV280: a] :
( ( ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1634,plain,
! [SV281: a,SV121: a,SV381: a] :
( ( ( less_eq @ SV381 @ SV121 )
= $false )
| ( ( less_eq @ SV381 @ SV281 )
= $true )
| ( ( less_eq @ SV121 @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1635,plain,
! [SV382: a,SV282: a,SV122: a] :
( ( ( ~ ( less_eq @ SV122 @ SV282 ) )
= $false )
| ( ( less_eq @ SV122 @ ( inf @ SV282 @ SV382 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1636,plain,
! [SV282: a,SV382: a,SV122: a] :
( ( ( ~ ( less_eq @ SV122 @ SV382 ) )
= $false )
| ( ( less_eq @ SV122 @ ( inf @ SV282 @ SV382 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1637,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1638,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1639,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1640,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1641,plain,
! [SV286: a,SV385: a,SV126: a] :
( ( ( less_eq @ SV126 @ SV385 )
= $false )
| ( ( less_eq @ SV126 @ ( inf @ SV286 @ SV385 ) )
= $true )
| ( ( less_eq @ SV126 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1642,plain,
! [SV128: a,SV386: a,SV288: a] :
( ( ( less @ SV288 @ SV386 )
= $false )
| ( ( less @ SV128 @ SV386 )
= $true )
| ( ( less_eq @ SV128 @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1643,plain,
! [SV289: a,SV129: a,SV387: a] :
( ( ( less_eq @ SV387 @ SV129 )
= $false )
| ( ( less @ SV387 @ SV289 )
= $true )
| ( ( less @ SV129 @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1644,plain,
! [SV130: set_a,SV290: a] :
( ( ( member_a @ ( sK2_SY819 @ SV290 @ SV130 ) @ SV130 )
= $true )
| ( ( condit1001553558elow_a @ less_eq @ SV130 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1645,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ! [SY821: a] :
( ~ ( SV132 @ SY821 )
| ( less_eq @ SY821 @ SV292 ) ) )
= $false )
| ( ( ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) )
| ( SV388 @ ( greatest_a @ less_eq @ SV132 ) ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1646,plain,
! [SV293: a,SV389: a,SV133: a > a > a] :
( ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false )
| ( ( ~ ! [SY666: a,SY667: a] : ( less_eq @ ( SV133 @ SY666 @ SY667 ) @ SY667 )
| ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1537]) ).
thf(1647,plain,
! [SV135: a > a > a,SV295: a,SV391: a] :
( ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false )
| ( ( ~ ! [SY677: a,SY678: a] : ( less_eq @ SY678 @ ( SV135 @ SY677 @ SY678 ) )
| ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1538]) ).
thf(1648,plain,
! [SV296: a,SV136: a,SV417: a,SV392: a] :
( ( ( ~ ( less_eq @ SV392 @ SV417 ) )
= $true )
| ( ( less_eq @ ( inf @ SV136 @ SV392 ) @ ( inf @ SV296 @ SV417 ) )
= $true )
| ( ( less_eq @ SV136 @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1649,plain,
! [SV137: a,SV297: a] :
( ( ( less_eq @ SV297 @ SV137 )
= $false )
| ( ( less @ SV297 @ SV137 )
= $true )
| ( ( SV137 = SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1650,plain,
! [SV143: a,SV303: a,SV395: a] :
( ( ( ! [SY916: a] :
( ( inf @ ( sK5_SX3 @ SV395 @ SV303 @ SV143 ) @ ( sup @ ( sK10_SY911 @ SV143 @ SV303 @ SV395 ) @ SY916 ) )
= ( sup @ ( inf @ ( sK5_SX3 @ SV395 @ SV303 @ SV143 ) @ ( sK10_SY911 @ SV143 @ SV303 @ SV395 ) ) @ ( inf @ ( sK5_SX3 @ SV395 @ SV303 @ SV143 ) @ SY916 ) ) ) )
= $false )
| ( ( ( sup @ SV143 @ ( inf @ SV303 @ SV395 ) )
= ( inf @ ( sup @ SV143 @ SV303 ) @ ( sup @ SV143 @ SV395 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1541]) ).
thf(1651,plain,
! [SV144: a,SV304: a,SV396: a] :
( ( ( less_eq @ SV396 @ SV304 )
= $false )
| ( ( less_eq @ ( sup @ SV144 @ SV396 ) @ SV304 )
= $true )
| ( ( less_eq @ SV144 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1652,plain,
! [SV305: a,SV145: a > $o] :
( ( ( ~ ( SV145 @ ( sK11_SY850 @ SV305 @ SV145 ) )
| ( less_eq @ SV305 @ ( sK11_SY850 @ SV305 @ SV145 ) ) )
= $false )
| ( ( ( least_a @ less_eq @ SV145 )
= SV305 )
= $true )
| ( ( SV145 @ SV305 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1543]) ).
thf(1653,plain,
! [SV306: a,SV146: a,SV418: a,SV397: a] :
( ( ( ~ ( less_eq @ SV397 @ SV418 ) )
= $true )
| ( ( less_eq @ ( sup @ SV146 @ SV397 ) @ ( sup @ SV306 @ SV418 ) )
= $true )
| ( ( less_eq @ SV146 @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1654,plain,
! [SV308: a,SV398: a,SV148: a] :
( ( ( ~ ( less_eq @ SV148 @ SV398 ) )
= $false )
| ( ( less_eq @ ( sup @ SV148 @ SV308 ) @ SV398 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1655,plain,
! [SV148: a,SV398: a,SV308: a] :
( ( ( ~ ( less_eq @ SV308 @ SV398 ) )
= $false )
| ( ( less_eq @ ( sup @ SV148 @ SV308 ) @ SV398 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1656,plain,
! [SV149: a,SV309: a,SV399: a] :
( ( ( less_eq @ SV399 @ SV309 )
= $false )
| ( ( less_eq @ ( sup @ SV149 @ SV399 ) @ SV309 )
= $true )
| ( ( less_eq @ SV149 @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1657,plain,
! [SV311: a,SV401: a,SV151: a] :
( ( ( ~ ( less @ SV151 @ SV401 ) )
= $false )
| ( ( less @ ( sup @ SV151 @ SV311 ) @ SV401 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1658,plain,
! [SV151: a,SV401: a,SV311: a] :
( ( ( ~ ( less @ SV311 @ SV401 ) )
= $false )
| ( ( less @ ( sup @ SV151 @ SV311 ) @ SV401 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1659,plain,
! [SV313: a,SV153: a] :
( ( ( less_eq @ SV153 @ SV313 )
= $false )
| ( ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1660,plain,
! [SV313: a,SV153: a] :
( ( ( ~ ( less_eq @ SV153 @ SV313 ) )
= $false )
| ( ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1661,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) )
= $false )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1662,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) )
= $true )
| ( ( ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1551]) ).
thf(1663,plain,
! [SV156: set_a] :
( ( ( ~ ( condit1001553558elow_a @ less_eq @ SV156 ) )
= $false )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1664,plain,
! [SV156: set_a] :
( ( ( ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1665,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ! [SY917: a] :
( ~ ( member_a @ SY917 @ SV156 )
| ( less_eq @ SV422 @ SY917 ) ) )
= $true )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1666,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ! [SY860: a] :
( ~ ( SV158 @ SY860 )
| ( less_eq @ SV317 @ SY860 ) ) )
= $false )
| ( ( ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) )
| ( SV404 @ ( least_a @ less_eq @ SV158 ) ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1667,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1668,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) )
= $false )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1669,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) )
= $false )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1670,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) )
= $true )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1557]) ).
thf(1671,plain,
! [SV322: a,SV408: a,SV163: a] :
( ( ( ~ ( less_eq @ SV163 @ SV408 ) )
= $false )
| ( ( less_eq @ ( sup @ SV163 @ SV322 ) @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1672,plain,
! [SV163: a,SV408: a,SV322: a] :
( ( ( ~ ( less_eq @ SV322 @ SV408 ) )
= $false )
| ( ( less_eq @ ( sup @ SV163 @ SV322 ) @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1673,plain,
! [SV323: a,SV164: a] :
( ( ( SV164 = SV323 )
= $true )
| ( ( less @ SV164 @ SV323 )
= $true )
| ( ( less_eq @ SV164 @ SV323 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1674,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1675,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1676,plain,
! [SV166: a,SV325: a,SV410: a] :
( ( ( ! [SY918: a] :
( ( sup @ ( sK6_SX3 @ SV410 @ SV325 @ SV166 ) @ ( inf @ ( sK12_SY913 @ SV166 @ SV325 @ SV410 ) @ SY918 ) )
= ( inf @ ( sup @ ( sK6_SX3 @ SV410 @ SV325 @ SV166 ) @ ( sK12_SY913 @ SV166 @ SV325 @ SV410 ) ) @ ( sup @ ( sK6_SX3 @ SV410 @ SV325 @ SV166 ) @ SY918 ) ) ) )
= $false )
| ( ( ( inf @ SV166 @ ( sup @ SV325 @ SV410 ) )
= ( sup @ ( inf @ SV166 @ SV325 ) @ ( inf @ SV166 @ SV410 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1561]) ).
thf(1677,plain,
! [SV167: a,SV411: a,SV326: a] :
( ( ( less_eq @ SV326 @ SV411 )
= $false )
| ( ( less @ SV167 @ SV411 )
= $true )
| ( ( less @ SV167 @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1678,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1679,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) )
= $false )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1680,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( less_eq @ SV13 @ SV181 ) )
= $false )
| ( ( less_eq @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1681,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) )
= $false )
| ( ( less_eq @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1682,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) )
= $false )
| ( ( less @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1683,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( less_eq @ SV13 @ SV181 )
| ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) )
= $false )
| ( ( SV181 = SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1684,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( less_eq @ SV14 @ SV182 ) )
= $false )
| ( ( less_eq @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1685,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) )
= $false )
| ( ( less_eq @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1686,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) )
= $false )
| ( ( less @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1687,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( less_eq @ SV14 @ SV182 )
| ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) )
= $false )
| ( ( SV14 = SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1688,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( less_eq @ SV15 @ SV183 ) )
= $false )
| ( ( less_eq @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1570]) ).
thf(1689,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) )
= $false )
| ( ( less_eq @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1570]) ).
thf(1690,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) )
= $false )
| ( ( less @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1691,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( less_eq @ SV15 @ SV183 )
| ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) )
= $false )
| ( ( SV15 = SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1692,plain,
! [SV184: a,SV16: a] :
( ( ( ~ ( less_eq @ SV16 @ SV184 ) )
= $false )
| ( ( less_eq @ SV16 @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1693,plain,
! [SV184: a,SV16: a] :
( ( ( ( inf @ SV16 @ SV184 )
!= SV16 )
= $false )
| ( ( less_eq @ SV16 @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1694,plain,
! [SV184: a,SV16: a] :
( ( ( ~ ( less_eq @ SV16 @ SV184 ) )
= $false )
| ( ( ( inf @ SV16 @ SV184 )
= SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1695,plain,
! [SV184: a,SV16: a] :
( ( ( ( inf @ SV16 @ SV184 )
!= SV16 )
= $false )
| ( ( ( inf @ SV16 @ SV184 )
= SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1696,plain,
! [SV185: a,SV17: a] :
( ( ( ~ ( less_eq @ SV17 @ SV185 ) )
= $false )
| ( ( less_eq @ SV17 @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1697,plain,
! [SV17: a,SV185: a] :
( ( ( ( inf @ SV185 @ SV17 )
!= SV17 )
= $false )
| ( ( less_eq @ SV17 @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1698,plain,
! [SV185: a,SV17: a] :
( ( ( ~ ( less_eq @ SV17 @ SV185 ) )
= $false )
| ( ( ( inf @ SV185 @ SV17 )
= SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1576]) ).
thf(1699,plain,
! [SV17: a,SV185: a] :
( ( ( ( inf @ SV185 @ SV17 )
!= SV17 )
= $false )
| ( ( ( inf @ SV185 @ SV17 )
= SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1576]) ).
thf(1700,plain,
! [SV188: a,SV20: a] :
( ( ( ~ ( less_eq @ SV20 @ SV188 ) )
= $false )
| ( ( less_eq @ SV20 @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1701,plain,
! [SV188: a,SV20: a] :
( ( ( SV20
!= ( inf @ SV20 @ SV188 ) )
= $false )
| ( ( less_eq @ SV20 @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1702,plain,
! [SV188: a,SV20: a] :
( ( ( ~ ( less_eq @ SV20 @ SV188 ) )
= $false )
| ( ( SV20
= ( inf @ SV20 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1703,plain,
! [SV188: a,SV20: a] :
( ( ( SV20
!= ( inf @ SV20 @ SV188 ) )
= $false )
| ( ( SV20
= ( inf @ SV20 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1704,plain,
! [SV191: a,SV23: a] :
( ( ( ~ ( less_eq @ SV23 @ SV191 ) )
= $false )
| ( ( less_eq @ SV23 @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1705,plain,
! [SV191: a,SV23: a] :
( ( ( ( inf @ SV23 @ SV191 )
!= SV23 )
= $false )
| ( ( less_eq @ SV23 @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1706,plain,
! [SV191: a,SV23: a] :
( ( ( ~ ( less_eq @ SV23 @ SV191 ) )
= $false )
| ( ( ( inf @ SV23 @ SV191 )
= SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1707,plain,
! [SV191: a,SV23: a] :
( ( ( ( inf @ SV23 @ SV191 )
!= SV23 )
= $false )
| ( ( ( inf @ SV23 @ SV191 )
= SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1708,plain,
! [SV192: a,SV24: a] :
( ( ( ~ ( less_eq @ SV24 @ SV192 ) )
= $false )
| ( ( less_eq @ SV24 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1581]) ).
thf(1709,plain,
! [SV192: a,SV24: a] :
( ( ( ( sup @ SV24 @ SV192 )
!= SV192 )
= $false )
| ( ( less_eq @ SV24 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1581]) ).
thf(1710,plain,
! [SV192: a,SV24: a] :
( ( ( ~ ( less_eq @ SV24 @ SV192 ) )
= $false )
| ( ( ( sup @ SV24 @ SV192 )
= SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1711,plain,
! [SV192: a,SV24: a] :
( ( ( ( sup @ SV24 @ SV192 )
!= SV192 )
= $false )
| ( ( ( sup @ SV24 @ SV192 )
= SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1712,plain,
! [SV193: a,SV25: a] :
( ( ( ~ ( less_eq @ SV25 @ SV193 ) )
= $false )
| ( ( less_eq @ SV25 @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1713,plain,
! [SV25: a,SV193: a] :
( ( ( ( sup @ SV193 @ SV25 )
!= SV193 )
= $false )
| ( ( less_eq @ SV25 @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1714,plain,
! [SV193: a,SV25: a] :
( ( ( ~ ( less_eq @ SV25 @ SV193 ) )
= $false )
| ( ( ( sup @ SV193 @ SV25 )
= SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1584]) ).
thf(1715,plain,
! [SV25: a,SV193: a] :
( ( ( ( sup @ SV193 @ SV25 )
!= SV193 )
= $false )
| ( ( ( sup @ SV193 @ SV25 )
= SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1584]) ).
thf(1716,plain,
! [SV194: a,SV26: a] :
( ( ( ~ ( less_eq @ SV26 @ SV194 ) )
= $false )
| ( ( less_eq @ SV26 @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1585]) ).
thf(1717,plain,
! [SV194: a,SV26: a] :
( ( ( ( sup @ SV26 @ SV194 )
!= SV194 )
= $false )
| ( ( less_eq @ SV26 @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1585]) ).
thf(1718,plain,
! [SV194: a,SV26: a] :
( ( ( ~ ( less_eq @ SV26 @ SV194 ) )
= $false )
| ( ( ( sup @ SV26 @ SV194 )
= SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1719,plain,
! [SV194: a,SV26: a] :
( ( ( ( sup @ SV26 @ SV194 )
!= SV194 )
= $false )
| ( ( ( sup @ SV26 @ SV194 )
= SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1720,plain,
! [SV197: a,SV29: a] :
( ( ( ~ ( less_eq @ SV29 @ SV197 ) )
= $false )
| ( ( less_eq @ SV29 @ SV197 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1721,plain,
! [SV29: a,SV197: a] :
( ( ( SV197
!= ( sup @ SV197 @ SV29 ) )
= $false )
| ( ( less_eq @ SV29 @ SV197 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1722,plain,
! [SV197: a,SV29: a] :
( ( ( ~ ( less_eq @ SV29 @ SV197 ) )
= $false )
| ( ( SV197
= ( sup @ SV197 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1723,plain,
! [SV29: a,SV197: a] :
( ( ( SV197
!= ( sup @ SV197 @ SV29 ) )
= $false )
| ( ( SV197
= ( sup @ SV197 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1724,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( ~ ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ~ ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) )
= $false )
| ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1725,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( ~ ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
| ~ ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) )
= $false )
| ( ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1726,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less @ SV67 @ SV229 ) )
= $false )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1727,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) )
= $false )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1728,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less_eq @ SV67 @ SV229 ) )
= $true )
| ( ( ~ ( ( SV67 != SV229 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1729,plain,
! [SV234: a,SV72: a] :
( ( ( ( less_eq @ SV72 @ SV234 )
| ( SV72 = SV234 ) )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV72 @ SV234 )
| ( SV72 != SV234 ) ) )
= $true )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1730,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( less @ SV73 @ SV235 ) )
= $false )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1597]) ).
thf(1731,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) )
= $false )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1597]) ).
thf(1732,plain,
! [SV235: a,SV73: a] :
( ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
= $true )
| ( ( ~ ( ( SV73 != SV235 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1733,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ( less @ SV74 @ SV236 ) )
= $false )
| ( ( ~ ( ~ ~ ( less @ SV74 @ SV236 )
| ( SV74 != SV236 ) ) )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1734,plain,
! [SV236: a,SV74: a] :
( ( ( SV74 = SV236 )
= $false )
| ( ( ~ ( ~ ~ ( less @ SV74 @ SV236 )
| ( SV74 != SV236 ) ) )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1735,plain,
! [SV413: a,SV237: a] :
( ( ( SV237 = SV413 )
= $false )
| ( ( ~ ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1736,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) )
= $false )
| ( ( ~ ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1737,plain,
! [SV360: a,SV238: a,SV76: a] :
( ( ( less @ SV76 @ SV238 )
= $true )
| ( ( less @ SV76 @ ( inf @ SV238 @ SV360 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1601]) ).
thf(1738,plain,
! [SV238: a,SV360: a,SV76: a] :
( ( ( less @ SV76 @ SV360 )
= $true )
| ( ( less @ SV76 @ ( inf @ SV238 @ SV360 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1739,plain,
! [SV80: a,SV242: a] :
( ( ( less_eq @ SV242 @ SV80 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV242 @ SV80 )
| ( SV242 != SV80 ) ) )
= $true )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1740,plain,
! [SV80: a,SV242: a] :
( ( ( SV242 = SV80 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV242 @ SV80 )
| ( SV242 != SV80 ) ) )
= $true )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1741,plain,
! [SV247: a,SV85: a,SV414: a,SV364: a] :
( ( ( less_eq @ SV364 @ SV414 )
= $false )
| ( ( less_eq @ ( sup @ SV85 @ SV364 ) @ ( sup @ SV247 @ SV414 ) )
= $true )
| ( ( less_eq @ SV85 @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1742,plain,
! [SV415: a,SV250: a] :
( ( ( SV250 = SV415 )
= $false )
| ( ( ~ ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1608]) ).
thf(1743,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) )
= $false )
| ( ( ~ ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1608]) ).
thf(1744,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ~ ( ~ ( SV89 @ SV419 )
| ~ ! [SY903: a] :
( ~ ( SV89 @ SY903 )
| ( less_eq @ SV419 @ SY903 ) ) ) )
= $true )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1745,plain,
! [SV416: a,SV258: a] :
( ( ( SV258 = SV416 )
= $false )
| ( ( ~ ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1746,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) )
= $false )
| ( ( ~ ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1747,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less @ SV102 @ SV263 ) )
= $false )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1748,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) )
= $false )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1749,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less_eq @ SV102 @ SV263 ) )
= $true )
| ( ( ~ ( ( SV263 != SV102 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1750,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ~ ~ ( ~ ( SV103 @ SV420 )
| ~ ! [SY906: a] :
( ~ ( SV103 @ SY906 )
| ( less_eq @ SV420 @ SY906 ) ) )
| ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1751,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less @ SV105 @ SV266 ) )
= $false )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1752,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) )
= $false )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1753,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less_eq @ SV105 @ SV266 ) )
= $true )
| ( ( ~ ( ( SV105 != SV266 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1754,plain,
! [SV267: a,SV106: a > $o] :
( ( ( ~ ( SV106 @ ( sK7_SY804 @ SV267 @ SV106 ) ) )
= $false )
| ( ( ( greatest_a @ less_eq @ SV106 )
= SV267 )
= $true )
| ( ( SV106 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1755,plain,
! [SV106: a > $o,SV267: a] :
( ( ( less_eq @ ( sK7_SY804 @ SV267 @ SV106 ) @ SV267 )
= $false )
| ( ( ( greatest_a @ less_eq @ SV106 )
= SV267 )
= $true )
| ( ( SV106 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1756,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) )
= $false )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1757,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1758,plain,
! [SV376: a,SV273: a,SV112: a] :
( ( ( less_eq @ SV112 @ SV273 )
= $true )
| ( ( less_eq @ SV112 @ ( inf @ SV273 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1759,plain,
! [SV273: a,SV376: a,SV112: a] :
( ( ( less_eq @ SV112 @ SV376 )
= $true )
| ( ( less_eq @ SV112 @ ( inf @ SV273 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1760,plain,
! [SV277: a,SV116: a] :
( ( ( less_eq @ SV116 @ SV277 )
= $true )
| ( ( ( min_a @ less_eq @ SV116 @ SV277 )
= SV277 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1761,plain,
! [SV118: set_a] :
( ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $true )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1762,plain,
! [SV118: set_a] :
( ( ( ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $true )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1763,plain,
! [SV421: a,SV118: set_a] :
( ( ( ! [SY915: a] :
( ~ ( member_a @ SY915 @ SV118 )
| ( less_eq @ SY915 @ SV421 ) ) )
= $false )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1764,plain,
! [SV280: a,SV120: a] :
( ( ( ~ ( less @ SV120 @ SV280 ) )
= $false )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1765,plain,
! [SV120: a,SV280: a] :
( ( ( ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) )
= $false )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1766,plain,
! [SV120: a,SV280: a] :
( ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
= $true )
| ( ( ~ ( ( SV280 != SV120 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1767,plain,
! [SV382: a,SV282: a,SV122: a] :
( ( ( less_eq @ SV122 @ SV282 )
= $true )
| ( ( less_eq @ SV122 @ ( inf @ SV282 @ SV382 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1768,plain,
! [SV282: a,SV382: a,SV122: a] :
( ( ( less_eq @ SV122 @ SV382 )
= $true )
| ( ( less_eq @ SV122 @ ( inf @ SV282 @ SV382 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1769,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) )
= $false )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1637]) ).
thf(1770,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1771,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) )
= $false )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1772,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1640]) ).
thf(1773,plain,
! [SV292: a,SV388: a > $o,SV132: a > $o] :
( ( ( ~ ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
| ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 ) )
= $false )
| ( ( ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) )
| ( SV388 @ ( greatest_a @ less_eq @ SV132 ) ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1645]) ).
thf(1774,plain,
! [SV389: a,SV293: a,SV133: a > a > a] :
( ( ( ~ ! [SY666: a,SY667: a] : ( less_eq @ ( SV133 @ SY666 @ SY667 ) @ SY667 ) )
= $true )
| ( ( ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1775,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( ~ ! [SY677: a,SY678: a] : ( less_eq @ SY678 @ ( SV135 @ SY677 @ SY678 ) ) )
= $true )
| ( ( ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) ) )
= $true )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1776,plain,
! [SV296: a,SV136: a,SV417: a,SV392: a] :
( ( ( less_eq @ SV392 @ SV417 )
= $false )
| ( ( less_eq @ ( inf @ SV136 @ SV392 ) @ ( inf @ SV296 @ SV417 ) )
= $true )
| ( ( less_eq @ SV136 @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1777,plain,
! [SV143: a,SV303: a,SV395: a] :
( ( ( ( inf @ ( sK5_SX3 @ SV395 @ SV303 @ SV143 ) @ ( sup @ ( sK10_SY911 @ SV143 @ SV303 @ SV395 ) @ ( sK14_SY916 @ SV143 @ SV303 @ SV395 ) ) )
= ( sup @ ( inf @ ( sK5_SX3 @ SV395 @ SV303 @ SV143 ) @ ( sK10_SY911 @ SV143 @ SV303 @ SV395 ) ) @ ( inf @ ( sK5_SX3 @ SV395 @ SV303 @ SV143 ) @ ( sK14_SY916 @ SV143 @ SV303 @ SV395 ) ) ) )
= $false )
| ( ( ( sup @ SV143 @ ( inf @ SV303 @ SV395 ) )
= ( inf @ ( sup @ SV143 @ SV303 ) @ ( sup @ SV143 @ SV395 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1650]) ).
thf(1778,plain,
! [SV305: a,SV145: a > $o] :
( ( ( ~ ( SV145 @ ( sK11_SY850 @ SV305 @ SV145 ) ) )
= $false )
| ( ( ( least_a @ less_eq @ SV145 )
= SV305 )
= $true )
| ( ( SV145 @ SV305 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1779,plain,
! [SV145: a > $o,SV305: a] :
( ( ( less_eq @ SV305 @ ( sK11_SY850 @ SV305 @ SV145 ) )
= $false )
| ( ( ( least_a @ less_eq @ SV145 )
= SV305 )
= $true )
| ( ( SV145 @ SV305 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1780,plain,
! [SV306: a,SV146: a,SV418: a,SV397: a] :
( ( ( less_eq @ SV397 @ SV418 )
= $false )
| ( ( less_eq @ ( sup @ SV146 @ SV397 ) @ ( sup @ SV306 @ SV418 ) )
= $true )
| ( ( less_eq @ SV146 @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1781,plain,
! [SV308: a,SV398: a,SV148: a] :
( ( ( less_eq @ SV148 @ SV398 )
= $true )
| ( ( less_eq @ ( sup @ SV148 @ SV308 ) @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1782,plain,
! [SV148: a,SV398: a,SV308: a] :
( ( ( less_eq @ SV308 @ SV398 )
= $true )
| ( ( less_eq @ ( sup @ SV148 @ SV308 ) @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1783,plain,
! [SV311: a,SV401: a,SV151: a] :
( ( ( less @ SV151 @ SV401 )
= $true )
| ( ( less @ ( sup @ SV151 @ SV311 ) @ SV401 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1784,plain,
! [SV151: a,SV401: a,SV311: a] :
( ( ( less @ SV311 @ SV401 )
= $true )
| ( ( less @ ( sup @ SV151 @ SV311 ) @ SV401 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1785,plain,
! [SV313: a,SV153: a] :
( ( ( less_eq @ SV153 @ SV313 )
= $true )
| ( ( ( max_a @ less_eq @ SV153 @ SV313 )
= SV153 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1786,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less @ SV154 @ SV314 ) )
= $false )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1787,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) )
= $false )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1788,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less_eq @ SV154 @ SV314 ) )
= $true )
| ( ( ~ ~ ( less_eq @ SV314 @ SV154 ) )
= $true )
| ( ( ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1789,plain,
! [SV156: set_a] :
( ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $true )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1790,plain,
! [SV156: set_a] :
( ( ( ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $true )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1791,plain,
! [SV422: a,SV156: set_a] :
( ( ( ! [SY917: a] :
( ~ ( member_a @ SY917 @ SV156 )
| ( less_eq @ SV422 @ SY917 ) ) )
= $false )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1792,plain,
! [SV317: a,SV404: a > $o,SV158: a > $o] :
( ( ( ~ ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
| ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) ) )
= $false )
| ( ( ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) )
| ( SV404 @ ( least_a @ less_eq @ SV158 ) ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1666]) ).
thf(1793,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) )
= $false )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1794,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) )
= $true )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1795,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 ) )
= $false )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1796,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) )
= $false )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1797,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ~ ( less_eq @ SV161 @ SV320 ) )
= $true )
| ( ( ~ ~ ( less_eq @ SV320 @ SV161 ) )
= $true )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1798,plain,
! [SV322: a,SV408: a,SV163: a] :
( ( ( less_eq @ SV163 @ SV408 )
= $true )
| ( ( less_eq @ ( sup @ SV163 @ SV322 ) @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1799,plain,
! [SV163: a,SV408: a,SV322: a] :
( ( ( less_eq @ SV322 @ SV408 )
= $true )
| ( ( less_eq @ ( sup @ SV163 @ SV322 ) @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1800,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) )
= $false )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1801,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1802,plain,
! [SV166: a,SV325: a,SV410: a] :
( ( ( ( sup @ ( sK6_SX3 @ SV410 @ SV325 @ SV166 ) @ ( inf @ ( sK12_SY913 @ SV166 @ SV325 @ SV410 ) @ ( sK16_SY918 @ SV166 @ SV325 @ SV410 ) ) )
= ( inf @ ( sup @ ( sK6_SX3 @ SV410 @ SV325 @ SV166 ) @ ( sK12_SY913 @ SV166 @ SV325 @ SV410 ) ) @ ( sup @ ( sK6_SX3 @ SV410 @ SV325 @ SV166 ) @ ( sK16_SY918 @ SV166 @ SV325 @ SV410 ) ) ) )
= $false )
| ( ( ( inf @ SV166 @ ( sup @ SV325 @ SV410 ) )
= ( sup @ ( inf @ SV166 @ SV325 ) @ ( inf @ SV166 @ SV410 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1676]) ).
thf(1803,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1804,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1805,plain,
! [SV181: a,SV13: a] :
( ( ( less_eq @ SV13 @ SV181 )
= $true )
| ( ( less_eq @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1806,plain,
! [SV181: a,SV13: a] :
( ( ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) )
= $true )
| ( ( less_eq @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1807,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( less_eq @ SV13 @ SV181 ) )
= $false )
| ( ( less @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1808,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) )
= $false )
| ( ( less @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1809,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( less_eq @ SV13 @ SV181 ) )
= $false )
| ( ( SV181 = SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(1810,plain,
! [SV181: a,SV13: a] :
( ( ( ~ ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) ) )
= $false )
| ( ( SV181 = SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(1811,plain,
! [SV182: a,SV14: a] :
( ( ( less_eq @ SV14 @ SV182 )
= $true )
| ( ( less_eq @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1684]) ).
thf(1812,plain,
! [SV182: a,SV14: a] :
( ( ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) )
= $true )
| ( ( less_eq @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1685]) ).
thf(1813,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( less_eq @ SV14 @ SV182 ) )
= $false )
| ( ( less @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1814,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) )
= $false )
| ( ( less @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1815,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( less_eq @ SV14 @ SV182 ) )
= $false )
| ( ( SV14 = SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1816,plain,
! [SV182: a,SV14: a] :
( ( ( ~ ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) ) )
= $false )
| ( ( SV14 = SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1817,plain,
! [SV183: a,SV15: a] :
( ( ( less_eq @ SV15 @ SV183 )
= $true )
| ( ( less_eq @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1818,plain,
! [SV183: a,SV15: a] :
( ( ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) )
= $true )
| ( ( less_eq @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1819,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( less_eq @ SV15 @ SV183 ) )
= $false )
| ( ( less @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1820,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) )
= $false )
| ( ( less @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1821,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( less_eq @ SV15 @ SV183 ) )
= $false )
| ( ( SV15 = SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1822,plain,
! [SV183: a,SV15: a] :
( ( ( ~ ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) ) )
= $false )
| ( ( SV15 = SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1823,plain,
! [SV184: a,SV16: a] :
( ( ( less_eq @ SV16 @ SV184 )
= $true )
| ( ( less_eq @ SV16 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1824,plain,
! [SV184: a,SV16: a] :
( ( ( ( inf @ SV16 @ SV184 )
= SV16 )
= $true )
| ( ( less_eq @ SV16 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1825,plain,
! [SV184: a,SV16: a] :
( ( ( less_eq @ SV16 @ SV184 )
= $true )
| ( ( ( inf @ SV16 @ SV184 )
= SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1826,plain,
! [SV184: a,SV16: a] :
( ( ( ( inf @ SV16 @ SV184 )
= SV16 )
= $true )
| ( ( ( inf @ SV16 @ SV184 )
= SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1827,plain,
! [SV185: a,SV17: a] :
( ( ( less_eq @ SV17 @ SV185 )
= $true )
| ( ( less_eq @ SV17 @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1696]) ).
thf(1828,plain,
! [SV17: a,SV185: a] :
( ( ( ( inf @ SV185 @ SV17 )
= SV17 )
= $true )
| ( ( less_eq @ SV17 @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1829,plain,
! [SV185: a,SV17: a] :
( ( ( less_eq @ SV17 @ SV185 )
= $true )
| ( ( ( inf @ SV185 @ SV17 )
= SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1830,plain,
! [SV17: a,SV185: a] :
( ( ( ( inf @ SV185 @ SV17 )
= SV17 )
= $true )
| ( ( ( inf @ SV185 @ SV17 )
= SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(1831,plain,
! [SV188: a,SV20: a] :
( ( ( less_eq @ SV20 @ SV188 )
= $true )
| ( ( less_eq @ SV20 @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1832,plain,
! [SV188: a,SV20: a] :
( ( ( SV20
= ( inf @ SV20 @ SV188 ) )
= $true )
| ( ( less_eq @ SV20 @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1833,plain,
! [SV188: a,SV20: a] :
( ( ( less_eq @ SV20 @ SV188 )
= $true )
| ( ( SV20
= ( inf @ SV20 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1834,plain,
! [SV188: a,SV20: a] :
( ( ( SV20
= ( inf @ SV20 @ SV188 ) )
= $true )
| ( ( SV20
= ( inf @ SV20 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1835,plain,
! [SV191: a,SV23: a] :
( ( ( less_eq @ SV23 @ SV191 )
= $true )
| ( ( less_eq @ SV23 @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1836,plain,
! [SV191: a,SV23: a] :
( ( ( ( inf @ SV23 @ SV191 )
= SV23 )
= $true )
| ( ( less_eq @ SV23 @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1705]) ).
thf(1837,plain,
! [SV191: a,SV23: a] :
( ( ( less_eq @ SV23 @ SV191 )
= $true )
| ( ( ( inf @ SV23 @ SV191 )
= SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1838,plain,
! [SV191: a,SV23: a] :
( ( ( ( inf @ SV23 @ SV191 )
= SV23 )
= $true )
| ( ( ( inf @ SV23 @ SV191 )
= SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1707]) ).
thf(1839,plain,
! [SV192: a,SV24: a] :
( ( ( less_eq @ SV24 @ SV192 )
= $true )
| ( ( less_eq @ SV24 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1840,plain,
! [SV192: a,SV24: a] :
( ( ( ( sup @ SV24 @ SV192 )
= SV192 )
= $true )
| ( ( less_eq @ SV24 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1841,plain,
! [SV192: a,SV24: a] :
( ( ( less_eq @ SV24 @ SV192 )
= $true )
| ( ( ( sup @ SV24 @ SV192 )
= SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1842,plain,
! [SV192: a,SV24: a] :
( ( ( ( sup @ SV24 @ SV192 )
= SV192 )
= $true )
| ( ( ( sup @ SV24 @ SV192 )
= SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(1843,plain,
! [SV193: a,SV25: a] :
( ( ( less_eq @ SV25 @ SV193 )
= $true )
| ( ( less_eq @ SV25 @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1844,plain,
! [SV25: a,SV193: a] :
( ( ( ( sup @ SV193 @ SV25 )
= SV193 )
= $true )
| ( ( less_eq @ SV25 @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1845,plain,
! [SV193: a,SV25: a] :
( ( ( less_eq @ SV25 @ SV193 )
= $true )
| ( ( ( sup @ SV193 @ SV25 )
= SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1846,plain,
! [SV25: a,SV193: a] :
( ( ( ( sup @ SV193 @ SV25 )
= SV193 )
= $true )
| ( ( ( sup @ SV193 @ SV25 )
= SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1847,plain,
! [SV194: a,SV26: a] :
( ( ( less_eq @ SV26 @ SV194 )
= $true )
| ( ( less_eq @ SV26 @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1716]) ).
thf(1848,plain,
! [SV194: a,SV26: a] :
( ( ( ( sup @ SV26 @ SV194 )
= SV194 )
= $true )
| ( ( less_eq @ SV26 @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1849,plain,
! [SV194: a,SV26: a] :
( ( ( less_eq @ SV26 @ SV194 )
= $true )
| ( ( ( sup @ SV26 @ SV194 )
= SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1850,plain,
! [SV194: a,SV26: a] :
( ( ( ( sup @ SV26 @ SV194 )
= SV194 )
= $true )
| ( ( ( sup @ SV26 @ SV194 )
= SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1851,plain,
! [SV197: a,SV29: a] :
( ( ( less_eq @ SV29 @ SV197 )
= $true )
| ( ( less_eq @ SV29 @ SV197 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1852,plain,
! [SV29: a,SV197: a] :
( ( ( SV197
= ( sup @ SV197 @ SV29 ) )
= $true )
| ( ( less_eq @ SV29 @ SV197 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1721]) ).
thf(1853,plain,
! [SV197: a,SV29: a] :
( ( ( less_eq @ SV29 @ SV197 )
= $true )
| ( ( SV197
= ( sup @ SV197 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1722]) ).
thf(1854,plain,
! [SV29: a,SV197: a] :
( ( ( SV197
= ( sup @ SV197 @ SV29 ) )
= $true )
| ( ( SV197
= ( sup @ SV197 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1855,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( ~ ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 ) )
= $false )
| ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1856,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( ~ ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) )
= $false )
| ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1857,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( ~ ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 ) )
= $false )
| ( ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1858,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( ~ ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) ) )
= $false )
| ( ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1859,plain,
! [SV229: a,SV67: a] :
( ( ( less @ SV67 @ SV229 )
= $true )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1860,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) )
= $true )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1861,plain,
! [SV229: a,SV67: a] :
( ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( ~ ( ( SV67 != SV229 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1862,plain,
! [SV234: a,SV72: a] :
( ( ( less_eq @ SV72 @ SV234 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV72 @ SV234 )
| ( SV72 != SV234 ) ) )
= $true )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1729]) ).
thf(1863,plain,
! [SV234: a,SV72: a] :
( ( ( SV72 = SV234 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV72 @ SV234 )
| ( SV72 != SV234 ) ) )
= $true )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1729]) ).
thf(1864,plain,
! [SV235: a,SV73: a] :
( ( ( less @ SV73 @ SV235 )
= $true )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1865,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) )
= $true )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1866,plain,
! [SV235: a,SV73: a] :
( ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( ~ ( ( SV73 != SV235 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1867,plain,
! [SV236: a,SV74: a] :
( ( ( less @ SV74 @ SV236 )
= $true )
| ( ( ~ ( ~ ~ ( less @ SV74 @ SV236 )
| ( SV74 != SV236 ) ) )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1733]) ).
thf(1868,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ~ ( less @ SV74 @ SV236 )
| ( SV74 != SV236 ) )
= $false )
| ( ( SV74 = SV236 )
= $false )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1869,plain,
! [SV413: a,SV237: a] :
( ( ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) )
= $false )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1870,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) )
= $true )
| ( ( ~ ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1871,plain,
! [SV80: a,SV242: a] :
( ( ( ~ ( less_eq @ SV242 @ SV80 )
| ( SV242 != SV80 ) )
= $false )
| ( ( less_eq @ SV242 @ SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1872,plain,
! [SV80: a,SV242: a] :
( ( ( ~ ( less_eq @ SV242 @ SV80 )
| ( SV242 != SV80 ) )
= $false )
| ( ( SV242 = SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1873,plain,
! [SV415: a,SV250: a] :
( ( ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) )
= $false )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1874,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) )
= $true )
| ( ( ~ ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1875,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( ~ ( SV89 @ SV419 )
| ~ ! [SY903: a] :
( ~ ( SV89 @ SY903 )
| ( less_eq @ SV419 @ SY903 ) ) ) )
= $false )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1876,plain,
! [SV416: a,SV258: a] :
( ( ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) )
= $false )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1877,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) )
= $true )
| ( ( ~ ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1878,plain,
! [SV263: a,SV102: a] :
( ( ( less @ SV102 @ SV263 )
= $true )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1879,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) )
= $true )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1880,plain,
! [SV263: a,SV102: a] :
( ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( ~ ( ( SV263 != SV102 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1881,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ~ ~ ( ~ ( SV103 @ SV420 )
| ~ ! [SY906: a] :
( ~ ( SV103 @ SY906 )
| ( less_eq @ SV420 @ SY906 ) ) ) )
= $true )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1882,plain,
! [SV266: a,SV105: a] :
( ( ( less @ SV105 @ SV266 )
= $true )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(1883,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) )
= $true )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(1884,plain,
! [SV266: a,SV105: a] :
( ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( ~ ( ( SV105 != SV266 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1885,plain,
! [SV267: a,SV106: a > $o] :
( ( ( SV106 @ ( sK7_SY804 @ SV267 @ SV106 ) )
= $true )
| ( ( ( greatest_a @ less_eq @ SV106 )
= SV267 )
= $true )
| ( ( SV106 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1886,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) ) )
= $false )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1756]) ).
thf(1887,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) )
= $false )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1756]) ).
thf(1888,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ SV268 ) )
= $true )
| ( ( ~ ( less_eq @ SV107 @ SV374 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(1889,plain,
! [SV118: set_a] :
( ( ( ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1890,plain,
! [SV118: set_a,SV421: a] :
( ( ( ~ ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
| ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 ) )
= $false )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1763]) ).
thf(1891,plain,
! [SV280: a,SV120: a] :
( ( ( less @ SV120 @ SV280 )
= $true )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1892,plain,
! [SV120: a,SV280: a] :
( ( ( ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) )
= $true )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1893,plain,
! [SV120: a,SV280: a] :
( ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( ~ ( ( SV280 != SV120 ) ) )
= $true )
| ( ( ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1894,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 ) )
= $false )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1769]) ).
thf(1895,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) )
= $false )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1769]) ).
thf(1896,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ( less_eq @ SV124 @ SV383 ) )
= $true )
| ( ( ~ ( less_eq @ SV284 @ SV383 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1897,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) ) )
= $false )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1898,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) )
= $false )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1899,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ SV285 ) )
= $true )
| ( ( ~ ( less_eq @ SV125 @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1900,plain,
! [SV292: a,SV388: a > $o,SV132: a > $o] :
( ( ( ~ ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) ) )
= $false )
| ( ( ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) )
| ( SV388 @ ( greatest_a @ less_eq @ SV132 ) ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1773]) ).
thf(1901,plain,
! [SV132: a > $o,SV292: a,SV388: a > $o] :
( ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) )
| ( SV388 @ ( greatest_a @ less_eq @ SV132 ) ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1773]) ).
thf(1902,plain,
! [SV389: a,SV293: a,SV133: a > a > a] :
( ( ( ! [SY666: a,SY667: a] : ( less_eq @ ( SV133 @ SY666 @ SY667 ) @ SY667 ) )
= $false )
| ( ( ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1903,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( ! [SY677: a,SY678: a] : ( less_eq @ SY678 @ ( SV135 @ SY677 @ SY678 ) ) )
= $false )
| ( ( ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) ) )
= $true )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1904,plain,
! [SV305: a,SV145: a > $o] :
( ( ( SV145 @ ( sK11_SY850 @ SV305 @ SV145 ) )
= $true )
| ( ( ( least_a @ less_eq @ SV145 )
= SV305 )
= $true )
| ( ( SV145 @ SV305 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1905,plain,
! [SV314: a,SV154: a] :
( ( ( less @ SV154 @ SV314 )
= $true )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1906,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) )
= $true )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1907,plain,
! [SV314: a,SV154: a] :
( ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( ~ ~ ( less_eq @ SV314 @ SV154 ) )
= $true )
| ( ( ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1908,plain,
! [SV156: set_a] :
( ( ( ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1909,plain,
! [SV156: set_a,SV422: a] :
( ( ( ~ ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
| ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) ) )
= $false )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1791]) ).
thf(1910,plain,
! [SV317: a,SV404: a > $o,SV158: a > $o] :
( ( ( ~ ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) ) )
= $false )
| ( ( ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) )
| ( SV404 @ ( least_a @ less_eq @ SV158 ) ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1911,plain,
! [SV158: a > $o,SV404: a > $o,SV317: a] :
( ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) )
| ( SV404 @ ( least_a @ less_eq @ SV158 ) ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1912,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 ) )
= $false )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1793]) ).
thf(1913,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) )
= $false )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1793]) ).
thf(1914,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) ) )
= $true )
| ( ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) )
= $true )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1915,plain,
! [SV320: a,SV161: a] :
( ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $true )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1916,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) )
= $true )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1796]) ).
thf(1917,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( less_eq @ SV161 @ SV320 ) )
= $false )
| ( ( ~ ~ ( less_eq @ SV320 @ SV161 ) )
= $true )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1918,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 ) )
= $false )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1800]) ).
thf(1919,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) )
= $false )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1800]) ).
thf(1920,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ( less_eq @ SV165 @ SV409 ) )
= $true )
| ( ( ~ ( less_eq @ SV324 @ SV409 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(1921,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1803]) ).
thf(1922,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1803]) ).
thf(1923,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(1924,plain,
! [SV181: a,SV13: a] :
( ( ( less @ SV13 @ SV181 )
= $true )
| ( ( SV181 = SV13 )
= $true )
| ( ( less_eq @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(1925,plain,
! [SV181: a,SV13: a] :
( ( ( less_eq @ SV13 @ SV181 )
= $true )
| ( ( less @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1926,plain,
! [SV181: a,SV13: a] :
( ( ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) )
= $true )
| ( ( less @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1927,plain,
! [SV181: a,SV13: a] :
( ( ( less_eq @ SV13 @ SV181 )
= $true )
| ( ( SV181 = SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1928,plain,
! [SV181: a,SV13: a] :
( ( ( ( less @ SV13 @ SV181 )
| ( SV181 = SV13 ) )
= $true )
| ( ( SV181 = SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1810]) ).
thf(1929,plain,
! [SV182: a,SV14: a] :
( ( ( less @ SV14 @ SV182 )
= $true )
| ( ( SV14 = SV182 )
= $true )
| ( ( less_eq @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(1930,plain,
! [SV182: a,SV14: a] :
( ( ( less_eq @ SV14 @ SV182 )
= $true )
| ( ( less @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1931,plain,
! [SV182: a,SV14: a] :
( ( ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) )
= $true )
| ( ( less @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1932,plain,
! [SV182: a,SV14: a] :
( ( ( less_eq @ SV14 @ SV182 )
= $true )
| ( ( SV14 = SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1933,plain,
! [SV182: a,SV14: a] :
( ( ( ( less @ SV14 @ SV182 )
| ( SV14 = SV182 ) )
= $true )
| ( ( SV14 = SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1934,plain,
! [SV183: a,SV15: a] :
( ( ( less @ SV15 @ SV183 )
= $true )
| ( ( SV15 = SV183 )
= $true )
| ( ( less_eq @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(1935,plain,
! [SV183: a,SV15: a] :
( ( ( less_eq @ SV15 @ SV183 )
= $true )
| ( ( less @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1819]) ).
thf(1936,plain,
! [SV183: a,SV15: a] :
( ( ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) )
= $true )
| ( ( less @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1937,plain,
! [SV183: a,SV15: a] :
( ( ( less_eq @ SV15 @ SV183 )
= $true )
| ( ( SV15 = SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1938,plain,
! [SV183: a,SV15: a] :
( ( ( ( less @ SV15 @ SV183 )
| ( SV15 = SV183 ) )
= $true )
| ( ( SV15 = SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1939,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= $true )
| ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1940,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) )
= $true )
| ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1941,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( modula1962211574trib_a @ inf @ less @ sup @ SV47 @ SV209 @ SV338 )
= $true )
| ( ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(1942,plain,
! [SV338: a,SV209: a,SV47: a] :
( ( ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) )
= $true )
| ( ( less @ ( sup @ ( inf @ SV47 @ SV209 ) @ ( inf @ SV338 @ SV47 ) ) @ ( inf @ SV47 @ ( sup @ SV209 @ SV338 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(1943,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) )
= $false )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1944,plain,
! [SV229: a,SV67: a] :
( ( ( SV67 != SV229 )
= $false )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1945,plain,
! [SV234: a,SV72: a] :
( ( ( ~ ( less_eq @ SV72 @ SV234 )
| ( SV72 != SV234 ) )
= $false )
| ( ( less_eq @ SV72 @ SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1946,plain,
! [SV234: a,SV72: a] :
( ( ( ~ ( less_eq @ SV72 @ SV234 )
| ( SV72 != SV234 ) )
= $false )
| ( ( SV72 = SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(1947,plain,
! [SV235: a,SV73: a] :
( ( ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) )
= $false )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(1948,plain,
! [SV235: a,SV73: a] :
( ( ( SV73 != SV235 )
= $false )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(1949,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ~ ( less @ SV74 @ SV236 )
| ( SV74 != SV236 ) )
= $false )
| ( ( less @ SV74 @ SV236 )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1950,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ~ ( less @ SV74 @ SV236 ) )
= $false )
| ( ( SV74 = SV236 )
= $false )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(1951,plain,
! [SV236: a,SV74: a] :
( ( ( SV74 != SV236 )
= $false )
| ( ( SV74 = SV236 )
= $false )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(1952,plain,
! [SV413: a,SV237: a] :
( ( ( SV237 != SV413 )
= $false )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(1953,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) )
= $false )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(1954,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ( less_eq @ SV413 @ SV237 ) )
= $true )
| ( ( ~ ( less_eq @ SV237 @ SV413 ) )
= $true )
| ( ( ~ ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(1955,plain,
! [SV80: a,SV242: a] :
( ( ( ~ ( less_eq @ SV242 @ SV80 ) )
= $false )
| ( ( less_eq @ SV242 @ SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1956,plain,
! [SV80: a,SV242: a] :
( ( ( SV242 != SV80 )
= $false )
| ( ( less_eq @ SV242 @ SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1957,plain,
! [SV80: a,SV242: a] :
( ( ( ~ ( less_eq @ SV242 @ SV80 ) )
= $false )
| ( ( SV242 = SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1958,plain,
! [SV80: a,SV242: a] :
( ( ( SV242 != SV80 )
= $false )
| ( ( SV242 = SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1959,plain,
! [SV415: a,SV250: a] :
( ( ( SV250 != SV415 )
= $false )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1960,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) )
= $false )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1961,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( less_eq @ SV250 @ SV415 ) )
= $true )
| ( ( ~ ( less_eq @ SV415 @ SV250 ) )
= $true )
| ( ( ~ ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(1962,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ SV419 )
| ~ ! [SY903: a] :
( ~ ( SV89 @ SY903 )
| ( less_eq @ SV419 @ SY903 ) ) )
= $true )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1875]) ).
thf(1963,plain,
! [SV416: a,SV258: a] :
( ( ( SV258 != SV416 )
= $false )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1964,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) )
= $false )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1965,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( less_eq @ SV258 @ SV416 ) )
= $true )
| ( ( ~ ( less_eq @ SV416 @ SV258 ) )
= $true )
| ( ( ~ ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(1966,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) )
= $false )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1967,plain,
! [SV102: a,SV263: a] :
( ( ( SV263 != SV102 )
= $false )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(1968,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ~ ( ~ ( SV103 @ SV420 )
| ~ ! [SY906: a] :
( ~ ( SV103 @ SY906 )
| ( less_eq @ SV420 @ SY906 ) ) ) )
= $false )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(1969,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) )
= $false )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(1970,plain,
! [SV266: a,SV105: a] :
( ( ( SV105 != SV266 )
= $false )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1971,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $true )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(1972,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) )
= $true )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1887]) ).
thf(1973,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( ~ ( less_eq @ SV107 @ SV374 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1974,plain,
! [SV118: set_a] :
( ( ( ~ ! [SY919: a] :
( ~ ( member_a @ SY919 @ SV118 )
| ( less_eq @ SY919 @ ( sK19_SY633 @ SV118 ) ) ) )
= $false )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1889]) ).
thf(1975,plain,
! [SV118: set_a,SV421: a] :
( ( ( ~ ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 ) )
= $false )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1976,plain,
! [SV118: set_a,SV421: a] :
( ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1977,plain,
! [SV120: a,SV280: a] :
( ( ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) )
= $false )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(1978,plain,
! [SV120: a,SV280: a] :
( ( ( SV280 != SV120 )
= $false )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1979,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $true )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(1980,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) )
= $true )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1895]) ).
thf(1981,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( ~ ( less_eq @ SV284 @ SV383 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(1982,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $true )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(1983,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) )
= $true )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(1984,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( ~ ( less_eq @ SV125 @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(1985,plain,
! [SV292: a,SV388: a > $o,SV132: a > $o] :
( ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) )
| ( SV388 @ ( greatest_a @ less_eq @ SV132 ) ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(1986,plain,
! [SV292: a,SV388: a > $o,SV132: a > $o] :
( ( ( ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(1987,plain,
! [SV293: a,SV389: a,SV133: a > a > a] :
( ( ( ! [SY920: a] : ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ SY920 ) @ SY920 ) )
= $false )
| ( ( ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1902]) ).
thf(1988,plain,
! [SV295: a,SV391: a,SV135: a > a > a] :
( ( ( ! [SY921: a] : ( less_eq @ SY921 @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ SY921 ) ) )
= $false )
| ( ( ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) ) )
= $true )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1903]) ).
thf(1989,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) )
= $false )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(1990,plain,
! [SV154: a,SV314: a] :
( ( ( ~ ( less_eq @ SV314 @ SV154 ) )
= $false )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(1991,plain,
! [SV156: set_a] :
( ( ( ~ ! [SY922: a] :
( ~ ( member_a @ SY922 @ SV156 )
| ( less_eq @ ( sK22_SY720 @ SV156 ) @ SY922 ) ) )
= $false )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1908]) ).
thf(1992,plain,
! [SV156: set_a,SV422: a] :
( ( ( ~ ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 ) )
= $false )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1909]) ).
thf(1993,plain,
! [SV156: set_a,SV422: a] :
( ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1909]) ).
thf(1994,plain,
! [SV317: a,SV404: a > $o,SV158: a > $o] :
( ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) )
| ( SV404 @ ( least_a @ less_eq @ SV158 ) ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(1995,plain,
! [SV317: a,SV404: a > $o,SV158: a > $o] :
( ( ( ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) ) )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1996,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $true )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1997,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) )
= $true )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1998,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) )
= $true )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1999,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) )
= $false )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2000,plain,
! [SV320: a,SV161: a] :
( ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( ~ ~ ( less_eq @ SV320 @ SV161 ) )
= $true )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1917]) ).
thf(2001,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $true )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(2002,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) )
= $true )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(2003,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( ~ ( less_eq @ SV324 @ SV409 ) )
= $true )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2004,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1921]) ).
thf(2005,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1922]) ).
thf(2006,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $false )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2007,plain,
! [SV181: a,SV13: a] :
( ( ( less @ SV13 @ SV181 )
= $true )
| ( ( SV181 = SV13 )
= $true )
| ( ( less @ SV13 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2008,plain,
! [SV181: a,SV13: a] :
( ( ( less @ SV13 @ SV181 )
= $true )
| ( ( SV181 = SV13 )
= $true )
| ( ( SV181 = SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2009,plain,
! [SV182: a,SV14: a] :
( ( ( less @ SV14 @ SV182 )
= $true )
| ( ( SV14 = SV182 )
= $true )
| ( ( less @ SV14 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2010,plain,
! [SV182: a,SV14: a] :
( ( ( less @ SV14 @ SV182 )
= $true )
| ( ( SV14 = SV182 )
= $true )
| ( ( SV14 = SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2011,plain,
! [SV183: a,SV15: a] :
( ( ( less @ SV15 @ SV183 )
= $true )
| ( ( SV15 = SV183 )
= $true )
| ( ( less @ SV15 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(2012,plain,
! [SV183: a,SV15: a] :
( ( ( less @ SV15 @ SV183 )
= $true )
| ( ( SV15 = SV183 )
= $true )
| ( ( SV15 = SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(2013,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less_eq @ SV67 @ SV229 ) )
= $false )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(2014,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( ( SV67 != SV229 ) ) )
= $false )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(2015,plain,
! [SV229: a,SV67: a] :
( ( ( SV67 = SV229 )
= $true )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( ~ ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2016,plain,
! [SV234: a,SV72: a] :
( ( ( ~ ( less_eq @ SV72 @ SV234 ) )
= $false )
| ( ( less_eq @ SV72 @ SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1945]) ).
thf(2017,plain,
! [SV234: a,SV72: a] :
( ( ( SV72 != SV234 )
= $false )
| ( ( less_eq @ SV72 @ SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1945]) ).
thf(2018,plain,
! [SV234: a,SV72: a] :
( ( ( ~ ( less_eq @ SV72 @ SV234 ) )
= $false )
| ( ( SV72 = SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2019,plain,
! [SV234: a,SV72: a] :
( ( ( SV72 != SV234 )
= $false )
| ( ( SV72 = SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2020,plain,
! [SV235: a,SV73: a] :
( ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(2021,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( ( SV73 != SV235 ) ) )
= $false )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(2022,plain,
! [SV235: a,SV73: a] :
( ( ( SV73 = SV235 )
= $true )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( ~ ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(2023,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ~ ( less @ SV74 @ SV236 ) )
= $false )
| ( ( less @ SV74 @ SV236 )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(2024,plain,
! [SV236: a,SV74: a] :
( ( ( SV74 != SV236 )
= $false )
| ( ( less @ SV74 @ SV236 )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(2025,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ( less @ SV74 @ SV236 ) )
= $true )
| ( ( SV74 = SV236 )
= $false )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1950]) ).
thf(2026,plain,
! [SV236: a,SV74: a] :
( ( ( SV74 = SV236 )
= $true )
| ( ( SV74 = SV236 )
= $false )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(2027,plain,
! [SV413: a,SV237: a] :
( ( ( SV237 = SV413 )
= $true )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2028,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) )
= $true )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1953]) ).
thf(2029,plain,
! [SV237: a,SV413: a] :
( ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( ~ ( less_eq @ SV237 @ SV413 ) )
= $true )
| ( ( ~ ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2030,plain,
! [SV80: a,SV242: a] :
( ( ( less_eq @ SV242 @ SV80 )
= $true )
| ( ( less_eq @ SV242 @ SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(2031,plain,
! [SV80: a,SV242: a] :
( ( ( SV242 = SV80 )
= $true )
| ( ( less_eq @ SV242 @ SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1956]) ).
thf(2032,plain,
! [SV80: a,SV242: a] :
( ( ( less_eq @ SV242 @ SV80 )
= $true )
| ( ( SV242 = SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1957]) ).
thf(2033,plain,
! [SV80: a,SV242: a] :
( ( ( SV242 = SV80 )
= $true )
| ( ( SV242 = SV80 )
= $false )
| ( ( less_eq @ SV80 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1958]) ).
thf(2034,plain,
! [SV415: a,SV250: a] :
( ( ( SV250 = SV415 )
= $true )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1959]) ).
thf(2035,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) )
= $true )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1960]) ).
thf(2036,plain,
! [SV415: a,SV250: a] :
( ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( ~ ( less_eq @ SV415 @ SV250 ) )
= $true )
| ( ( ~ ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2037,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ SV419 ) )
= $true )
| ( ( ~ ! [SY903: a] :
( ~ ( SV89 @ SY903 )
| ( less_eq @ SV419 @ SY903 ) ) )
= $true )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2038,plain,
! [SV416: a,SV258: a] :
( ( ( SV258 = SV416 )
= $true )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1963]) ).
thf(2039,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) )
= $true )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1964]) ).
thf(2040,plain,
! [SV416: a,SV258: a] :
( ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( ~ ( less_eq @ SV416 @ SV258 ) )
= $true )
| ( ( ~ ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2041,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less_eq @ SV102 @ SV263 ) )
= $false )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1966]) ).
thf(2042,plain,
! [SV102: a,SV263: a] :
( ( ( ~ ( ( SV263 != SV102 ) ) )
= $false )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1966]) ).
thf(2043,plain,
! [SV102: a,SV263: a] :
( ( ( SV263 = SV102 )
= $true )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( ~ ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2044,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV420 )
| ~ ! [SY906: a] :
( ~ ( SV103 @ SY906 )
| ( less_eq @ SV420 @ SY906 ) ) )
= $true )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1968]) ).
thf(2045,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less_eq @ SV105 @ SV266 ) )
= $false )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1969]) ).
thf(2046,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( ( SV105 != SV266 ) ) )
= $false )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1969]) ).
thf(2047,plain,
! [SV266: a,SV105: a] :
( ( ( SV105 = SV266 )
= $true )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( ~ ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1970]) ).
thf(2048,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) )
= $false )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2049,plain,
! [SV268: a,SV374: a,SV107: a] :
( ( ( less_eq @ SV107 @ SV374 )
= $false )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2050,plain,
! [SV118: set_a] :
( ( ( ! [SY919: a] :
( ~ ( member_a @ SY919 @ SV118 )
| ( less_eq @ SY919 @ ( sK19_SY633 @ SV118 ) ) ) )
= $true )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2051,plain,
! [SV118: set_a,SV421: a] :
( ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true )
| ( ( ~ ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(2052,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2053,plain,
! [SV120: a,SV280: a] :
( ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2054,plain,
! [SV120: a,SV280: a] :
( ( ( ~ ( ( SV280 != SV120 ) ) )
= $false )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2055,plain,
! [SV120: a,SV280: a] :
( ( ( SV280 = SV120 )
= $true )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( ~ ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(2056,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) )
= $false )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2057,plain,
! [SV124: a,SV383: a,SV284: a] :
( ( ( less_eq @ SV284 @ SV383 )
= $false )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2058,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) )
= $false )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2059,plain,
! [SV285: a,SV384: a,SV125: a] :
( ( ( less_eq @ SV125 @ SV384 )
= $false )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( ~ ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2060,plain,
! [SV292: a,SV388: a > $o,SV132: a > $o] :
( ( ( ~ ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2061,plain,
! [SV292: a,SV388: a > $o,SV132: a > $o] :
( ( ( ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2062,plain,
! [SV293: a,SV389: a,SV133: a > a > a] :
( ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) )
| ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1987]) ).
thf(2063,plain,
! [SV135: a > a > a,SV391: a,SV295: a] :
( ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) )
| ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) ) )
= $true )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1988]) ).
thf(2064,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less_eq @ SV154 @ SV314 ) )
= $false )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1989]) ).
thf(2065,plain,
! [SV154: a,SV314: a] :
( ( ( ~ ~ ( less_eq @ SV314 @ SV154 ) )
= $false )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1989]) ).
thf(2066,plain,
! [SV154: a,SV314: a] :
( ( ( less_eq @ SV314 @ SV154 )
= $true )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( ~ ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2067,plain,
! [SV156: set_a] :
( ( ( ! [SY922: a] :
( ~ ( member_a @ SY922 @ SV156 )
| ( less_eq @ ( sK22_SY720 @ SV156 ) @ SY922 ) ) )
= $true )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1991]) ).
thf(2068,plain,
! [SV156: set_a,SV422: a] :
( ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true )
| ( ( ~ ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2069,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2070,plain,
! [SV317: a,SV404: a > $o,SV158: a > $o] :
( ( ( ~ ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) ) )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2071,plain,
! [SV317: a,SV404: a > $o,SV158: a > $o] :
( ( ( ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2072,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) )
= $false )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2073,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
= $true )
| ( ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) )
= $true )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2074,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ~ ( less_eq @ SV161 @ SV320 ) )
= $false )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2075,plain,
! [SV161: a,SV320: a] :
( ( ( ~ ~ ( less_eq @ SV320 @ SV161 ) )
= $false )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2076,plain,
! [SV161: a,SV320: a] :
( ( ( ~ ( less_eq @ SV320 @ SV161 ) )
= $false )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2077,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) )
= $false )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2078,plain,
! [SV165: a,SV409: a,SV324: a] :
( ( ( less_eq @ SV324 @ SV409 )
= $false )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( ~ ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2079,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2080,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2081,plain,
! [SV229: a,SV67: a] :
( ( ( less_eq @ SV67 @ SV229 )
= $true )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2013]) ).
thf(2082,plain,
! [SV229: a,SV67: a] :
( ( ( SV67 != SV229 )
= $true )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2083,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less @ SV67 @ SV229 )
| ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) )
= $false )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2084,plain,
! [SV234: a,SV72: a] :
( ( ( less_eq @ SV72 @ SV234 )
= $true )
| ( ( less_eq @ SV72 @ SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2016]) ).
thf(2085,plain,
! [SV234: a,SV72: a] :
( ( ( SV72 = SV234 )
= $true )
| ( ( less_eq @ SV72 @ SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2086,plain,
! [SV234: a,SV72: a] :
( ( ( less_eq @ SV72 @ SV234 )
= $true )
| ( ( SV72 = SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2018]) ).
thf(2087,plain,
! [SV234: a,SV72: a] :
( ( ( SV72 = SV234 )
= $true )
| ( ( SV72 = SV234 )
= $false )
| ( ( less @ SV72 @ SV234 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2019]) ).
thf(2088,plain,
! [SV235: a,SV73: a] :
( ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $true )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2020]) ).
thf(2089,plain,
! [SV235: a,SV73: a] :
( ( ( SV73 != SV235 )
= $true )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2021]) ).
thf(2090,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( less @ SV73 @ SV235 )
| ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) )
= $false )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2091,plain,
! [SV236: a,SV74: a] :
( ( ( ~ ( less @ SV74 @ SV236 ) )
= $true )
| ( ( less @ SV74 @ SV236 )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2092,plain,
! [SV236: a,SV74: a] :
( ( ( SV74 = SV236 )
= $true )
| ( ( less @ SV74 @ SV236 )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2024]) ).
thf(2093,plain,
! [SV236: a,SV74: a] :
( ( ( less @ SV74 @ SV236 )
= $false )
| ( ( SV74 = SV236 )
= $false )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2094,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) )
= $false )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2095,plain,
! [SV413: a,SV237: a] :
( ( ( less_eq @ SV237 @ SV413 )
= $false )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( ~ ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2096,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) )
= $false )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2097,plain,
! [SV250: a,SV415: a] :
( ( ( less_eq @ SV415 @ SV250 )
= $false )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( ~ ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2098,plain,
! [SV419: a,SV89: a > $o] :
( ( ( SV89 @ SV419 )
= $false )
| ( ( ~ ! [SY903: a] :
( ~ ( SV89 @ SY903 )
| ( less_eq @ SV419 @ SY903 ) ) )
= $true )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2099,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) )
= $false )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2100,plain,
! [SV258: a,SV416: a] :
( ( ( less_eq @ SV416 @ SV258 )
= $false )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( ~ ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2101,plain,
! [SV263: a,SV102: a] :
( ( ( less_eq @ SV102 @ SV263 )
= $true )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2102,plain,
! [SV102: a,SV263: a] :
( ( ( SV263 != SV102 )
= $true )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2103,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less @ SV102 @ SV263 )
| ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) )
= $false )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2104,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV420 ) )
= $true )
| ( ( ~ ! [SY906: a] :
( ~ ( SV103 @ SY906 )
| ( less_eq @ SV420 @ SY906 ) ) )
= $true )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2105,plain,
! [SV266: a,SV105: a] :
( ( ( less_eq @ SV105 @ SV266 )
= $true )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2045]) ).
thf(2106,plain,
! [SV266: a,SV105: a] :
( ( ( SV105 != SV266 )
= $true )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2046]) ).
thf(2107,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less @ SV105 @ SV266 )
| ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) )
= $false )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2108,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ SV268 ) )
= $false )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2048]) ).
thf(2109,plain,
! [SV268: a,SV374: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ SV374 ) )
= $false )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2048]) ).
thf(2110,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
| ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) )
= $false )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2111,plain,
! [SV118: set_a,SV423: a] :
( ( ( ~ ( member_a @ SV423 @ SV118 )
| ( less_eq @ SV423 @ ( sK19_SY633 @ SV118 ) ) )
= $true )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2112,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ( condit1627435690bove_a @ less_eq @ SV118 )
| ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2113,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ( condit1627435690bove_a @ less_eq @ SV118 ) )
= $false )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2052]) ).
thf(2114,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2052]) ).
thf(2115,plain,
! [SV120: a,SV280: a] :
( ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $true )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2116,plain,
! [SV120: a,SV280: a] :
( ( ( SV280 != SV120 )
= $true )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2117,plain,
! [SV280: a,SV120: a] :
( ( ( ~ ( less @ SV120 @ SV280 )
| ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) )
= $false )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2118,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ( less_eq @ SV124 @ SV383 ) )
= $false )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2056]) ).
thf(2119,plain,
! [SV124: a,SV383: a,SV284: a] :
( ( ( ~ ( less_eq @ SV284 @ SV383 ) )
= $false )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2056]) ).
thf(2120,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
| ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) )
= $false )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2121,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ SV285 ) )
= $false )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2058]) ).
thf(2122,plain,
! [SV285: a,SV384: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ SV384 ) )
= $false )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2058]) ).
thf(2123,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
| ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) )
= $false )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2124,plain,
! [SV292: a,SV388: a > $o,SV132: a > $o] :
( ( ( ! [SY876: a] :
( ~ ( SV132 @ SY876 )
| ~ ! [SY661: a] :
( ~ ( SV132 @ SY661 )
| ( less_eq @ SY661 @ SY876 ) )
| ( SV388 @ SY876 ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2125,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ( SV132 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) )
| ~ ! [SY923: a] :
( ~ ( SV132 @ SY923 )
| ( less_eq @ SY923 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) ) )
| ( SV388 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2061]) ).
thf(2126,plain,
! [SV389: a,SV293: a,SV133: a > a > a] :
( ( ( ~ ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) ) )
= $true )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2127,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( ~ ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) ) )
= $true )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2128,plain,
! [SV314: a,SV154: a] :
( ( ( less_eq @ SV154 @ SV314 )
= $true )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2129,plain,
! [SV154: a,SV314: a] :
( ( ( ~ ( less_eq @ SV314 @ SV154 ) )
= $true )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2130,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less @ SV154 @ SV314 )
| ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) )
= $false )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2131,plain,
! [SV156: set_a,SV424: a] :
( ( ( ~ ( member_a @ SV424 @ SV156 )
| ( less_eq @ ( sK22_SY720 @ SV156 ) @ SV424 ) )
= $true )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2132,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ( condit1001553558elow_a @ less_eq @ SV156 )
| ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2133,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ( condit1001553558elow_a @ less_eq @ SV156 ) )
= $false )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2134,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2135,plain,
! [SV317: a,SV404: a > $o,SV158: a > $o] :
( ( ( ! [SY898: a] :
( ~ ( SV158 @ SY898 )
| ~ ! [SY727: a] :
( ~ ( SV158 @ SY727 )
| ( less_eq @ SY898 @ SY727 ) )
| ( SV404 @ SY898 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2136,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ( SV158 @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) )
| ~ ! [SY924: a] :
( ~ ( SV158 @ SY924 )
| ( less_eq @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) @ SY924 ) )
| ( SV404 @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2071]) ).
thf(2137,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) ) )
= $false )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2138,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) )
= $false )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2139,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
= $true )
| ( ( ~ ( less @ SV160 @ SV319 ) )
= $true )
| ( ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) )
= $true )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2140,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( less_eq @ SV161 @ SV320 ) )
= $true )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2141,plain,
! [SV161: a,SV320: a] :
( ( ( ~ ( less_eq @ SV320 @ SV161 ) )
= $true )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2142,plain,
! [SV161: a,SV320: a] :
( ( ( less_eq @ SV320 @ SV161 )
= $true )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( ~ ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2143,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ( less_eq @ SV165 @ SV409 ) )
= $false )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2144,plain,
! [SV165: a,SV409: a,SV324: a] :
( ( ( ~ ( less_eq @ SV324 @ SV409 ) )
= $false )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2145,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
| ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) )
= $false )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2146,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2079]) ).
thf(2147,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2079]) ).
thf(2148,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2080]) ).
thf(2149,plain,
! [SV229: a,SV67: a] :
( ( ( SV67 = SV229 )
= $false )
| ( ( less @ SV67 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2150,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less @ SV67 @ SV229 ) )
= $false )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2083]) ).
thf(2151,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) )
= $false )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2083]) ).
thf(2152,plain,
! [SV235: a,SV73: a] :
( ( ( SV73 = SV235 )
= $false )
| ( ( less @ SV73 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2153,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( less @ SV73 @ SV235 ) )
= $false )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2154,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) )
= $false )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2155,plain,
! [SV236: a,SV74: a] :
( ( ( less @ SV74 @ SV236 )
= $false )
| ( ( less @ SV74 @ SV236 )
= $true )
| ( ( less_eq @ SV74 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2156,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ( less_eq @ SV413 @ SV237 ) )
= $false )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2157,plain,
! [SV413: a,SV237: a] :
( ( ( ~ ( less_eq @ SV237 @ SV413 ) )
= $false )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2158,plain,
! [SV413: a,SV237: a] :
( ( ( ( SV237 != SV413 )
| ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) )
= $false )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2159,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( less_eq @ SV250 @ SV415 ) )
= $false )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2096]) ).
thf(2160,plain,
! [SV250: a,SV415: a] :
( ( ( ~ ( less_eq @ SV415 @ SV250 ) )
= $false )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2096]) ).
thf(2161,plain,
! [SV415: a,SV250: a] :
( ( ( ( SV250 != SV415 )
| ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) )
= $false )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2162,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ! [SY903: a] :
( ~ ( SV89 @ SY903 )
| ( less_eq @ SV419 @ SY903 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2163,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( less_eq @ SV258 @ SV416 ) )
= $false )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2099]) ).
thf(2164,plain,
! [SV258: a,SV416: a] :
( ( ( ~ ( less_eq @ SV416 @ SV258 ) )
= $false )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2099]) ).
thf(2165,plain,
! [SV416: a,SV258: a] :
( ( ( ( SV258 != SV416 )
| ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) )
= $false )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2166,plain,
! [SV102: a,SV263: a] :
( ( ( SV263 = SV102 )
= $false )
| ( ( less @ SV102 @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2167,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less @ SV102 @ SV263 ) )
= $false )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2168,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) )
= $false )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2169,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( SV103 @ SV420 )
= $false )
| ( ( ~ ! [SY906: a] :
( ~ ( SV103 @ SY906 )
| ( less_eq @ SV420 @ SY906 ) ) )
= $true )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2170,plain,
! [SV266: a,SV105: a] :
( ( ( SV105 = SV266 )
= $false )
| ( ( less @ SV105 @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2171,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less @ SV105 @ SV266 ) )
= $false )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2107]) ).
thf(2172,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) )
= $false )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2107]) ).
thf(2173,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( less_eq @ SV107 @ SV268 )
= $true )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2174,plain,
! [SV268: a,SV374: a,SV107: a] :
( ( ( less_eq @ SV107 @ SV374 )
= $true )
| ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2109]) ).
thf(2175,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) ) )
= $false )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2110]) ).
thf(2176,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) )
= $false )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2110]) ).
thf(2177,plain,
! [SV118: set_a,SV423: a] :
( ( ( ~ ( member_a @ SV423 @ SV118 ) )
= $true )
| ( ( less_eq @ SV423 @ ( sK19_SY633 @ SV118 ) )
= $true )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2178,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ( condit1627435690bove_a @ less_eq @ SV118 ) )
= $false )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2179,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2180,plain,
! [SV421: a,SV118: set_a] :
( ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $true )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2113]) ).
thf(2181,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $true )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2182,plain,
! [SV120: a,SV280: a] :
( ( ( SV280 = SV120 )
= $false )
| ( ( less @ SV120 @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2183,plain,
! [SV280: a,SV120: a] :
( ( ( ~ ( less @ SV120 @ SV280 ) )
= $false )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2184,plain,
! [SV120: a,SV280: a] :
( ( ( ~ ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) )
= $false )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2185,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( less_eq @ SV124 @ SV383 )
= $true )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2118]) ).
thf(2186,plain,
! [SV124: a,SV383: a,SV284: a] :
( ( ( less_eq @ SV284 @ SV383 )
= $true )
| ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2119]) ).
thf(2187,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( ~ ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 ) )
= $false )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2120]) ).
thf(2188,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) )
= $false )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2120]) ).
thf(2189,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( less_eq @ SV125 @ SV285 )
= $true )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2190,plain,
! [SV285: a,SV384: a,SV125: a] :
( ( ( less_eq @ SV125 @ SV384 )
= $true )
| ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2122]) ).
thf(2191,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) ) )
= $false )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2192,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) )
= $false )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2193,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ( SV132 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) )
| ~ ! [SY925: a] :
( ~ ( SV132 @ SY925 )
| ( less_eq @ SY925 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) ) )
| ( SV388 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2124]) ).
thf(2194,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ( SV132 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2125]) ).
thf(2195,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ! [SY923: a] :
( ~ ( SV132 @ SY923 )
| ( less_eq @ SY923 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) ) )
| ( SV388 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2125]) ).
thf(2196,plain,
! [SV389: a,SV293: a,SV133: a > a > a] :
( ( ( ! [SY668: a,SY669: a,SY670: a] :
( ~ ( less_eq @ SY668 @ SY669 )
| ~ ( less_eq @ SY668 @ SY670 )
| ( less_eq @ SY668 @ ( SV133 @ SY669 @ SY670 ) ) ) )
= $false )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2197,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( ! [SY679: a,SY680: a,SY681: a] :
( ~ ( less_eq @ SY680 @ SY679 )
| ~ ( less_eq @ SY681 @ SY679 )
| ( less_eq @ ( SV135 @ SY680 @ SY681 ) @ SY679 ) ) )
= $false )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2198,plain,
! [SV154: a,SV314: a] :
( ( ( less_eq @ SV314 @ SV154 )
= $false )
| ( ( less @ SV154 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2199,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less @ SV154 @ SV314 ) )
= $false )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2130]) ).
thf(2200,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) )
= $false )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2130]) ).
thf(2201,plain,
! [SV156: set_a,SV424: a] :
( ( ( ~ ( member_a @ SV424 @ SV156 ) )
= $true )
| ( ( less_eq @ ( sK22_SY720 @ SV156 ) @ SV424 )
= $true )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2202,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ( condit1001553558elow_a @ less_eq @ SV156 ) )
= $false )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2203,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2204,plain,
! [SV422: a,SV156: set_a] :
( ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $true )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2133]) ).
thf(2205,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $true )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2134]) ).
thf(2206,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ( SV158 @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) )
| ~ ! [SY926: a] :
( ~ ( SV158 @ SY926 )
| ( less_eq @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) @ SY926 ) )
| ( SV404 @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2135]) ).
thf(2207,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ( SV158 @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2208,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ! [SY924: a] :
( ~ ( SV158 @ SY924 )
| ( less_eq @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) @ SY924 ) )
| ( SV404 @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2209,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) ) )
= $true )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2210,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $true )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2211,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ~ ( less @ SV160 @ SV319 ) )
= $true )
| ( ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) )
= $true )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2212,plain,
! [SV320: a,SV161: a] :
( ( ( less_eq @ SV161 @ SV320 )
= $false )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2213,plain,
! [SV161: a,SV320: a] :
( ( ( less_eq @ SV320 @ SV161 )
= $false )
| ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2214,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
| ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) )
= $false )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2215,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( less_eq @ SV165 @ SV409 )
= $true )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2143]) ).
thf(2216,plain,
! [SV165: a,SV409: a,SV324: a] :
( ( ( less_eq @ SV324 @ SV409 )
= $true )
| ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2217,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( ~ ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 ) )
= $false )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2145]) ).
thf(2218,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) )
= $false )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2145]) ).
thf(2219,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2146]) ).
thf(2220,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2221,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2222,plain,
! [SV229: a,SV67: a] :
( ( ( less @ SV67 @ SV229 )
= $true )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2223,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) ) )
= $true )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2224,plain,
! [SV235: a,SV73: a] :
( ( ( less @ SV73 @ SV235 )
= $true )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2153]) ).
thf(2225,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) ) )
= $true )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2154]) ).
thf(2226,plain,
! [SV237: a,SV413: a] :
( ( ( less_eq @ SV413 @ SV237 )
= $true )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2156]) ).
thf(2227,plain,
! [SV413: a,SV237: a] :
( ( ( less_eq @ SV237 @ SV413 )
= $true )
| ( ( SV237 = SV413 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2157]) ).
thf(2228,plain,
! [SV413: a,SV237: a] :
( ( ( SV237 != SV413 )
= $false )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2229,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) )
= $false )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2230,plain,
! [SV415: a,SV250: a] :
( ( ( less_eq @ SV250 @ SV415 )
= $true )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2159]) ).
thf(2231,plain,
! [SV250: a,SV415: a] :
( ( ( less_eq @ SV415 @ SV250 )
= $true )
| ( ( SV250 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2232,plain,
! [SV415: a,SV250: a] :
( ( ( SV250 != SV415 )
= $false )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2233,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) )
= $false )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2234,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
| ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2162]) ).
thf(2235,plain,
! [SV416: a,SV258: a] :
( ( ( less_eq @ SV258 @ SV416 )
= $true )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2163]) ).
thf(2236,plain,
! [SV258: a,SV416: a] :
( ( ( less_eq @ SV416 @ SV258 )
= $true )
| ( ( SV258 = SV416 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2237,plain,
! [SV416: a,SV258: a] :
( ( ( SV258 != SV416 )
= $false )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2165]) ).
thf(2238,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) )
= $false )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2165]) ).
thf(2239,plain,
! [SV263: a,SV102: a] :
( ( ( less @ SV102 @ SV263 )
= $true )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2167]) ).
thf(2240,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) ) )
= $true )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2168]) ).
thf(2241,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ! [SY906: a] :
( ~ ( SV103 @ SY906 )
| ( less_eq @ SV420 @ SY906 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2242,plain,
! [SV266: a,SV105: a] :
( ( ( less @ SV105 @ SV266 )
= $true )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2171]) ).
thf(2243,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) ) )
= $true )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2172]) ).
thf(2244,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( less_eq @ SV107 @ ( inf @ SV268 @ SV374 ) )
= $true )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2245,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) ) )
= $true )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2246,plain,
! [SV118: set_a,SV423: a] :
( ( ( member_a @ SV423 @ SV118 )
= $false )
| ( ( less_eq @ SV423 @ ( sK19_SY633 @ SV118 ) )
= $true )
| ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2247,plain,
! [SV421: a,SV118: set_a] :
( ( ( condit1627435690bove_a @ less_eq @ SV118 )
= $true )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2178]) ).
thf(2248,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $true )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2179]) ).
thf(2249,plain,
! [SV421: a,SV118: set_a] :
( ( ( ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2250,plain,
! [SV280: a,SV120: a] :
( ( ( less @ SV120 @ SV280 )
= $true )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2251,plain,
! [SV120: a,SV280: a] :
( ( ( ~ ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) ) )
= $true )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2184]) ).
thf(2252,plain,
! [SV383: a,SV284: a,SV124: a] :
( ( ( less_eq @ ( sup @ SV124 @ SV284 ) @ SV383 )
= $true )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2187]) ).
thf(2253,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) ) )
= $true )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2254,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( less_eq @ SV125 @ ( inf @ SV285 @ SV384 ) )
= $true )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2255,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) ) )
= $true )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2192]) ).
thf(2256,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ( SV132 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2257,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ! [SY925: a] :
( ~ ( SV132 @ SY925 )
| ( less_eq @ SY925 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) ) )
| ( SV388 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2258,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( SV132 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2259,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ! [SY923: a] :
( ~ ( SV132 @ SY923 )
| ( less_eq @ SY923 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2260,plain,
! [SV132: a > $o,SV292: a,SV388: a > $o] :
( ( ( SV388 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2261,plain,
! [SV133: a > a > a,SV293: a,SV389: a] :
( ( ( ! [SY927: a,SY928: a] :
( ~ ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ SY927 )
| ~ ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ SY928 )
| ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( SV133 @ SY927 @ SY928 ) ) ) )
= $false )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2196]) ).
thf(2262,plain,
! [SV135: a > a > a,SV295: a,SV391: a] :
( ( ( ! [SY929: a,SY930: a] :
( ~ ( less_eq @ SY929 @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
| ~ ( less_eq @ SY930 @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
| ( less_eq @ ( SV135 @ SY929 @ SY930 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) ) ) )
= $false )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2197]) ).
thf(2263,plain,
! [SV314: a,SV154: a] :
( ( ( less @ SV154 @ SV314 )
= $true )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2199]) ).
thf(2264,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) ) )
= $true )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2200]) ).
thf(2265,plain,
! [SV156: set_a,SV424: a] :
( ( ( member_a @ SV424 @ SV156 )
= $false )
| ( ( less_eq @ ( sK22_SY720 @ SV156 ) @ SV424 )
= $true )
| ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2266,plain,
! [SV422: a,SV156: set_a] :
( ( ( condit1001553558elow_a @ less_eq @ SV156 )
= $true )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2267,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $true )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2203]) ).
thf(2268,plain,
! [SV422: a,SV156: set_a] :
( ( ( ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2269,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ( SV158 @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2270,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ! [SY926: a] :
( ~ ( SV158 @ SY926 )
| ( less_eq @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) @ SY926 ) )
| ( SV404 @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2271,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( SV158 @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2272,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ! [SY924: a] :
( ~ ( SV158 @ SY924 )
| ( less_eq @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) @ SY924 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2273,plain,
! [SV158: a > $o,SV317: a,SV404: a > $o] :
( ( ( SV404 @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2274,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
= $false )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2275,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) )
= $true )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2276,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 ) )
= $false )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2214]) ).
thf(2277,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) )
= $false )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2214]) ).
thf(2278,plain,
! [SV409: a,SV324: a,SV165: a] :
( ( ( less_eq @ ( sup @ SV165 @ SV324 ) @ SV409 )
= $true )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2279,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) ) )
= $true )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2218]) ).
thf(2280,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2281,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2282,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less_eq @ SV67 @ SV229 )
| ~ ( ( SV67 != SV229 ) ) )
= $false )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2283,plain,
! [SV235: a,SV73: a] :
( ( ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
| ~ ( ( SV73 != SV235 ) ) )
= $false )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2284,plain,
! [SV413: a,SV237: a] :
( ( ( SV237 = SV413 )
= $true )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2285,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) ) )
= $true )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2229]) ).
thf(2286,plain,
! [SV415: a,SV250: a] :
( ( ( SV250 = SV415 )
= $true )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2232]) ).
thf(2287,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) ) )
= $true )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2233]) ).
thf(2288,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2289,plain,
! [SV89: a > $o,SV419: a] :
( ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2290,plain,
! [SV416: a,SV258: a] :
( ( ( SV258 = SV416 )
= $true )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2237]) ).
thf(2291,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) ) )
= $true )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2238]) ).
thf(2292,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less_eq @ SV102 @ SV263 )
| ~ ( ( SV263 != SV102 ) ) )
= $false )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2293,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
| ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2241]) ).
thf(2294,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less_eq @ SV105 @ SV266 )
| ~ ( ( SV105 != SV266 ) ) )
= $false )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2295,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ SV268 )
| ~ ( less_eq @ SV107 @ SV374 ) )
= $false )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2296,plain,
! [SV421: a,SV118: set_a] :
( ( ( ! [SY633: a] :
~ ! [SY634: a] :
( ~ ( member_a @ SY634 @ SV118 )
| ( less_eq @ SY634 @ SY633 ) ) )
= $false )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2297,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ! [SY931: a] :
( ~ ( member_a @ SY931 @ SV118 )
| ( less_eq @ SY931 @ ( sK33_SY633 @ SV421 @ SV118 ) ) ) )
= $false )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2249]) ).
thf(2298,plain,
! [SV120: a,SV280: a] :
( ( ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
| ~ ( ( SV280 != SV120 ) ) )
= $false )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2299,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ( less_eq @ SV124 @ SV383 )
| ~ ( less_eq @ SV284 @ SV383 ) )
= $false )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2300,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ SV285 )
| ~ ( less_eq @ SV125 @ SV384 ) )
= $false )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2301,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( SV132 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2256]) ).
thf(2302,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ~ ! [SY925: a] :
( ~ ( SV132 @ SY925 )
| ( less_eq @ SY925 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) ) ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2257]) ).
thf(2303,plain,
! [SV132: a > $o,SV292: a,SV388: a > $o] :
( ( ( SV388 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) )
= $false )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2257]) ).
thf(2304,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ! [SY923: a] :
( ~ ( SV132 @ SY923 )
| ( less_eq @ SY923 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) ) ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2259]) ).
thf(2305,plain,
! [SV133: a > a > a,SV293: a,SV389: a] :
( ( ( ! [SY932: a] :
( ~ ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( sK34_SY927 @ SV133 @ SV293 @ SV389 ) )
| ~ ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ SY932 )
| ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( SV133 @ ( sK34_SY927 @ SV133 @ SV293 @ SV389 ) @ SY932 ) ) ) )
= $false )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2261]) ).
thf(2306,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( ! [SY933: a] :
( ~ ( less_eq @ ( sK35_SY929 @ SV135 @ SV295 @ SV391 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
| ~ ( less_eq @ SY933 @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
| ( less_eq @ ( SV135 @ ( sK35_SY929 @ SV135 @ SV295 @ SV391 ) @ SY933 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) ) ) )
= $false )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2262]) ).
thf(2307,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less_eq @ SV154 @ SV314 )
| ~ ~ ( less_eq @ SV314 @ SV154 ) )
= $false )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2308,plain,
! [SV422: a,SV156: set_a] :
( ( ( ! [SY720: a] :
~ ! [SY721: a] :
( ~ ( member_a @ SY721 @ SV156 )
| ( less_eq @ SY720 @ SY721 ) ) )
= $false )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2309,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ! [SY934: a] :
( ~ ( member_a @ SY934 @ SV156 )
| ( less_eq @ ( sK36_SY720 @ SV422 @ SV156 ) @ SY934 ) ) )
= $false )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2268]) ).
thf(2310,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( SV158 @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2269]) ).
thf(2311,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ~ ! [SY926: a] :
( ~ ( SV158 @ SY926 )
| ( less_eq @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) @ SY926 ) ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2270]) ).
thf(2312,plain,
! [SV158: a > $o,SV317: a,SV404: a > $o] :
( ( ( SV404 @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) )
= $false )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2270]) ).
thf(2313,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ! [SY924: a] :
( ~ ( SV158 @ SY924 )
| ( less_eq @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) @ SY924 ) ) )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2272]) ).
thf(2314,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2315,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( ~ ( less @ SV160 @ SV319 ) )
= $false )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2316,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ~ ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2317,plain,
! [SV320: a,SV161: a] :
( ( ( modula1727524044comp_a @ less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2276]) ).
thf(2318,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) ) )
= $true )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2277]) ).
thf(2319,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ( less_eq @ SV165 @ SV409 )
| ~ ( less_eq @ SV324 @ SV409 ) )
= $false )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2320,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2280]) ).
thf(2321,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2280]) ).
thf(2322,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) ) )
= $true )
| ( ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2323,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( less_eq @ SV67 @ SV229 ) )
= $false )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2324,plain,
! [SV229: a,SV67: a] :
( ( ( ~ ( ( SV67 != SV229 ) ) )
= $false )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2325,plain,
! [SV235: a,SV73: a] :
( ( ( SV73
!= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2326,plain,
! [SV235: a,SV73: a] :
( ( ( ~ ( ( SV73 != SV235 ) ) )
= $false )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2327,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ( less_eq @ SV413 @ SV237 )
| ~ ( less_eq @ SV237 @ SV413 ) )
= $false )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2328,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( less_eq @ SV250 @ SV415 )
| ~ ( less_eq @ SV415 @ SV250 ) )
= $false )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2329,plain,
! [SV419: a,SV89: a > $o] :
( ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( ~ ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2288]) ).
thf(2330,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2331,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( less_eq @ SV258 @ SV416 )
| ~ ( less_eq @ SV416 @ SV258 ) )
= $false )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2332,plain,
! [SV263: a,SV102: a] :
( ( ( ~ ( less_eq @ SV102 @ SV263 ) )
= $false )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2292]) ).
thf(2333,plain,
! [SV102: a,SV263: a] :
( ( ( ~ ( ( SV263 != SV102 ) ) )
= $false )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2292]) ).
thf(2334,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2335,plain,
! [SV103: a > $o,SV264: a,SV420: a] :
( ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2336,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( less_eq @ SV105 @ SV266 ) )
= $false )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2294]) ).
thf(2337,plain,
! [SV266: a,SV105: a] :
( ( ( ~ ( ( SV105 != SV266 ) ) )
= $false )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2294]) ).
thf(2338,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ SV268 ) )
= $false )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2295]) ).
thf(2339,plain,
! [SV268: a,SV374: a,SV107: a] :
( ( ( ~ ( less_eq @ SV107 @ SV374 ) )
= $false )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2295]) ).
thf(2340,plain,
! [SV421: a,SV118: set_a] :
( ( ( ~ ! [SY935: a] :
( ~ ( member_a @ SY935 @ SV118 )
| ( less_eq @ SY935 @ ( sK37_SY633 @ SV421 @ SV118 ) ) ) )
= $false )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2296]) ).
thf(2341,plain,
! [SV421: a,SV118: set_a] :
( ( ( ! [SY931: a] :
( ~ ( member_a @ SY931 @ SV118 )
| ( less_eq @ SY931 @ ( sK33_SY633 @ SV421 @ SV118 ) ) ) )
= $true )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2297]) ).
thf(2342,plain,
! [SV120: a,SV280: a] :
( ( ( SV280
!= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2343,plain,
! [SV120: a,SV280: a] :
( ( ( ~ ( ( SV280 != SV120 ) ) )
= $false )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2344,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( ~ ( less_eq @ SV124 @ SV383 ) )
= $false )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2299]) ).
thf(2345,plain,
! [SV124: a,SV383: a,SV284: a] :
( ( ( ~ ( less_eq @ SV284 @ SV383 ) )
= $false )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2299]) ).
thf(2346,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ SV285 ) )
= $false )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2300]) ).
thf(2347,plain,
! [SV285: a,SV384: a,SV125: a] :
( ( ( ~ ( less_eq @ SV125 @ SV384 ) )
= $false )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2300]) ).
thf(2348,plain,
! [SV388: a > $o,SV292: a,SV132: a > $o] :
( ( ( ! [SY925: a] :
( ~ ( SV132 @ SY925 )
| ( less_eq @ SY925 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) ) ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2302]) ).
thf(2349,plain,
! [SV388: a > $o,SV292: a,SV425: a,SV132: a > $o] :
( ( ( ~ ( SV132 @ SV425 )
| ( less_eq @ SV425 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2350,plain,
! [SV133: a > a > a,SV293: a,SV389: a] :
( ( ( ~ ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( sK34_SY927 @ SV133 @ SV293 @ SV389 ) )
| ~ ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( sK38_SY932 @ SV133 @ SV293 @ SV389 ) )
| ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( SV133 @ ( sK34_SY927 @ SV133 @ SV293 @ SV389 ) @ ( sK38_SY932 @ SV133 @ SV293 @ SV389 ) ) ) )
= $false )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2305]) ).
thf(2351,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( ~ ( less_eq @ ( sK35_SY929 @ SV135 @ SV295 @ SV391 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
| ~ ( less_eq @ ( sK39_SY933 @ SV391 @ SV295 @ SV135 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
| ( less_eq @ ( SV135 @ ( sK35_SY929 @ SV135 @ SV295 @ SV391 ) @ ( sK39_SY933 @ SV391 @ SV295 @ SV135 ) ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) ) )
= $false )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2306]) ).
thf(2352,plain,
! [SV314: a,SV154: a] :
( ( ( ~ ( less_eq @ SV154 @ SV314 ) )
= $false )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2307]) ).
thf(2353,plain,
! [SV154: a,SV314: a] :
( ( ( ~ ~ ( less_eq @ SV314 @ SV154 ) )
= $false )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2307]) ).
thf(2354,plain,
! [SV422: a,SV156: set_a] :
( ( ( ~ ! [SY936: a] :
( ~ ( member_a @ SY936 @ SV156 )
| ( less_eq @ ( sK40_SY720 @ SV422 @ SV156 ) @ SY936 ) ) )
= $false )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2308]) ).
thf(2355,plain,
! [SV422: a,SV156: set_a] :
( ( ( ! [SY934: a] :
( ~ ( member_a @ SY934 @ SV156 )
| ( less_eq @ ( sK36_SY720 @ SV422 @ SV156 ) @ SY934 ) ) )
= $true )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2356,plain,
! [SV404: a > $o,SV317: a,SV158: a > $o] :
( ( ( ! [SY926: a] :
( ~ ( SV158 @ SY926 )
| ( less_eq @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) @ SY926 ) ) )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2311]) ).
thf(2357,plain,
! [SV404: a > $o,SV317: a,SV426: a,SV158: a > $o] :
( ( ( ~ ( SV158 @ SV426 )
| ( less_eq @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) @ SV426 ) )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2358,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $true )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2314]) ).
thf(2359,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( less @ SV160 @ SV319 )
= $true )
| ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2315]) ).
thf(2360,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
| ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2361,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ~ ( less_eq @ SV161 @ SV320 )
| ~ ~ ( less_eq @ SV320 @ SV161 ) )
= $false )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2362,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( ~ ( less_eq @ SV165 @ SV409 ) )
= $false )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2319]) ).
thf(2363,plain,
! [SV165: a,SV409: a,SV324: a] :
( ( ( ~ ( less_eq @ SV324 @ SV409 ) )
= $false )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2319]) ).
thf(2364,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2320]) ).
thf(2365,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2321]) ).
thf(2366,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2367,plain,
! [SV229: a,SV67: a] :
( ( ( less_eq @ SV67 @ SV229 )
= $true )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2323]) ).
thf(2368,plain,
! [SV229: a,SV67: a] :
( ( ( SV67 != SV229 )
= $true )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2324]) ).
thf(2369,plain,
! [SV235: a,SV73: a] :
( ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $true )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2325]) ).
thf(2370,plain,
! [SV235: a,SV73: a] :
( ( ( SV73 != SV235 )
= $true )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2326]) ).
thf(2371,plain,
! [SV237: a,SV413: a] :
( ( ( ~ ( less_eq @ SV413 @ SV237 ) )
= $false )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2327]) ).
thf(2372,plain,
! [SV413: a,SV237: a] :
( ( ( ~ ( less_eq @ SV237 @ SV413 ) )
= $false )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2327]) ).
thf(2373,plain,
! [SV415: a,SV250: a] :
( ( ( ~ ( less_eq @ SV250 @ SV415 ) )
= $false )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2328]) ).
thf(2374,plain,
! [SV250: a,SV415: a] :
( ( ( ~ ( less_eq @ SV415 @ SV250 ) )
= $false )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2328]) ).
thf(2375,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ! [SY904: a] :
( ~ ~ ( ~ ( SV89 @ SY904 )
| ~ ! [SY584: a] :
( ~ ( SV89 @ SY584 )
| ( less_eq @ SY904 @ SY584 ) ) )
| ( SY904 = SV419 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2376,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ~ ( ~ ( SV89 @ ( sK41_SY904 @ SV419 @ SV89 ) )
| ~ ! [SY937: a] :
( ~ ( SV89 @ SY937 )
| ( less_eq @ ( sK41_SY904 @ SV419 @ SV89 ) @ SY937 ) ) )
| ( ( sK41_SY904 @ SV419 @ SV89 )
= SV419 ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2330]) ).
thf(2377,plain,
! [SV416: a,SV258: a] :
( ( ( ~ ( less_eq @ SV258 @ SV416 ) )
= $false )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2331]) ).
thf(2378,plain,
! [SV258: a,SV416: a] :
( ( ( ~ ( less_eq @ SV416 @ SV258 ) )
= $false )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2331]) ).
thf(2379,plain,
! [SV263: a,SV102: a] :
( ( ( less_eq @ SV102 @ SV263 )
= $true )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2332]) ).
thf(2380,plain,
! [SV102: a,SV263: a] :
( ( ( SV263 != SV102 )
= $true )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2381,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( ~ ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2382,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2383,plain,
! [SV266: a,SV105: a] :
( ( ( less_eq @ SV105 @ SV266 )
= $true )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2336]) ).
thf(2384,plain,
! [SV266: a,SV105: a] :
( ( ( SV105 != SV266 )
= $true )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2337]) ).
thf(2385,plain,
! [SV374: a,SV268: a,SV107: a] :
( ( ( less_eq @ SV107 @ SV268 )
= $true )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2386,plain,
! [SV268: a,SV374: a,SV107: a] :
( ( ( less_eq @ SV107 @ SV374 )
= $true )
| ( ( less_eq @ SV107 @ SV268 )
= $false )
| ( ( less_eq @ SV107 @ SV374 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2339]) ).
thf(2387,plain,
! [SV421: a,SV118: set_a] :
( ( ( ! [SY935: a] :
( ~ ( member_a @ SY935 @ SV118 )
| ( less_eq @ SY935 @ ( sK37_SY633 @ SV421 @ SV118 ) ) ) )
= $true )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2340]) ).
thf(2388,plain,
! [SV421: a,SV118: set_a,SV427: a] :
( ( ( ~ ( member_a @ SV427 @ SV118 )
| ( less_eq @ SV427 @ ( sK33_SY633 @ SV421 @ SV118 ) ) )
= $true )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2389,plain,
! [SV120: a,SV280: a] :
( ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $true )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2390,plain,
! [SV120: a,SV280: a] :
( ( ( SV280 != SV120 )
= $true )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2343]) ).
thf(2391,plain,
! [SV284: a,SV383: a,SV124: a] :
( ( ( less_eq @ SV124 @ SV383 )
= $true )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2344]) ).
thf(2392,plain,
! [SV124: a,SV383: a,SV284: a] :
( ( ( less_eq @ SV284 @ SV383 )
= $true )
| ( ( less_eq @ SV124 @ SV383 )
= $false )
| ( ( less_eq @ SV284 @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2393,plain,
! [SV384: a,SV285: a,SV125: a] :
( ( ( less_eq @ SV125 @ SV285 )
= $true )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2346]) ).
thf(2394,plain,
! [SV285: a,SV384: a,SV125: a] :
( ( ( less_eq @ SV125 @ SV384 )
= $true )
| ( ( less_eq @ SV125 @ SV285 )
= $false )
| ( ( less_eq @ SV125 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2347]) ).
thf(2395,plain,
! [SV388: a > $o,SV292: a,SV428: a,SV132: a > $o] :
( ( ( ~ ( SV132 @ SV428 )
| ( less_eq @ SV428 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2396,plain,
! [SV388: a > $o,SV292: a,SV425: a,SV132: a > $o] :
( ( ( ~ ( SV132 @ SV425 ) )
= $true )
| ( ( less_eq @ SV425 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2397,plain,
! [SV133: a > a > a,SV293: a,SV389: a] :
( ( ( ~ ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( sK34_SY927 @ SV133 @ SV293 @ SV389 ) ) )
= $false )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2350]) ).
thf(2398,plain,
! [SV133: a > a > a,SV293: a,SV389: a] :
( ( ( ~ ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( sK38_SY932 @ SV133 @ SV293 @ SV389 ) )
| ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( SV133 @ ( sK34_SY927 @ SV133 @ SV293 @ SV389 ) @ ( sK38_SY932 @ SV133 @ SV293 @ SV389 ) ) ) )
= $false )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2350]) ).
thf(2399,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( ~ ( less_eq @ ( sK35_SY929 @ SV135 @ SV295 @ SV391 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) ) )
= $false )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2400,plain,
! [SV135: a > a > a,SV295: a,SV391: a] :
( ( ( ~ ( less_eq @ ( sK39_SY933 @ SV391 @ SV295 @ SV135 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
| ( less_eq @ ( SV135 @ ( sK35_SY929 @ SV135 @ SV295 @ SV391 ) @ ( sK39_SY933 @ SV391 @ SV295 @ SV135 ) ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) ) )
= $false )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2401,plain,
! [SV314: a,SV154: a] :
( ( ( less_eq @ SV154 @ SV314 )
= $true )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2402,plain,
! [SV154: a,SV314: a] :
( ( ( ~ ( less_eq @ SV314 @ SV154 ) )
= $true )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2353]) ).
thf(2403,plain,
! [SV422: a,SV156: set_a] :
( ( ( ! [SY936: a] :
( ~ ( member_a @ SY936 @ SV156 )
| ( less_eq @ ( sK40_SY720 @ SV422 @ SV156 ) @ SY936 ) ) )
= $true )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2354]) ).
thf(2404,plain,
! [SV422: a,SV156: set_a,SV429: a] :
( ( ( ~ ( member_a @ SV429 @ SV156 )
| ( less_eq @ ( sK36_SY720 @ SV422 @ SV156 ) @ SV429 ) )
= $true )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2405,plain,
! [SV404: a > $o,SV317: a,SV430: a,SV158: a > $o] :
( ( ( ~ ( SV158 @ SV430 )
| ( less_eq @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) @ SV430 ) )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2406,plain,
! [SV404: a > $o,SV317: a,SV426: a,SV158: a > $o] :
( ( ( ~ ( SV158 @ SV426 ) )
= $true )
| ( ( less_eq @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) @ SV426 )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2407,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( ~ ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2408,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2409,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ~ ( less_eq @ SV161 @ SV320 ) )
= $false )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2410,plain,
! [SV161: a,SV320: a] :
( ( ( ~ ~ ( less_eq @ SV320 @ SV161 ) )
= $false )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2411,plain,
! [SV324: a,SV409: a,SV165: a] :
( ( ( less_eq @ SV165 @ SV409 )
= $true )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2362]) ).
thf(2412,plain,
! [SV165: a,SV409: a,SV324: a] :
( ( ( less_eq @ SV324 @ SV409 )
= $true )
| ( ( less_eq @ SV165 @ SV409 )
= $false )
| ( ( less_eq @ SV324 @ SV409 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2363]) ).
thf(2413,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2414,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
= $true )
| ( ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2366]) ).
thf(2415,plain,
! [SV229: a,SV67: a] :
( ( ( SV67 = SV229 )
= $false )
| ( ( less_eq @ SV67 @ SV229 )
= $false )
| ( ( SV67 = SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2416,plain,
! [SV235: a,SV73: a] :
( ( ( SV73 = SV235 )
= $false )
| ( ( SV73
= ( inf @ SV73 @ SV235 ) )
= $false )
| ( ( SV73 = SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2417,plain,
! [SV237: a,SV413: a] :
( ( ( less_eq @ SV413 @ SV237 )
= $true )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2371]) ).
thf(2418,plain,
! [SV413: a,SV237: a] :
( ( ( less_eq @ SV237 @ SV413 )
= $true )
| ( ( less_eq @ SV413 @ SV237 )
= $false )
| ( ( less_eq @ SV237 @ SV413 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2419,plain,
! [SV415: a,SV250: a] :
( ( ( less_eq @ SV250 @ SV415 )
= $true )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2373]) ).
thf(2420,plain,
! [SV250: a,SV415: a] :
( ( ( less_eq @ SV415 @ SV250 )
= $true )
| ( ( less_eq @ SV250 @ SV415 )
= $false )
| ( ( less_eq @ SV415 @ SV250 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2374]) ).
thf(2421,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ~ ( ~ ( SV89 @ ( sK42_SY904 @ SV419 @ SV89 ) )
| ~ ! [SY938: a] :
( ~ ( SV89 @ SY938 )
| ( less_eq @ ( sK42_SY904 @ SV419 @ SV89 ) @ SY938 ) ) )
| ( ( sK42_SY904 @ SV419 @ SV89 )
= SV419 ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2375]) ).
thf(2422,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ~ ( ~ ( SV89 @ ( sK41_SY904 @ SV419 @ SV89 ) )
| ~ ! [SY937: a] :
( ~ ( SV89 @ SY937 )
| ( less_eq @ ( sK41_SY904 @ SV419 @ SV89 ) @ SY937 ) ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2423,plain,
! [SV89: a > $o,SV419: a] :
( ( ( ( sK41_SY904 @ SV419 @ SV89 )
= SV419 )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2424,plain,
! [SV416: a,SV258: a] :
( ( ( less_eq @ SV258 @ SV416 )
= $true )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2377]) ).
thf(2425,plain,
! [SV258: a,SV416: a] :
( ( ( less_eq @ SV416 @ SV258 )
= $true )
| ( ( less_eq @ SV258 @ SV416 )
= $false )
| ( ( less_eq @ SV416 @ SV258 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2426,plain,
! [SV102: a,SV263: a] :
( ( ( SV263 = SV102 )
= $false )
| ( ( less_eq @ SV102 @ SV263 )
= $false )
| ( ( SV263 = SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2427,plain,
! [SV264: a,SV420: a,SV103: a > $o] :
( ( ( ! [SY907: a] :
( ~ ~ ( ~ ( SV103 @ SY907 )
| ~ ! [SY610: a] :
( ~ ( SV103 @ SY610 )
| ( less_eq @ SY907 @ SY610 ) ) )
| ( SY907 = SV420 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2428,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ~ ( ~ ( SV103 @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) )
| ~ ! [SY939: a] :
( ~ ( SV103 @ SY939 )
| ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SY939 ) ) )
| ( ( sK43_SY907 @ SV264 @ SV420 @ SV103 )
= SV420 ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2382]) ).
thf(2429,plain,
! [SV266: a,SV105: a] :
( ( ( SV105 = SV266 )
= $false )
| ( ( less_eq @ SV105 @ SV266 )
= $false )
| ( ( SV105 = SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2430,plain,
! [SV421: a,SV118: set_a,SV431: a] :
( ( ( ~ ( member_a @ SV431 @ SV118 )
| ( less_eq @ SV431 @ ( sK37_SY633 @ SV421 @ SV118 ) ) )
= $true )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2431,plain,
! [SV421: a,SV118: set_a,SV427: a] :
( ( ( ~ ( member_a @ SV427 @ SV118 ) )
= $true )
| ( ( less_eq @ SV427 @ ( sK33_SY633 @ SV421 @ SV118 ) )
= $true )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2432,plain,
! [SV120: a,SV280: a] :
( ( ( SV280 = SV120 )
= $false )
| ( ( SV280
= ( sup @ SV280 @ SV120 ) )
= $false )
| ( ( SV280 = SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2433,plain,
! [SV388: a > $o,SV292: a,SV428: a,SV132: a > $o] :
( ( ( ~ ( SV132 @ SV428 ) )
= $true )
| ( ( less_eq @ SV428 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2434,plain,
! [SV388: a > $o,SV292: a,SV425: a,SV132: a > $o] :
( ( ( SV132 @ SV425 )
= $false )
| ( ( less_eq @ SV425 @ ( sK25_SY876 @ SV292 @ SV388 @ SV132 ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( less_eq @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) @ SV292 )
= $false )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2435,plain,
! [SV133: a > a > a,SV293: a,SV389: a] :
( ( ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( sK34_SY927 @ SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2436,plain,
! [SV133: a > a > a,SV293: a,SV389: a] :
( ( ( ~ ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( sK38_SY932 @ SV133 @ SV293 @ SV389 ) ) )
= $false )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2437,plain,
! [SV133: a > a > a,SV293: a,SV389: a] :
( ( ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( SV133 @ ( sK34_SY927 @ SV133 @ SV293 @ SV389 ) @ ( sK38_SY932 @ SV133 @ SV293 @ SV389 ) ) )
= $false )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2438,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( less_eq @ ( sK35_SY929 @ SV135 @ SV295 @ SV391 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
= $true )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2439,plain,
! [SV135: a > a > a,SV295: a,SV391: a] :
( ( ( ~ ( less_eq @ ( sK39_SY933 @ SV391 @ SV295 @ SV135 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) ) )
= $false )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2440,plain,
! [SV391: a,SV295: a,SV135: a > a > a] :
( ( ( less_eq @ ( SV135 @ ( sK35_SY929 @ SV135 @ SV295 @ SV391 ) @ ( sK39_SY933 @ SV391 @ SV295 @ SV135 ) ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
= $false )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2441,plain,
! [SV154: a,SV314: a] :
( ( ( less_eq @ SV314 @ SV154 )
= $false )
| ( ( less_eq @ SV154 @ SV314 )
= $false )
| ( ( less_eq @ SV314 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2442,plain,
! [SV422: a,SV156: set_a,SV432: a] :
( ( ( ~ ( member_a @ SV432 @ SV156 )
| ( less_eq @ ( sK40_SY720 @ SV422 @ SV156 ) @ SV432 ) )
= $true )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2443,plain,
! [SV422: a,SV156: set_a,SV429: a] :
( ( ( ~ ( member_a @ SV429 @ SV156 ) )
= $true )
| ( ( less_eq @ ( sK36_SY720 @ SV422 @ SV156 ) @ SV429 )
= $true )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2444,plain,
! [SV404: a > $o,SV317: a,SV430: a,SV158: a > $o] :
( ( ( ~ ( SV158 @ SV430 ) )
= $true )
| ( ( less_eq @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) @ SV430 )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2445,plain,
! [SV404: a > $o,SV317: a,SV426: a,SV158: a > $o] :
( ( ( SV158 @ SV426 )
= $false )
| ( ( less_eq @ ( sK26_SY898 @ SV317 @ SV404 @ SV158 ) @ SV426 )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( less_eq @ SV317 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $false )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2446,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( modula397570059tice_a @ inf @ less @ sup @ SV160 @ SV319 @ SV406 )
= $true )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2407]) ).
thf(2447,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) ) )
= $true )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2408]) ).
thf(2448,plain,
! [SV320: a,SV161: a] :
( ( ( ~ ( less_eq @ SV161 @ SV320 ) )
= $true )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2409]) ).
thf(2449,plain,
! [SV161: a,SV320: a] :
( ( ( ~ ( less_eq @ SV320 @ SV161 ) )
= $true )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2410]) ).
thf(2450,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2413]) ).
thf(2451,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2413]) ).
thf(2452,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
= $true )
| ( ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2453,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ~ ( ~ ( SV89 @ ( sK42_SY904 @ SV419 @ SV89 ) )
| ~ ! [SY938: a] :
( ~ ( SV89 @ SY938 )
| ( less_eq @ ( sK42_SY904 @ SV419 @ SV89 ) @ SY938 ) ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2421]) ).
thf(2454,plain,
! [SV89: a > $o,SV419: a] :
( ( ( ( sK42_SY904 @ SV419 @ SV89 )
= SV419 )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2421]) ).
thf(2455,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( ~ ( SV89 @ ( sK41_SY904 @ SV419 @ SV89 ) )
| ~ ! [SY937: a] :
( ~ ( SV89 @ SY937 )
| ( less_eq @ ( sK41_SY904 @ SV419 @ SV89 ) @ SY937 ) ) ) )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2422]) ).
thf(2456,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ~ ( ~ ( SV103 @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) )
| ~ ! [SY940: a] :
( ~ ( SV103 @ SY940 )
| ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SY940 ) ) )
| ( ( sK44_SY907 @ SV264 @ SV420 @ SV103 )
= SV420 ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2427]) ).
thf(2457,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ~ ( ~ ( SV103 @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) )
| ~ ! [SY939: a] :
( ~ ( SV103 @ SY939 )
| ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SY939 ) ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2458,plain,
! [SV103: a > $o,SV420: a,SV264: a] :
( ( ( ( sK43_SY907 @ SV264 @ SV420 @ SV103 )
= SV420 )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2459,plain,
! [SV421: a,SV118: set_a,SV431: a] :
( ( ( ~ ( member_a @ SV431 @ SV118 ) )
= $true )
| ( ( less_eq @ SV431 @ ( sK37_SY633 @ SV421 @ SV118 ) )
= $true )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2460,plain,
! [SV421: a,SV118: set_a,SV427: a] :
( ( ( member_a @ SV427 @ SV118 )
= $false )
| ( ( less_eq @ SV427 @ ( sK33_SY633 @ SV421 @ SV118 ) )
= $true )
| ( ( less_eq @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2461,plain,
! [SV388: a > $o,SV292: a,SV428: a,SV132: a > $o] :
( ( ( SV132 @ SV428 )
= $false )
| ( ( less_eq @ SV428 @ ( sK27_SY876 @ SV292 @ SV388 @ SV132 ) )
= $true )
| ( ( SV388 @ ( greatest_a @ less_eq @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK13_SY821 @ SV388 @ SV292 @ SV132 ) )
= $true )
| ( ( SV132 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2462,plain,
! [SV133: a > a > a,SV293: a,SV389: a] :
( ( ( less_eq @ ( sK30_SY668 @ SV389 @ SV293 @ SV133 ) @ ( sK38_SY932 @ SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( ( inf @ SV293 @ SV389 )
= ( SV133 @ SV293 @ SV389 ) )
= $true )
| ( ( less_eq @ ( SV133 @ ( sK20_SY666 @ SV389 @ SV293 @ SV133 ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) ) @ ( sK23_SY920 @ SV293 @ SV389 @ SV133 ) )
= $false )
| ( ( less_eq @ ( SV133 @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) @ ( sK8_SY909 @ SV293 @ SV389 @ SV133 ) ) @ ( sK3_SY664 @ SV389 @ SV293 @ SV133 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2463,plain,
! [SV135: a > a > a,SV295: a,SV391: a] :
( ( ( less_eq @ ( sK39_SY933 @ SV391 @ SV295 @ SV135 ) @ ( sK31_SY679 @ SV391 @ SV295 @ SV135 ) )
= $true )
| ( ( ( sup @ SV295 @ SV391 )
= ( SV135 @ SV295 @ SV391 ) )
= $true )
| ( ( less_eq @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) @ ( SV135 @ ( sK21_SY677 @ SV391 @ SV295 @ SV135 ) @ ( sK24_SY921 @ SV295 @ SV391 @ SV135 ) ) )
= $false )
| ( ( less_eq @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( SV135 @ ( sK4_SY675 @ SV391 @ SV295 @ SV135 ) @ ( sK9_SY910 @ SV135 @ SV295 @ SV391 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2439]) ).
thf(2464,plain,
! [SV422: a,SV156: set_a,SV432: a] :
( ( ( ~ ( member_a @ SV432 @ SV156 ) )
= $true )
| ( ( less_eq @ ( sK40_SY720 @ SV422 @ SV156 ) @ SV432 )
= $true )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2465,plain,
! [SV422: a,SV156: set_a,SV429: a] :
( ( ( member_a @ SV429 @ SV156 )
= $false )
| ( ( less_eq @ ( sK36_SY720 @ SV422 @ SV156 ) @ SV429 )
= $true )
| ( ( less_eq @ SV422 @ ( sK18_SY917 @ SV422 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2466,plain,
! [SV404: a > $o,SV317: a,SV430: a,SV158: a > $o] :
( ( ( SV158 @ SV430 )
= $false )
| ( ( less_eq @ ( sK28_SY898 @ SV317 @ SV404 @ SV158 ) @ SV430 )
= $true )
| ( ( SV404 @ ( least_a @ less_eq @ SV158 ) )
= $true )
| ( ( SV158 @ ( sK15_SY860 @ SV404 @ SV317 @ SV158 ) )
= $true )
| ( ( SV158 @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2467,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
| ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2468,plain,
! [SV320: a,SV161: a] :
( ( ( less_eq @ SV161 @ SV320 )
= $false )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2469,plain,
! [SV161: a,SV320: a] :
( ( ( less_eq @ SV320 @ SV161 )
= $false )
| ( ( less_eq @ SV161 @ SV320 )
= $true )
| ( ( less_eq @ SV320 @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2470,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) ) )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2450]) ).
thf(2471,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2451]) ).
thf(2472,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2473,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( ~ ( SV89 @ ( sK42_SY904 @ SV419 @ SV89 ) )
| ~ ! [SY938: a] :
( ~ ( SV89 @ SY938 )
| ( less_eq @ ( sK42_SY904 @ SV419 @ SV89 ) @ SY938 ) ) ) )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2453]) ).
thf(2474,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ ( sK41_SY904 @ SV419 @ SV89 ) )
| ~ ! [SY937: a] :
( ~ ( SV89 @ SY937 )
| ( less_eq @ ( sK41_SY904 @ SV419 @ SV89 ) @ SY937 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2475,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ~ ( ~ ( SV103 @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) )
| ~ ! [SY940: a] :
( ~ ( SV103 @ SY940 )
| ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SY940 ) ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2456]) ).
thf(2476,plain,
! [SV103: a > $o,SV420: a,SV264: a] :
( ( ( ( sK44_SY907 @ SV264 @ SV420 @ SV103 )
= SV420 )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2456]) ).
thf(2477,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( ~ ( SV103 @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) )
| ~ ! [SY939: a] :
( ~ ( SV103 @ SY939 )
| ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SY939 ) ) ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2457]) ).
thf(2478,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV264 ) )
= $true )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( ( sK43_SY907 @ SV264 @ SV420 @ SV103 )
= SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2479,plain,
! [SV421: a,SV118: set_a,SV431: a] :
( ( ( member_a @ SV431 @ SV118 )
= $false )
| ( ( less_eq @ SV431 @ ( sK37_SY633 @ SV421 @ SV118 ) )
= $true )
| ( ( member_a @ ( sK17_SY915 @ SV421 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2480,plain,
! [SV422: a,SV156: set_a,SV432: a] :
( ( ( member_a @ SV432 @ SV156 )
= $false )
| ( ( less_eq @ ( sK40_SY720 @ SV422 @ SV156 ) @ SV432 )
= $true )
| ( ( member_a @ ( sK18_SY917 @ SV422 @ SV156 ) @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2481,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2482,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( sup @ SV160 @ SV406 )
!= ( sup @ SV319 @ SV406 ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2483,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2484,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2485,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ ( sK42_SY904 @ SV419 @ SV89 ) )
| ~ ! [SY938: a] :
( ~ ( SV89 @ SY938 )
| ( less_eq @ ( sK42_SY904 @ SV419 @ SV89 ) @ SY938 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2486,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ ( sK41_SY904 @ SV419 @ SV89 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2474]) ).
thf(2487,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ! [SY937: a] :
( ~ ( SV89 @ SY937 )
| ( less_eq @ ( sK41_SY904 @ SV419 @ SV89 ) @ SY937 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2474]) ).
thf(2488,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( ~ ( SV103 @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) )
| ~ ! [SY940: a] :
( ~ ( SV103 @ SY940 )
| ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SY940 ) ) ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2475]) ).
thf(2489,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV264 ) )
= $true )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( ( sK44_SY907 @ SV264 @ SV420 @ SV103 )
= SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2490,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) )
| ~ ! [SY939: a] :
( ~ ( SV103 @ SY939 )
| ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SY939 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2491,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( SV103 @ SV264 )
= $false )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( ( sK43_SY907 @ SV264 @ SV420 @ SV103 )
= SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2492,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ~ ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) ) )
= $true )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2481]) ).
thf(2493,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $true )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2482]) ).
thf(2494,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2483]) ).
thf(2495,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2483]) ).
thf(2496,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2497,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ ( sK42_SY904 @ SV419 @ SV89 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2498,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ~ ! [SY938: a] :
( ~ ( SV89 @ SY938 )
| ( less_eq @ ( sK42_SY904 @ SV419 @ SV89 ) @ SY938 ) ) )
= $false )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2499,plain,
! [SV419: a,SV89: a > $o] :
( ( ( SV89 @ ( sK41_SY904 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2500,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ! [SY937: a] :
( ~ ( SV89 @ SY937 )
| ( less_eq @ ( sK41_SY904 @ SV419 @ SV89 ) @ SY937 ) ) )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2487]) ).
thf(2501,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) )
| ~ ! [SY940: a] :
( ~ ( SV103 @ SY940 )
| ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SY940 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2502,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( SV103 @ SV264 )
= $false )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( ( sK44_SY907 @ SV264 @ SV420 @ SV103 )
= SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2503,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2490]) ).
thf(2504,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ! [SY939: a] :
( ~ ( SV103 @ SY939 )
| ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SY939 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2490]) ).
thf(2505,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
| ~ ( less @ SV160 @ SV319 ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2506,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2494]) ).
thf(2507,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $true )
| ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2508,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $true )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2509,plain,
! [SV419: a,SV89: a > $o] :
( ( ( SV89 @ ( sK42_SY904 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2497]) ).
thf(2510,plain,
! [SV419: a,SV89: a > $o] :
( ( ( ! [SY938: a] :
( ~ ( SV89 @ SY938 )
| ( less_eq @ ( sK42_SY904 @ SV419 @ SV89 ) @ SY938 ) ) )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2498]) ).
thf(2511,plain,
! [SV419: a,SV433: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ SV433 )
| ( less_eq @ ( sK41_SY904 @ SV419 @ SV89 ) @ SV433 ) )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(2512,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2513,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ! [SY940: a] :
( ~ ( SV103 @ SY940 )
| ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SY940 ) ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2514,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( SV103 @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2503]) ).
thf(2515,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ! [SY939: a] :
( ~ ( SV103 @ SY939 )
| ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SY939 ) ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2504]) ).
thf(2516,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( inf @ SV160 @ SV406 )
!= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2505]) ).
thf(2517,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( ~ ( less @ SV160 @ SV319 ) )
= $false )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2505]) ).
thf(2518,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ~ ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2519,plain,
! [SV419: a,SV434: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ SV434 )
| ( less_eq @ ( sK42_SY904 @ SV419 @ SV89 ) @ SV434 ) )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2520,plain,
! [SV419: a,SV433: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ SV433 ) )
= $true )
| ( ( less_eq @ ( sK41_SY904 @ SV419 @ SV89 ) @ SV433 )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2521,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( SV103 @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2512]) ).
thf(2522,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ! [SY940: a] :
( ~ ( SV103 @ SY940 )
| ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SY940 ) ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2513]) ).
thf(2523,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV264 ) )
= $true )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2524,plain,
! [SV420: a,SV264: a,SV435: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV435 )
| ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SV435 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(2525,plain,
! [SV319: a,SV406: a,SV160: a] :
( ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $true )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2516]) ).
thf(2526,plain,
! [SV406: a,SV319: a,SV160: a] :
( ( ( less @ SV160 @ SV319 )
= $true )
| ( ( less @ SV160 @ SV319 )
= $false )
| ( ( ( inf @ SV160 @ SV406 )
= ( inf @ SV319 @ SV406 ) )
= $false )
| ( ( ( sup @ SV160 @ SV406 )
= ( sup @ SV319 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2517]) ).
thf(2527,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2528,plain,
! [SV419: a,SV434: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ SV434 ) )
= $true )
| ( ( less_eq @ ( sK42_SY904 @ SV419 @ SV89 ) @ SV434 )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2529,plain,
! [SV419: a,SV433: a,SV89: a > $o] :
( ( ( SV89 @ SV433 )
= $false )
| ( ( less_eq @ ( sK41_SY904 @ SV419 @ SV89 ) @ SV433 )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( less_eq @ SV419 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $false )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2530,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV264 ) )
= $true )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2521]) ).
thf(2531,plain,
! [SV420: a,SV264: a,SV436: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV436 )
| ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SV436 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(2532,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( SV103 @ SV264 )
= $false )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2533,plain,
! [SV420: a,SV264: a,SV435: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV435 ) )
= $true )
| ( ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SV435 )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2534,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2535,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2536,plain,
! [SV419: a,SV434: a,SV89: a > $o] :
( ( ( SV89 @ SV434 )
= $false )
| ( ( less_eq @ ( sK42_SY904 @ SV419 @ SV89 ) @ SV434 )
= $true )
| ( ( SV89 @ SV419 )
= $false )
| ( ( SV89 @ ( sK29_SY903 @ SV419 @ SV89 ) )
= $true )
| ( ( SV89 @ ( least_a @ less_eq @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2537,plain,
! [SV420: a,SV264: a,SV103: a > $o] :
( ( ( SV103 @ SV264 )
= $false )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(2538,plain,
! [SV420: a,SV264: a,SV436: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV436 ) )
= $true )
| ( ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SV436 )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2539,plain,
! [SV420: a,SV264: a,SV435: a,SV103: a > $o] :
( ( ( SV103 @ SV435 )
= $false )
| ( ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SV435 )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(2540,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( modula1376131916tice_a @ inf @ less @ sup @ SV168 @ SV327 @ SV412 )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2534]) ).
thf(2541,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2535]) ).
thf(2542,plain,
! [SV420: a,SV264: a,SV436: a,SV103: a > $o] :
( ( ( SV103 @ SV436 )
= $false )
| ( ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SV436 )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( ~ ( SV103 @ SV264 )
| ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2543,plain,
! [SV435: a,SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV264 ) )
= $true )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SV435 )
= $true )
| ( ( SV103 @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2544,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
| ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2545,plain,
! [SV436: a,SV420: a,SV264: a,SV103: a > $o] :
( ( ( ~ ( SV103 @ SV264 ) )
= $true )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SV436 )
= $true )
| ( ( SV103 @ SV436 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2542]) ).
thf(2546,plain,
! [SV435: a,SV420: a,SV264: a,SV103: a > $o] :
( ( ( SV103 @ SV264 )
= $false )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( less_eq @ SV420 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $false )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ ( sK43_SY907 @ SV264 @ SV420 @ SV103 ) @ SV435 )
= $true )
| ( ( SV103 @ SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2547,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2548,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2549,plain,
! [SV436: a,SV420: a,SV264: a,SV103: a > $o] :
( ( ( SV103 @ SV264 )
= $false )
| ( ( less_eq @ ( least_a @ less_eq @ SV103 ) @ SV264 )
= $true )
| ( ( SV103 @ ( sK32_SY906 @ SV264 @ SV420 @ SV103 ) )
= $true )
| ( ( SV103 @ SV420 )
= $false )
| ( ( less_eq @ ( sK44_SY907 @ SV264 @ SV420 @ SV103 ) @ SV436 )
= $true )
| ( ( SV103 @ SV436 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2550,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2547]) ).
thf(2551,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2552,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
| ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2553,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2554,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( sup @ SV412 @ SV168 )
!= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2555,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2553]) ).
thf(2556,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2554]) ).
thf(2557,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
| ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2558,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2557]) ).
thf(2559,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( sup @ SV168 @ SV327 )
!= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2557]) ).
thf(2560,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ~ ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2561,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2559]) ).
thf(2562,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
| ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2563,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( inf @ SV168 @ SV327 )
!= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2562]) ).
thf(2564,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( inf @ SV412 @ SV168 )
!= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2562]) ).
thf(2565,plain,
! [SV412: a,SV327: a,SV168: a] :
( ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2563]) ).
thf(2566,plain,
! [SV327: a,SV168: a,SV412: a] :
( ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $true )
| ( ( ( sup @ SV412 @ SV168 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV412 @ SV168 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( inf @ SV168 @ SV327 )
= ( inf @ SV327 @ SV412 ) )
= $false )
| ( ( ( sup @ SV168 @ SV327 )
= ( sup @ SV327 @ SV412 ) )
= $false )
| ( ( less @ ( inf @ SV168 @ SV327 ) @ ( sup @ SV168 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2564]) ).
thf(2567,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[443,2566,2565,2561,2556,2551,2549,2546,2540,2537,2536,2532,2529,2526,2525,2509,2507,2506,2502,2499,2493,2491,2480,2479,2471,2469,2468,2466,2465,2463,2462,2461,2460,2454,2446,2445,2441,2440,2438,2437,2435,2434,2432,2429,2426,2425,2424,2423,2420,2419,2418,2417,2416,2415,2412,2411,2401,2394,2393,2392,2391,2389,2386,2385,2383,2379,2369,2367,2365,2359,2358,2317,2312,2310,2303,2301,2290,2286,2284,2278,2273,2271,2266,2265,2263,2260,2258,2254,2252,2250,2247,2246,2244,2242,2239,2236,2235,2231,2230,2227,2226,2224,2222,2220,2216,2215,2213,2212,2210,2204,2198,2190,2189,2186,2185,2182,2180,2174,2173,2170,2166,2155,2152,2149,2128,2115,2105,2101,2093,2092,2088,2087,2086,2085,2084,2081,2038,2034,2033,2032,2031,2030,2027,2026,2012,2011,2010,2009,2008,2007,2004,2001,1996,1982,1979,1971,1942,1941,1940,1939,1937,1935,1934,1932,1930,1929,1927,1925,1924,1915,1905,1904,1891,1885,1882,1878,1864,1859,1854,1853,1852,1851,1850,1849,1848,1847,1846,1845,1844,1843,1842,1841,1840,1839,1838,1837,1836,1835,1834,1833,1832,1831,1830,1829,1828,1827,1826,1825,1824,1823,1817,1811,1805,1802,1799,1798,1789,1785,1784,1783,1782,1781,1780,1779,1777,1776,1768,1767,1761,1760,1759,1758,1755,1741,1738,1737,1677,1673,1659,1656,1651,1649,1644,1643,1642,1641,1634,1631,1626,1623,1617,1613,1611,1610,1606,1605,1603,1595,1594,1593,1535,1534,1518,1511,1502,1489,1453,1450,1446,1442,1440,1433,1432,1431,1427,1411,1407,1406,1404,1396,1395,1393,1389,1388,1385,1380,1379,1375,1373,1368,1352,1348,1342,1338,1327,1322,1321,1307,1305,1303,1301,1286,1285,1284,1277,1270,1269,1263,1262,1260,1255,1253,1242,1222,1214,1179,1163,1159,1153,1143,1129,1126,1119,1117,1116,1115,1114,1113,1112,1111,1110,1109,1108,1107,1106,1105,1104,1103,1102,1100,1099,1098,1096,1094,1092,1090,1088,1086,1084,1082,1080,1078,1076,1075,1074,1073,1072,1071,1070,1069,1056,1017,964,947,946,944,943,942,941,940,939,938,935,934,932,931,926,925,923,922,915,912,909,906,860,832,822,808,798,776,773,770,767,766,765,622,621,620,619,618,617,616,615,612,611,610,609,604,446,444]) ).
thf(2568,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2567]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP123^1 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.07/0.18 % Computer : n009.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 11:18:17 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 108.60/18.32 .
% 108.60/18.32
% 108.60/18.32 No.of.Axioms: 185
% 108.60/18.32
% 108.60/18.32 Length.of.Defs: 0
% 108.60/18.32
% 108.60/18.32 Contains.Choice.Funs: false
% 108.60/18.32 ..............................................................................
% 108.60/18.32
% 108.60/18.32 ********************************
% 108.60/18.32 * All subproblems solved! *
% 108.60/18.32 ********************************
% 108.60/18.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:185,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2567,loop_count:0,foatp_calls:1,translation:fof_full)
% 108.60/18.32
% 108.60/18.32 %**** Beginning of derivation protocol ****
% 108.60/18.32 % SZS output start CNFRefutation
% See solution above
% 108.60/18.34
% 108.60/18.34 %**** End of derivation protocol ****
% 108.60/18.34 %**** no. of clauses in derivation: 2500 ****
% 108.60/18.34 %**** clause counter: 2567 ****
% 108.60/18.34
% 108.60/18.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:185,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2567,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------