%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP122^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:43 AM UTC 2026
% Result : Theorem 12.21s 3.20s
% Output : Refutation 12.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 161 ( 88 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 1428 ( 43 ~; 16 |; 0 &;1366 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 12 con; 0-5 aty)
% Number of variables : 93 ( 0 ^; 93 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
set_a: $tType ).
thf(func_def_0,type,
set_a: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
thf(func_def_3,type,
condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
thf(func_def_4,type,
finite40241356em_a_a: ( a > a > a ) > $o ).
thf(func_def_5,type,
finite_finite_a: set_a > $o ).
thf(func_def_6,type,
abel_semigroup_a: ( a > a > a ) > $o ).
thf(func_def_7,type,
semigroup_a: ( a > a > a ) > $o ).
thf(func_def_8,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(func_def_9,type,
semilattice_a: ( a > a > a ) > $o ).
thf(func_def_10,type,
lattic247676691_fin_a: ( a > a > a ) > set_a > a ).
thf(func_def_11,type,
lattic1885654924_set_a: ( a > a > a ) > $o ).
thf(func_def_12,type,
lattic1781219155_fin_a: ( a > a > a ) > set_a > a ).
thf(func_def_13,type,
modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_14,type,
modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_15,type,
modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_16,type,
modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_17,type,
modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_18,type,
modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
thf(func_def_19,type,
bot_bot_set_a: set_a ).
thf(func_def_20,type,
least_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_21,type,
max_a: ( a > a > $o ) > a > a > a ).
thf(func_def_22,type,
min_a: ( a > a > $o ) > a > a > a ).
thf(func_def_23,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_24,type,
greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_25,type,
antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
thf(func_def_26,type,
mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
thf(func_def_27,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_28,type,
insert_a: a > set_a > set_a ).
thf(func_def_29,type,
set_atLeast_a: ( a > a > $o ) > a > set_a ).
thf(func_def_30,type,
set_atMost_a: ( a > a > $o ) > a > set_a ).
thf(func_def_31,type,
member_a: a > set_a > $o ).
thf(func_def_32,type,
a2: a ).
thf(func_def_33,type,
b: a ).
thf(func_def_34,type,
c: a ).
thf(func_def_35,type,
inf: a > a > a ).
thf(func_def_36,type,
less_eq: a > a > $o ).
thf(func_def_37,type,
sup: a > a > a ).
thf(func_def_52,type,
sK0: ( a > a > a ) > a ).
thf(func_def_53,type,
sK1: ( a > a > a ) > a ).
thf(func_def_54,type,
sK2: ( a > a > a ) > a ).
thf(func_def_55,type,
sK3: ( a > a > a ) > a ).
thf(func_def_56,type,
sK4: ( a > a > a ) > a ).
thf(func_def_57,type,
sK5: ( a > a > a ) > a ).
thf(func_def_58,type,
sK6: ( a > a > a ) > a ).
thf(func_def_59,type,
sK7: ( a > a > a ) > a ).
thf(func_def_60,type,
sK8: ( a > a > a ) > a ).
thf(func_def_61,type,
sK9: ( a > a > a ) > a ).
thf(func_def_62,type,
sK10: ( a > a > a ) > a ).
thf(func_def_63,type,
sK11: ( a > a > a ) > a ).
thf(func_def_64,type,
sK12: ( a > a > a ) > a ).
thf(func_def_65,type,
sK13: ( a > a > a ) > a ).
thf(func_def_66,type,
sK14: a ).
thf(func_def_67,type,
sK15: a ).
thf(func_def_68,type,
sK16: a ).
thf(func_def_69,type,
sK17: a ).
thf(func_def_70,type,
sK18: a ).
thf(func_def_71,type,
sK19: a ).
thf(func_def_73,type,
ph21:
!>[X0: $tType] : X0 ).
thf(f1077,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1076,f921]) ).
thf(f921,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f920,f836]) ).
thf(f836,plain,
! [X0: a,X1: a] :
( ( inf @ X0 @ X1 )
= ( inf @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f648]) ).
thf(f648,plain,
! [X0: a,X1: a] :
( ( inf @ X0 @ X1 )
= ( inf @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
! [X3: a,X2: a] :
( ( inf @ X3 @ X2 )
= ( inf @ X2 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_14_local_Oinf_Ocommute) ).
thf(f920,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ a2 @ c ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f917,f881]) ).
thf(f881,plain,
! [X0: a,X1: a] :
( ( sup @ X0 @ X1 )
= ( sup @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f671]) ).
thf(f671,plain,
! [X0: a,X1: a] :
( ( sup @ X0 @ X1 )
= ( sup @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,axiom,
! [X1: a,X0: a] :
( ( sup @ X0 @ X1 )
= ( sup @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_23_local_Osup__commute) ).
thf(f917,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ a2 @ c ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ a2 @ c ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f906,f881]) ).
thf(f906,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ a2 @ c ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ c @ a2 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f904,f836]) ).
thf(f904,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ c @ a2 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f903,f843]) ).
thf(f843,plain,
! [X2: a,X0: a,X1: a] :
( ( sup @ ( sup @ X2 @ X0 ) @ X1 )
= ( sup @ X2 @ ( sup @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f668]) ).
thf(f668,plain,
! [X0: a,X1: a,X2: a] :
( ( sup @ ( sup @ X2 @ X0 ) @ X1 )
= ( sup @ X2 @ ( sup @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,axiom,
! [X1: a,X11: a,X0: a] :
( ( sup @ ( sup @ X0 @ X1 ) @ X11 )
= ( sup @ X0 @ ( sup @ X1 @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_22_local_Osup__assoc) ).
thf(f903,plain,
( ( less_eq @ ( sup @ ( sup @ ( inf @ a2 @ b ) @ ( inf @ b @ c ) ) @ ( inf @ c @ a2 ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ c @ a2 ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f902,f866]) ).
thf(f866,plain,
! [X2: a,X0: a,X1: a] :
( ( inf @ ( inf @ X0 @ X1 ) @ X2 )
= ( inf @ X0 @ ( inf @ X1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f657]) ).
thf(f657,plain,
! [X0: a,X1: a,X2: a] :
( ( inf @ ( inf @ X0 @ X1 ) @ X2 )
= ( inf @ X0 @ ( inf @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,axiom,
! [X0: a,X1: a,X11: a] :
( ( inf @ ( inf @ X0 @ X1 ) @ X11 )
= ( inf @ X0 @ ( inf @ X1 @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_16_local_Oinf__assoc) ).
thf(f902,plain,
( ( less_eq @ ( sup @ ( sup @ ( inf @ a2 @ b ) @ ( inf @ b @ c ) ) @ ( inf @ c @ a2 ) ) @ ( inf @ ( inf @ ( sup @ a2 @ b ) @ ( sup @ b @ c ) ) @ ( sup @ c @ a2 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f901,f808]) ).
thf(f808,plain,
! [X2: a,X0: a,X1: a] :
( ( inf @ ( inf @ ( sup @ X2 @ X1 ) @ ( sup @ X1 @ X0 ) ) @ ( sup @ X0 @ X2 ) )
= ( modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f643]) ).
thf(f643,plain,
! [X0: a,X1: a,X2: a] :
( ( inf @ ( inf @ ( sup @ X2 @ X1 ) @ ( sup @ X1 @ X0 ) ) @ ( sup @ X0 @ X2 ) )
= ( modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,axiom,
! [X8: a,X2: a,X3: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( inf @ ( inf @ ( sup @ X3 @ X2 ) @ ( sup @ X2 @ X8 ) ) @ ( sup @ X8 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_92_local_Oe__aux__def) ).
thf(f901,plain,
( ( less_eq @ ( sup @ ( sup @ ( inf @ a2 @ b ) @ ( inf @ b @ c ) ) @ ( inf @ c @ a2 ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f830,f879]) ).
thf(f879,plain,
! [X2: a,X0: a,X1: a] :
( ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 )
= ( sup @ ( sup @ ( inf @ X2 @ X0 ) @ ( inf @ X0 @ X1 ) ) @ ( inf @ X1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f632]) ).
thf(f632,plain,
! [X0: a,X1: a,X2: a] :
( ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 )
= ( sup @ ( sup @ ( inf @ X2 @ X0 ) @ ( inf @ X0 @ X1 ) ) @ ( inf @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f87]) ).
thf(f87,axiom,
! [X2: a,X8: a,X3: a] :
( ( modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( sup @ ( sup @ ( inf @ X3 @ X2 ) @ ( inf @ X2 @ X8 ) ) @ ( inf @ X8 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_86_local_Od__aux__def) ).
thf(f830,plain,
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f262]) ).
thf(f262,plain,
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) )
= $true ),
inference(fool_elimination,[status(thm)],[f261]) ).
thf(f261,plain,
less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ),
inference(rectify,[status(thm)],[f255]) ).
thf(f255,axiom,
less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',conj_0) ).
thf(f1076,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1075,f836]) ).
thf(f1075,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ a2 @ c ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1074,f881]) ).
thf(f1074,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ c @ a2 ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1073,f866]) ).
thf(f1073,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( inf @ ( sup @ a2 @ b ) @ ( sup @ b @ c ) ) @ ( sup @ c @ a2 ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1072,f808]) ).
thf(f1072,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1071,f852]) ).
thf(f852,plain,
! [X2: a,X0: a,X1: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 )
= ( modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f645]) ).
thf(f645,plain,
! [X0: a,X1: a,X2: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 )
= ( modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f94]) ).
thf(f94,axiom,
! [X3: a,X8: a,X2: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( modula1144073633_aux_a @ inf @ sup @ X2 @ X8 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_93_local_Oe__b__c__a) ).
thf(f1071,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1070,f852]) ).
thf(f1070,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1069]) ).
thf(f1069,plain,
( ( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true )
| ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1068,f836]) ).
thf(f1068,plain,
( ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ a2 @ c ) ) )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) ) )
| ( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1067,f881]) ).
thf(f1067,plain,
( ( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ a2 @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true )
| ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ a2 @ c ) ) )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1066,f881]) ).
thf(f1066,plain,
( ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ c @ a2 ) ) ) )
| ( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ a2 @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1065,f836]) ).
thf(f1065,plain,
( ( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true )
| ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ c @ a2 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1064,f866]) ).
thf(f1064,plain,
( ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) )
!= ( inf @ ( inf @ ( sup @ a2 @ b ) @ ( sup @ b @ c ) ) @ ( sup @ c @ a2 ) ) )
| ( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1063,f843]) ).
thf(f1063,plain,
( ( ( less_eq @ ( sup @ ( sup @ ( inf @ a2 @ b ) @ ( inf @ b @ c ) ) @ ( inf @ c @ a2 ) ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true )
| ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) )
!= ( inf @ ( inf @ ( sup @ a2 @ b ) @ ( sup @ b @ c ) ) @ ( sup @ c @ a2 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1062,f879]) ).
thf(f1062,plain,
( ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true )
| ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) )
!= ( inf @ ( inf @ ( sup @ a2 @ b ) @ ( sup @ b @ c ) ) @ ( sup @ c @ a2 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1061,f808]) ).
thf(f1061,plain,
( ( ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) ) )
| ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1060,f822]) ).
thf(f822,plain,
! [X2: a,X0: a,X1: a] :
( ( modula1936294176_aux_a @ inf @ sup @ X2 @ X1 @ X0 )
= ( modula1936294176_aux_a @ inf @ sup @ X1 @ X0 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f636]) ).
thf(f636,plain,
! [X0: a,X1: a,X2: a] :
( ( modula1936294176_aux_a @ inf @ sup @ X2 @ X1 @ X0 )
= ( modula1936294176_aux_a @ inf @ sup @ X1 @ X0 @ X2 ) ),
inference(rectify,[status(thm)],[f89]) ).
thf(f89,axiom,
! [X2: a,X3: a,X8: a] :
( ( modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( modula1936294176_aux_a @ inf @ sup @ X8 @ X3 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_88_local_Od__c__a__b) ).
thf(f1060,plain,
( ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true )
| ( ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1059,f852]) ).
thf(f1059,plain,
( ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) )
!= ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
| ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1058,f822]) ).
thf(f1058,plain,
( ( $true
!= ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) ) )
| ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) )
!= ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) ) ),
inference(forward_demodulation,[status(thm)],[f1051,f852]) ).
thf(f1051,plain,
( ( ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) )
!= ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) )
| ( $true
!= ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) ) ) ),
inference(superposition,[status(thm)],[f919,f938]) ).
thf(f938,plain,
! [X2: a,X0: a,X1: a] :
( ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ X0 @ X1 @ X2 ) @ ( modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X0 ) )
= ( modula1144073633_aux_a @ inf @ sup @ X0 @ X1 @ X2 ) )
| ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X0 @ X1 @ X2 ) @ ( modula1144073633_aux_a @ inf @ sup @ X0 @ X1 @ X2 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f853,f797]) ).
thf(f797,plain,
! [X2: a,X0: a,X1: a] :
( ( modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1 )
= ( modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f673]) ).
thf(f673,plain,
! [X0: a,X1: a,X2: a] :
( ( modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1 )
= ( modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X0 ) ),
inference(rectify,[status(thm)],[f133]) ).
thf(f133,axiom,
! [X8: a,X3: a,X2: a] :
( ( modula1373251614_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( modula17988509_aux_a @ inf @ sup @ X2 @ X8 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_132_local_Ob__a) ).
thf(f853,plain,
! [X2: a,X0: a,X1: a] :
( ( ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 )
= ( sup @ ( modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) @ ( modula1373251614_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) ) )
| ( $true
!= ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) @ ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f693]) ).
thf(f693,plain,
! [X0: a,X1: a,X2: a] :
( ( ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 )
= ( sup @ ( modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) @ ( modula1373251614_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) ) )
| ( $true
!= ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) @ ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f345]) ).
thf(f345,plain,
! [X0: a,X1: a,X2: a] :
( ( $true
= ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) @ ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) ) )
=> ( ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 )
= ( sup @ ( modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) @ ( modula1373251614_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f344]) ).
thf(f344,plain,
! [X0: a,X1: a,X2: a] :
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) @ ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) )
=> ( ( modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1 )
= ( sup @ ( modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) @ ( modula1373251614_aux_a @ inf @ sup @ X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f136]) ).
thf(f136,axiom,
! [X3: a,X8: a,X2: a] :
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8 ) @ ( modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8 ) )
=> ( ( modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( sup @ ( modula17988509_aux_a @ inf @ sup @ X3 @ X2 @ X8 ) @ ( modula1373251614_aux_a @ inf @ sup @ X3 @ X2 @ X8 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_135_a__join__b__eq__e) ).
thf(f919,plain,
( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ a2 @ c ) @ ( sup @ b @ c ) ) ) ),
inference(forward_demodulation,[status(thm)],[f918,f836]) ).
thf(f918,plain,
( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ a2 @ c ) ) ) ),
inference(backward_demodulation,[status(thm)],[f892,f881]) ).
thf(f892,plain,
( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) )
!= ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ b @ c ) @ ( sup @ c @ a2 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f891,f866]) ).
thf(f891,plain,
( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) )
!= ( inf @ ( inf @ ( sup @ a2 @ b ) @ ( sup @ b @ c ) ) @ ( sup @ c @ a2 ) ) ),
inference(backward_demodulation,[status(thm)],[f792,f808]) ).
thf(f792,plain,
( ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(cnf_transformation,[status(thm)],[f629]) ).
thf(f629,plain,
( ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(flattening,[status(thm)],[f257]) ).
thf(f257,negated_conjecture,
( ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(negated_conjecture,[status(cth)],[f256]) ).
thf(f256,conjecture,
( ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c )
= ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP122^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n004.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:26:56 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP122^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer Modular_Distrib_Lattice problem prob_265__3262952_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : Modular_Distrib_Lattice/prob_265__3262952_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 294 ( 126 unt; 38 typ; 0 def)
% 0.30/0.46 % Number of atoms : 639 ( 205 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.30/0.46 % Number of connectives : 2161 ( 35 ~; 0 |; 29 &;1841 @)
% 0.30/0.46 % ( 0 <=>; 256 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 16 ( 6 avg)
% 0.30/0.46 % Number of types : 3 ( 2 usr)
% 0.30/0.46 % Number of type conns : 188 ( 188 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 37 ( 36 usr; 4 con; 0-5 aty)
% 0.30/0.46 % Number of variables : 615 ( 22 ^; 585 !; 8 ?; 615 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:44:43.847
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (2)
% 0.30/0.46 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 set_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (36)
% 0.30/0.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a,type,
% 0.30/0.46 condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a,type,
% 0.30/0.46 condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 0.30/0.46 finite40241356em_a_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
% 0.30/0.46 finite_finite_a: set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 0.30/0.46 abel_semigroup_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 0.30/0.46 semigroup_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 inf_inf_set_a: set_a > set_a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 0.30/0.46 semilattice_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin_001tf__a,type,
% 0.30/0.46 lattic247676691_fin_a: ( a > a > a ) > set_a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 0.30/0.46 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin_001tf__a,type,
% 0.30/0.46 lattic1781219155_fin_a: ( a > a > a ) > set_a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 0.30/0.46 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 0.30/0.46 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 0.30/0.46 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 0.30/0.46 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 0.30/0.46 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oincomp_001tf__a,type,
% 0.30/0.46 modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 bot_bot_set_a: set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord_OLeast_001tf__a,type,
% 0.30/0.46 least_a: ( a > a > $o ) > ( a > $o ) > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord_Omax_001tf__a,type,
% 0.30/0.46 max_a: ( a > a > $o ) > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord_Omin_001tf__a,type,
% 0.30/0.46 min_a: ( a > a > $o ) > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder_OGreatest_001tf__a,type,
% 0.30/0.46 greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder_Oantimono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder_Omono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.30/0.46 collect_a: ( a > $o ) > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.30/0.46 insert_a: a > set_a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set__Interval_Oord_OatLeast_001tf__a,type,
% 0.30/0.46 set_atLeast_a: ( a > a > $o ) > a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set__Interval_Oord_OatMost_001tf__a,type,
% 0.30/0.46 set_atMost_a: ( a > a > $o ) > a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001tf__a,type,
% 0.30/0.46 member_a: a > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_a,type,
% 0.30/0.46 a2: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_b,type,
% 0.30/0.46 b: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_c,type,
% 0.30/0.46 c: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_inf,type,
% 0.30/0.46 inf: a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_less__eq,type,
% 0.30/0.46 less_eq: a > a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_sup,type,
% 0.30/0.46 sup: a > a > a ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (254)
% 0.30/0.46 thf(fact_0_local_Oantisym,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antisym
% 0.30/0.46 thf(fact_1_local_Oantisym__conv,axiom,
% 0.30/0.46 ! [Y: a,X: a] :
% 0.30/0.46 ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antisym_conv
% 0.30/0.46 thf(fact_2_local_Odual__order_Oantisym,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( less_eq @ A @ B )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.dual_order.antisym
% 0.30/0.46 thf(fact_3_local_Odual__order_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.30/0.46 = ( ^ [A2: a,B2: a] :
% 0.30/0.46 ( ( less_eq @ B2 @ A2 )
% 0.30/0.46 & ( less_eq @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.dual_order.eq_iff
% 0.30/0.46 thf(fact_4_local_Odual__order_Otrans,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( less_eq @ C @ B )
% 0.30/0.46 => ( less_eq @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.dual_order.trans
% 0.30/0.46 thf(fact_5_local_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.30/0.46 = ( ^ [X2: a,Y3: a] :
% 0.30/0.46 ( ( less_eq @ X2 @ Y3 )
% 0.30/0.46 & ( less_eq @ Y3 @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.eq_iff
% 0.30/0.46 thf(fact_6_local_Oeq__refl,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( X = Y )
% 0.30/0.46 => ( less_eq @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.eq_refl
% 0.30/0.46 thf(fact_7_local_Oord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( less_eq @ B @ C )
% 0.30/0.46 => ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.ord_eq_le_trans
% 0.30/0.46 thf(fact_8_local_Oord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( B = C )
% 0.30/0.46 => ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.ord_le_eq_trans
% 0.30/0.46 thf(fact_9_local_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( less_eq @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.order.antisym
% 0.30/0.46 thf(fact_10_local_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.30/0.46 = ( ^ [A2: a,B2: a] :
% 0.30/0.46 ( ( less_eq @ A2 @ B2 )
% 0.30/0.46 & ( less_eq @ B2 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.order.eq_iff
% 0.30/0.46 thf(fact_11_local_Oorder_Otrans,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( less_eq @ B @ C )
% 0.30/0.46 => ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.order.trans
% 0.30/0.46 thf(fact_12_local_Oorder__trans,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( less_eq @ Y @ Z2 )
% 0.30/0.46 => ( less_eq @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.order_trans
% 0.30/0.46 thf(fact_13_local_Oinf_Oassoc,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( inf @ ( inf @ A @ B ) @ C )
% 0.30/0.46 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.assoc
% 0.30/0.46 thf(fact_14_local_Oinf_Ocommute,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( inf @ A @ B )
% 0.30/0.46 = ( inf @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.commute
% 0.30/0.46 thf(fact_15_local_Oinf_Oleft__commute,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( inf @ B @ ( inf @ A @ C ) )
% 0.30/0.46 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.left_commute
% 0.30/0.46 thf(fact_16_local_Oinf__assoc,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( inf @ ( inf @ X @ Y ) @ Z2 )
% 0.30/0.46 = ( inf @ X @ ( inf @ Y @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_assoc
% 0.30/0.46 thf(fact_17_local_Oinf__commute,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( inf @ X @ Y )
% 0.30/0.46 = ( inf @ Y @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_commute
% 0.30/0.46 thf(fact_18_local_Oinf__left__commute,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( inf @ X @ ( inf @ Y @ Z2 ) )
% 0.30/0.46 = ( inf @ Y @ ( inf @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_left_commute
% 0.30/0.46 thf(fact_19_local_Osup_Oassoc,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( sup @ ( sup @ A @ B ) @ C )
% 0.30/0.46 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.assoc
% 0.30/0.46 thf(fact_20_local_Osup_Ocommute,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( sup @ A @ B )
% 0.30/0.46 = ( sup @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.commute
% 0.30/0.46 thf(fact_21_local_Osup_Oleft__commute,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( sup @ B @ ( sup @ A @ C ) )
% 0.30/0.46 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.left_commute
% 0.30/0.46 thf(fact_22_local_Osup__assoc,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( sup @ ( sup @ X @ Y ) @ Z2 )
% 0.30/0.46 = ( sup @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_assoc
% 0.30/0.46 thf(fact_23_local_Osup__commute,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( sup @ X @ Y )
% 0.30/0.46 = ( sup @ Y @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_commute
% 0.30/0.46 thf(fact_24_local_Osup__left__commute,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( sup @ X @ ( sup @ Y @ Z2 ) )
% 0.30/0.46 = ( sup @ Y @ ( sup @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_left_commute
% 0.30/0.46 thf(fact_25_local_Oinf_Oabsorb1,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( inf @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.absorb1
% 0.30/0.46 thf(fact_26_local_Oinf_Oabsorb2,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( inf @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.absorb2
% 0.30/0.46 thf(fact_27_local_Oinf_Oabsorb__iff1,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 = ( ( inf @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.absorb_iff1
% 0.30/0.46 thf(fact_28_local_Oinf_Oabsorb__iff2,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 = ( ( inf @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.absorb_iff2
% 0.30/0.46 thf(fact_29_local_Oinf_OboundedE,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 0.30/0.46 => ~ ( ( less_eq @ A @ B )
% 0.30/0.46 => ~ ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.boundedE
% 0.30/0.46 thf(fact_30_local_Oinf_OboundedI,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( less_eq @ A @ C )
% 0.30/0.46 => ( less_eq @ A @ ( inf @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.boundedI
% 0.30/0.46 thf(fact_31_local_Oinf_Ocobounded1,axiom,
% 0.30/0.46 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.cobounded1
% 0.30/0.46 thf(fact_32_local_Oinf_Ocobounded2,axiom,
% 0.30/0.46 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.cobounded2
% 0.30/0.46 thf(fact_33_local_Oinf_OcoboundedI1,axiom,
% 0.30/0.46 ! [A: a,C: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ C )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.coboundedI1
% 0.30/0.46 thf(fact_34_local_Oinf_OcoboundedI2,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ C )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.coboundedI2
% 0.30/0.46 thf(fact_35_local_Oinf_OorderE,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( A
% 0.30/0.46 = ( inf @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.orderE
% 0.30/0.46 thf(fact_36_local_Oinf_OorderI,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( inf @ A @ B ) )
% 0.30/0.46 => ( less_eq @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.orderI
% 0.30/0.46 thf(fact_37_local_Oinf_Oorder__iff,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 = ( A
% 0.30/0.46 = ( inf @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.order_iff
% 0.30/0.46 thf(fact_38_local_Oinf__absorb1,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( inf @ X @ Y )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_absorb1
% 0.30/0.46 thf(fact_39_local_Oinf__absorb2,axiom,
% 0.30/0.46 ! [Y: a,X: a] :
% 0.30/0.46 ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( ( inf @ X @ Y )
% 0.30/0.46 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_absorb2
% 0.30/0.46 thf(fact_40_local_Oinf__greatest,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( less_eq @ X @ Z2 )
% 0.30/0.46 => ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_greatest
% 0.30/0.46 thf(fact_41_local_Oinf__le1,axiom,
% 0.30/0.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_le1
% 0.30/0.46 thf(fact_42_local_Oinf__le2,axiom,
% 0.30/0.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_le2
% 0.30/0.46 thf(fact_43_local_Oinf__mono,axiom,
% 0.30/0.46 ! [A: a,C: a,B: a,D: a] :
% 0.30/0.46 ( ( less_eq @ A @ C )
% 0.30/0.46 => ( ( less_eq @ B @ D )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_mono
% 0.30/0.46 thf(fact_44_local_Oinf__unique,axiom,
% 0.30/0.46 ! [F: a > a > a,X: a,Y: a] :
% 0.30/0.46 ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
% 0.30/0.46 => ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
% 0.30/0.46 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.30/0.46 ( ( less_eq @ X3 @ Y4 )
% 0.30/0.46 => ( ( less_eq @ X3 @ Z3 )
% 0.30/0.46 => ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 0.30/0.46 => ( ( inf @ X @ Y )
% 0.30/0.46 = ( F @ X @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_unique
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: a,P: a > $o] :
% 0.30/0.46 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.30/0.46 = ( P @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( collect_a
% 0.30/0.46 @ ^ [X2: a] : ( member_a @ X2 @ A3 ) )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [P: a > $o,Q: a > $o] :
% 0.30/0.46 ( ! [X3: a] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 = ( Q @ X3 ) )
% 0.30/0.46 => ( ( collect_a @ P )
% 0.30/0.46 = ( collect_a @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_local_Ole__iff__inf,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 = ( ( inf @ X @ Y )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_iff_inf
% 0.30/0.46 thf(fact_49_local_Ole__infE,axiom,
% 0.30/0.46 ! [X: a,A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ X @ ( inf @ A @ B ) )
% 0.30/0.46 => ~ ( ( less_eq @ X @ A )
% 0.30/0.46 => ~ ( less_eq @ X @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_infE
% 0.30/0.46 thf(fact_50_local_Ole__infI,axiom,
% 0.30/0.46 ! [X: a,A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ X @ A )
% 0.30/0.46 => ( ( less_eq @ X @ B )
% 0.30/0.46 => ( less_eq @ X @ ( inf @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_infI
% 0.30/0.46 thf(fact_51_local_Ole__infI1,axiom,
% 0.30/0.46 ! [A: a,X: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ X )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_infI1
% 0.30/0.46 thf(fact_52_local_Ole__infI2,axiom,
% 0.30/0.46 ! [B: a,X: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ X )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_infI2
% 0.30/0.46 thf(fact_53_local_Ole__iff__sup,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 = ( ( sup @ X @ Y )
% 0.30/0.46 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_iff_sup
% 0.30/0.46 thf(fact_54_local_Ole__supE,axiom,
% 0.30/0.46 ! [A: a,B: a,X: a] :
% 0.30/0.46 ( ( less_eq @ ( sup @ A @ B ) @ X )
% 0.30/0.46 => ~ ( ( less_eq @ A @ X )
% 0.30/0.46 => ~ ( less_eq @ B @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_supE
% 0.30/0.46 thf(fact_55_local_Ole__supI,axiom,
% 0.30/0.46 ! [A: a,X: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ X )
% 0.30/0.46 => ( ( less_eq @ B @ X )
% 0.30/0.46 => ( less_eq @ ( sup @ A @ B ) @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_supI
% 0.30/0.46 thf(fact_56_local_Ole__supI1,axiom,
% 0.30/0.46 ! [X: a,A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ X @ A )
% 0.30/0.46 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_supI1
% 0.30/0.46 thf(fact_57_local_Ole__supI2,axiom,
% 0.30/0.46 ! [X: a,B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ X @ B )
% 0.30/0.46 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_supI2
% 0.30/0.46 thf(fact_58_local_Osup_Oabsorb1,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( sup @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.absorb1
% 0.30/0.46 thf(fact_59_local_Osup_Oabsorb2,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( sup @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.absorb2
% 0.30/0.46 thf(fact_60_local_Osup_Oabsorb__iff1,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 = ( ( sup @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.absorb_iff1
% 0.30/0.46 thf(fact_61_local_Osup_Oabsorb__iff2,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 = ( ( sup @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.absorb_iff2
% 0.30/0.46 thf(fact_62_local_Osup_OboundedE,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 0.30/0.46 => ~ ( ( less_eq @ B @ A )
% 0.30/0.46 => ~ ( less_eq @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.boundedE
% 0.30/0.46 thf(fact_63_local_Osup_OboundedI,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( less_eq @ C @ A )
% 0.30/0.46 => ( less_eq @ ( sup @ B @ C ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.boundedI
% 0.30/0.46 thf(fact_64_local_Osup_Ocobounded1,axiom,
% 0.30/0.46 ! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.cobounded1
% 0.30/0.46 thf(fact_65_local_Osup_Ocobounded2,axiom,
% 0.30/0.46 ! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.cobounded2
% 0.30/0.46 thf(fact_66_local_Osup_OcoboundedI1,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ C @ A )
% 0.30/0.46 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.coboundedI1
% 0.30/0.46 thf(fact_67_local_Osup_OcoboundedI2,axiom,
% 0.30/0.46 ! [C: a,B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ C @ B )
% 0.30/0.46 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.coboundedI2
% 0.30/0.46 thf(fact_68_local_Osup_Omono,axiom,
% 0.30/0.46 ! [C: a,A: a,D: a,B: a] :
% 0.30/0.46 ( ( less_eq @ C @ A )
% 0.30/0.46 => ( ( less_eq @ D @ B )
% 0.30/0.46 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.mono
% 0.30/0.46 thf(fact_69_local_Osup_OorderE,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( A
% 0.30/0.46 = ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.orderE
% 0.30/0.46 thf(fact_70_local_Osup_OorderI,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( sup @ A @ B ) )
% 0.30/0.46 => ( less_eq @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.orderI
% 0.30/0.46 thf(fact_71_local_Osup_Oorder__iff,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 = ( A
% 0.30/0.46 = ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.order_iff
% 0.30/0.46 thf(fact_72_local_Osup__absorb1,axiom,
% 0.30/0.46 ! [Y: a,X: a] :
% 0.30/0.46 ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( ( sup @ X @ Y )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_absorb1
% 0.30/0.46 thf(fact_73_local_Osup__absorb2,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( sup @ X @ Y )
% 0.30/0.46 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_absorb2
% 0.30/0.46 thf(fact_74_local_Osup__ge1,axiom,
% 0.30/0.46 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_ge1
% 0.30/0.46 thf(fact_75_local_Osup__ge2,axiom,
% 0.30/0.46 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_ge2
% 0.30/0.46 thf(fact_76_local_Osup__least,axiom,
% 0.30/0.46 ! [Y: a,X: a,Z2: a] :
% 0.30/0.46 ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( ( less_eq @ Z2 @ X )
% 0.30/0.46 => ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_least
% 0.30/0.46 thf(fact_77_local_Osup__mono,axiom,
% 0.30/0.46 ! [A: a,C: a,B: a,D: a] :
% 0.30/0.46 ( ( less_eq @ A @ C )
% 0.30/0.46 => ( ( less_eq @ B @ D )
% 0.30/0.46 => ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_mono
% 0.30/0.46 thf(fact_78_local_Osup__unique,axiom,
% 0.30/0.46 ! [F: a > a > a,X: a,Y: a] :
% 0.30/0.46 ( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
% 0.30/0.46 => ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
% 0.30/0.46 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.30/0.46 ( ( less_eq @ Y4 @ X3 )
% 0.30/0.46 => ( ( less_eq @ Z3 @ X3 )
% 0.30/0.46 => ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
% 0.30/0.46 => ( ( sup @ X @ Y )
% 0.30/0.46 = ( F @ X @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_unique
% 0.30/0.46 thf(fact_79_local_Odistrib__imp1,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ! [X3: a,Y4: a,Z3: a] :
% 0.30/0.46 ( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
% 0.30/0.46 = ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
% 0.30/0.46 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.30/0.46 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.distrib_imp1
% 0.30/0.46 thf(fact_80_local_Odistrib__imp2,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ! [X3: a,Y4: a,Z3: a] :
% 0.30/0.46 ( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
% 0.30/0.46 = ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
% 0.30/0.46 => ( ( inf @ X @ ( sup @ Y @ Z2 ) )
% 0.30/0.46 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.distrib_imp2
% 0.30/0.46 thf(fact_81_local_Oa__join__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.a_join_d
% 0.30/0.46 thf(fact_82_a__meet__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % a_meet_d
% 0.30/0.46 thf(fact_83_local_Ob__join__d,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.b_join_d
% 0.30/0.46 thf(fact_84_b__meet__d,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( inf @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ ( inf @ B @ C ) @ ( inf @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % b_meet_d
% 0.30/0.46 thf(fact_85_c__meet__d,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( inf @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ ( inf @ C @ A ) @ ( inf @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % c_meet_d
% 0.30/0.46 thf(fact_86_local_Od__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.d_aux_def
% 0.30/0.46 thf(fact_87_local_Od__b__c__a,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.d_b_c_a
% 0.30/0.46 thf(fact_88_local_Od__c__a__b,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.d_c_a_b
% 0.30/0.46 thf(fact_89_local_Oa__meet__e,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.a_meet_e
% 0.30/0.46 thf(fact_90_local_Ob__meet__e,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.b_meet_e
% 0.30/0.46 thf(fact_91_local_Oc__meet__e,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.c_meet_e
% 0.30/0.46 thf(fact_92_local_Oe__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.e_aux_def
% 0.30/0.46 thf(fact_93_local_Oe__b__c__a,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 0.30/0.46 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.e_b_c_a
% 0.30/0.46 thf(fact_94_local_Oe__c__a__b,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 0.30/0.46 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.e_c_a_b
% 0.30/0.46 thf(fact_95_local_Odistrib__inf__le,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.distrib_inf_le
% 0.30/0.46 thf(fact_96_local_Odistrib__sup__le,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.distrib_sup_le
% 0.30/0.46 thf(fact_97_local_Omodular,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.30/0.46 = ( inf @ Y @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.modular
% 0.30/0.46 thf(fact_98_local_Oincomp__def,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( modula1727524044comp_a @ less_eq @ X @ Y )
% 0.30/0.46 = ( ~ ( less_eq @ X @ Y )
% 0.30/0.46 & ~ ( less_eq @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.incomp_def
% 0.30/0.46 thf(fact_99_local_Oorder_Orefl,axiom,
% 0.30/0.46 ! [A: a] : ( less_eq @ A @ A ) ).
% 0.30/0.46
% 0.30/0.46 % local.order.refl
% 0.30/0.46 thf(fact_100_local_Oorder__refl,axiom,
% 0.30/0.46 ! [X: a] : ( less_eq @ X @ X ) ).
% 0.30/0.46
% 0.30/0.46 % local.order_refl
% 0.30/0.46 thf(fact_101_local_Oinf_Oidem,axiom,
% 0.30/0.46 ! [A: a] :
% 0.30/0.46 ( ( inf @ A @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.idem
% 0.30/0.46 thf(fact_102_local_Oinf_Oleft__idem,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( inf @ A @ ( inf @ A @ B ) )
% 0.30/0.46 = ( inf @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.left_idem
% 0.30/0.46 thf(fact_103_local_Oinf_Oright__idem,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( inf @ ( inf @ A @ B ) @ B )
% 0.30/0.46 = ( inf @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.right_idem
% 0.30/0.46 thf(fact_104_local_Oinf__idem,axiom,
% 0.30/0.46 ! [X: a] :
% 0.30/0.46 ( ( inf @ X @ X )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_idem
% 0.30/0.46 thf(fact_105_local_Oinf__left__idem,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( inf @ X @ ( inf @ X @ Y ) )
% 0.30/0.46 = ( inf @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_left_idem
% 0.30/0.46 thf(fact_106_local_Oinf__right__idem,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 0.30/0.46 = ( inf @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_right_idem
% 0.30/0.46 thf(fact_107_local_Osup_Oidem,axiom,
% 0.30/0.46 ! [A: a] :
% 0.30/0.46 ( ( sup @ A @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.idem
% 0.30/0.46 thf(fact_108_local_Osup_Oleft__idem,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( sup @ A @ ( sup @ A @ B ) )
% 0.30/0.46 = ( sup @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.left_idem
% 0.30/0.46 thf(fact_109_local_Osup_Oright__idem,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( sup @ ( sup @ A @ B ) @ B )
% 0.30/0.46 = ( sup @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.right_idem
% 0.30/0.46 thf(fact_110_local_Osup__idem,axiom,
% 0.30/0.46 ! [X: a] :
% 0.30/0.46 ( ( sup @ X @ X )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_idem
% 0.30/0.46 thf(fact_111_local_Osup__left__idem,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( sup @ X @ ( sup @ X @ Y ) )
% 0.30/0.46 = ( sup @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_left_idem
% 0.30/0.46 thf(fact_112_local_OGreatestI2__order,axiom,
% 0.30/0.46 ! [P: a > $o,X: a,Q: a > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y4: a] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( less_eq @ Y4 @ X ) )
% 0.30/0.46 => ( ! [X3: a] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( ! [Y5: a] :
% 0.30/0.46 ( ( P @ Y5 )
% 0.30/0.46 => ( less_eq @ Y5 @ X3 ) )
% 0.30/0.46 => ( Q @ X3 ) ) )
% 0.30/0.46 => ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.GreatestI2_order
% 0.30/0.46 thf(fact_113_local_OGreatest__equality,axiom,
% 0.30/0.46 ! [P: a > $o,X: a] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y4: a] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( less_eq @ Y4 @ X ) )
% 0.30/0.46 => ( ( greatest_a @ less_eq @ P )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Greatest_equality
% 0.30/0.46 thf(fact_114_local_Omax__def,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( max_a @ less_eq @ A @ B )
% 0.30/0.46 = B ) )
% 0.30/0.46 & ( ~ ( less_eq @ A @ B )
% 0.30/0.46 => ( ( max_a @ less_eq @ A @ B )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.max_def
% 0.30/0.46 thf(fact_115_local_Omin__def,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( min_a @ less_eq @ A @ B )
% 0.30/0.46 = A ) )
% 0.30/0.46 & ( ~ ( less_eq @ A @ B )
% 0.30/0.46 => ( ( min_a @ less_eq @ A @ B )
% 0.30/0.46 = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.min_def
% 0.30/0.46 thf(fact_116_local_Oa__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.a_aux_def
% 0.30/0.46 thf(fact_117_a__def__equiv,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( inf @ ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % a_def_equiv
% 0.30/0.46 thf(fact_118_local_Oinf_Obounded__iff,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 0.30/0.46 = ( ( less_eq @ A @ B )
% 0.30/0.46 & ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.bounded_iff
% 0.30/0.46 thf(fact_119_local_Ole__inf__iff,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
% 0.30/0.46 = ( ( less_eq @ X @ Y )
% 0.30/0.46 & ( less_eq @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_inf_iff
% 0.30/0.46 thf(fact_120_local_Ole__sup__iff,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
% 0.30/0.46 = ( ( less_eq @ X @ Z2 )
% 0.30/0.46 & ( less_eq @ Y @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_sup_iff
% 0.30/0.46 thf(fact_121_local_Osup_Obounded__iff,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 0.30/0.46 = ( ( less_eq @ B @ A )
% 0.30/0.46 & ( less_eq @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.bounded_iff
% 0.30/0.46 thf(fact_122_local_Oinf__sup__absorb,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( inf @ X @ ( sup @ X @ Y ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_sup_absorb
% 0.30/0.46 thf(fact_123_local_Osup__inf__absorb,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( sup @ X @ ( inf @ X @ Y ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_inf_absorb
% 0.30/0.46 thf(fact_124_local_OLeast1I,axiom,
% 0.30/0.46 ! [P: a > $o] :
% 0.30/0.46 ( ? [X4: a] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 & ! [Y4: a] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( less_eq @ X4 @ Y4 ) )
% 0.30/0.46 & ! [Y4: a] :
% 0.30/0.46 ( ( ( P @ Y4 )
% 0.30/0.46 & ! [Ya: a] :
% 0.30/0.46 ( ( P @ Ya )
% 0.30/0.46 => ( less_eq @ Y4 @ Ya ) ) )
% 0.30/0.46 => ( Y4 = X4 ) ) )
% 0.30/0.46 => ( P @ ( least_a @ less_eq @ P ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Least1I
% 0.30/0.46 thf(fact_125_local_OLeast1__le,axiom,
% 0.30/0.46 ! [P: a > $o,Z2: a] :
% 0.30/0.46 ( ? [X4: a] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 & ! [Y4: a] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( less_eq @ X4 @ Y4 ) )
% 0.30/0.46 & ! [Y4: a] :
% 0.30/0.46 ( ( ( P @ Y4 )
% 0.30/0.46 & ! [Ya: a] :
% 0.30/0.46 ( ( P @ Ya )
% 0.30/0.46 => ( less_eq @ Y4 @ Ya ) ) )
% 0.30/0.46 => ( Y4 = X4 ) ) )
% 0.30/0.46 => ( ( P @ Z2 )
% 0.30/0.46 => ( less_eq @ ( least_a @ less_eq @ P ) @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Least1_le
% 0.30/0.46 thf(fact_126_local_OLeastI2__order,axiom,
% 0.30/0.46 ! [P: a > $o,X: a,Q: a > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y4: a] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( less_eq @ X @ Y4 ) )
% 0.30/0.46 => ( ! [X3: a] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( ! [Y5: a] :
% 0.30/0.46 ( ( P @ Y5 )
% 0.30/0.46 => ( less_eq @ X3 @ Y5 ) )
% 0.30/0.46 => ( Q @ X3 ) ) )
% 0.30/0.46 => ( Q @ ( least_a @ less_eq @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.LeastI2_order
% 0.30/0.46 thf(fact_127_local_OLeast__equality,axiom,
% 0.30/0.46 ! [P: a > $o,X: a] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y4: a] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( less_eq @ X @ Y4 ) )
% 0.30/0.46 => ( ( least_a @ less_eq @ P )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Least_equality
% 0.30/0.46 thf(fact_128_local_Oc__a,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.c_a
% 0.30/0.46 thf(fact_129_local_Oc__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.c_aux_def
% 0.30/0.46 thf(fact_130_c__def__equiv,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( inf @ ( sup @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % c_def_equiv
% 0.30/0.46 thf(fact_131_c__meet__a__eq__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( inf @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % c_meet_a_eq_d
% 0.30/0.46 thf(fact_132_local_Ob__a,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.b_a
% 0.30/0.46 thf(fact_133_local_Ob__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.b_aux_def
% 0.30/0.46 thf(fact_134_b__def__equiv,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( inf @ ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % b_def_equiv
% 0.30/0.46 thf(fact_135_a__join__b__eq__e,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % a_join_b_eq_e
% 0.30/0.46 thf(fact_136_a__meet__b__eq__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % a_meet_b_eq_d
% 0.30/0.46 thf(fact_137_lattice_Oa__aux_Ocong,axiom,
% 0.30/0.46 modula17988509_aux_a = modula17988509_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.a_aux.cong
% 0.30/0.46 thf(fact_138_lattice_Od__aux_Ocong,axiom,
% 0.30/0.46 modula1936294176_aux_a = modula1936294176_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.d_aux.cong
% 0.30/0.46 thf(fact_139_lattice_Oe__aux_Ocong,axiom,
% 0.30/0.46 modula1144073633_aux_a = modula1144073633_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.e_aux.cong
% 0.30/0.46 thf(fact_140_local_Ocomp__fun__idem__sup,axiom,
% 0.30/0.46 finite40241356em_a_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.comp_fun_idem_sup
% 0.30/0.46 thf(fact_141_local_Ocomp__fun__idem__inf,axiom,
% 0.30/0.46 finite40241356em_a_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.comp_fun_idem_inf
% 0.30/0.46 thf(fact_142_b__join__c__eq__e,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( sup @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % b_join_c_eq_e
% 0.30/0.46 thf(fact_143_b__meet__c__eq__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( inf @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % b_meet_c_eq_d
% 0.30/0.46 thf(fact_144_local_Osup_Osemigroup__axioms,axiom,
% 0.30/0.46 semigroup_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.sup.semigroup_axioms
% 0.30/0.46 thf(fact_145_local_Oinf_Osemigroup__axioms,axiom,
% 0.30/0.46 semigroup_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.inf.semigroup_axioms
% 0.30/0.46 thf(fact_146_local_Osup_Osemilattice__axioms,axiom,
% 0.30/0.46 semilattice_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.sup.semilattice_axioms
% 0.30/0.46 thf(fact_147_local_Oinf_Osemilattice__axioms,axiom,
% 0.30/0.46 semilattice_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.inf.semilattice_axioms
% 0.30/0.46 thf(fact_148_local_Osup_Oabel__semigroup__axioms,axiom,
% 0.30/0.46 abel_semigroup_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.sup.abel_semigroup_axioms
% 0.30/0.46 thf(fact_149_local_Oinf_Oabel__semigroup__axioms,axiom,
% 0.30/0.46 abel_semigroup_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.inf.abel_semigroup_axioms
% 0.30/0.46 thf(fact_150_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 0.30/0.46 lattic1885654924_set_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.semilattice_set_axioms
% 0.30/0.46 thf(fact_151_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 0.30/0.46 lattic1885654924_set_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.semilattice_set_axioms
% 0.30/0.46 thf(fact_152_lattice_Oincomp_Ocong,axiom,
% 0.30/0.46 modula1727524044comp_a = modula1727524044comp_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.incomp.cong
% 0.30/0.46 thf(fact_153_lattice_Oc__aux_Ocong,axiom,
% 0.30/0.46 modula581031071_aux_a = modula581031071_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.c_aux.cong
% 0.30/0.46 thf(fact_154_lattice_Ob__aux_Ocong,axiom,
% 0.30/0.46 modula1373251614_aux_a = modula1373251614_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.b_aux.cong
% 0.30/0.46 thf(fact_155_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ( abel_semigroup_a @ F )
% 0.30/0.46 => ( semigroup_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % abel_semigroup.axioms(1)
% 0.30/0.46 thf(fact_156_semilattice__set__def,axiom,
% 0.30/0.46 lattic1885654924_set_a = semilattice_a ).
% 0.30/0.46
% 0.30/0.46 % semilattice_set_def
% 0.30/0.46 thf(fact_157_semilattice__set_Ointro,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( lattic1885654924_set_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_set.intro
% 0.30/0.46 thf(fact_158_abel__semigroup_Oleft__commute,axiom,
% 0.30/0.46 ! [F: a > a > a,B: a,A: a,C: a] :
% 0.30/0.46 ( ( abel_semigroup_a @ F )
% 0.30/0.46 => ( ( F @ B @ ( F @ A @ C ) )
% 0.30/0.46 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % abel_semigroup.left_commute
% 0.30/0.46 thf(fact_159_abel__semigroup_Ocommute,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a,B: a] :
% 0.30/0.46 ( ( abel_semigroup_a @ F )
% 0.30/0.46 => ( ( F @ A @ B )
% 0.30/0.46 = ( F @ B @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % abel_semigroup.commute
% 0.30/0.46 thf(fact_160_semigroup_Ointro,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ! [A4: a,B3: a,C2: a] :
% 0.30/0.46 ( ( F @ ( F @ A4 @ B3 ) @ C2 )
% 0.30/0.46 = ( F @ A4 @ ( F @ B3 @ C2 ) ) )
% 0.30/0.46 => ( semigroup_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % semigroup.intro
% 0.30/0.46 thf(fact_161_semigroup_Oassoc,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.30/0.46 ( ( semigroup_a @ F )
% 0.30/0.46 => ( ( F @ ( F @ A @ B ) @ C )
% 0.30/0.46 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semigroup.assoc
% 0.30/0.46 thf(fact_162_semigroup__def,axiom,
% 0.30/0.46 ( semigroup_a
% 0.30/0.46 = ( ^ [F2: a > a > a] :
% 0.30/0.46 ! [A2: a,B2: a,C3: a] :
% 0.30/0.46 ( ( F2 @ ( F2 @ A2 @ B2 ) @ C3 )
% 0.30/0.46 = ( F2 @ A2 @ ( F2 @ B2 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semigroup_def
% 0.30/0.46 thf(fact_163_semilattice__set_Oaxioms,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ( lattic1885654924_set_a @ F )
% 0.30/0.46 => ( semilattice_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_set.axioms
% 0.30/0.46 thf(fact_164_semilattice_Oaxioms_I1_J,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( abel_semigroup_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice.axioms(1)
% 0.30/0.46 thf(fact_165_local_Obdd__above__def,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 0.30/0.46 = ( ? [M: a] :
% 0.30/0.46 ! [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A3 )
% 0.30/0.46 => ( less_eq @ X2 @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_def
% 0.30/0.46 thf(fact_166_local_Obdd__below__def,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 0.30/0.46 = ( ? [M2: a] :
% 0.30/0.46 ! [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A3 )
% 0.30/0.46 => ( less_eq @ M2 @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_def
% 0.30/0.46 thf(fact_167_local_Obdd__belowI,axiom,
% 0.30/0.46 ! [A3: set_a,M3: a] :
% 0.30/0.46 ( ! [X3: a] :
% 0.30/0.46 ( ( member_a @ X3 @ A3 )
% 0.30/0.46 => ( less_eq @ M3 @ X3 ) )
% 0.30/0.46 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_belowI
% 0.30/0.46 thf(fact_168_local_Obdd__aboveI,axiom,
% 0.30/0.46 ! [A3: set_a,M4: a] :
% 0.30/0.46 ( ! [X3: a] :
% 0.30/0.46 ( ( member_a @ X3 @ A3 )
% 0.30/0.46 => ( less_eq @ X3 @ M4 ) )
% 0.30/0.46 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_aboveI
% 0.30/0.46 thf(fact_169_semilattice_Oidem,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( ( F @ A @ A )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice.idem
% 0.30/0.46 thf(fact_170_semilattice_Oleft__idem,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a,B: a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( ( F @ A @ ( F @ A @ B ) )
% 0.30/0.46 = ( F @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice.left_idem
% 0.30/0.46 thf(fact_171_semilattice_Oright__idem,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a,B: a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( ( F @ ( F @ A @ B ) @ B )
% 0.30/0.46 = ( F @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice.right_idem
% 0.30/0.46 thf(fact_172_local_Obdd__above__mono,axiom,
% 0.30/0.46 ! [B4: set_a,A3: set_a] :
% 0.30/0.46 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.30/0.46 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_mono
% 0.30/0.46 thf(fact_173_local_Obdd__below__mono,axiom,
% 0.30/0.46 ! [B4: set_a,A3: set_a] :
% 0.30/0.46 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.30/0.46 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_mono
% 0.30/0.46 thf(fact_174_local_Obdd__above__finite,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_finite
% 0.30/0.46 thf(fact_175_local_Ofinite__has__maximal2,axiom,
% 0.30/0.46 ! [A3: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( member_a @ A @ A3 )
% 0.30/0.46 => ? [X3: a] :
% 0.30/0.46 ( ( member_a @ X3 @ A3 )
% 0.30/0.46 & ( less_eq @ A @ X3 )
% 0.30/0.46 & ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ A3 )
% 0.30/0.46 => ( ( less_eq @ X3 @ Xa )
% 0.30/0.46 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.finite_has_maximal2
% 0.30/0.46 thf(fact_176_local_Ofinite__has__minimal2,axiom,
% 0.30/0.46 ! [A3: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( member_a @ A @ A3 )
% 0.30/0.46 => ? [X3: a] :
% 0.30/0.46 ( ( member_a @ X3 @ A3 )
% 0.30/0.46 & ( less_eq @ X3 @ A )
% 0.30/0.46 & ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ A3 )
% 0.30/0.46 => ( ( less_eq @ Xa @ X3 )
% 0.30/0.46 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.finite_has_minimal2
% 0.30/0.46 thf(fact_177_local_Obdd__below__finite,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_finite
% 0.30/0.46 thf(fact_178_local_OantimonoD,axiom,
% 0.30/0.46 ! [F: a > set_a,X: a,Y: a] :
% 0.30/0.46 ( ( antimono_a_set_a @ less_eq @ F )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antimonoD
% 0.30/0.46 thf(fact_179_local_OantimonoE,axiom,
% 0.30/0.46 ! [F: a > set_a,X: a,Y: a] :
% 0.30/0.46 ( ( antimono_a_set_a @ less_eq @ F )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antimonoE
% 0.30/0.46 thf(fact_180_local_OantimonoI,axiom,
% 0.30/0.46 ! [F: a > set_a] :
% 0.30/0.46 ( ! [X3: a,Y4: a] :
% 0.30/0.46 ( ( less_eq @ X3 @ Y4 )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.30/0.46 => ( antimono_a_set_a @ less_eq @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antimonoI
% 0.30/0.46 thf(fact_181_local_Oantimono__def,axiom,
% 0.30/0.46 ! [F: a > set_a] :
% 0.30/0.46 ( ( antimono_a_set_a @ less_eq @ F )
% 0.30/0.46 = ( ! [X2: a,Y3: a] :
% 0.30/0.46 ( ( less_eq @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antimono_def
% 0.30/0.46 thf(fact_182_local_Omono__def,axiom,
% 0.30/0.46 ! [F: a > set_a] :
% 0.30/0.46 ( ( mono_a_set_a @ less_eq @ F )
% 0.30/0.46 = ( ! [X2: a,Y3: a] :
% 0.30/0.46 ( ( less_eq @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.mono_def
% 0.30/0.46 thf(fact_183_local_OmonoI,axiom,
% 0.30/0.46 ! [F: a > set_a] :
% 0.30/0.46 ( ! [X3: a,Y4: a] :
% 0.30/0.46 ( ( less_eq @ X3 @ Y4 )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( mono_a_set_a @ less_eq @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.monoI
% 0.30/0.46 thf(fact_184_local_OmonoE,axiom,
% 0.30/0.46 ! [F: a > set_a,X: a,Y: a] :
% 0.30/0.46 ( ( mono_a_set_a @ less_eq @ F )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.monoE
% 0.30/0.46 thf(fact_185_local_OmonoD,axiom,
% 0.30/0.46 ! [F: a > set_a,X: a,Y: a] :
% 0.30/0.46 ( ( mono_a_set_a @ less_eq @ F )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.monoD
% 0.30/0.46 thf(fact_186_local_OSup__fin_OcoboundedI,axiom,
% 0.30/0.46 ! [A3: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( member_a @ A @ A3 )
% 0.30/0.46 => ( less_eq @ A @ ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.coboundedI
% 0.30/0.46 thf(fact_187_local_OInf__fin_OcoboundedI,axiom,
% 0.30/0.46 ! [A3: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( member_a @ A @ A3 )
% 0.30/0.46 => ( less_eq @ ( lattic247676691_fin_a @ inf @ A3 ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.coboundedI
% 0.30/0.46 thf(fact_188_local_OSup__fin_Oin__idem,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( member_a @ X @ A3 )
% 0.30/0.46 => ( ( sup @ X @ ( lattic1781219155_fin_a @ sup @ A3 ) )
% 0.30/0.46 = ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.in_idem
% 0.30/0.46 thf(fact_189_local_OInf__fin_Oin__idem,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( member_a @ X @ A3 )
% 0.30/0.46 => ( ( inf @ X @ ( lattic247676691_fin_a @ inf @ A3 ) )
% 0.30/0.46 = ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.in_idem
% 0.30/0.46 thf(fact_190_local_Oinf__Sup__absorb,axiom,
% 0.30/0.46 ! [A3: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( member_a @ A @ A3 )
% 0.30/0.46 => ( ( inf @ A @ ( lattic1781219155_fin_a @ sup @ A3 ) )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_Sup_absorb
% 0.30/0.46 thf(fact_191_local_Osup__Inf__absorb,axiom,
% 0.30/0.46 ! [A3: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( member_a @ A @ A3 )
% 0.30/0.46 => ( ( sup @ ( lattic247676691_fin_a @ inf @ A3 ) @ A )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_Inf_absorb
% 0.30/0.46 thf(fact_192_semilattice__sup_OSup__fin_Ocong,axiom,
% 0.30/0.46 lattic1781219155_fin_a = lattic1781219155_fin_a ).
% 0.30/0.46
% 0.30/0.46 % semilattice_sup.Sup_fin.cong
% 0.30/0.46 thf(fact_193_semilattice__inf_OInf__fin_Ocong,axiom,
% 0.30/0.46 lattic247676691_fin_a = lattic247676691_fin_a ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf.Inf_fin.cong
% 0.30/0.46 thf(fact_194_local_OInf__fin__le__Sup__fin,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( less_eq @ ( lattic247676691_fin_a @ inf @ A3 ) @ ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin_le_Sup_fin
% 0.30/0.46 thf(fact_195_local_OSup__fin_Osubset__imp,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ( finite_finite_a @ B4 )
% 0.30/0.46 => ( less_eq @ ( lattic1781219155_fin_a @ sup @ A3 ) @ ( lattic1781219155_fin_a @ sup @ B4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.subset_imp
% 0.30/0.46 thf(fact_196_local_Ofinite__has__minimal,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ? [X3: a] :
% 0.30/0.46 ( ( member_a @ X3 @ A3 )
% 0.30/0.46 & ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ A3 )
% 0.30/0.46 => ( ( less_eq @ Xa @ X3 )
% 0.30/0.46 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.finite_has_minimal
% 0.30/0.46 thf(fact_197_local_Ofinite__has__maximal,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ? [X3: a] :
% 0.30/0.46 ( ( member_a @ X3 @ A3 )
% 0.30/0.46 & ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ A3 )
% 0.30/0.46 => ( ( less_eq @ X3 @ Xa )
% 0.30/0.46 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.finite_has_maximal
% 0.30/0.46 thf(fact_198_local_OInf__fin_Osubset,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( B4 != bot_bot_set_a )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 0.30/0.46 => ( ( inf @ ( lattic247676691_fin_a @ inf @ B4 ) @ ( lattic247676691_fin_a @ inf @ A3 ) )
% 0.30/0.46 = ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.subset
% 0.30/0.46 thf(fact_199_local_OSup__fin_Osubset,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( B4 != bot_bot_set_a )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 0.30/0.46 => ( ( sup @ ( lattic1781219155_fin_a @ sup @ B4 ) @ ( lattic1781219155_fin_a @ sup @ A3 ) )
% 0.30/0.46 = ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.subset
% 0.30/0.46 thf(fact_200_local_OInf__fin_Obounded__iff,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A3 ) )
% 0.30/0.46 = ( ! [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A3 )
% 0.30/0.46 => ( less_eq @ X @ X2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.bounded_iff
% 0.30/0.46 thf(fact_201_local_OInf__fin_OboundedI,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ! [A4: a] :
% 0.30/0.46 ( ( member_a @ A4 @ A3 )
% 0.30/0.46 => ( less_eq @ X @ A4 ) )
% 0.30/0.46 => ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.boundedI
% 0.30/0.46 thf(fact_202_local_OInf__fin_OboundedE,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A3 ) )
% 0.30/0.46 => ! [A5: a] :
% 0.30/0.46 ( ( member_a @ A5 @ A3 )
% 0.30/0.46 => ( less_eq @ X @ A5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.boundedE
% 0.30/0.46 thf(fact_203_local_OSup__fin_Obounded__iff,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ( less_eq @ ( lattic1781219155_fin_a @ sup @ A3 ) @ X )
% 0.30/0.46 = ( ! [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A3 )
% 0.30/0.46 => ( less_eq @ X2 @ X ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.bounded_iff
% 0.30/0.46 thf(fact_204_local_OSup__fin_OboundedI,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ! [A4: a] :
% 0.30/0.46 ( ( member_a @ A4 @ A3 )
% 0.30/0.46 => ( less_eq @ A4 @ X ) )
% 0.30/0.46 => ( less_eq @ ( lattic1781219155_fin_a @ sup @ A3 ) @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.boundedI
% 0.30/0.46 thf(fact_205_local_OSup__fin_OboundedE,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ( less_eq @ ( lattic1781219155_fin_a @ sup @ A3 ) @ X )
% 0.30/0.46 => ! [A5: a] :
% 0.30/0.46 ( ( member_a @ A5 @ A3 )
% 0.30/0.46 => ( less_eq @ A5 @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.boundedE
% 0.30/0.46 thf(fact_206_local_OInf__fin_Osubset__imp,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ( finite_finite_a @ B4 )
% 0.30/0.46 => ( less_eq @ ( lattic247676691_fin_a @ inf @ B4 ) @ ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.subset_imp
% 0.30/0.46 thf(fact_207_local_Obdd__below__empty,axiom,
% 0.30/0.46 condit1001553558elow_a @ less_eq @ bot_bot_set_a ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_empty
% 0.30/0.46 thf(fact_208_local_Obdd__above__empty,axiom,
% 0.30/0.46 condit1627435690bove_a @ less_eq @ bot_bot_set_a ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_empty
% 0.30/0.46 thf(fact_209_local_Onot__empty__eq__Iic__eq__empty,axiom,
% 0.30/0.46 ! [H: a] :
% 0.30/0.46 ( bot_bot_set_a
% 0.30/0.46 != ( set_atMost_a @ less_eq @ H ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.not_empty_eq_Iic_eq_empty
% 0.30/0.46 thf(fact_210_local_Onot__empty__eq__Ici__eq__empty,axiom,
% 0.30/0.46 ! [L: a] :
% 0.30/0.46 ( bot_bot_set_a
% 0.30/0.46 != ( set_atLeast_a @ less_eq @ L ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.not_empty_eq_Ici_eq_empty
% 0.30/0.46 thf(fact_211_local_OatLeast__iff,axiom,
% 0.30/0.46 ! [I: a,K: a] :
% 0.30/0.46 ( ( member_a @ I @ ( set_atLeast_a @ less_eq @ K ) )
% 0.30/0.46 = ( less_eq @ K @ I ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.atLeast_iff
% 0.30/0.46 thf(fact_212_local_OatMost__iff,axiom,
% 0.30/0.46 ! [I: a,K: a] :
% 0.30/0.46 ( ( member_a @ I @ ( set_atMost_a @ less_eq @ K ) )
% 0.30/0.46 = ( less_eq @ I @ K ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.atMost_iff
% 0.30/0.46 thf(fact_213_local_Obdd__below__Ici,axiom,
% 0.30/0.46 ! [A: a] : ( condit1001553558elow_a @ less_eq @ ( set_atLeast_a @ less_eq @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_Ici
% 0.30/0.46 thf(fact_214_local_Obdd__above__Iic,axiom,
% 0.30/0.46 ! [B: a] : ( condit1627435690bove_a @ less_eq @ ( set_atMost_a @ less_eq @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_Iic
% 0.30/0.46 thf(fact_215_subset__empty,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A3 @ bot_bot_set_a )
% 0.30/0.46 = ( A3 = bot_bot_set_a ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_empty
% 0.30/0.46 thf(fact_216_empty__subsetI,axiom,
% 0.30/0.46 ! [A3: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A3 ) ).
% 0.30/0.46
% 0.30/0.46 % empty_subsetI
% 0.30/0.46 thf(fact_217_subset__antisym,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 0.30/0.46 => ( A3 = B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_218_subsetI,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ! [X3: a] :
% 0.30/0.46 ( ( member_a @ X3 @ A3 )
% 0.30/0.46 => ( member_a @ X3 @ B4 ) )
% 0.30/0.46 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_219_Collect__mono__iff,axiom,
% 0.30/0.46 ! [P: a > $o,Q: a > $o] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.30/0.46 = ( ! [X2: a] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( Q @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono_iff
% 0.30/0.46 thf(fact_220_set__eq__subset,axiom,
% 0.30/0.46 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.30/0.46 = ( ^ [A6: set_a,B5: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A6 @ B5 )
% 0.30/0.46 & ( ord_less_eq_set_a @ B5 @ A6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_eq_subset
% 0.30/0.46 thf(fact_221_subset__trans,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a,C4: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ B4 @ C4 )
% 0.30/0.46 => ( ord_less_eq_set_a @ A3 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_trans
% 0.30/0.46 thf(fact_222_Collect__mono,axiom,
% 0.30/0.46 ! [P: a > $o,Q: a > $o] :
% 0.30/0.46 ( ! [X3: a] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( Q @ X3 ) )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono
% 0.30/0.46 thf(fact_223_subset__refl,axiom,
% 0.30/0.46 ! [A3: set_a] : ( ord_less_eq_set_a @ A3 @ A3 ) ).
% 0.30/0.46
% 0.30/0.46 % subset_refl
% 0.30/0.46 thf(fact_224_subset__iff,axiom,
% 0.30/0.46 ( ord_less_eq_set_a
% 0.30/0.46 = ( ^ [A6: set_a,B5: set_a] :
% 0.30/0.46 ! [T: a] :
% 0.30/0.46 ( ( member_a @ T @ A6 )
% 0.30/0.46 => ( member_a @ T @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_iff
% 0.30/0.46 thf(fact_225_equalityD2,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( A3 = B4 )
% 0.30/0.46 => ( ord_less_eq_set_a @ B4 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD2
% 0.30/0.46 thf(fact_226_equalityD1,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( A3 = B4 )
% 0.30/0.46 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD1
% 0.30/0.46 thf(fact_227_subset__eq,axiom,
% 0.30/0.46 ( ord_less_eq_set_a
% 0.30/0.46 = ( ^ [A6: set_a,B5: set_a] :
% 0.30/0.46 ! [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A6 )
% 0.30/0.46 => ( member_a @ X2 @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_eq
% 0.30/0.46 thf(fact_228_equalityE,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( A3 = B4 )
% 0.30/0.46 => ~ ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.30/0.46 => ~ ( ord_less_eq_set_a @ B4 @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityE
% 0.30/0.46 thf(fact_229_subsetD,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.30/0.46 => ( ( member_a @ C @ A3 )
% 0.30/0.46 => ( member_a @ C @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetD
% 0.30/0.46 thf(fact_230_in__mono,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a,X: a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.30/0.46 => ( ( member_a @ X @ A3 )
% 0.30/0.46 => ( member_a @ X @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mono
% 0.30/0.46 thf(fact_231_local_Omono__inf,axiom,
% 0.30/0.46 ! [F: a > set_a,A3: a,B4: a] :
% 0.30/0.46 ( ( mono_a_set_a @ less_eq @ F )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ ( inf @ A3 @ B4 ) ) @ ( inf_inf_set_a @ ( F @ A3 ) @ ( F @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.mono_inf
% 0.30/0.46 thf(fact_232_local_OSup__fin_Oclosed,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ! [X3: a,Y4: a] : ( member_a @ ( sup @ X3 @ Y4 ) @ ( insert_a @ X3 @ ( insert_a @ Y4 @ bot_bot_set_a ) ) )
% 0.30/0.46 => ( member_a @ ( lattic1781219155_fin_a @ sup @ A3 ) @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.closed
% 0.30/0.46 thf(fact_233_local_Obdd__above__Int1,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 0.30/0.46 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_Int1
% 0.30/0.46 thf(fact_234_local_Obdd__above__Int2,axiom,
% 0.30/0.46 ! [B4: set_a,A3: set_a] :
% 0.30/0.46 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 0.30/0.46 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_Int2
% 0.30/0.46 thf(fact_235_local_Obdd__below__Int1,axiom,
% 0.30/0.46 ! [A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 0.30/0.46 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_Int1
% 0.30/0.46 thf(fact_236_local_Obdd__below__Int2,axiom,
% 0.30/0.46 ! [B4: set_a,A3: set_a] :
% 0.30/0.46 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 0.30/0.46 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_Int2
% 0.30/0.46 thf(fact_237_Int__subset__iff,axiom,
% 0.30/0.46 ! [C4: set_a,A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ C4 @ ( inf_inf_set_a @ A3 @ B4 ) )
% 0.30/0.46 = ( ( ord_less_eq_set_a @ C4 @ A3 )
% 0.30/0.46 & ( ord_less_eq_set_a @ C4 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_subset_iff
% 0.30/0.46 thf(fact_238_semilattice__inf__class_Oinf__right__idem,axiom,
% 0.30/0.46 ! [X: set_a,Y: set_a] :
% 0.30/0.46 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Y )
% 0.30/0.46 = ( inf_inf_set_a @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf_class.inf_right_idem
% 0.30/0.46 thf(fact_239_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 0.30/0.46 ! [A: set_a,B: set_a] :
% 0.30/0.46 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
% 0.30/0.46 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf_class.inf.right_idem
% 0.30/0.46 thf(fact_240_semilattice__inf__class_Oinf__left__idem,axiom,
% 0.30/0.46 ! [X: set_a,Y: set_a] :
% 0.30/0.46 ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 0.30/0.46 = ( inf_inf_set_a @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf_class.inf_left_idem
% 0.30/0.46 thf(fact_241_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 0.30/0.46 ! [A: set_a,B: set_a] :
% 0.30/0.46 ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
% 0.30/0.46 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf_class.inf.left_idem
% 0.30/0.46 thf(fact_242_semilattice__inf__class_Oinf__idem,axiom,
% 0.30/0.46 ! [X: set_a] :
% 0.30/0.46 ( ( inf_inf_set_a @ X @ X )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf_class.inf_idem
% 0.30/0.46 thf(fact_243_semilattice__inf__class_Oinf_Oidem,axiom,
% 0.30/0.46 ! [A: set_a] :
% 0.30/0.46 ( ( inf_inf_set_a @ A @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf_class.inf.idem
% 0.30/0.46 thf(fact_244_local_OInf__fin_Oinsert__not__elem,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ~ ( member_a @ X @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ( lattic247676691_fin_a @ inf @ ( insert_a @ X @ A3 ) )
% 0.30/0.46 = ( inf @ X @ ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.insert_not_elem
% 0.30/0.46 thf(fact_245_local_OInf__fin_Oclosed,axiom,
% 0.30/0.46 ! [A3: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ! [X3: a,Y4: a] : ( member_a @ ( inf @ X3 @ Y4 ) @ ( insert_a @ X3 @ ( insert_a @ Y4 @ bot_bot_set_a ) ) )
% 0.30/0.46 => ( member_a @ ( lattic247676691_fin_a @ inf @ A3 ) @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.closed
% 0.30/0.46 thf(fact_246_local_OSup__fin_Oinsert__not__elem,axiom,
% 0.30/0.46 ! [A3: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A3 )
% 0.30/0.46 => ( ~ ( member_a @ X @ A3 )
% 0.30/0.46 => ( ( A3 != bot_bot_set_a )
% 0.30/0.46 => ( ( lattic1781219155_fin_a @ sup @ ( insert_a @ X @ A3 ) )
% 0.30/0.46 = ( sup @ X @ ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.insert_not_elem
% 0.30/0.46 thf(fact_247_semilattice__inf__class_Ole__inf__iff,axiom,
% 0.30/0.46 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ X @ ( inf_inf_set_a @ Y @ Z2 ) )
% 0.30/0.46 = ( ( ord_less_eq_set_a @ X @ Y )
% 0.30/0.46 & ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf_class.le_inf_iff
% 0.30/0.46 thf(fact_248_semilattice__inf__class_Oinf_Obounded__iff,axiom,
% 0.30/0.46 ! [A: set_a,B: set_a,C: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 0.30/0.46 = ( ( ord_less_eq_set_a @ A @ B )
% 0.30/0.46 & ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf_class.inf.bounded_iff
% 0.30/0.46 thf(fact_249_inf__bot__right,axiom,
% 0.30/0.46 ! [X: set_a] :
% 0.30/0.46 ( ( inf_inf_set_a @ X @ bot_bot_set_a )
% 0.30/0.46 = bot_bot_set_a ) ).
% 0.30/0.46
% 0.30/0.46 % inf_bot_right
% 0.30/0.46 thf(fact_250_inf__bot__left,axiom,
% 0.30/0.46 ! [X: set_a] :
% 0.30/0.46 ( ( inf_inf_set_a @ bot_bot_set_a @ X )
% 0.30/0.46 = bot_bot_set_a ) ).
% 0.30/0.46
% 0.30/0.46 % inf_bot_left
% 0.30/0.46 thf(fact_251_insert__subset,axiom,
% 0.30/0.46 ! [X: a,A3: set_a,B4: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ ( insert_a @ X @ A3 ) @ B4 )
% 0.30/0.46 = ( ( member_a @ X @ B4 )
% 0.30/0.46 & ( ord_less_eq_set_a @ A3 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_subset
% 0.30/0.46 thf(fact_252_singleton__insert__inj__eq,axiom,
% 0.30/0.46 ! [B: a,A: a,A3: set_a] :
% 0.30/0.46 ( ( ( insert_a @ B @ bot_bot_set_a )
% 0.30/0.46 = ( insert_a @ A @ A3 ) )
% 0.30/0.46 = ( ( A = B )
% 0.30/0.46 & ( ord_less_eq_set_a @ A3 @ ( insert_a @ B @ bot_bot_set_a ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_insert_inj_eq
% 0.30/0.46 thf(fact_253_singleton__insert__inj__eq_H,axiom,
% 0.30/0.46 ! [A: a,A3: set_a,B: a] :
% 0.30/0.46 ( ( ( insert_a @ A @ A3 )
% 0.30/0.46 = ( insert_a @ B @ bot_bot_set_a ) )
% 0.30/0.46 = ( ( A = B )
% 0.30/0.46 & ( ord_less_eq_set_a @ A3 @ ( insert_a @ B @ bot_bot_set_a ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_insert_inj_eq'
% 0.30/0.46
% 0.30/0.46 % Conjectures (2)
% 0.30/0.46 thf(conj_0,hypothesis,
% 0.30/0.46 less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ).
% 0.30/0.46
% 0.30/0.46 thf(conj_1,conjecture,
% 0.30/0.46 ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) )
% 0.30/0.46 = ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 3.08/1.76 ---- Embedded in THF ---
% 3.08/1.76 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.08/1.76 %%% Generated on Tue Feb 24 08:26:57 EST 2026
% 3.08/1.76 %%% using '$$dhol' embedding, version 1.3.0.
% 3.08/1.76 %%% Logic specification used:
% 3.08/1.76 %%% thf(spec, logic, $$dhol).
% 3.08/1.76
% 3.08/1.76 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2DTF5856.p
% See solution above
% 3.08/1.76 ------------------------
% 3.19/1.80 ---- Cleaned THF ---
% 3.19/1.80 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 3.19/1.80 set_a: $tType ).
% 3.19/1.80
% 3.19/1.80 thf(ty_n_tf__a,type,
% 3.19/1.80 a: $tType ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a,type,
% 3.19/1.80 condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a,type,
% 3.19/1.80 condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 3.19/1.80 finite40241356em_a_a: ( a > a > a ) > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
% 3.19/1.80 finite_finite_a: set_a > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 3.19/1.80 abel_semigroup_a: ( a > a > a ) > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 3.19/1.80 semigroup_a: ( a > a > a ) > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
% 3.19/1.80 inf_inf_set_a: set_a > set_a > set_a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 3.19/1.80 semilattice_a: ( a > a > a ) > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin_001tf__a,type,
% 3.19/1.80 lattic247676691_fin_a: ( a > a > a ) > set_a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 3.19/1.80 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin_001tf__a,type,
% 3.19/1.80 lattic1781219155_fin_a: ( a > a > a ) > set_a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 3.19/1.80 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 3.19/1.80 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 3.19/1.80 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 3.19/1.80 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 3.19/1.80 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oincomp_001tf__a,type,
% 3.19/1.80 modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 3.19/1.80 bot_bot_set_a: set_a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Orderings_Oord_OLeast_001tf__a,type,
% 3.19/1.80 least_a: ( a > a > $o ) > ( a > $o ) > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Orderings_Oord_Omax_001tf__a,type,
% 3.19/1.80 max_a: ( a > a > $o ) > a > a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Orderings_Oord_Omin_001tf__a,type,
% 3.19/1.80 min_a: ( a > a > $o ) > a > a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 3.19/1.80 ord_less_eq_set_a: set_a > set_a > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Orderings_Oorder_OGreatest_001tf__a,type,
% 3.19/1.80 greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Orderings_Oorder_Oantimono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 3.19/1.80 antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Orderings_Oorder_Omono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 3.19/1.80 mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Set_OCollect_001tf__a,type,
% 3.19/1.80 collect_a: ( a > $o ) > set_a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Set_Oinsert_001tf__a,type,
% 3.19/1.80 insert_a: a > set_a > set_a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Set__Interval_Oord_OatLeast_001tf__a,type,
% 3.19/1.80 set_atLeast_a: ( a > a > $o ) > a > set_a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_Set__Interval_Oord_OatMost_001tf__a,type,
% 3.19/1.80 set_atMost_a: ( a > a > $o ) > a > set_a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_c_member_001tf__a,type,
% 3.19/1.80 member_a: a > set_a > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_v_a,type,
% 3.19/1.80 a2: a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_v_b,type,
% 3.19/1.80 b: a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_v_c,type,
% 3.19/1.80 c: a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_v_inf,type,
% 3.19/1.80 inf: a > a > a ).
% 3.19/1.80
% 3.19/1.80 thf(sy_v_less__eq,type,
% 3.19/1.80 less_eq: a > a > $o ).
% 3.19/1.80
% 3.19/1.80 thf(sy_v_sup,type,
% 3.19/1.80 sup: a > a > a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_0_local_Oantisym,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ( less_eq @ Y @ X )
% 3.19/1.80 => ( X = Y ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_1_local_Oantisym__conv,axiom,
% 3.19/1.80 ! [Y: a,X: a] :
% 3.19/1.80 ( ( less_eq @ Y @ X )
% 3.19/1.80 => ( ( less_eq @ X @ Y )
% 3.19/1.80 = ( X = Y ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_2_local_Odual__order_Oantisym,axiom,
% 3.19/1.80 ! [B: a,A: a] :
% 3.19/1.80 ( ( less_eq @ B @ A )
% 3.19/1.80 => ( ( less_eq @ A @ B )
% 3.19/1.80 => ( A = B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_3_local_Odual__order_Oeq__iff,axiom,
% 3.19/1.80 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 3.19/1.80 = ( ^ [A2: a,B2: a] :
% 3.19/1.80 ( ( less_eq @ B2 @ A2 )
% 3.19/1.80 & ( less_eq @ A2 @ B2 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_4_local_Odual__order_Otrans,axiom,
% 3.19/1.80 ! [B: a,A: a,C: a] :
% 3.19/1.80 ( ( less_eq @ B @ A )
% 3.19/1.80 => ( ( less_eq @ C @ B )
% 3.19/1.80 => ( less_eq @ C @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_5_local_Oeq__iff,axiom,
% 3.19/1.80 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 3.19/1.80 = ( ^ [X2: a,Y3: a] :
% 3.19/1.80 ( ( less_eq @ X2 @ Y3 )
% 3.19/1.80 & ( less_eq @ Y3 @ X2 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_6_local_Oeq__refl,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( X = Y )
% 3.19/1.80 => ( less_eq @ X @ Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_7_local_Oord__eq__le__trans,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( A = B )
% 3.19/1.80 => ( ( less_eq @ B @ C )
% 3.19/1.80 => ( less_eq @ A @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_8_local_Oord__le__eq__trans,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 => ( ( B = C )
% 3.19/1.80 => ( less_eq @ A @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_9_local_Oorder_Oantisym,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 => ( ( less_eq @ B @ A )
% 3.19/1.80 => ( A = B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_10_local_Oorder_Oeq__iff,axiom,
% 3.19/1.80 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 3.19/1.80 = ( ^ [A2: a,B2: a] :
% 3.19/1.80 ( ( less_eq @ A2 @ B2 )
% 3.19/1.80 & ( less_eq @ B2 @ A2 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_11_local_Oorder_Otrans,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 => ( ( less_eq @ B @ C )
% 3.19/1.80 => ( less_eq @ A @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_12_local_Oorder__trans,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ( less_eq @ Y @ Z2 )
% 3.19/1.80 => ( less_eq @ X @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_13_local_Oinf_Oassoc,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( inf @ ( inf @ A @ B ) @ C )
% 3.19/1.80 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_14_local_Oinf_Ocommute,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( inf @ A @ B )
% 3.19/1.80 = ( inf @ B @ A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_15_local_Oinf_Oleft__commute,axiom,
% 3.19/1.80 ! [B: a,A: a,C: a] :
% 3.19/1.80 ( ( inf @ B @ ( inf @ A @ C ) )
% 3.19/1.80 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_16_local_Oinf__assoc,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ( inf @ ( inf @ X @ Y ) @ Z2 )
% 3.19/1.80 = ( inf @ X @ ( inf @ Y @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_17_local_Oinf__commute,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( inf @ X @ Y )
% 3.19/1.80 = ( inf @ Y @ X ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_18_local_Oinf__left__commute,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ( inf @ X @ ( inf @ Y @ Z2 ) )
% 3.19/1.80 = ( inf @ Y @ ( inf @ X @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_19_local_Osup_Oassoc,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( sup @ ( sup @ A @ B ) @ C )
% 3.19/1.80 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_20_local_Osup_Ocommute,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( sup @ A @ B )
% 3.19/1.80 = ( sup @ B @ A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_21_local_Osup_Oleft__commute,axiom,
% 3.19/1.80 ! [B: a,A: a,C: a] :
% 3.19/1.80 ( ( sup @ B @ ( sup @ A @ C ) )
% 3.19/1.80 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_22_local_Osup__assoc,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ( sup @ ( sup @ X @ Y ) @ Z2 )
% 3.19/1.80 = ( sup @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_23_local_Osup__commute,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( sup @ X @ Y )
% 3.19/1.80 = ( sup @ Y @ X ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_24_local_Osup__left__commute,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ( sup @ X @ ( sup @ Y @ Z2 ) )
% 3.19/1.80 = ( sup @ Y @ ( sup @ X @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_25_local_Oinf_Oabsorb1,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 => ( ( inf @ A @ B )
% 3.19/1.80 = A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_26_local_Oinf_Oabsorb2,axiom,
% 3.19/1.80 ! [B: a,A: a] :
% 3.19/1.80 ( ( less_eq @ B @ A )
% 3.19/1.80 => ( ( inf @ A @ B )
% 3.19/1.80 = B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_27_local_Oinf_Oabsorb__iff1,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 = ( ( inf @ A @ B )
% 3.19/1.80 = A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_28_local_Oinf_Oabsorb__iff2,axiom,
% 3.19/1.80 ! [B: a,A: a] :
% 3.19/1.80 ( ( less_eq @ B @ A )
% 3.19/1.80 = ( ( inf @ A @ B )
% 3.19/1.80 = B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_29_local_Oinf_OboundedE,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 3.19/1.80 => ~ ( ( less_eq @ A @ B )
% 3.19/1.80 => ~ ( less_eq @ A @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_30_local_Oinf_OboundedI,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 => ( ( less_eq @ A @ C )
% 3.19/1.80 => ( less_eq @ A @ ( inf @ B @ C ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_31_local_Oinf_Ocobounded1,axiom,
% 3.19/1.80 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_32_local_Oinf_Ocobounded2,axiom,
% 3.19/1.80 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_33_local_Oinf_OcoboundedI1,axiom,
% 3.19/1.80 ! [A: a,C: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ C )
% 3.19/1.80 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_34_local_Oinf_OcoboundedI2,axiom,
% 3.19/1.80 ! [B: a,C: a,A: a] :
% 3.19/1.80 ( ( less_eq @ B @ C )
% 3.19/1.80 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_35_local_Oinf_OorderE,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 => ( A
% 3.19/1.80 = ( inf @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_36_local_Oinf_OorderI,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( A
% 3.19/1.80 = ( inf @ A @ B ) )
% 3.19/1.80 => ( less_eq @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_37_local_Oinf_Oorder__iff,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 = ( A
% 3.19/1.80 = ( inf @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_38_local_Oinf__absorb1,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ( inf @ X @ Y )
% 3.19/1.80 = X ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_39_local_Oinf__absorb2,axiom,
% 3.19/1.80 ! [Y: a,X: a] :
% 3.19/1.80 ( ( less_eq @ Y @ X )
% 3.19/1.80 => ( ( inf @ X @ Y )
% 3.19/1.80 = Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_40_local_Oinf__greatest,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ( less_eq @ X @ Z2 )
% 3.19/1.80 => ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_41_local_Oinf__le1,axiom,
% 3.19/1.80 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_42_local_Oinf__le2,axiom,
% 3.19/1.80 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_43_local_Oinf__mono,axiom,
% 3.19/1.80 ! [A: a,C: a,B: a,D: a] :
% 3.19/1.80 ( ( less_eq @ A @ C )
% 3.19/1.80 => ( ( less_eq @ B @ D )
% 3.19/1.80 => ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_44_local_Oinf__unique,axiom,
% 3.19/1.80 ! [F: a > a > a,X: a,Y: a] :
% 3.19/1.80 ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
% 3.19/1.80 => ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
% 3.19/1.80 => ( ! [X3: a,Y4: a,Z3: a] :
% 3.19/1.80 ( ( less_eq @ X3 @ Y4 )
% 3.19/1.80 => ( ( less_eq @ X3 @ Z3 )
% 3.19/1.80 => ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 3.19/1.80 => ( ( inf @ X @ Y )
% 3.19/1.80 = ( F @ X @ Y ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_45_mem__Collect__eq,axiom,
% 3.19/1.80 ! [A: a,P: a > $o] :
% 3.19/1.80 ( ( member_a @ A @ ( collect_a @ P ) )
% 3.19/1.80 = ( P @ A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_46_Collect__mem__eq,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( collect_a
% 3.19/1.80 @ ^ [X2: a] : ( member_a @ X2 @ A3 ) )
% 3.19/1.80 = A3 ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_47_Collect__cong,axiom,
% 3.19/1.80 ! [P: a > $o,Q: a > $o] :
% 3.19/1.80 ( ! [X3: a] :
% 3.19/1.80 ( ( P @ X3 )
% 3.19/1.80 = ( Q @ X3 ) )
% 3.19/1.80 => ( ( collect_a @ P )
% 3.19/1.80 = ( collect_a @ Q ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_48_local_Ole__iff__inf,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( less_eq @ X @ Y )
% 3.19/1.80 = ( ( inf @ X @ Y )
% 3.19/1.80 = X ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_49_local_Ole__infE,axiom,
% 3.19/1.80 ! [X: a,A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ X @ ( inf @ A @ B ) )
% 3.19/1.80 => ~ ( ( less_eq @ X @ A )
% 3.19/1.80 => ~ ( less_eq @ X @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_50_local_Ole__infI,axiom,
% 3.19/1.80 ! [X: a,A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ X @ A )
% 3.19/1.80 => ( ( less_eq @ X @ B )
% 3.19/1.80 => ( less_eq @ X @ ( inf @ A @ B ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_51_local_Ole__infI1,axiom,
% 3.19/1.80 ! [A: a,X: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ X )
% 3.19/1.80 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_52_local_Ole__infI2,axiom,
% 3.19/1.80 ! [B: a,X: a,A: a] :
% 3.19/1.80 ( ( less_eq @ B @ X )
% 3.19/1.80 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_53_local_Ole__iff__sup,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( less_eq @ X @ Y )
% 3.19/1.80 = ( ( sup @ X @ Y )
% 3.19/1.80 = Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_54_local_Ole__supE,axiom,
% 3.19/1.80 ! [A: a,B: a,X: a] :
% 3.19/1.80 ( ( less_eq @ ( sup @ A @ B ) @ X )
% 3.19/1.80 => ~ ( ( less_eq @ A @ X )
% 3.19/1.80 => ~ ( less_eq @ B @ X ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_55_local_Ole__supI,axiom,
% 3.19/1.80 ! [A: a,X: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ X )
% 3.19/1.80 => ( ( less_eq @ B @ X )
% 3.19/1.80 => ( less_eq @ ( sup @ A @ B ) @ X ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_56_local_Ole__supI1,axiom,
% 3.19/1.80 ! [X: a,A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ X @ A )
% 3.19/1.80 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_57_local_Ole__supI2,axiom,
% 3.19/1.80 ! [X: a,B: a,A: a] :
% 3.19/1.80 ( ( less_eq @ X @ B )
% 3.19/1.80 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_58_local_Osup_Oabsorb1,axiom,
% 3.19/1.80 ! [B: a,A: a] :
% 3.19/1.80 ( ( less_eq @ B @ A )
% 3.19/1.80 => ( ( sup @ A @ B )
% 3.19/1.80 = A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_59_local_Osup_Oabsorb2,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 => ( ( sup @ A @ B )
% 3.19/1.80 = B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_60_local_Osup_Oabsorb__iff1,axiom,
% 3.19/1.80 ! [B: a,A: a] :
% 3.19/1.80 ( ( less_eq @ B @ A )
% 3.19/1.80 = ( ( sup @ A @ B )
% 3.19/1.80 = A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_61_local_Osup_Oabsorb__iff2,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ A @ B )
% 3.19/1.80 = ( ( sup @ A @ B )
% 3.19/1.80 = B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_62_local_Osup_OboundedE,axiom,
% 3.19/1.80 ! [B: a,C: a,A: a] :
% 3.19/1.80 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 3.19/1.80 => ~ ( ( less_eq @ B @ A )
% 3.19/1.80 => ~ ( less_eq @ C @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_63_local_Osup_OboundedI,axiom,
% 3.19/1.80 ! [B: a,A: a,C: a] :
% 3.19/1.80 ( ( less_eq @ B @ A )
% 3.19/1.80 => ( ( less_eq @ C @ A )
% 3.19/1.80 => ( less_eq @ ( sup @ B @ C ) @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_64_local_Osup_Ocobounded1,axiom,
% 3.19/1.80 ! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_65_local_Osup_Ocobounded2,axiom,
% 3.19/1.80 ! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_66_local_Osup_OcoboundedI1,axiom,
% 3.19/1.80 ! [C: a,A: a,B: a] :
% 3.19/1.80 ( ( less_eq @ C @ A )
% 3.19/1.80 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_67_local_Osup_OcoboundedI2,axiom,
% 3.19/1.80 ! [C: a,B: a,A: a] :
% 3.19/1.80 ( ( less_eq @ C @ B )
% 3.19/1.80 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_68_local_Osup_Omono,axiom,
% 3.19/1.80 ! [C: a,A: a,D: a,B: a] :
% 3.19/1.80 ( ( less_eq @ C @ A )
% 3.19/1.80 => ( ( less_eq @ D @ B )
% 3.19/1.80 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_69_local_Osup_OorderE,axiom,
% 3.19/1.80 ! [B: a,A: a] :
% 3.19/1.80 ( ( less_eq @ B @ A )
% 3.19/1.80 => ( A
% 3.19/1.80 = ( sup @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_70_local_Osup_OorderI,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( A
% 3.19/1.80 = ( sup @ A @ B ) )
% 3.19/1.80 => ( less_eq @ B @ A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_71_local_Osup_Oorder__iff,axiom,
% 3.19/1.80 ! [B: a,A: a] :
% 3.19/1.80 ( ( less_eq @ B @ A )
% 3.19/1.80 = ( A
% 3.19/1.80 = ( sup @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_72_local_Osup__absorb1,axiom,
% 3.19/1.80 ! [Y: a,X: a] :
% 3.19/1.80 ( ( less_eq @ Y @ X )
% 3.19/1.80 => ( ( sup @ X @ Y )
% 3.19/1.80 = X ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_73_local_Osup__absorb2,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ( sup @ X @ Y )
% 3.19/1.80 = Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_74_local_Osup__ge1,axiom,
% 3.19/1.80 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_75_local_Osup__ge2,axiom,
% 3.19/1.80 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_76_local_Osup__least,axiom,
% 3.19/1.80 ! [Y: a,X: a,Z2: a] :
% 3.19/1.80 ( ( less_eq @ Y @ X )
% 3.19/1.80 => ( ( less_eq @ Z2 @ X )
% 3.19/1.80 => ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_77_local_Osup__mono,axiom,
% 3.19/1.80 ! [A: a,C: a,B: a,D: a] :
% 3.19/1.80 ( ( less_eq @ A @ C )
% 3.19/1.80 => ( ( less_eq @ B @ D )
% 3.19/1.80 => ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_78_local_Osup__unique,axiom,
% 3.19/1.80 ! [F: a > a > a,X: a,Y: a] :
% 3.19/1.80 ( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
% 3.19/1.80 => ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
% 3.19/1.80 => ( ! [X3: a,Y4: a,Z3: a] :
% 3.19/1.80 ( ( less_eq @ Y4 @ X3 )
% 3.19/1.80 => ( ( less_eq @ Z3 @ X3 )
% 3.19/1.80 => ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
% 3.19/1.80 => ( ( sup @ X @ Y )
% 3.19/1.80 = ( F @ X @ Y ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_79_local_Odistrib__imp1,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ! [X3: a,Y4: a,Z3: a] :
% 3.19/1.80 ( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
% 3.19/1.80 = ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
% 3.19/1.80 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 3.19/1.80 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_80_local_Odistrib__imp2,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ! [X3: a,Y4: a,Z3: a] :
% 3.19/1.80 ( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
% 3.19/1.80 = ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
% 3.19/1.80 => ( ( inf @ X @ ( sup @ Y @ Z2 ) )
% 3.19/1.80 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_81_local_Oa__join__d,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_82_a__meet__d,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_83_local_Ob__join__d,axiom,
% 3.19/1.80 ! [B: a,A: a,C: a] :
% 3.19/1.80 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_84_b__meet__d,axiom,
% 3.19/1.80 ! [B: a,A: a,C: a] :
% 3.19/1.80 ( ( inf @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( sup @ ( inf @ B @ C ) @ ( inf @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_85_c__meet__d,axiom,
% 3.19/1.80 ! [C: a,A: a,B: a] :
% 3.19/1.80 ( ( inf @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( sup @ ( inf @ C @ A ) @ ( inf @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_86_local_Od__aux__def,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_87_local_Od__b__c__a,axiom,
% 3.19/1.80 ! [B: a,C: a,A: a] :
% 3.19/1.80 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 3.19/1.80 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_88_local_Od__c__a__b,axiom,
% 3.19/1.80 ! [C: a,A: a,B: a] :
% 3.19/1.80 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 3.19/1.80 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_89_local_Oa__meet__e,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_90_local_Ob__meet__e,axiom,
% 3.19/1.80 ! [B: a,A: a,C: a] :
% 3.19/1.80 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_91_local_Oc__meet__e,axiom,
% 3.19/1.80 ! [C: a,A: a,B: a] :
% 3.19/1.80 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_92_local_Oe__aux__def,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_93_local_Oe__b__c__a,axiom,
% 3.19/1.80 ! [B: a,C: a,A: a] :
% 3.19/1.80 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 3.19/1.80 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_94_local_Oe__c__a__b,axiom,
% 3.19/1.80 ! [C: a,A: a,B: a] :
% 3.19/1.80 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 3.19/1.80 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_95_local_Odistrib__inf__le,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_96_local_Odistrib__sup__le,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_97_local_Omodular,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 3.19/1.80 = ( inf @ Y @ ( sup @ X @ Z2 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_98_local_Oincomp__def,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( modula1727524044comp_a @ less_eq @ X @ Y )
% 3.19/1.80 = ( ~ ( less_eq @ X @ Y )
% 3.19/1.80 & ~ ( less_eq @ Y @ X ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_99_local_Oorder_Orefl,axiom,
% 3.19/1.80 ! [A: a] : ( less_eq @ A @ A ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_100_local_Oorder__refl,axiom,
% 3.19/1.80 ! [X: a] : ( less_eq @ X @ X ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_101_local_Oinf_Oidem,axiom,
% 3.19/1.80 ! [A: a] :
% 3.19/1.80 ( ( inf @ A @ A )
% 3.19/1.80 = A ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_102_local_Oinf_Oleft__idem,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( inf @ A @ ( inf @ A @ B ) )
% 3.19/1.80 = ( inf @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_103_local_Oinf_Oright__idem,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( inf @ ( inf @ A @ B ) @ B )
% 3.19/1.80 = ( inf @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_104_local_Oinf__idem,axiom,
% 3.19/1.80 ! [X: a] :
% 3.19/1.80 ( ( inf @ X @ X )
% 3.19/1.80 = X ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_105_local_Oinf__left__idem,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( inf @ X @ ( inf @ X @ Y ) )
% 3.19/1.80 = ( inf @ X @ Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_106_local_Oinf__right__idem,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 3.19/1.80 = ( inf @ X @ Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_107_local_Osup_Oidem,axiom,
% 3.19/1.80 ! [A: a] :
% 3.19/1.80 ( ( sup @ A @ A )
% 3.19/1.80 = A ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_108_local_Osup_Oleft__idem,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( sup @ A @ ( sup @ A @ B ) )
% 3.19/1.80 = ( sup @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_109_local_Osup_Oright__idem,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( sup @ ( sup @ A @ B ) @ B )
% 3.19/1.80 = ( sup @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_110_local_Osup__idem,axiom,
% 3.19/1.80 ! [X: a] :
% 3.19/1.80 ( ( sup @ X @ X )
% 3.19/1.80 = X ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_111_local_Osup__left__idem,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( sup @ X @ ( sup @ X @ Y ) )
% 3.19/1.80 = ( sup @ X @ Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_112_local_OGreatestI2__order,axiom,
% 3.19/1.80 ! [P: a > $o,X: a,Q: a > $o] :
% 3.19/1.80 ( ( P @ X )
% 3.19/1.80 => ( ! [Y4: a] :
% 3.19/1.80 ( ( P @ Y4 )
% 3.19/1.80 => ( less_eq @ Y4 @ X ) )
% 3.19/1.80 => ( ! [X3: a] :
% 3.19/1.80 ( ( P @ X3 )
% 3.19/1.80 => ( ! [Y5: a] :
% 3.19/1.80 ( ( P @ Y5 )
% 3.19/1.80 => ( less_eq @ Y5 @ X3 ) )
% 3.19/1.80 => ( Q @ X3 ) ) )
% 3.19/1.80 => ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_113_local_OGreatest__equality,axiom,
% 3.19/1.80 ! [P: a > $o,X: a] :
% 3.19/1.80 ( ( P @ X )
% 3.19/1.80 => ( ! [Y4: a] :
% 3.19/1.80 ( ( P @ Y4 )
% 3.19/1.80 => ( less_eq @ Y4 @ X ) )
% 3.19/1.80 => ( ( greatest_a @ less_eq @ P )
% 3.19/1.80 = X ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_114_local_Omax__def,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( ( less_eq @ A @ B )
% 3.19/1.80 => ( ( max_a @ less_eq @ A @ B )
% 3.19/1.80 = B ) )
% 3.19/1.80 & ( ~ ( less_eq @ A @ B )
% 3.19/1.80 => ( ( max_a @ less_eq @ A @ B )
% 3.19/1.80 = A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_115_local_Omin__def,axiom,
% 3.19/1.80 ! [A: a,B: a] :
% 3.19/1.80 ( ( ( less_eq @ A @ B )
% 3.19/1.80 => ( ( min_a @ less_eq @ A @ B )
% 3.19/1.80 = A ) )
% 3.19/1.80 & ( ~ ( less_eq @ A @ B )
% 3.19/1.80 => ( ( min_a @ less_eq @ A @ B )
% 3.19/1.80 = B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_116_local_Oa__aux__def,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_117_a__def__equiv,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 => ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( inf @ ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_118_local_Oinf_Obounded__iff,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 3.19/1.80 = ( ( less_eq @ A @ B )
% 3.19/1.80 & ( less_eq @ A @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_119_local_Ole__inf__iff,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
% 3.19/1.80 = ( ( less_eq @ X @ Y )
% 3.19/1.80 & ( less_eq @ X @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_120_local_Ole__sup__iff,axiom,
% 3.19/1.80 ! [X: a,Y: a,Z2: a] :
% 3.19/1.80 ( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
% 3.19/1.80 = ( ( less_eq @ X @ Z2 )
% 3.19/1.80 & ( less_eq @ Y @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_121_local_Osup_Obounded__iff,axiom,
% 3.19/1.80 ! [B: a,C: a,A: a] :
% 3.19/1.80 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 3.19/1.80 = ( ( less_eq @ B @ A )
% 3.19/1.80 & ( less_eq @ C @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_122_local_Oinf__sup__absorb,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( inf @ X @ ( sup @ X @ Y ) )
% 3.19/1.80 = X ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_123_local_Osup__inf__absorb,axiom,
% 3.19/1.80 ! [X: a,Y: a] :
% 3.19/1.80 ( ( sup @ X @ ( inf @ X @ Y ) )
% 3.19/1.80 = X ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_124_local_OLeast1I,axiom,
% 3.19/1.80 ! [P: a > $o] :
% 3.19/1.80 ( ? [X4: a] :
% 3.19/1.80 ( ( P @ X4 )
% 3.19/1.80 & ! [Y4: a] :
% 3.19/1.80 ( ( P @ Y4 )
% 3.19/1.80 => ( less_eq @ X4 @ Y4 ) )
% 3.19/1.80 & ! [Y4: a] :
% 3.19/1.80 ( ( ( P @ Y4 )
% 3.19/1.80 & ! [Ya: a] :
% 3.19/1.80 ( ( P @ Ya )
% 3.19/1.80 => ( less_eq @ Y4 @ Ya ) ) )
% 3.19/1.80 => ( Y4 = X4 ) ) )
% 3.19/1.80 => ( P @ ( least_a @ less_eq @ P ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_125_local_OLeast1__le,axiom,
% 3.19/1.80 ! [P: a > $o,Z2: a] :
% 3.19/1.80 ( ? [X4: a] :
% 3.19/1.80 ( ( P @ X4 )
% 3.19/1.80 & ! [Y4: a] :
% 3.19/1.80 ( ( P @ Y4 )
% 3.19/1.80 => ( less_eq @ X4 @ Y4 ) )
% 3.19/1.80 & ! [Y4: a] :
% 3.19/1.80 ( ( ( P @ Y4 )
% 3.19/1.80 & ! [Ya: a] :
% 3.19/1.80 ( ( P @ Ya )
% 3.19/1.80 => ( less_eq @ Y4 @ Ya ) ) )
% 3.19/1.80 => ( Y4 = X4 ) ) )
% 3.19/1.80 => ( ( P @ Z2 )
% 3.19/1.80 => ( less_eq @ ( least_a @ less_eq @ P ) @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_126_local_OLeastI2__order,axiom,
% 3.19/1.80 ! [P: a > $o,X: a,Q: a > $o] :
% 3.19/1.80 ( ( P @ X )
% 3.19/1.80 => ( ! [Y4: a] :
% 3.19/1.80 ( ( P @ Y4 )
% 3.19/1.80 => ( less_eq @ X @ Y4 ) )
% 3.19/1.80 => ( ! [X3: a] :
% 3.19/1.80 ( ( P @ X3 )
% 3.19/1.80 => ( ! [Y5: a] :
% 3.19/1.80 ( ( P @ Y5 )
% 3.19/1.80 => ( less_eq @ X3 @ Y5 ) )
% 3.19/1.80 => ( Q @ X3 ) ) )
% 3.19/1.80 => ( Q @ ( least_a @ less_eq @ P ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_127_local_OLeast__equality,axiom,
% 3.19/1.80 ! [P: a > $o,X: a] :
% 3.19/1.80 ( ( P @ X )
% 3.19/1.80 => ( ! [Y4: a] :
% 3.19/1.80 ( ( P @ Y4 )
% 3.19/1.80 => ( less_eq @ X @ Y4 ) )
% 3.19/1.80 => ( ( least_a @ less_eq @ P )
% 3.19/1.80 = X ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_128_local_Oc__a,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_129_local_Oc__aux__def,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_130_c__def__equiv,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 => ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( inf @ ( sup @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_131_c__meet__a__eq__d,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 => ( ( inf @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_132_local_Ob__a,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_133_local_Ob__aux__def,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_134_b__def__equiv,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 => ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 3.19/1.80 = ( inf @ ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_135_a__join__b__eq__e,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 => ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_136_a__meet__b__eq__d,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 => ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_137_lattice_Oa__aux_Ocong,axiom,
% 3.19/1.80 modula17988509_aux_a = modula17988509_aux_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_138_lattice_Od__aux_Ocong,axiom,
% 3.19/1.80 modula1936294176_aux_a = modula1936294176_aux_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_139_lattice_Oe__aux_Ocong,axiom,
% 3.19/1.80 modula1144073633_aux_a = modula1144073633_aux_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_140_local_Ocomp__fun__idem__sup,axiom,
% 3.19/1.80 finite40241356em_a_a @ sup ).
% 3.19/1.80
% 3.19/1.80 thf(fact_141_local_Ocomp__fun__idem__inf,axiom,
% 3.19/1.80 finite40241356em_a_a @ inf ).
% 3.19/1.80
% 3.19/1.80 thf(fact_142_b__join__c__eq__e,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 => ( ( sup @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_143_b__meet__c__eq__d,axiom,
% 3.19/1.80 ! [A: a,B: a,C: a] :
% 3.19/1.80 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 => ( ( inf @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) )
% 3.19/1.80 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_144_local_Osup_Osemigroup__axioms,axiom,
% 3.19/1.80 semigroup_a @ sup ).
% 3.19/1.80
% 3.19/1.80 thf(fact_145_local_Oinf_Osemigroup__axioms,axiom,
% 3.19/1.80 semigroup_a @ inf ).
% 3.19/1.80
% 3.19/1.80 thf(fact_146_local_Osup_Osemilattice__axioms,axiom,
% 3.19/1.80 semilattice_a @ sup ).
% 3.19/1.80
% 3.19/1.80 thf(fact_147_local_Oinf_Osemilattice__axioms,axiom,
% 3.19/1.80 semilattice_a @ inf ).
% 3.19/1.80
% 3.19/1.80 thf(fact_148_local_Osup_Oabel__semigroup__axioms,axiom,
% 3.19/1.80 abel_semigroup_a @ sup ).
% 3.19/1.80
% 3.19/1.80 thf(fact_149_local_Oinf_Oabel__semigroup__axioms,axiom,
% 3.19/1.80 abel_semigroup_a @ inf ).
% 3.19/1.80
% 3.19/1.80 thf(fact_150_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 3.19/1.80 lattic1885654924_set_a @ sup ).
% 3.19/1.80
% 3.19/1.80 thf(fact_151_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 3.19/1.80 lattic1885654924_set_a @ inf ).
% 3.19/1.80
% 3.19/1.80 thf(fact_152_lattice_Oincomp_Ocong,axiom,
% 3.19/1.80 modula1727524044comp_a = modula1727524044comp_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_153_lattice_Oc__aux_Ocong,axiom,
% 3.19/1.80 modula581031071_aux_a = modula581031071_aux_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_154_lattice_Ob__aux_Ocong,axiom,
% 3.19/1.80 modula1373251614_aux_a = modula1373251614_aux_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_155_abel__semigroup_Oaxioms_I1_J,axiom,
% 3.19/1.80 ! [F: a > a > a] :
% 3.19/1.80 ( ( abel_semigroup_a @ F )
% 3.19/1.80 => ( semigroup_a @ F ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_156_semilattice__set__def,axiom,
% 3.19/1.80 lattic1885654924_set_a = semilattice_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_157_semilattice__set_Ointro,axiom,
% 3.19/1.80 ! [F: a > a > a] :
% 3.19/1.80 ( ( semilattice_a @ F )
% 3.19/1.80 => ( lattic1885654924_set_a @ F ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_158_abel__semigroup_Oleft__commute,axiom,
% 3.19/1.80 ! [F: a > a > a,B: a,A: a,C: a] :
% 3.19/1.80 ( ( abel_semigroup_a @ F )
% 3.19/1.80 => ( ( F @ B @ ( F @ A @ C ) )
% 3.19/1.80 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_159_abel__semigroup_Ocommute,axiom,
% 3.19/1.80 ! [F: a > a > a,A: a,B: a] :
% 3.19/1.80 ( ( abel_semigroup_a @ F )
% 3.19/1.80 => ( ( F @ A @ B )
% 3.19/1.80 = ( F @ B @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_160_semigroup_Ointro,axiom,
% 3.19/1.80 ! [F: a > a > a] :
% 3.19/1.80 ( ! [A4: a,B3: a,C2: a] :
% 3.19/1.80 ( ( F @ ( F @ A4 @ B3 ) @ C2 )
% 3.19/1.80 = ( F @ A4 @ ( F @ B3 @ C2 ) ) )
% 3.19/1.80 => ( semigroup_a @ F ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_161_semigroup_Oassoc,axiom,
% 3.19/1.80 ! [F: a > a > a,A: a,B: a,C: a] :
% 3.19/1.80 ( ( semigroup_a @ F )
% 3.19/1.80 => ( ( F @ ( F @ A @ B ) @ C )
% 3.19/1.80 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_162_semigroup__def,axiom,
% 3.19/1.80 ( semigroup_a
% 3.19/1.80 = ( ^ [F2: a > a > a] :
% 3.19/1.80 ! [A2: a,B2: a,C3: a] :
% 3.19/1.80 ( ( F2 @ ( F2 @ A2 @ B2 ) @ C3 )
% 3.19/1.80 = ( F2 @ A2 @ ( F2 @ B2 @ C3 ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_163_semilattice__set_Oaxioms,axiom,
% 3.19/1.80 ! [F: a > a > a] :
% 3.19/1.80 ( ( lattic1885654924_set_a @ F )
% 3.19/1.80 => ( semilattice_a @ F ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_164_semilattice_Oaxioms_I1_J,axiom,
% 3.19/1.80 ! [F: a > a > a] :
% 3.19/1.80 ( ( semilattice_a @ F )
% 3.19/1.80 => ( abel_semigroup_a @ F ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_165_local_Obdd__above__def,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 3.19/1.80 = ( ? [M: a] :
% 3.19/1.80 ! [X2: a] :
% 3.19/1.80 ( ( member_a @ X2 @ A3 )
% 3.19/1.80 => ( less_eq @ X2 @ M ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_166_local_Obdd__below__def,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 3.19/1.80 = ( ? [M2: a] :
% 3.19/1.80 ! [X2: a] :
% 3.19/1.80 ( ( member_a @ X2 @ A3 )
% 3.19/1.80 => ( less_eq @ M2 @ X2 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_167_local_Obdd__belowI,axiom,
% 3.19/1.80 ! [A3: set_a,M3: a] :
% 3.19/1.80 ( ! [X3: a] :
% 3.19/1.80 ( ( member_a @ X3 @ A3 )
% 3.19/1.80 => ( less_eq @ M3 @ X3 ) )
% 3.19/1.80 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_168_local_Obdd__aboveI,axiom,
% 3.19/1.80 ! [A3: set_a,M4: a] :
% 3.19/1.80 ( ! [X3: a] :
% 3.19/1.80 ( ( member_a @ X3 @ A3 )
% 3.19/1.80 => ( less_eq @ X3 @ M4 ) )
% 3.19/1.80 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_169_semilattice_Oidem,axiom,
% 3.19/1.80 ! [F: a > a > a,A: a] :
% 3.19/1.80 ( ( semilattice_a @ F )
% 3.19/1.80 => ( ( F @ A @ A )
% 3.19/1.80 = A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_170_semilattice_Oleft__idem,axiom,
% 3.19/1.80 ! [F: a > a > a,A: a,B: a] :
% 3.19/1.80 ( ( semilattice_a @ F )
% 3.19/1.80 => ( ( F @ A @ ( F @ A @ B ) )
% 3.19/1.80 = ( F @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_171_semilattice_Oright__idem,axiom,
% 3.19/1.80 ! [F: a > a > a,A: a,B: a] :
% 3.19/1.80 ( ( semilattice_a @ F )
% 3.19/1.80 => ( ( F @ ( F @ A @ B ) @ B )
% 3.19/1.80 = ( F @ A @ B ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_172_local_Obdd__above__mono,axiom,
% 3.19/1.80 ! [B4: set_a,A3: set_a] :
% 3.19/1.80 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 3.19/1.80 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 3.19/1.80 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_173_local_Obdd__below__mono,axiom,
% 3.19/1.80 ! [B4: set_a,A3: set_a] :
% 3.19/1.80 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 3.19/1.80 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 3.19/1.80 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_174_local_Obdd__above__finite,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_175_local_Ofinite__has__maximal2,axiom,
% 3.19/1.80 ! [A3: set_a,A: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( member_a @ A @ A3 )
% 3.19/1.80 => ? [X3: a] :
% 3.19/1.80 ( ( member_a @ X3 @ A3 )
% 3.19/1.80 & ( less_eq @ A @ X3 )
% 3.19/1.80 & ! [Xa: a] :
% 3.19/1.80 ( ( member_a @ Xa @ A3 )
% 3.19/1.80 => ( ( less_eq @ X3 @ Xa )
% 3.19/1.80 => ( X3 = Xa ) ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_176_local_Ofinite__has__minimal2,axiom,
% 3.19/1.80 ! [A3: set_a,A: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( member_a @ A @ A3 )
% 3.19/1.80 => ? [X3: a] :
% 3.19/1.80 ( ( member_a @ X3 @ A3 )
% 3.19/1.80 & ( less_eq @ X3 @ A )
% 3.19/1.80 & ! [Xa: a] :
% 3.19/1.80 ( ( member_a @ Xa @ A3 )
% 3.19/1.80 => ( ( less_eq @ Xa @ X3 )
% 3.19/1.80 => ( X3 = Xa ) ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_177_local_Obdd__below__finite,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_178_local_OantimonoD,axiom,
% 3.19/1.80 ! [F: a > set_a,X: a,Y: a] :
% 3.19/1.80 ( ( antimono_a_set_a @ less_eq @ F )
% 3.19/1.80 => ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_179_local_OantimonoE,axiom,
% 3.19/1.80 ! [F: a > set_a,X: a,Y: a] :
% 3.19/1.80 ( ( antimono_a_set_a @ less_eq @ F )
% 3.19/1.80 => ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_180_local_OantimonoI,axiom,
% 3.19/1.80 ! [F: a > set_a] :
% 3.19/1.80 ( ! [X3: a,Y4: a] :
% 3.19/1.80 ( ( less_eq @ X3 @ Y4 )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 3.19/1.80 => ( antimono_a_set_a @ less_eq @ F ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_181_local_Oantimono__def,axiom,
% 3.19/1.80 ! [F: a > set_a] :
% 3.19/1.80 ( ( antimono_a_set_a @ less_eq @ F )
% 3.19/1.80 = ( ! [X2: a,Y3: a] :
% 3.19/1.80 ( ( less_eq @ X2 @ Y3 )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_182_local_Omono__def,axiom,
% 3.19/1.80 ! [F: a > set_a] :
% 3.19/1.80 ( ( mono_a_set_a @ less_eq @ F )
% 3.19/1.80 = ( ! [X2: a,Y3: a] :
% 3.19/1.80 ( ( less_eq @ X2 @ Y3 )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_183_local_OmonoI,axiom,
% 3.19/1.80 ! [F: a > set_a] :
% 3.19/1.80 ( ! [X3: a,Y4: a] :
% 3.19/1.80 ( ( less_eq @ X3 @ Y4 )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.19/1.80 => ( mono_a_set_a @ less_eq @ F ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_184_local_OmonoE,axiom,
% 3.19/1.80 ! [F: a > set_a,X: a,Y: a] :
% 3.19/1.80 ( ( mono_a_set_a @ less_eq @ F )
% 3.19/1.80 => ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_185_local_OmonoD,axiom,
% 3.19/1.80 ! [F: a > set_a,X: a,Y: a] :
% 3.19/1.80 ( ( mono_a_set_a @ less_eq @ F )
% 3.19/1.80 => ( ( less_eq @ X @ Y )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_186_local_OSup__fin_OcoboundedI,axiom,
% 3.19/1.80 ! [A3: set_a,A: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( member_a @ A @ A3 )
% 3.19/1.80 => ( less_eq @ A @ ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_187_local_OInf__fin_OcoboundedI,axiom,
% 3.19/1.80 ! [A3: set_a,A: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( member_a @ A @ A3 )
% 3.19/1.80 => ( less_eq @ ( lattic247676691_fin_a @ inf @ A3 ) @ A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_188_local_OSup__fin_Oin__idem,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( member_a @ X @ A3 )
% 3.19/1.80 => ( ( sup @ X @ ( lattic1781219155_fin_a @ sup @ A3 ) )
% 3.19/1.80 = ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_189_local_OInf__fin_Oin__idem,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( member_a @ X @ A3 )
% 3.19/1.80 => ( ( inf @ X @ ( lattic247676691_fin_a @ inf @ A3 ) )
% 3.19/1.80 = ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_190_local_Oinf__Sup__absorb,axiom,
% 3.19/1.80 ! [A3: set_a,A: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( member_a @ A @ A3 )
% 3.19/1.80 => ( ( inf @ A @ ( lattic1781219155_fin_a @ sup @ A3 ) )
% 3.19/1.80 = A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_191_local_Osup__Inf__absorb,axiom,
% 3.19/1.80 ! [A3: set_a,A: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( member_a @ A @ A3 )
% 3.19/1.80 => ( ( sup @ ( lattic247676691_fin_a @ inf @ A3 ) @ A )
% 3.19/1.80 = A ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_192_semilattice__sup_OSup__fin_Ocong,axiom,
% 3.19/1.80 lattic1781219155_fin_a = lattic1781219155_fin_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_193_semilattice__inf_OInf__fin_Ocong,axiom,
% 3.19/1.80 lattic247676691_fin_a = lattic247676691_fin_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_194_local_OInf__fin__le__Sup__fin,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( less_eq @ ( lattic247676691_fin_a @ inf @ A3 ) @ ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_195_local_OSup__fin_Osubset__imp,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ( finite_finite_a @ B4 )
% 3.19/1.80 => ( less_eq @ ( lattic1781219155_fin_a @ sup @ A3 ) @ ( lattic1781219155_fin_a @ sup @ B4 ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_196_local_Ofinite__has__minimal,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ? [X3: a] :
% 3.19/1.80 ( ( member_a @ X3 @ A3 )
% 3.19/1.80 & ! [Xa: a] :
% 3.19/1.80 ( ( member_a @ Xa @ A3 )
% 3.19/1.80 => ( ( less_eq @ Xa @ X3 )
% 3.19/1.80 => ( X3 = Xa ) ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_197_local_Ofinite__has__maximal,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ? [X3: a] :
% 3.19/1.80 ( ( member_a @ X3 @ A3 )
% 3.19/1.80 & ! [Xa: a] :
% 3.19/1.80 ( ( member_a @ Xa @ A3 )
% 3.19/1.80 => ( ( less_eq @ X3 @ Xa )
% 3.19/1.80 => ( X3 = Xa ) ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_198_local_OInf__fin_Osubset,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( B4 != bot_bot_set_a )
% 3.19/1.80 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 3.19/1.80 => ( ( inf @ ( lattic247676691_fin_a @ inf @ B4 ) @ ( lattic247676691_fin_a @ inf @ A3 ) )
% 3.19/1.80 = ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_199_local_OSup__fin_Osubset,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( B4 != bot_bot_set_a )
% 3.19/1.80 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 3.19/1.80 => ( ( sup @ ( lattic1781219155_fin_a @ sup @ B4 ) @ ( lattic1781219155_fin_a @ sup @ A3 ) )
% 3.19/1.80 = ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_200_local_OInf__fin_Obounded__iff,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A3 ) )
% 3.19/1.80 = ( ! [X2: a] :
% 3.19/1.80 ( ( member_a @ X2 @ A3 )
% 3.19/1.80 => ( less_eq @ X @ X2 ) ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_201_local_OInf__fin_OboundedI,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ! [A4: a] :
% 3.19/1.80 ( ( member_a @ A4 @ A3 )
% 3.19/1.80 => ( less_eq @ X @ A4 ) )
% 3.19/1.80 => ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_202_local_OInf__fin_OboundedE,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A3 ) )
% 3.19/1.80 => ! [A5: a] :
% 3.19/1.80 ( ( member_a @ A5 @ A3 )
% 3.19/1.80 => ( less_eq @ X @ A5 ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_203_local_OSup__fin_Obounded__iff,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ( less_eq @ ( lattic1781219155_fin_a @ sup @ A3 ) @ X )
% 3.19/1.80 = ( ! [X2: a] :
% 3.19/1.80 ( ( member_a @ X2 @ A3 )
% 3.19/1.80 => ( less_eq @ X2 @ X ) ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_204_local_OSup__fin_OboundedI,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ! [A4: a] :
% 3.19/1.80 ( ( member_a @ A4 @ A3 )
% 3.19/1.80 => ( less_eq @ A4 @ X ) )
% 3.19/1.80 => ( less_eq @ ( lattic1781219155_fin_a @ sup @ A3 ) @ X ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_205_local_OSup__fin_OboundedE,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ( less_eq @ ( lattic1781219155_fin_a @ sup @ A3 ) @ X )
% 3.19/1.80 => ! [A5: a] :
% 3.19/1.80 ( ( member_a @ A5 @ A3 )
% 3.19/1.80 => ( less_eq @ A5 @ X ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_206_local_OInf__fin_Osubset__imp,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ( finite_finite_a @ B4 )
% 3.19/1.80 => ( less_eq @ ( lattic247676691_fin_a @ inf @ B4 ) @ ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_207_local_Obdd__below__empty,axiom,
% 3.19/1.80 condit1001553558elow_a @ less_eq @ bot_bot_set_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_208_local_Obdd__above__empty,axiom,
% 3.19/1.80 condit1627435690bove_a @ less_eq @ bot_bot_set_a ).
% 3.19/1.80
% 3.19/1.80 thf(fact_209_local_Onot__empty__eq__Iic__eq__empty,axiom,
% 3.19/1.80 ! [H: a] :
% 3.19/1.80 ( bot_bot_set_a
% 3.19/1.80 != ( set_atMost_a @ less_eq @ H ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_210_local_Onot__empty__eq__Ici__eq__empty,axiom,
% 3.19/1.80 ! [L: a] :
% 3.19/1.80 ( bot_bot_set_a
% 3.19/1.80 != ( set_atLeast_a @ less_eq @ L ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_211_local_OatLeast__iff,axiom,
% 3.19/1.80 ! [I: a,K: a] :
% 3.19/1.80 ( ( member_a @ I @ ( set_atLeast_a @ less_eq @ K ) )
% 3.19/1.80 = ( less_eq @ K @ I ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_212_local_OatMost__iff,axiom,
% 3.19/1.80 ! [I: a,K: a] :
% 3.19/1.80 ( ( member_a @ I @ ( set_atMost_a @ less_eq @ K ) )
% 3.19/1.80 = ( less_eq @ I @ K ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_213_local_Obdd__below__Ici,axiom,
% 3.19/1.80 ! [A: a] : ( condit1001553558elow_a @ less_eq @ ( set_atLeast_a @ less_eq @ A ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_214_local_Obdd__above__Iic,axiom,
% 3.19/1.80 ! [B: a] : ( condit1627435690bove_a @ less_eq @ ( set_atMost_a @ less_eq @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_215_subset__empty,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ A3 @ bot_bot_set_a )
% 3.19/1.80 = ( A3 = bot_bot_set_a ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_216_empty__subsetI,axiom,
% 3.19/1.80 ! [A3: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A3 ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_217_subset__antisym,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 3.19/1.80 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 3.19/1.80 => ( A3 = B4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_218_subsetI,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ! [X3: a] :
% 3.19/1.80 ( ( member_a @ X3 @ A3 )
% 3.19/1.80 => ( member_a @ X3 @ B4 ) )
% 3.19/1.80 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_219_Collect__mono__iff,axiom,
% 3.19/1.80 ! [P: a > $o,Q: a > $o] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 3.19/1.80 = ( ! [X2: a] :
% 3.19/1.80 ( ( P @ X2 )
% 3.19/1.80 => ( Q @ X2 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_220_set__eq__subset,axiom,
% 3.19/1.80 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 3.19/1.80 = ( ^ [A6: set_a,B5: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ A6 @ B5 )
% 3.19/1.80 & ( ord_less_eq_set_a @ B5 @ A6 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_221_subset__trans,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a,C4: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 3.19/1.80 => ( ( ord_less_eq_set_a @ B4 @ C4 )
% 3.19/1.80 => ( ord_less_eq_set_a @ A3 @ C4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_222_Collect__mono,axiom,
% 3.19/1.80 ! [P: a > $o,Q: a > $o] :
% 3.19/1.80 ( ! [X3: a] :
% 3.19/1.80 ( ( P @ X3 )
% 3.19/1.80 => ( Q @ X3 ) )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_223_subset__refl,axiom,
% 3.19/1.80 ! [A3: set_a] : ( ord_less_eq_set_a @ A3 @ A3 ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_224_subset__iff,axiom,
% 3.19/1.80 ( ord_less_eq_set_a
% 3.19/1.80 = ( ^ [A6: set_a,B5: set_a] :
% 3.19/1.80 ! [T: a] :
% 3.19/1.80 ( ( member_a @ T @ A6 )
% 3.19/1.80 => ( member_a @ T @ B5 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_225_equalityD2,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( A3 = B4 )
% 3.19/1.80 => ( ord_less_eq_set_a @ B4 @ A3 ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_226_equalityD1,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( A3 = B4 )
% 3.19/1.80 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_227_subset__eq,axiom,
% 3.19/1.80 ( ord_less_eq_set_a
% 3.19/1.80 = ( ^ [A6: set_a,B5: set_a] :
% 3.19/1.80 ! [X2: a] :
% 3.19/1.80 ( ( member_a @ X2 @ A6 )
% 3.19/1.80 => ( member_a @ X2 @ B5 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_228_equalityE,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( A3 = B4 )
% 3.19/1.80 => ~ ( ( ord_less_eq_set_a @ A3 @ B4 )
% 3.19/1.80 => ~ ( ord_less_eq_set_a @ B4 @ A3 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_229_subsetD,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a,C: a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 3.19/1.80 => ( ( member_a @ C @ A3 )
% 3.19/1.80 => ( member_a @ C @ B4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_230_in__mono,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a,X: a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 3.19/1.80 => ( ( member_a @ X @ A3 )
% 3.19/1.80 => ( member_a @ X @ B4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_231_local_Omono__inf,axiom,
% 3.19/1.80 ! [F: a > set_a,A3: a,B4: a] :
% 3.19/1.80 ( ( mono_a_set_a @ less_eq @ F )
% 3.19/1.80 => ( ord_less_eq_set_a @ ( F @ ( inf @ A3 @ B4 ) ) @ ( inf_inf_set_a @ ( F @ A3 ) @ ( F @ B4 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_232_local_OSup__fin_Oclosed,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ! [X3: a,Y4: a] : ( member_a @ ( sup @ X3 @ Y4 ) @ ( insert_a @ X3 @ ( insert_a @ Y4 @ bot_bot_set_a ) ) )
% 3.19/1.80 => ( member_a @ ( lattic1781219155_fin_a @ sup @ A3 ) @ A3 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_233_local_Obdd__above__Int1,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 3.19/1.80 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_234_local_Obdd__above__Int2,axiom,
% 3.19/1.80 ! [B4: set_a,A3: set_a] :
% 3.19/1.80 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 3.19/1.80 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_235_local_Obdd__below__Int1,axiom,
% 3.19/1.80 ! [A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 3.19/1.80 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_236_local_Obdd__below__Int2,axiom,
% 3.19/1.80 ! [B4: set_a,A3: set_a] :
% 3.19/1.80 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 3.19/1.80 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_237_Int__subset__iff,axiom,
% 3.19/1.80 ! [C4: set_a,A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ C4 @ ( inf_inf_set_a @ A3 @ B4 ) )
% 3.19/1.80 = ( ( ord_less_eq_set_a @ C4 @ A3 )
% 3.19/1.80 & ( ord_less_eq_set_a @ C4 @ B4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_238_semilattice__inf__class_Oinf__right__idem,axiom,
% 3.19/1.80 ! [X: set_a,Y: set_a] :
% 3.19/1.80 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Y )
% 3.19/1.80 = ( inf_inf_set_a @ X @ Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_239_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 3.19/1.80 ! [A: set_a,B: set_a] :
% 3.19/1.80 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
% 3.19/1.80 = ( inf_inf_set_a @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_240_semilattice__inf__class_Oinf__left__idem,axiom,
% 3.19/1.80 ! [X: set_a,Y: set_a] :
% 3.19/1.80 ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 3.19/1.80 = ( inf_inf_set_a @ X @ Y ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_241_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 3.19/1.80 ! [A: set_a,B: set_a] :
% 3.19/1.80 ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
% 3.19/1.80 = ( inf_inf_set_a @ A @ B ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_242_semilattice__inf__class_Oinf__idem,axiom,
% 3.19/1.80 ! [X: set_a] :
% 3.19/1.80 ( ( inf_inf_set_a @ X @ X )
% 3.19/1.80 = X ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_243_semilattice__inf__class_Oinf_Oidem,axiom,
% 3.19/1.80 ! [A: set_a] :
% 3.19/1.80 ( ( inf_inf_set_a @ A @ A )
% 3.19/1.80 = A ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_244_local_OInf__fin_Oinsert__not__elem,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ~ ( member_a @ X @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ( lattic247676691_fin_a @ inf @ ( insert_a @ X @ A3 ) )
% 3.19/1.80 = ( inf @ X @ ( lattic247676691_fin_a @ inf @ A3 ) ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_245_local_OInf__fin_Oclosed,axiom,
% 3.19/1.80 ! [A3: set_a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ! [X3: a,Y4: a] : ( member_a @ ( inf @ X3 @ Y4 ) @ ( insert_a @ X3 @ ( insert_a @ Y4 @ bot_bot_set_a ) ) )
% 3.19/1.80 => ( member_a @ ( lattic247676691_fin_a @ inf @ A3 ) @ A3 ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_246_local_OSup__fin_Oinsert__not__elem,axiom,
% 3.19/1.80 ! [A3: set_a,X: a] :
% 3.19/1.80 ( ( finite_finite_a @ A3 )
% 3.19/1.80 => ( ~ ( member_a @ X @ A3 )
% 3.19/1.80 => ( ( A3 != bot_bot_set_a )
% 3.19/1.80 => ( ( lattic1781219155_fin_a @ sup @ ( insert_a @ X @ A3 ) )
% 3.19/1.80 = ( sup @ X @ ( lattic1781219155_fin_a @ sup @ A3 ) ) ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_247_semilattice__inf__class_Ole__inf__iff,axiom,
% 3.19/1.80 ! [X: set_a,Y: set_a,Z2: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ X @ ( inf_inf_set_a @ Y @ Z2 ) )
% 3.19/1.80 = ( ( ord_less_eq_set_a @ X @ Y )
% 3.19/1.80 & ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_248_semilattice__inf__class_Oinf_Obounded__iff,axiom,
% 3.19/1.80 ! [A: set_a,B: set_a,C: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 3.19/1.80 = ( ( ord_less_eq_set_a @ A @ B )
% 3.19/1.80 & ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_249_inf__bot__right,axiom,
% 3.19/1.80 ! [X: set_a] :
% 3.19/1.80 ( ( inf_inf_set_a @ X @ bot_bot_set_a )
% 3.19/1.80 = bot_bot_set_a ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_250_inf__bot__left,axiom,
% 3.19/1.80 ! [X: set_a] :
% 3.19/1.80 ( ( inf_inf_set_a @ bot_bot_set_a @ X )
% 3.19/1.80 = bot_bot_set_a ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_251_insert__subset,axiom,
% 3.19/1.80 ! [X: a,A3: set_a,B4: set_a] :
% 3.19/1.80 ( ( ord_less_eq_set_a @ ( insert_a @ X @ A3 ) @ B4 )
% 3.19/1.80 = ( ( member_a @ X @ B4 )
% 3.19/1.80 & ( ord_less_eq_set_a @ A3 @ B4 ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_252_singleton__insert__inj__eq,axiom,
% 3.19/1.80 ! [B: a,A: a,A3: set_a] :
% 3.19/1.80 ( ( ( insert_a @ B @ bot_bot_set_a )
% 3.19/1.80 = ( insert_a @ A @ A3 ) )
% 3.19/1.80 = ( ( A = B )
% 3.19/1.80 & ( ord_less_eq_set_a @ A3 @ ( insert_a @ B @ bot_bot_set_a ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(fact_253_singleton__insert__inj__eq_H,axiom,
% 3.19/1.80 ! [A: a,A3: set_a,B: a] :
% 3.19/1.80 ( ( ( insert_a @ A @ A3 )
% 3.19/1.80 = ( insert_a @ B @ bot_bot_set_a ) )
% 3.19/1.80 = ( ( A = B )
% 3.19/1.80 & ( ord_less_eq_set_a @ A3 @ ( insert_a @ B @ bot_bot_set_a ) ) ) ) ).
% 3.19/1.80
% 3.19/1.80 thf(conj_0,hypothesis,
% 3.19/1.80 less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ).
% 3.19/1.80
% 3.19/1.80 thf(conj_1,conjecture,
% 3.19/1.80 ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) )
% 3.19/1.80 = ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) ).
% 3.19/1.80 ------------------------
% 3.19/1.84 % (5968)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/275Mi)
% 3.19/1.84 % (5965)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/27Mi)
% 3.19/1.84 % (5966)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/2Mi)
% 3.19/1.84 % (5963)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/183Mi)
% 3.19/1.84 % (5969)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/18Mi)
% 3.19/1.84 % (5967)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/2Mi)
% 3.19/1.84 % (5964)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/4Mi)
% 3.19/1.84 % (5966)Instruction limit reached!
% 3.19/1.84 % (5966)------------------------------
% 3.19/1.84 % (5966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.84 % (5966)Termination reason: Unknown
% 3.19/1.84 % (5966)Termination phase: shuffling
% 3.19/1.84
% 3.19/1.84 % (5966)Memory used [KB]: 1151
% 3.19/1.84 % (5966)Time elapsed: 0.003 s
% 3.19/1.84 % (5966)Instructions burned: 2 (million)
% 3.19/1.84 % (5966)------------------------------
% 3.19/1.84 % (5966)------------------------------
% 3.19/1.84 % (5967)Instruction limit reached!
% 3.19/1.84 % (5967)------------------------------
% 3.19/1.84 % (5967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.84 % (5967)Termination reason: Unknown
% 3.19/1.84 % (5967)Termination phase: shuffling
% 3.19/1.84
% 3.19/1.84 % (5967)Memory used [KB]: 1279
% 3.19/1.84 % (5967)Time elapsed: 0.003 s
% 3.19/1.84 % (5967)Instructions burned: 2 (million)
% 3.19/1.84 % (5967)------------------------------
% 3.19/1.84 % (5967)------------------------------
% 3.19/1.84 % (5964)Instruction limit reached!
% 3.19/1.84 % (5964)------------------------------
% 3.19/1.84 % (5964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.84 % (5964)Termination reason: Unknown
% 3.19/1.84 % (5964)Termination phase: shuffling
% 3.19/1.84
% 3.19/1.84 % (5964)Memory used [KB]: 1279
% 3.19/1.84 % (5964)Time elapsed: 0.005 s
% 3.19/1.84 % (5964)Instructions burned: 5 (million)
% 3.19/1.84 % (5964)------------------------------
% 3.19/1.84 % (5964)------------------------------
% 3.19/1.85 % (5969)Instruction limit reached!
% 3.19/1.85 % (5969)------------------------------
% 3.19/1.85 % (5969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.85 % (5969)Termination reason: Unknown
% 3.19/1.85 % (5969)Termination phase: Property scanning
% 3.19/1.85
% 3.19/1.85 % (5969)Memory used [KB]: 1407
% 3.19/1.85 % (5969)Time elapsed: 0.012 s
% 3.19/1.85 % (5969)Instructions burned: 19 (million)
% 3.19/1.85 % (5969)------------------------------
% 3.19/1.85 % (5969)------------------------------
% 3.19/1.85 % (5965)Instruction limit reached!
% 3.19/1.85 % (5965)------------------------------
% 3.19/1.85 % (5965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.85 % (5965)Termination reason: Unknown
% 3.19/1.85 % (5965)Termination phase: Property scanning
% 3.19/1.85
% 3.19/1.85 % (5965)Memory used [KB]: 1535
% 3.19/1.85 % (5965)Time elapsed: 0.016 s
% 3.19/1.85 % (5965)Instructions burned: 27 (million)
% 3.19/1.85 % (5965)------------------------------
% 3.19/1.85 % (5965)------------------------------
% 3.19/1.86 % (5970)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/3Mi)
% 3.19/1.86 % (5971)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/37Mi)
% 3.19/1.86 % (5972)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/15Mi)
% 3.19/1.86 % (5970)Instruction limit reached!
% 3.19/1.86 % (5970)------------------------------
% 3.19/1.86 % (5970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.86 % (5970)Termination reason: Unknown
% 3.19/1.86 % (5970)Termination phase: shuffling
% 3.19/1.86
% 3.19/1.86 % (5970)Memory used [KB]: 1279
% 3.19/1.86 % (5970)Time elapsed: 0.003 s
% 3.19/1.86 % (5970)Instructions burned: 3 (million)
% 3.19/1.86 % (5970)------------------------------
% 3.19/1.86 % (5970)------------------------------
% 3.19/1.87 % (5972)Instruction limit reached!
% 3.19/1.87 % (5972)------------------------------
% 3.19/1.87 % (5972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.87 % (5972)Termination reason: Unknown
% 3.19/1.87 % (5972)Termination phase: shuffling
% 3.19/1.87
% 3.19/1.87 % (5972)Memory used [KB]: 1407
% 3.19/1.87 % (5972)Time elapsed: 0.010 s
% 3.19/1.87 % (5972)Instructions burned: 15 (million)
% 3.19/1.87 % (5972)------------------------------
% 3.19/1.87 % (5972)------------------------------
% 3.19/1.87 % (5973)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/3Mi)
% 3.19/1.87 % (5973)Instruction limit reached!
% 3.19/1.87 % (5973)------------------------------
% 3.19/1.87 % (5973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.87 % (5973)Termination reason: Unknown
% 3.19/1.87 % (5973)Termination phase: shuffling
% 3.19/1.87
% 3.19/1.87 % (5973)Memory used [KB]: 1279
% 3.19/1.87 % (5973)Time elapsed: 0.003 s
% 3.19/1.87 % (5973)Instructions burned: 3 (million)
% 3.19/1.87 % (5973)------------------------------
% 3.19/1.87 % (5973)------------------------------
% 3.19/1.87 % (5974)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/1041Mi)
% 3.19/1.88 % (5971)Instruction limit reached!
% 3.19/1.88 % (5971)------------------------------
% 3.19/1.88 % (5971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.88 % (5971)Termination reason: Unknown
% 3.19/1.88 % (5971)Termination phase: Property scanning
% 3.19/1.88
% 3.19/1.88 % (5971)Memory used [KB]: 1918
% 3.19/1.88 % (5971)Time elapsed: 0.020 s
% 3.19/1.88 % (5971)Instructions burned: 37 (million)
% 3.19/1.88 % (5971)------------------------------
% 3.19/1.88 % (5971)------------------------------
% 3.19/1.88 % (5975)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/7Mi)
% 3.19/1.88 % (5975)Instruction limit reached!
% 3.19/1.88 % (5975)------------------------------
% 3.19/1.88 % (5975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.88 % (5975)Termination reason: Unknown
% 3.19/1.88 % (5975)Termination phase: shuffling
% 3.19/1.88
% 3.19/1.88 % (5975)Memory used [KB]: 1279
% 3.19/1.88 % (5975)Time elapsed: 0.006 s
% 3.19/1.88 % (5975)Instructions burned: 8 (million)
% 3.19/1.88 % (5975)------------------------------
% 3.19/1.88 % (5975)------------------------------
% 3.19/1.89 % (5976)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/16Mi)
% 3.19/1.89 % (5977)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/3Mi)
% 3.19/1.89 % (5977)Instruction limit reached!
% 3.19/1.89 % (5977)------------------------------
% 3.19/1.89 % (5977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.89 % (5977)Termination reason: Unknown
% 3.19/1.89 % (5977)Termination phase: shuffling
% 3.19/1.89
% 3.19/1.89 % (5977)Memory used [KB]: 1279
% 3.19/1.89 % (5977)Time elapsed: 0.004 s
% 3.19/1.89 % (5977)Instructions burned: 3 (million)
% 3.19/1.89 % (5977)------------------------------
% 3.19/1.89 % (5977)------------------------------
% 3.19/1.90 % (5976)Instruction limit reached!
% 3.19/1.90 % (5976)------------------------------
% 3.19/1.90 % (5976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.90 % (5976)Termination reason: Unknown
% 3.19/1.90 % (5976)Termination phase: shuffling
% 3.19/1.90
% 3.19/1.90 % (5976)Memory used [KB]: 1407
% 3.19/1.90 % (5976)Time elapsed: 0.010 s
% 3.19/1.90 % (5976)Instructions burned: 16 (million)
% 3.19/1.90 % (5976)------------------------------
% 3.19/1.90 % (5976)------------------------------
% 3.22/1.90 % (5978)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/3Mi)
% 3.22/1.90 % (5978)Instruction limit reached!
% 3.22/1.90 % (5978)------------------------------
% 3.22/1.90 % (5978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.90 % (5978)Termination reason: Unknown
% 3.22/1.90 % (5978)Termination phase: shuffling
% 3.22/1.90
% 3.22/1.90 % (5978)Memory used [KB]: 1279
% 3.22/1.90 % (5978)Time elapsed: 0.004 s
% 3.22/1.90 % (5978)Instructions burned: 3 (million)
% 3.22/1.90 % (5978)------------------------------
% 3.22/1.90 % (5978)------------------------------
% 3.22/1.90 % (5979)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/7Mi)
% 3.22/1.91 % (5979)Instruction limit reached!
% 3.22/1.91 % (5979)------------------------------
% 3.22/1.91 % (5979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.91 % (5979)Termination reason: Unknown
% 3.22/1.91 % (5979)Termination phase: shuffling
% 3.22/1.91
% 3.22/1.91 % (5979)Memory used [KB]: 1279
% 3.22/1.91 % (5979)Time elapsed: 0.005 s
% 3.22/1.91 % (5979)Instructions burned: 8 (million)
% 3.22/1.91 % (5979)------------------------------
% 3.22/1.91 % (5979)------------------------------
% 3.22/1.91 % (5980)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/3Mi)
% 3.22/1.91 % (5980)Instruction limit reached!
% 3.22/1.91 % (5980)------------------------------
% 3.22/1.91 % (5980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.91 % (5980)Termination reason: Unknown
% 3.22/1.91 % (5980)Termination phase: shuffling
% 3.22/1.91
% 3.22/1.91 % (5980)Memory used [KB]: 1279
% 3.22/1.91 % (5980)Time elapsed: 0.003 s
% 3.22/1.91 % (5980)Instructions burned: 3 (million)
% 3.22/1.91 % (5980)------------------------------
% 3.22/1.91 % (5980)------------------------------
% 3.22/1.91 % (5981)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/4Mi)
% 3.22/1.92 % (5982)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/18Mi)
% 3.22/1.92 % (5981)Instruction limit reached!
% 3.22/1.92 % (5981)------------------------------
% 3.22/1.92 % (5981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.92 % (5981)Termination reason: Unknown
% 3.22/1.92 % (5981)Termination phase: shuffling
% 3.22/1.92
% 3.22/1.92 % (5981)Memory used [KB]: 1279
% 3.22/1.92 % (5981)Time elapsed: 0.005 s
% 3.22/1.92 % (5981)Instructions burned: 6 (million)
% 3.22/1.92 % (5981)------------------------------
% 3.22/1.92 % (5981)------------------------------
% 3.22/1.93 % (5983)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/710Mi)
% 3.22/1.93 % (5982)Instruction limit reached!
% 3.22/1.93 % (5982)------------------------------
% 3.22/1.93 % (5982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.93 % (5982)Termination reason: Unknown
% 3.22/1.93 % (5982)Termination phase: Property scanning
% 3.22/1.93
% 3.22/1.93 % (5982)Memory used [KB]: 1407
% 3.22/1.93 % (5982)Time elapsed: 0.012 s
% 3.22/1.93 % (5982)Instructions burned: 19 (million)
% 3.22/1.93 % (5982)------------------------------
% 3.22/1.93 % (5982)------------------------------
% 3.22/1.93 % (5984)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5856 for (2999ds/6Mi)
% 3.22/1.93 % (5984)Instruction limit reached!
% 3.22/1.93 % (5984)------------------------------
% 3.22/1.93 % (5984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.93 % (5984)Termination reason: Unknown
% 3.22/1.93 % (5984)Termination phase: shuffling
% 3.22/1.93
% 3.22/1.93 % (5984)Memory used [KB]: 1279
% 3.22/1.93 % (5984)Time elapsed: 0.005 s
% 3.22/1.93 % (5984)Instructions burned: 6 (million)
% 3.22/1.93 % (5984)------------------------------
% 3.22/1.93 % (5984)------------------------------
% 3.22/1.94 % (5985)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_5856 for (2998ds/902Mi)
% 3.22/1.94 % (5963)Instruction limit reached!
% 3.22/1.94 % (5963)------------------------------
% 3.22/1.94 % (5963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.94 % (5963)Termination reason: Unknown
% 3.22/1.94 % (5963)Termination phase: Saturation
% 3.22/1.94
% 3.22/1.94 % (5963)Memory used [KB]: 6908
% 3.22/1.94 % (5963)Time elapsed: 0.102 s
% 3.22/1.94 % (5963)Instructions burned: 184 (million)
% 3.22/1.94 % (5963)------------------------------
% 3.22/1.94 % (5963)------------------------------
% 3.22/1.94 % (5986)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_5856 for (2998ds/21Mi)
% 3.22/1.95 % (5987)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5856 for (2998ds/5Mi)
% 3.22/1.96 % (5987)Instruction limit reached!
% 3.22/1.96 % (5987)------------------------------
% 3.22/1.96 % (5987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.96 % (5987)Termination reason: Unknown
% 3.22/1.96 % (5987)Termination phase: shuffling
% 3.22/1.96
% 3.22/1.96 % (5987)Memory used [KB]: 1279
% 3.22/1.96 % (5987)Time elapsed: 0.005 s
% 3.22/1.96 % (5987)Instructions burned: 6 (million)
% 3.22/1.96 % (5987)------------------------------
% 3.22/1.96 % (5987)------------------------------
% 3.22/1.96 % (5986)Instruction limit reached!
% 3.22/1.96 % (5986)------------------------------
% 3.22/1.96 % (5986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.96 % (5986)Termination reason: Unknown
% 3.22/1.96 % (5986)Termination phase: shuffling
% 3.22/1.96
% 3.22/1.96 % (5986)Memory used [KB]: 1535
% 3.22/1.96 % (5986)Time elapsed: 0.013 s
% 3.22/1.96 % (5986)Instructions burned: 22 (million)
% 3.22/1.96 % (5986)------------------------------
% 3.22/1.96 % (5986)------------------------------
% 3.22/1.96 % (5988)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_5856 for (2998ds/6Mi)
% 3.22/1.96 % (5988)Instruction limit reached!
% 3.22/1.96 % (5988)------------------------------
% 3.22/1.96 % (5988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.96 % (5988)Termination reason: Unknown
% 3.22/1.96 % (5988)Termination phase: shuffling
% 3.22/1.96
% 3.22/1.96 % (5988)Memory used [KB]: 1279
% 3.22/1.96 % (5988)Time elapsed: 0.005 s
% 3.22/1.96 % (5988)Instructions burned: 7 (million)
% 3.22/1.96 % (5988)------------------------------
% 3.22/1.96 % (5988)------------------------------
% 3.22/1.97 % (5989)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5856 for (2998ds/377Mi)
% 3.22/1.98 % (5990)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_5856 for (2998ds/779Mi)
% 3.22/1.98 % (5968)Instruction limit reached!
% 3.22/1.98 % (5968)------------------------------
% 3.22/1.98 % (5968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.98 % (5968)Termination reason: Unknown
% 3.22/1.98 % (5968)Termination phase: Saturation
% 3.22/1.98
% 3.22/1.98 % (5968)Memory used [KB]: 6396
% 3.22/1.98 % (5968)Time elapsed: 0.145 s
% 3.22/1.98 % (5968)Instructions burned: 276 (million)
% 3.22/1.98 % (5968)------------------------------
% 3.22/1.98 % (5968)------------------------------
% 3.22/1.98 % (5991)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_5856 for (2998ds/19Mi)
% 3.22/1.99 % (5991)Instruction limit reached!
% 3.22/1.99 % (5991)------------------------------
% 3.22/1.99 % (5991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.99 % (5991)Termination reason: Unknown
% 3.22/1.99 % (5991)Termination phase: shuffling
% 3.22/1.99
% 3.22/1.99 % (5991)Memory used [KB]: 1535
% 3.22/1.99 % (5991)Time elapsed: 0.011 s
% 3.22/1.99 % (5991)Instructions burned: 19 (million)
% 3.22/1.99 % (5991)------------------------------
% 3.22/1.99 % (5991)------------------------------
% 3.22/2.00 % (5992)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5856 for (2998ds/879Mi)
% 3.22/2.01 % (5993)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5856 for (2998ds/17Mi)
% 3.22/2.02 % (5993)Instruction limit reached!
% 3.22/2.02 % (5993)------------------------------
% 3.22/2.02 % (5993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/2.02 % (5993)Termination reason: Unknown
% 3.22/2.02 % (5993)Termination phase: shuffling
% 3.22/2.02
% 3.22/2.02 % (5993)Memory used [KB]: 1407
% 3.22/2.02 % (5993)Time elapsed: 0.012 s
% 3.22/2.02 % (5993)Instructions burned: 18 (million)
% 3.22/2.02 % (5993)------------------------------
% 3.22/2.02 % (5993)------------------------------
% 4.57/2.04 % (5994)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5856 for (2997ds/3Mi)
% 4.57/2.05 % (5994)Instruction limit reached!
% 4.57/2.05 % (5994)------------------------------
% 4.57/2.05 % (5994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.05 % (5994)Termination reason: Unknown
% 4.57/2.05 % (5994)Termination phase: shuffling
% 4.57/2.05
% 4.57/2.05 % (5994)Memory used [KB]: 1279
% 4.57/2.05 % (5994)Time elapsed: 0.004 s
% 4.57/2.05 % (5994)Instructions burned: 4 (million)
% 4.57/2.05 % (5994)------------------------------
% 4.57/2.05 % (5994)------------------------------
% 4.57/2.07 % (5995)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5856 for (2997ds/30Mi)
% 4.57/2.08 % (5995)Instruction limit reached!
% 4.57/2.08 % (5995)------------------------------
% 4.57/2.08 % (5995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.08 % (5995)Termination reason: Unknown
% 4.57/2.08 % (5995)Termination phase: Property scanning
% 4.57/2.08
% 4.57/2.08 % (5995)Memory used [KB]: 1535
% 4.57/2.08 % (5995)Time elapsed: 0.018 s
% 4.57/2.08 % (5995)Instructions burned: 31 (million)
% 4.57/2.08 % (5995)------------------------------
% 4.57/2.08 % (5995)------------------------------
% 4.57/2.11 % (5996)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5856 for (2997ds/127Mi)
% 5.29/2.17 % (5996)Instruction limit reached!
% 5.29/2.17 % (5996)------------------------------
% 5.29/2.17 % (5996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.29/2.17 % (5996)Termination reason: Unknown
% 5.29/2.17 % (5996)Termination phase: Saturation
% 5.29/2.17
% 5.29/2.17 % (5996)Memory used [KB]: 6652
% 5.29/2.17 % (5996)Time elapsed: 0.069 s
% 5.29/2.17 % (5996)Instructions burned: 128 (million)
% 5.29/2.17 % (5996)------------------------------
% 5.29/2.17 % (5996)------------------------------
% 5.29/2.19 % (5989)Instruction limit reached!
% 5.29/2.19 % (5989)------------------------------
% 5.29/2.19 % (5989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.29/2.19 % (5989)Termination reason: Unknown
% 5.29/2.19 % (5989)Termination phase: Saturation
% 5.29/2.19
% 5.29/2.19 % (5989)Memory used [KB]: 7291
% 5.29/2.19 % (5989)Time elapsed: 0.213 s
% 5.29/2.19 % (5989)Instructions burned: 378 (million)
% 5.29/2.19 % (5989)------------------------------
% 5.29/2.19 % (5989)------------------------------
% 5.29/2.19 % (5997)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_5856 for (2996ds/100Mi)
% 5.78/2.21 % (5998)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_5856 for (2996ds/3Mi)
% 5.78/2.21 % (5998)Instruction limit reached!
% 5.78/2.21 % (5998)------------------------------
% 5.78/2.21 % (5998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.21 % (5998)Termination reason: Unknown
% 5.78/2.21 % (5998)Termination phase: shuffling
% 5.78/2.21
% 5.78/2.21 % (5998)Memory used [KB]: 1279
% 5.78/2.21 % (5998)Time elapsed: 0.004 s
% 5.78/2.21 % (5998)Instructions burned: 4 (million)
% 5.78/2.21 % (5998)------------------------------
% 5.78/2.21 % (5998)------------------------------
% 5.78/2.23 % (5999)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_5856 for (2995ds/20Mi)
% 5.78/2.24 % (5999)Instruction limit reached!
% 5.78/2.24 % (5999)------------------------------
% 5.78/2.24 % (5999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.24 % (5999)Termination reason: Unknown
% 5.78/2.24 % (5999)Termination phase: Property scanning
% 5.78/2.24
% 5.78/2.24 % (5999)Memory used [KB]: 1407
% 5.78/2.24 % (5999)Time elapsed: 0.014 s
% 5.78/2.24 % (5999)Instructions burned: 22 (million)
% 5.78/2.24 % (5999)------------------------------
% 5.78/2.24 % (5999)------------------------------
% 5.78/2.24 % (5997)Instruction limit reached!
% 5.78/2.24 % (5997)------------------------------
% 5.78/2.24 % (5997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.24 % (5997)Termination reason: Unknown
% 5.78/2.24 % (5997)Termination phase: Property scanning
% 5.78/2.24
% 5.78/2.24 % (5997)Memory used [KB]: 1918
% 5.78/2.24 % (5997)Time elapsed: 0.052 s
% 5.78/2.24 % (5997)Instructions burned: 100 (million)
% 5.78/2.24 % (5997)------------------------------
% 5.78/2.24 % (5997)------------------------------
% 5.78/2.26 % (6000)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_5856 for (2995ds/86Mi)
% 5.78/2.26 % (6001)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_5856 for (2995ds/107Mi)
% 6.40/2.31 % (6000)Instruction limit reached!
% 6.40/2.31 % (6000)------------------------------
% 6.40/2.31 % (6000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.31 % (6000)Termination reason: Unknown
% 6.40/2.31 % (6000)Termination phase: Saturation
% 6.40/2.31
% 6.40/2.31 % (6000)Memory used [KB]: 6396
% 6.40/2.31 % (6000)Time elapsed: 0.047 s
% 6.40/2.31 % (6000)Instructions burned: 86 (million)
% 6.40/2.31 % (6000)------------------------------
% 6.40/2.31 % (6000)------------------------------
% 6.40/2.31 % (5983)Refutation not found, non-redundant clauses discarded% (5983)------------------------------
% 6.40/2.31 % (5983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.31 % (5983)Termination reason: Refutation not found, non-redundant clauses discarded
% 6.40/2.31
% 6.40/2.31 % (5983)Memory used [KB]: 7036
% 6.40/2.31 % (5983)Time elapsed: 0.385 s
% 6.40/2.31 % (5983)Instructions burned: 694 (million)
% 6.40/2.31 % (5983)------------------------------
% 6.40/2.31 % (5983)------------------------------
% 6.40/2.32 % (6001)Instruction limit reached!
% 6.40/2.32 % (6001)------------------------------
% 6.40/2.32 % (6001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.32 % (6001)Termination reason: Unknown
% 6.40/2.32 % (6001)Termination phase: Saturation
% 6.40/2.32
% 6.40/2.32 % (6001)Memory used [KB]: 6396
% 6.40/2.32 % (6001)Time elapsed: 0.060 s
% 6.40/2.32 % (6001)Instructions burned: 108 (million)
% 6.40/2.32 % (6001)------------------------------
% 6.40/2.32 % (6001)------------------------------
% 6.40/2.33 % (6002)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_5856 for (2994ds/39Mi)
% 6.40/2.33 % (6003)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_5856 for (2994ds/448Mi)
% 6.40/2.34 % (6004)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_5856 for (2994ds/46Mi)
% 6.40/2.35 % (6002)Instruction limit reached!
% 6.40/2.35 % (6002)------------------------------
% 6.40/2.35 % (6002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.35 % (6002)Termination reason: Unknown
% 6.40/2.35 % (6002)Termination phase: Property scanning
% 6.40/2.35
% 6.40/2.35 % (6002)Memory used [KB]: 1918
% 6.40/2.35 % (6002)Time elapsed: 0.022 s
% 6.40/2.35 % (6002)Instructions burned: 40 (million)
% 6.40/2.35 % (6002)------------------------------
% 6.40/2.35 % (6002)------------------------------
% 6.40/2.37 % (6004)Instruction limit reached!
% 6.40/2.37 % (6004)------------------------------
% 6.40/2.37 % (6004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.37 % (6004)Termination reason: Unknown
% 6.40/2.37 % (6004)Termination phase: Property scanning
% 6.40/2.37
% 6.40/2.37 % (6004)Memory used [KB]: 1535
% 6.40/2.37 % (6004)Time elapsed: 0.026 s
% 6.40/2.37 % (6004)Instructions burned: 46 (million)
% 6.40/2.37 % (6004)------------------------------
% 6.40/2.37 % (6004)------------------------------
% 6.40/2.37 % (6005)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_5856 for (2994ds/98Mi)
% 6.40/2.38 % (5990)Instruction limit reached!
% 6.40/2.38 % (5990)------------------------------
% 6.40/2.38 % (5990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.38 % (5990)Termination reason: Unknown
% 6.40/2.38 % (5990)Termination phase: Saturation
% 6.40/2.38
% 6.40/2.38 % (5990)Memory used [KB]: 7036
% 6.40/2.38 % (5990)Time elapsed: 0.410 s
% 6.40/2.38 % (5990)Instructions burned: 780 (million)
% 6.40/2.38 % (5990)------------------------------
% 6.40/2.38 % (5990)------------------------------
% 6.40/2.39 % (6006)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_5856 for (2994ds/507Mi)
% 7.05/2.40 % (6007)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_5856 for (2994ds/149Mi)
% 7.05/2.41 % (5985)Instruction limit reached!
% 7.05/2.41 % (5985)------------------------------
% 7.05/2.41 % (5985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.05/2.42 % (5985)Termination reason: Unknown
% 7.05/2.42 % (5985)Termination phase: Saturation
% 7.05/2.42
% 7.05/2.42 % (5985)Memory used [KB]: 7547
% 7.05/2.42 % (5985)Time elapsed: 0.481 s
% 7.05/2.42 % (5985)Instructions burned: 902 (million)
% 7.05/2.42 % (5985)------------------------------
% 7.05/2.42 % (5985)------------------------------
% 7.05/2.42 % (6005)Instruction limit reached!
% 7.05/2.42 % (6005)------------------------------
% 7.05/2.42 % (6005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.05/2.42 % (6005)Termination reason: Unknown
% 7.05/2.42 % (6005)Termination phase: Property scanning
% 7.05/2.42
% 7.05/2.42 % (6005)Memory used [KB]: 1918
% 7.05/2.42 % (6005)Time elapsed: 0.051 s
% 7.05/2.42 % (6005)Instructions burned: 98 (million)
% 7.05/2.42 % (6005)------------------------------
% 7.05/2.42 % (6005)------------------------------
% 7.05/2.44 % (6008)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_5856 for (2993ds/39Mi)
% 7.05/2.44 % (6009)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_5856 for (2993ds/6Mi)
% 7.05/2.44 % (6009)Instruction limit reached!
% 7.05/2.44 % (6009)------------------------------
% 7.05/2.44 % (6009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.05/2.44 % (6009)Termination reason: Unknown
% 7.05/2.44 % (6009)Termination phase: shuffling
% 7.05/2.44
% 7.05/2.44 % (6009)Memory used [KB]: 1279
% 7.05/2.44 % (6009)Time elapsed: 0.005 s
% 7.05/2.44 % (6009)Instructions burned: 6 (million)
% 7.05/2.44 % (6009)------------------------------
% 7.05/2.44 % (6009)------------------------------
% 7.05/2.46 % (5974)Instruction limit reached!
% 7.05/2.46 % (5974)------------------------------
% 7.05/2.46 % (5974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.05/2.46 % (5974)Termination reason: Unknown
% 7.05/2.46 % (5974)Termination phase: Saturation
% 7.05/2.46
% 7.05/2.46 % (5974)Memory used [KB]: 8059
% 7.05/2.46 % (5974)Time elapsed: 0.585 s
% 7.05/2.46 % (5974)Instructions burned: 1042 (million)
% 7.05/2.46 % (5974)------------------------------
% 7.05/2.46 % (5974)------------------------------
% 7.05/2.46 % (6008)Instruction limit reached!
% 7.05/2.46 % (6008)------------------------------
% 7.05/2.46 % (6008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.05/2.46 % (6008)Termination reason: Unknown
% 7.05/2.46 % (6008)Termination phase: Property scanning
% 7.05/2.46
% 7.05/2.46 % (6008)Memory used [KB]: 1663
% 7.05/2.46 % (6008)Time elapsed: 0.024 s
% 7.05/2.46 % (6008)Instructions burned: 40 (million)
% 7.05/2.46 % (6008)------------------------------
% 7.05/2.46 % (6008)------------------------------
% 7.05/2.46 % (6010)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_5856 for (2993ds/1087Mi)
% 7.05/2.48 % (6011)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_5856 for (2993ds/47Mi)
% 7.05/2.48 % (6012)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_5856 for (2993ds/44Mi)
% 7.05/2.48 % (5992)Instruction limit reached!
% 7.05/2.48 % (5992)------------------------------
% 7.05/2.48 % (5992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.05/2.48 % (5992)Termination reason: Unknown
% 7.05/2.48 % (5992)Termination phase: Saturation
% 7.05/2.48
% 7.05/2.48 % (5992)Memory used [KB]: 7675
% 7.05/2.48 % (5992)Time elapsed: 0.481 s
% 7.05/2.48 % (5992)Instructions burned: 879 (million)
% 7.05/2.48 % (5992)------------------------------
% 7.05/2.48 % (5992)------------------------------
% 7.05/2.49 % (6007)Instruction limit reached!
% 7.05/2.49 % (6007)------------------------------
% 7.05/2.49 % (6007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.05/2.49 % (6007)Termination reason: Unknown
% 7.05/2.49 % (6007)Termination phase: Saturation
% 7.05/2.49
% 7.05/2.49 % (6007)Memory used [KB]: 6652
% 7.05/2.49 % (6007)Time elapsed: 0.085 s
% 7.05/2.49 % (6007)Instructions burned: 149 (million)
% 7.05/2.49 % (6007)------------------------------
% 7.05/2.49 % (6007)------------------------------
% 7.49/2.50 % (6012)Instruction limit reached!
% 7.49/2.50 % (6012)------------------------------
% 7.49/2.50 % (6012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.50 % (6012)Termination reason: Unknown
% 7.49/2.50 % (6012)Termination phase: Property scanning
% 7.49/2.50
% 7.49/2.50 % (6012)Memory used [KB]: 1918
% 7.49/2.50 % (6012)Time elapsed: 0.025 s
% 7.49/2.50 % (6012)Instructions burned: 45 (million)
% 7.49/2.50 % (6012)------------------------------
% 7.49/2.50 % (6012)------------------------------
% 7.49/2.50 % (6011)Instruction limit reached!
% 7.49/2.50 % (6011)------------------------------
% 7.49/2.50 % (6011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.50 % (6011)Termination reason: Unknown
% 7.49/2.50 % (6011)Termination phase: Property scanning
% 7.49/2.50
% 7.49/2.50 % (6011)Memory used [KB]: 1663
% 7.49/2.50 % (6011)Time elapsed: 0.027 s
% 7.49/2.50 % (6011)Instructions burned: 48 (million)
% 7.49/2.50 % (6011)------------------------------
% 7.49/2.50 % (6011)------------------------------
% 7.49/2.50 % (6013)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_5856 for (2993ds/432Mi)
% 7.49/2.51 % (6014)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_5856 for (2993ds/62Mi)
% 7.49/2.52 % (6015)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_5856 for (2993ds/31Mi)
% 7.49/2.52 % (6016)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_5856 for (2993ds/96Mi)
% 7.49/2.54 % (6015)Instruction limit reached!
% 7.49/2.54 % (6015)------------------------------
% 7.49/2.54 % (6015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.54 % (6015)Termination reason: Unknown
% 7.49/2.54 % (6015)Termination phase: Preprocessing 1
% 7.49/2.54
% 7.49/2.54 % (6015)Memory used [KB]: 1535
% 7.49/2.54 % (6015)Time elapsed: 0.018 s
% 7.49/2.54 % (6015)Instructions burned: 31 (million)
% 7.49/2.54 % (6015)------------------------------
% 7.49/2.54 % (6015)------------------------------
% 7.49/2.54 % (6014)Instruction limit reached!
% 7.49/2.54 % (6014)------------------------------
% 7.49/2.54 % (6014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.54 % (6014)Termination reason: Unknown
% 7.49/2.54 % (6014)Termination phase: Property scanning
% 7.49/2.54
% 7.49/2.54 % (6014)Memory used [KB]: 1918
% 7.49/2.54 % (6014)Time elapsed: 0.034 s
% 7.49/2.54 % (6014)Instructions burned: 63 (million)
% 7.49/2.54 % (6014)------------------------------
% 7.49/2.54 % (6014)------------------------------
% 7.49/2.56 % (6018)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_5856 for (2992ds/71Mi)
% 7.49/2.56 % (6017)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_5856 for (2992ds/453Mi)
% 7.49/2.57 % (6003)Instruction limit reached!
% 7.49/2.57 % (6003)------------------------------
% 7.49/2.57 % (6003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.57 % (6003)Termination reason: Unknown
% 7.49/2.57 % (6003)Termination phase: Saturation
% 7.49/2.57
% 7.49/2.57 % (6003)Memory used [KB]: 7291
% 7.49/2.57 % (6003)Time elapsed: 0.246 s
% 7.49/2.57 % (6003)Instructions burned: 448 (million)
% 7.49/2.57 % (6003)------------------------------
% 7.49/2.57 % (6003)------------------------------
% 7.49/2.57 % (6016)Instruction limit reached!
% 7.49/2.57 % (6016)------------------------------
% 7.49/2.57 % (6016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.57 % (6016)Termination reason: Unknown
% 7.49/2.57 % (6016)Termination phase: Saturation
% 7.49/2.57
% 7.49/2.57 % (6016)Memory used [KB]: 6524
% 7.49/2.57 % (6016)Time elapsed: 0.052 s
% 7.49/2.57 % (6016)Instructions burned: 96 (million)
% 7.49/2.57 % (6016)------------------------------
% 7.49/2.57 % (6016)------------------------------
% 7.49/2.59 % (6019)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_5856 for (2992ds/83Mi)
% 7.49/2.59 % (6020)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_5856 for (2992ds/11Mi)
% 8.00/2.60 % (6018)Instruction limit reached!
% 8.00/2.60 % (6018)------------------------------
% 8.00/2.60 % (6018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.60 % (6018)Termination reason: Unknown
% 8.00/2.60 % (6018)Termination phase: Property scanning
% 8.00/2.60
% 8.00/2.60 % (6018)Memory used [KB]: 1791
% 8.00/2.60 % (6018)Time elapsed: 0.039 s
% 8.00/2.60 % (6018)Instructions burned: 71 (million)
% 8.00/2.60 % (6018)------------------------------
% 8.00/2.60 % (6018)------------------------------
% 8.00/2.60 % (6020)Instruction limit reached!
% 8.00/2.60 % (6020)------------------------------
% 8.00/2.60 % (6020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.60 % (6020)Termination reason: Unknown
% 8.00/2.60 % (6020)Termination phase: shuffling
% 8.00/2.60
% 8.00/2.60 % (6020)Memory used [KB]: 1407
% 8.00/2.60 % (6020)Time elapsed: 0.008 s
% 8.00/2.60 % (6020)Instructions burned: 11 (million)
% 8.00/2.60 % (6020)------------------------------
% 8.00/2.60 % (6020)------------------------------
% 8.00/2.62 % (6021)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_5856 for (2992ds/41Mi)
% 8.00/2.62 % (6022)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5856 for (2992ds/6Mi)
% 8.00/2.62 % (6022)Instruction limit reached!
% 8.00/2.62 % (6022)------------------------------
% 8.00/2.62 % (6022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.62 % (6022)Termination reason: Unknown
% 8.00/2.62 % (6022)Termination phase: shuffling
% 8.00/2.62
% 8.00/2.62 % (6022)Memory used [KB]: 1279
% 8.00/2.62 % (6022)Time elapsed: 0.006 s
% 8.00/2.62 % (6022)Instructions burned: 7 (million)
% 8.00/2.62 % (6022)------------------------------
% 8.00/2.62 % (6022)------------------------------
% 8.00/2.64 % (6021)Instruction limit reached!
% 8.00/2.64 % (6021)------------------------------
% 8.00/2.64 % (6021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.64 % (6021)Termination reason: Unknown
% 8.00/2.64 % (6021)Termination phase: Property scanning
% 8.00/2.64
% 8.00/2.64 % (6021)Memory used [KB]: 1791
% 8.00/2.64 % (6021)Time elapsed: 0.023 s
% 8.00/2.64 % (6021)Instructions burned: 42 (million)
% 8.00/2.64 % (6021)------------------------------
% 8.00/2.64 % (6021)------------------------------
% 8.00/2.64 % (6019)Instruction limit reached!
% 8.00/2.64 % (6019)------------------------------
% 8.00/2.64 % (6019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.64 % (6019)Termination reason: Unknown
% 8.00/2.64 % (6019)Termination phase: Saturation
% 8.00/2.64
% 8.00/2.64 % (6019)Memory used [KB]: 6140
% 8.00/2.64 % (6019)Time elapsed: 0.048 s
% 8.00/2.64 % (6019)Instructions burned: 83 (million)
% 8.00/2.64 % (6019)------------------------------
% 8.00/2.64 % (6019)------------------------------
% 8.00/2.64 % (6023)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_5856 for (2991ds/150Mi)
% 8.00/2.66 % (6024)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_5856 for (2991ds/343Mi)
% 8.00/2.66 % (6025)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_5856 for (2991ds/109Mi)
% 8.00/2.66 % (6006)Instruction limit reached!
% 8.00/2.66 % (6006)------------------------------
% 8.00/2.66 % (6006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.66 % (6006)Termination reason: Unknown
% 8.00/2.66 % (6006)Termination phase: Saturation
% 8.00/2.66
% 8.00/2.66 % (6006)Memory used [KB]: 7291
% 8.00/2.66 % (6006)Time elapsed: 0.275 s
% 8.00/2.66 % (6006)Instructions burned: 507 (million)
% 8.00/2.66 % (6006)------------------------------
% 8.00/2.66 % (6006)------------------------------
% 8.00/2.68 % (6026)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_5856 for (2991ds/253Mi)
% 8.51/2.72 % (6025)Instruction limit reached!
% 8.51/2.72 % (6025)------------------------------
% 8.51/2.72 % (6025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.51/2.72 % (6025)Termination reason: Unknown
% 8.51/2.72 % (6025)Termination phase: Saturation
% 8.51/2.72
% 8.51/2.72 % (6025)Memory used [KB]: 6524
% 8.51/2.72 % (6025)Time elapsed: 0.060 s
% 8.51/2.72 % (6025)Instructions burned: 109 (million)
% 8.51/2.72 % (6025)------------------------------
% 8.51/2.72 % (6025)------------------------------
% 8.51/2.73 % (6023)Instruction limit reached!
% 8.51/2.73 % (6023)------------------------------
% 8.51/2.73 % (6023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.51/2.73 % (6023)Termination reason: Unknown
% 8.51/2.73 % (6023)Termination phase: Saturation
% 8.51/2.73
% 8.51/2.73 % (6023)Memory used [KB]: 6652
% 8.51/2.73 % (6023)Time elapsed: 0.086 s
% 8.51/2.73 % (6023)Instructions burned: 150 (million)
% 8.51/2.73 % (6023)------------------------------
% 8.51/2.73 % (6023)------------------------------
% 8.51/2.73 % (6013)Instruction limit reached!
% 8.51/2.73 % (6013)------------------------------
% 8.51/2.73 % (6013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.51/2.73 % (6013)Termination reason: Unknown
% 8.51/2.73 % (6013)Termination phase: Saturation
% 8.51/2.73
% 8.51/2.73 % (6013)Memory used [KB]: 3454
% 8.51/2.73 % (6013)Time elapsed: 0.233 s
% 8.51/2.73 % (6013)Instructions burned: 432 (million)
% 8.51/2.73 % (6013)------------------------------
% 8.51/2.73 % (6013)------------------------------
% 8.51/2.74 % (6027)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_5856 for (2990ds/140Mi)
% 8.51/2.75 % (6028)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_5856 for (2990ds/614Mi)
% 8.51/2.76 % (6029)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_5856 for (2990ds/202Mi)
% 8.94/2.81 % (6017)Instruction limit reached!
% 8.94/2.81 % (6017)------------------------------
% 8.94/2.81 % (6017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.94/2.81 % (6017)Termination reason: Unknown
% 8.94/2.81 % (6017)Termination phase: Saturation
% 8.94/2.81
% 8.94/2.81 % (6017)Memory used [KB]: 7036
% 8.94/2.81 % (6017)Time elapsed: 0.253 s
% 8.94/2.81 % (6017)Instructions burned: 454 (million)
% 8.94/2.81 % (6017)------------------------------
% 8.94/2.81 % (6017)------------------------------
% 8.94/2.82 % (6026)Instruction limit reached!
% 8.94/2.82 % (6026)------------------------------
% 8.94/2.82 % (6026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.94/2.82 % (6026)Termination reason: Unknown
% 8.94/2.82 % (6026)Termination phase: Saturation
% 8.94/2.82
% 8.94/2.82 % (6026)Memory used [KB]: 6524
% 8.94/2.82 % (6026)Time elapsed: 0.134 s
% 8.94/2.82 % (6026)Instructions burned: 253 (million)
% 8.94/2.82 % (6026)------------------------------
% 8.94/2.82 % (6026)------------------------------
% 8.94/2.82 % (6027)Instruction limit reached!
% 8.94/2.82 % (6027)------------------------------
% 8.94/2.82 % (6027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.94/2.82 % (6027)Termination reason: Unknown
% 8.94/2.82 % (6027)Termination phase: Saturation
% 8.94/2.82
% 8.94/2.82 % (6027)Memory used [KB]: 6396
% 8.94/2.82 % (6027)Time elapsed: 0.080 s
% 8.94/2.82 % (6027)Instructions burned: 140 (million)
% 8.94/2.82 % (6027)------------------------------
% 8.94/2.82 % (6027)------------------------------
% 8.94/2.83 % (6030)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_5856 for (2990ds/339Mi)
% 8.94/2.84 % (6032)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_5856 for (2990ds/134Mi)
% 8.94/2.84 % (6031)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_5856 for (2990ds/283Mi)
% 8.94/2.85 % (6024)Instruction limit reached!
% 8.94/2.85 % (6024)------------------------------
% 8.94/2.85 % (6024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.94/2.85 % (6024)Termination reason: Unknown
% 8.94/2.85 % (6024)Termination phase: Saturation
% 8.94/2.85
% 8.94/2.85 % (6024)Memory used [KB]: 6908
% 8.94/2.85 % (6024)Time elapsed: 0.195 s
% 8.94/2.85 % (6024)Instructions burned: 343 (million)
% 8.94/2.85 % (6024)------------------------------
% 8.94/2.85 % (6024)------------------------------
% 8.94/2.86 % (6029)Instruction limit reached!
% 8.94/2.86 % (6029)------------------------------
% 8.94/2.86 % (6029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.94/2.86 % (6029)Termination reason: Unknown
% 8.94/2.86 % (6029)Termination phase: Saturation
% 8.94/2.86
% 8.94/2.86 % (6029)Memory used [KB]: 6524
% 8.94/2.86 % (6029)Time elapsed: 0.108 s
% 8.94/2.86 % (6029)Instructions burned: 202 (million)
% 8.94/2.86 % (6029)------------------------------
% 8.94/2.86 % (6029)------------------------------
% 8.94/2.87 % (6033)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_5856 for (2989ds/298Mi)
% 8.94/2.88 % (6034)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_5856 for (2989ds/192Mi)
% 9.81/2.91 % (6032)Instruction limit reached!
% 9.81/2.91 % (6032)------------------------------
% 9.81/2.91 % (6032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.81/2.91 % (6032)Termination reason: Unknown
% 9.81/2.91 % (6032)Termination phase: Saturation
% 9.81/2.91
% 9.81/2.91 % (6032)Memory used [KB]: 6780
% 9.81/2.91 % (6032)Time elapsed: 0.074 s
% 9.81/2.91 % (6032)Instructions burned: 135 (million)
% 9.81/2.91 % (6032)------------------------------
% 9.81/2.91 % (6032)------------------------------
% 9.81/2.93 % (6035)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_5856 for (2989ds/258Mi)
% 9.81/2.99 % (6034)Instruction limit reached!
% 9.81/2.99 % (6034)------------------------------
% 9.81/2.99 % (6034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.81/2.99 % (6034)Termination reason: Unknown
% 9.81/2.99 % (6034)Termination phase: Saturation
% 9.81/2.99
% 9.81/2.99 % (6034)Memory used [KB]: 7291
% 9.81/2.99 % (6034)Time elapsed: 0.105 s
% 9.81/2.99 % (6034)Instructions burned: 193 (million)
% 9.81/2.99 % (6034)------------------------------
% 9.81/2.99 % (6034)------------------------------
% 9.81/2.99 % (6031)Instruction limit reached!
% 9.81/2.99 % (6031)------------------------------
% 9.81/2.99 % (6031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.81/2.99 % (6031)Termination reason: Unknown
% 9.81/2.99 % (6031)Termination phase: Saturation
% 9.81/2.99
% 9.81/2.99 % (6031)Memory used [KB]: 7036
% 9.81/2.99 % (6031)Time elapsed: 0.156 s
% 9.81/2.99 % (6031)Instructions burned: 284 (million)
% 9.81/2.99 % (6031)------------------------------
% 9.81/2.99 % (6031)------------------------------
% 9.81/3.01 % (6036)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_5856 for (2988ds/90Mi)
% 9.81/3.01 % (6037)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_5856 for (2988ds/231Mi)
% 9.81/3.02 % (6030)Instruction limit reached!
% 9.81/3.02 % (6030)------------------------------
% 9.81/3.02 % (6030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.81/3.02 % (6030)Termination reason: Unknown
% 9.81/3.02 % (6030)Termination phase: Saturation
% 9.81/3.02
% 9.81/3.02 % (6030)Memory used [KB]: 6652
% 9.81/3.02 % (6030)Time elapsed: 0.189 s
% 9.81/3.02 % (6030)Instructions burned: 340 (million)
% 9.81/3.02 % (6030)------------------------------
% 9.81/3.02 % (6030)------------------------------
% 11.62/3.03 % (6033)Instruction limit reached!
% 11.62/3.03 % (6033)------------------------------
% 11.62/3.03 % (6033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.62/3.03 % (6033)Termination reason: Unknown
% 11.62/3.03 % (6033)Termination phase: Saturation
% 11.62/3.03
% 11.62/3.03 % (6033)Memory used [KB]: 7547
% 11.62/3.03 % (6033)Time elapsed: 0.162 s
% 11.62/3.03 % (6033)Instructions burned: 298 (million)
% 11.62/3.03 % (6033)------------------------------
% 11.62/3.03 % (6033)------------------------------
% 11.62/3.04 % (6038)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_5856 for (2988ds/458Mi)
% 11.62/3.05 % (6010)Instruction limit reached!
% 11.62/3.05 % (6010)------------------------------
% 11.62/3.05 % (6010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.62/3.05 % (6010)Termination reason: Unknown
% 11.62/3.05 % (6010)Termination phase: Saturation
% 11.62/3.05
% 11.62/3.05 % (6010)Memory used [KB]: 7419
% 11.62/3.05 % (6010)Time elapsed: 0.592 s
% 11.62/3.05 % (6010)Instructions burned: 1088 (million)
% 11.62/3.05 % (6010)------------------------------
% 11.62/3.05 % (6010)------------------------------
% 11.62/3.06 % (6036)Instruction limit reached!
% 11.62/3.06 % (6036)------------------------------
% 11.62/3.06 % (6036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.62/3.06 % (6036)Termination reason: Unknown
% 11.62/3.06 % (6036)Termination phase: Saturation
% 11.62/3.06
% 11.62/3.06 % (6036)Memory used [KB]: 6396
% 11.62/3.06 % (6036)Time elapsed: 0.050 s
% 11.62/3.06 % (6036)Instructions burned: 91 (million)
% 11.62/3.06 % (6036)------------------------------
% 11.62/3.06 % (6036)------------------------------
% 11.62/3.06 % (6039)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_5856 for (2987ds/31Mi)
% 11.62/3.07 % (6035)Instruction limit reached!
% 11.62/3.07 % (6035)------------------------------
% 11.62/3.07 % (6035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.62/3.07 % (6035)Termination reason: Unknown
% 11.62/3.07 % (6035)Termination phase: Saturation
% 11.62/3.07
% 11.62/3.07 % (6035)Memory used [KB]: 6524
% 11.62/3.07 % (6035)Time elapsed: 0.138 s
% 11.62/3.07 % (6035)Instructions burned: 258 (million)
% 11.62/3.07 % (6035)------------------------------
% 11.62/3.07 % (6035)------------------------------
% 11.62/3.07 % (6039)Instruction limit reached!
% 11.62/3.07 % (6039)------------------------------
% 11.62/3.07 % (6039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.62/3.07 % (6039)Termination reason: Unknown
% 11.62/3.07 % (6039)Termination phase: Preprocessing 1
% 11.62/3.07
% 11.62/3.07 % (6039)Memory used [KB]: 1535
% 11.62/3.07 % (6039)Time elapsed: 0.019 s
% 11.62/3.07 % (6039)Instructions burned: 31 (million)
% 11.62/3.07 % (6039)------------------------------
% 11.62/3.07 % (6039)------------------------------
% 11.62/3.07 % (6040)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_5856 for (2987ds/297Mi)
% 11.62/3.08 % (6041)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_5856 for (2987ds/987Mi)
% 11.62/3.09 % (6042)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_5856 for (2987ds/182Mi)
% 11.62/3.09 % (6028)Instruction limit reached!
% 11.62/3.09 % (6028)------------------------------
% 11.62/3.09 % (6028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.62/3.09 % (6028)Termination reason: Unknown
% 11.62/3.09 % (6028)Termination phase: Saturation
% 11.62/3.09
% 11.62/3.09 % (6028)Memory used [KB]: 8187
% 11.62/3.09 % (6028)Time elapsed: 0.348 s
% 11.62/3.09 % (6028)Instructions burned: 614 (million)
% 11.62/3.09 % (6028)------------------------------
% 11.62/3.09 % (6028)------------------------------
% 11.62/3.09 % (6043)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_5856 for (2987ds/182Mi)
% 11.62/3.12 % (6044)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_5856 for (2987ds/154Mi)
% 11.97/3.14 % (6037)Instruction limit reached!
% 11.97/3.14 % (6037)------------------------------
% 11.97/3.14 % (6037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.14 % (6037)Termination reason: Unknown
% 11.97/3.14 % (6037)Termination phase: Saturation
% 11.97/3.14
% 11.97/3.14 % (6037)Memory used [KB]: 7036
% 11.97/3.14 % (6037)Time elapsed: 0.130 s
% 11.97/3.14 % (6037)Instructions burned: 231 (million)
% 11.97/3.14 % (6037)------------------------------
% 11.97/3.14 % (6037)------------------------------
% 11.97/3.16 % (6045)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_5856 for (2986ds/79Mi)
% 11.97/3.19 % (6042)Instruction limit reached!
% 11.97/3.19 % (6042)------------------------------
% 11.97/3.19 % (6042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.19 % (6042)Termination reason: Unknown
% 11.97/3.19 % (6042)Termination phase: Saturation
% 11.97/3.19
% 11.97/3.19 % (6042)Memory used [KB]: 6908
% 11.97/3.19 % (6042)Time elapsed: 0.104 s
% 11.97/3.19 % (6042)Instructions burned: 182 (million)
% 11.97/3.19 % (6042)------------------------------
% 11.97/3.19 % (6042)------------------------------
% 11.97/3.19 % (6044)Refutation not found, incomplete strategy
% 11.97/3.19 % (6044)------------------------------
% 11.97/3.19 % (6044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.19 % (6044)Termination reason: Refutation not found, incomplete strategy
% 11.97/3.19
% 11.97/3.19
% 11.97/3.19 % (6044)Memory used [KB]: 6780
% 11.97/3.19 % (6044)Time elapsed: 0.078 s
% 11.97/3.19 % (6044)Instructions burned: 145 (million)
% 11.97/3.19 % (6044)------------------------------
% 11.97/3.19 % (6044)------------------------------
% 11.97/3.19 % (6038)First to succeed.
% 12.21/3.20 % (6043)Instruction limit reached!
% 12.21/3.20 % (6043)------------------------------
% 12.21/3.20 % (6043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.21/3.20 % (6043)Termination reason: Unknown
% 12.21/3.20 % (6043)Termination phase: Saturation
% 12.21/3.20
% 12.21/3.20 % (6043)Memory used [KB]: 6652
% 12.21/3.20 % (6043)Time elapsed: 0.104 s
% 12.21/3.20 % (6043)Instructions burned: 183 (million)
% 12.21/3.20 % (6043)------------------------------
% 12.21/3.20 % (6043)------------------------------
% 12.21/3.20 % (6045)Instruction limit reached!
% 12.21/3.20 % (6045)------------------------------
% 12.21/3.20 % (6045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.21/3.20 % (6045)Termination reason: Unknown
% 12.21/3.20 % (6045)Termination phase: Saturation
% 12.21/3.20
% 12.21/3.20 % (6045)Memory used [KB]: 6396
% 12.21/3.20 % (6045)Time elapsed: 0.042 s
% 12.21/3.20 % (6045)Instructions burned: 79 (million)
% 12.21/3.20 % (6045)------------------------------
% 12.21/3.20 % (6045)------------------------------
% 12.21/3.20 % (6038)Refutation found. Thanks to Tanya!
% 12.21/3.20 % SZS status Theorem for DTF2THF_5856
% 12.21/3.20 % SZS output start Proof for DTF2THF_5856
% 12.21/3.20 thf(type_def_5, type, a: $tType).
% 12.21/3.20 thf(type_def_7, type, set_a: $tType).
% 12.21/3.20 thf(func_def_0, type, set_a: $tType).
% 12.21/3.20 thf(func_def_1, type, a: $tType).
% 12.21/3.20 thf(func_def_2, type, condit1627435690bove_a: (a > a > $o) > set_a > $o).
% 12.21/3.20 thf(func_def_3, type, condit1001553558elow_a: (a > a > $o) > set_a > $o).
% 12.21/3.20 thf(func_def_4, type, finite40241356em_a_a: (a > a > a) > $o).
% 12.21/3.20 thf(func_def_5, type, finite_finite_a: set_a > $o).
% 12.21/3.20 thf(func_def_6, type, abel_semigroup_a: (a > a > a) > $o).
% 12.21/3.20 thf(func_def_7, type, semigroup_a: (a > a > a) > $o).
% 12.21/3.20 thf(func_def_8, type, inf_inf_set_a: set_a > set_a > set_a).
% 12.21/3.20 thf(func_def_9, type, semilattice_a: (a > a > a) > $o).
% 12.21/3.20 thf(func_def_10, type, lattic247676691_fin_a: (a > a > a) > set_a > a).
% 12.21/3.20 thf(func_def_11, type, lattic1885654924_set_a: (a > a > a) > $o).
% 12.21/3.20 thf(func_def_12, type, lattic1781219155_fin_a: (a > a > a) > set_a > a).
% 12.21/3.20 thf(func_def_13, type, modula17988509_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 12.21/3.20 thf(func_def_14, type, modula1373251614_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 12.21/3.20 thf(func_def_15, type, modula581031071_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 12.21/3.20 thf(func_def_16, type, modula1936294176_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 12.21/3.20 thf(func_def_17, type, modula1144073633_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 12.21/3.20 thf(func_def_18, type, modula1727524044comp_a: (a > a > $o) > a > a > $o).
% 12.21/3.20 thf(func_def_19, type, bot_bot_set_a: set_a).
% 12.21/3.20 thf(func_def_20, type, least_a: (a > a > $o) > (a > $o) > a).
% 12.21/3.20 thf(func_def_21, type, max_a: (a > a > $o) > a > a > a).
% 12.21/3.20 thf(func_def_22, type, min_a: (a > a > $o) > a > a > a).
% 12.21/3.20 thf(func_def_23, type, ord_less_eq_set_a: set_a > set_a > $o).
% 12.21/3.20 thf(func_def_24, type, greatest_a: (a > a > $o) > (a > $o) > a).
% 12.21/3.20 thf(func_def_25, type, antimono_a_set_a: (a > a > $o) > (a > set_a) > $o).
% 12.21/3.20 thf(func_def_26, type, mono_a_set_a: (a > a > $o) > (a > set_a) > $o).
% 12.21/3.20 thf(func_def_27, type, collect_a: (a > $o) > set_a).
% 12.21/3.20 thf(func_def_28, type, insert_a: a > set_a > set_a).
% 12.21/3.20 thf(func_def_29, type, set_atLeast_a: (a > a > $o) > a > set_a).
% 12.21/3.20 thf(func_def_30, type, set_atMost_a: (a > a > $o) > a > set_a).
% 12.21/3.20 thf(func_def_31, type, member_a: a > set_a > $o).
% 12.21/3.20 thf(func_def_32, type, a2: a).
% 12.21/3.20 thf(func_def_33, type, b: a).
% 12.21/3.20 thf(func_def_34, type, c: a).
% 12.21/3.20 thf(func_def_35, type, inf: a > a > a).
% 12.21/3.20 thf(func_def_36, type, less_eq: a > a > $o).
% 12.21/3.20 thf(func_def_37, type, sup: a > a > a).
% 12.21/3.20 thf(func_def_52, type, sK0: (a > a > a) > a).
% 12.21/3.20 thf(func_def_53, type, sK1: (a > a > a) > a).
% 12.21/3.20 thf(func_def_54, type, sK2: (a > a > a) > a).
% 12.21/3.20 thf(func_def_55, type, sK3: (a > a > a) > a).
% 12.21/3.20 thf(func_def_56, type, sK4: (a > a > a) > a).
% 12.21/3.20 thf(func_def_57, type, sK5: (a > a > a) > a).
% 12.21/3.20 thf(func_def_58, type, sK6: (a > a > a) > a).
% 12.21/3.20 thf(func_def_59, type, sK7: (a > a > a) > a).
% 12.21/3.20 thf(func_def_60, type, sK8: (a > a > a) > a).
% 12.21/3.20 thf(func_def_61, type, sK9: (a > a > a) > a).
% 12.21/3.20 thf(func_def_62, type, sK10: (a > a > a) > a).
% 12.21/3.20 thf(func_def_63, type, sK11: (a > a > a) > a).
% 12.21/3.20 thf(func_def_64, type, sK12: (a > a > a) > a).
% 12.21/3.20 thf(func_def_65, type, sK13: (a > a > a) > a).
% 12.21/3.20 thf(func_def_66, type, sK14: a).
% 12.21/3.20 thf(func_def_67, type, sK15: a).
% 12.21/3.20 thf(func_def_68, type, sK16: a).
% 12.21/3.20 thf(func_def_69, type, sK17: a).
% 12.21/3.20 thf(func_def_70, type, sK18: a).
% 12.21/3.20 thf(func_def_71, type, sK19: a).
% 12.21/3.20 thf(func_def_73, type, ph21: !>[X0: $tType]:(X0)).
% 12.21/3.20 thf(f1077,plain,(
% 12.21/3.20 $false),
% 12.21/3.20 inference(subsumption_resolution,[status(thm)],[f1076,f921])).
% 12.21/3.20 thf(f921,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) = $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f920,f836])).
% 12.21/3.20 thf(f836,plain,(
% 12.21/3.20 ( ! [X0 : a,X1 : a] : (((inf @ X0 @ X1) = (inf @ X1 @ X0))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f648])).
% 12.21/3.20 thf(f648,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a] : ((inf @ X0 @ X1) = (inf @ X1 @ X0))),
% 12.21/3.20 inference(rectify,[status(thm)],[f15])).
% 12.21/3.20 thf(f15,axiom,(
% 12.21/3.20 ! [X3 : a,X2 : a] : ((inf @ X3 @ X2) = (inf @ X2 @ X3))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_14_local_Oinf_Ocommute)).
% 12.21/3.20 thf(f920,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))) = $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f917,f881])).
% 12.21/3.20 thf(f881,plain,(
% 12.21/3.20 ( ! [X0 : a,X1 : a] : (((sup @ X0 @ X1) = (sup @ X1 @ X0))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f671])).
% 12.21/3.20 thf(f671,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a] : ((sup @ X0 @ X1) = (sup @ X1 @ X0))),
% 12.21/3.20 inference(rectify,[status(thm)],[f24])).
% 12.21/3.20 thf(f24,axiom,(
% 12.21/3.20 ! [X1 : a,X0 : a] : ((sup @ X0 @ X1) = (sup @ X1 @ X0))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_23_local_Osup__commute)).
% 12.21/3.20 thf(f917,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))) = $true)),
% 12.21/3.20 inference(backward_demodulation,[status(thm)],[f906,f881])).
% 12.21/3.20 thf(f906,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))) = $true)),
% 12.21/3.20 inference(backward_demodulation,[status(thm)],[f904,f836])).
% 12.21/3.20 thf(f904,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))) = $true)),
% 12.21/3.20 inference(backward_demodulation,[status(thm)],[f903,f843])).
% 12.21/3.20 thf(f843,plain,(
% 12.21/3.20 ( ! [X2 : a,X0 : a,X1 : a] : (((sup @ (sup @ X2 @ X0) @ X1) = (sup @ X2 @ (sup @ X0 @ X1)))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f668])).
% 12.21/3.20 thf(f668,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : ((sup @ (sup @ X2 @ X0) @ X1) = (sup @ X2 @ (sup @ X0 @ X1)))),
% 12.21/3.20 inference(rectify,[status(thm)],[f23])).
% 12.21/3.20 thf(f23,axiom,(
% 12.21/3.20 ! [X1 : a,X11 : a,X0 : a] : ((sup @ (sup @ X0 @ X1) @ X11) = (sup @ X0 @ (sup @ X1 @ X11)))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_22_local_Osup__assoc)).
% 12.21/3.20 thf(f903,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))) = $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f902,f866])).
% 12.21/3.20 thf(f866,plain,(
% 12.21/3.20 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ (inf @ X0 @ X1) @ X2) = (inf @ X0 @ (inf @ X1 @ X2)))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f657])).
% 12.21/3.20 thf(f657,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : ((inf @ (inf @ X0 @ X1) @ X2) = (inf @ X0 @ (inf @ X1 @ X2)))),
% 12.21/3.20 inference(rectify,[status(thm)],[f17])).
% 12.21/3.20 thf(f17,axiom,(
% 12.21/3.20 ! [X0 : a,X1 : a,X11 : a] : ((inf @ (inf @ X0 @ X1) @ X11) = (inf @ X0 @ (inf @ X1 @ X11)))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_16_local_Oinf__assoc)).
% 12.21/3.20 thf(f902,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2))) = $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f901,f808])).
% 12.21/3.20 thf(f808,plain,(
% 12.21/3.20 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ (inf @ (sup @ X2 @ X1) @ (sup @ X1 @ X0)) @ (sup @ X0 @ X2)) = (modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X0))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f643])).
% 12.21/3.20 thf(f643,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : ((inf @ (inf @ (sup @ X2 @ X1) @ (sup @ X1 @ X0)) @ (sup @ X0 @ X2)) = (modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X0))),
% 12.21/3.20 inference(rectify,[status(thm)],[f93])).
% 12.21/3.20 thf(f93,axiom,(
% 12.21/3.20 ! [X8 : a,X2 : a,X3 : a] : ((modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (inf @ (inf @ (sup @ X3 @ X2) @ (sup @ X2 @ X8)) @ (sup @ X8 @ X3)))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_92_local_Oe__aux__def)).
% 12.21/3.20 thf(f901,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f830,f879])).
% 12.21/3.20 thf(f879,plain,(
% 12.21/3.20 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1) = (sup @ (sup @ (inf @ X2 @ X0) @ (inf @ X0 @ X1)) @ (inf @ X1 @ X2)))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f632])).
% 12.21/3.20 thf(f632,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : ((modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1) = (sup @ (sup @ (inf @ X2 @ X0) @ (inf @ X0 @ X1)) @ (inf @ X1 @ X2)))),
% 12.21/3.20 inference(rectify,[status(thm)],[f87])).
% 12.21/3.20 thf(f87,axiom,(
% 12.21/3.20 ! [X2 : a,X8 : a,X3 : a] : ((modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (sup @ (sup @ (inf @ X3 @ X2) @ (inf @ X2 @ X8)) @ (inf @ X8 @ X3)))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_86_local_Od__aux__def)).
% 12.21/3.20 thf(f830,plain,(
% 12.21/3.20 ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f262])).
% 12.21/3.20 thf(f262,plain,(
% 12.21/3.20 ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 12.21/3.20 inference(fool_elimination,[status(thm)],[f261])).
% 12.21/3.20 thf(f261,plain,(
% 12.21/3.20 (less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))),
% 12.21/3.20 inference(rectify,[status(thm)],[f255])).
% 12.21/3.20 thf(f255,axiom,(
% 12.21/3.20 (less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',conj_0)).
% 12.21/3.20 thf(f1076,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1075,f836])).
% 12.21/3.20 thf(f1075,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1074,f881])).
% 12.21/3.20 thf(f1074,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1073,f866])).
% 12.21/3.20 thf(f1073,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2))) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1072,f808])).
% 12.21/3.20 thf(f1072,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1071,f852])).
% 12.21/3.20 thf(f852,plain,(
% 12.21/3.20 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1) = (modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X0))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f645])).
% 12.21/3.20 thf(f645,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : ((modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1) = (modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X0))),
% 12.21/3.20 inference(rectify,[status(thm)],[f94])).
% 12.21/3.20 thf(f94,axiom,(
% 12.21/3.20 ! [X3 : a,X8 : a,X2 : a] : ((modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (modula1144073633_aux_a @ inf @ sup @ X2 @ X8 @ X3))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_93_local_Oe__b__c__a)).
% 12.21/3.20 thf(f1071,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1070,f852])).
% 12.21/3.20 thf(f1070,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true)),
% 12.21/3.20 inference(trivial_inequality_removal,[status(thm)],[f1069])).
% 12.21/3.20 thf(f1069,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true) | ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1068,f836])).
% 12.21/3.20 thf(f1068,plain,(
% 12.21/3.20 ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) | ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1067,f881])).
% 12.21/3.20 thf(f1067,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true) | ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1066,f881])).
% 12.21/3.20 thf(f1066,plain,(
% 12.21/3.20 ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))) | ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1065,f836])).
% 12.21/3.20 thf(f1065,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true) | ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2))))),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1064,f866])).
% 12.21/3.20 thf(f1064,plain,(
% 12.21/3.20 ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2))) | ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1063,f843])).
% 12.21/3.20 thf(f1063,plain,(
% 12.21/3.20 ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true) | ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2)))),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1062,f879])).
% 12.21/3.20 thf(f1062,plain,(
% 12.21/3.20 ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true) | ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2)))),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1061,f808])).
% 12.21/3.20 thf(f1061,plain,(
% 12.21/3.20 ((modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) | ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1060,f822])).
% 12.21/3.20 thf(f822,plain,(
% 12.21/3.20 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1936294176_aux_a @ inf @ sup @ X2 @ X1 @ X0) = (modula1936294176_aux_a @ inf @ sup @ X1 @ X0 @ X2))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f636])).
% 12.21/3.20 thf(f636,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : ((modula1936294176_aux_a @ inf @ sup @ X2 @ X1 @ X0) = (modula1936294176_aux_a @ inf @ sup @ X1 @ X0 @ X2))),
% 12.21/3.20 inference(rectify,[status(thm)],[f89])).
% 12.21/3.20 thf(f89,axiom,(
% 12.21/3.20 ! [X2 : a,X3 : a,X8 : a] : ((modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (modula1936294176_aux_a @ inf @ sup @ X8 @ X3 @ X2))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_88_local_Od__c__a__b)).
% 12.21/3.20 thf(f1060,plain,(
% 12.21/3.20 ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ b @ c @ a2) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true) | ((modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1059,f852])).
% 12.21/3.20 thf(f1059,plain,(
% 12.21/3.20 ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) | ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ b @ c @ a2) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) != $true)),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1058,f822])).
% 12.21/3.20 thf(f1058,plain,(
% 12.21/3.20 ($true != (less_eq @ (modula1936294176_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b))) | ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2))),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f1051,f852])).
% 12.21/3.20 thf(f1051,plain,(
% 12.21/3.20 ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)) | ($true != (less_eq @ (modula1936294176_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b)))),
% 12.21/3.20 inference(superposition,[status(thm)],[f919,f938])).
% 12.21/3.20 thf(f938,plain,(
% 12.21/3.20 ( ! [X2 : a,X0 : a,X1 : a] : (((sup @ (modula17988509_aux_a @ inf @ sup @ X0 @ X1 @ X2) @ (modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X0)) = (modula1144073633_aux_a @ inf @ sup @ X0 @ X1 @ X2)) | ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ X0 @ X1 @ X2) @ (modula1144073633_aux_a @ inf @ sup @ X0 @ X1 @ X2)) != $true)) )),
% 12.21/3.20 inference(superposition,[status(thm)],[f853,f797])).
% 12.21/3.20 thf(f797,plain,(
% 12.21/3.20 ( ! [X2 : a,X0 : a,X1 : a] : (((modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1) = (modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X0))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f673])).
% 12.21/3.20 thf(f673,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : ((modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1) = (modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X0))),
% 12.21/3.20 inference(rectify,[status(thm)],[f133])).
% 12.21/3.20 thf(f133,axiom,(
% 12.21/3.20 ! [X8 : a,X3 : a,X2 : a] : ((modula1373251614_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (modula17988509_aux_a @ inf @ sup @ X2 @ X8 @ X3))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_132_local_Ob__a)).
% 12.21/3.20 thf(f853,plain,(
% 12.21/3.20 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1) = (sup @ (modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1) @ (modula1373251614_aux_a @ inf @ sup @ X0 @ X2 @ X1))) | ($true != (less_eq @ (modula1936294176_aux_a @ inf @ sup @ X0 @ X2 @ X1) @ (modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1)))) )),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f693])).
% 12.21/3.20 thf(f693,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : (((modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1) = (sup @ (modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1) @ (modula1373251614_aux_a @ inf @ sup @ X0 @ X2 @ X1))) | ($true != (less_eq @ (modula1936294176_aux_a @ inf @ sup @ X0 @ X2 @ X1) @ (modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1))))),
% 12.21/3.20 inference(ennf_transformation,[status(thm)],[f345])).
% 12.21/3.20 thf(f345,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : (($true = (less_eq @ (modula1936294176_aux_a @ inf @ sup @ X0 @ X2 @ X1) @ (modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1))) => ((modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1) = (sup @ (modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1) @ (modula1373251614_aux_a @ inf @ sup @ X0 @ X2 @ X1))))),
% 12.21/3.20 inference(fool_elimination,[status(thm)],[f344])).
% 12.21/3.20 thf(f344,plain,(
% 12.21/3.20 ! [X0 : a,X1 : a,X2 : a] : ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ X0 @ X2 @ X1) @ (modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1)) => ((modula1144073633_aux_a @ inf @ sup @ X0 @ X2 @ X1) = (sup @ (modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1) @ (modula1373251614_aux_a @ inf @ sup @ X0 @ X2 @ X1))))),
% 12.21/3.20 inference(rectify,[status(thm)],[f136])).
% 12.21/3.20 thf(f136,axiom,(
% 12.21/3.20 ! [X3 : a,X8 : a,X2 : a] : ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8)) => ((modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (sup @ (modula17988509_aux_a @ inf @ sup @ X3 @ X2 @ X8) @ (modula1373251614_aux_a @ inf @ sup @ X3 @ X2 @ X8))))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',fact_135_a__join__b__eq__e)).
% 12.21/3.20 thf(f919,plain,(
% 12.21/3.20 ((sup @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula17988509_aux_a @ inf @ sup @ a2 @ b @ c)) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f918,f836])).
% 12.21/3.20 thf(f918,plain,(
% 12.21/3.20 ((sup @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula17988509_aux_a @ inf @ sup @ a2 @ b @ c)) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c))))),
% 12.21/3.20 inference(backward_demodulation,[status(thm)],[f892,f881])).
% 12.21/3.20 thf(f892,plain,(
% 12.21/3.20 ((sup @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula17988509_aux_a @ inf @ sup @ a2 @ b @ c)) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2))))),
% 12.21/3.20 inference(forward_demodulation,[status(thm)],[f891,f866])).
% 12.21/3.20 thf(f891,plain,(
% 12.21/3.20 ((sup @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula17988509_aux_a @ inf @ sup @ a2 @ b @ c)) != (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2)))),
% 12.21/3.20 inference(backward_demodulation,[status(thm)],[f792,f808])).
% 12.21/3.20 thf(f792,plain,(
% 12.21/3.20 ((modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) != (sup @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula17988509_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 12.21/3.20 inference(cnf_transformation,[status(thm)],[f629])).
% 12.21/3.20 thf(f629,plain,(
% 12.21/3.20 ((modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) != (sup @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula17988509_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 12.21/3.20 inference(flattening,[status(thm)],[f257])).
% 12.21/3.20 thf(f257,negated_conjecture,(
% 12.21/3.20 ~((modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) = (sup @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula17988509_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 12.21/3.20 inference(negated_conjecture,[status(cth)],[f256])).
% 12.21/3.20 thf(f256,conjecture,(
% 12.21/3.20 ((modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) = (sup @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b) @ (modula17988509_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 12.21/3.20 file('/export/starexec/sandbox/tmp/tmp.TqXL5HrV6S/DTF2THF_5856.p',conj_1)).
% 12.21/3.20 % SZS output end Proof for DTF2THF_5856
% 12.21/3.20 % (6038)------------------------------
% 12.21/3.20 % (6038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.21/3.20 % (6038)Termination reason: Refutation
% 12.21/3.20
% 12.21/3.20 % (6038)Memory used [KB]: 6652
% 12.21/3.20 % (6038)Time elapsed: 0.183 s
% 12.21/3.20 % (6038)Instructions burned: 280 (million)
% 12.21/3.20 % (6038)------------------------------
% 12.21/3.20 % (6038)------------------------------
% 12.21/3.20 % (5962)Success in time 1.39 s
%------------------------------------------------------------------------------