%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP120^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 08:55:42 AM UTC 2026
% Result : Theorem 7.34s 2.20s
% Output : Refutation 7.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 159 ( 84 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 1388 ( 36 ~; 9 |; 0 &;1340 @)
% ( 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 : 56 ( 53 usr; 11 con; 0-5 aty)
% Number of variables : 91 ( 0 ^; 91 !; 0 ?; 91 :)
% 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,
if_a: $o > a > a > a ).
thf(func_def_9,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(func_def_10,type,
semilattice_a: ( a > a > a ) > $o ).
thf(func_def_11,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(func_def_12,type,
lattic1885654924_set_a: ( a > a > a ) > $o ).
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,
least_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_20,type,
max_a: ( a > a > $o ) > a > a > a ).
thf(func_def_21,type,
min_a: ( a > a > $o ) > a > a > a ).
thf(func_def_22,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_23,type,
greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_24,type,
antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
thf(func_def_25,type,
mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
thf(func_def_26,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_27,type,
member_a: a > set_a > $o ).
thf(func_def_28,type,
a2: a ).
thf(func_def_29,type,
b: a ).
thf(func_def_30,type,
c: a ).
thf(func_def_31,type,
inf: a > a > a ).
thf(func_def_32,type,
less_eq: a > a > $o ).
thf(func_def_33,type,
sup: a > a > a ).
thf(func_def_48,type,
sK0: a ).
thf(func_def_49,type,
sK1: a ).
thf(func_def_50,type,
sK2: a ).
thf(func_def_51,type,
sK3: ( a > a > a ) > a ).
thf(func_def_52,type,
sK4: ( a > a > a ) > a ).
thf(func_def_53,type,
sK5: ( a > a > a ) > a ).
thf(func_def_54,type,
sK6: ( a > a > a ) > a ).
thf(func_def_55,type,
sK7: ( a > a > a ) > a ).
thf(func_def_56,type,
sK8: ( a > a > a ) > a ).
thf(func_def_57,type,
sK9: ( a > a > a ) > a ).
thf(func_def_58,type,
sK10: ( a > a > a ) > a ).
thf(func_def_59,type,
sK11: ( a > a > a ) > a ).
thf(func_def_60,type,
sK12: ( a > a > a ) > a ).
thf(func_def_61,type,
sK13: ( a > a > a ) > a ).
thf(func_def_62,type,
sK14: ( a > a > a ) > a ).
thf(func_def_63,type,
sK15: ( a > a > a ) > a ).
thf(func_def_64,type,
sK16: ( a > a > a ) > a ).
thf(func_def_65,type,
sK17: a ).
thf(func_def_66,type,
sK18: a ).
thf(func_def_67,type,
sK19: a ).
thf(func_def_69,type,
ph21:
!>[X0: $tType] : X0 ).
thf(f914,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f913,f877]) ).
thf(f877,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)],[f876,f793]) ).
thf(f793,plain,
! [X0: a,X1: a] :
( ( inf @ X0 @ X1 )
= ( inf @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f621]) ).
thf(f621,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/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_14_local_Oinf_Ocommute) ).
thf(f876,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)],[f875,f815]) ).
thf(f815,plain,
! [X0: a,X1: a] :
( ( sup @ X0 @ X1 )
= ( sup @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,axiom,
! [X0: a,X1: a] :
( ( sup @ X0 @ X1 )
= ( sup @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_23_local_Osup__commute) ).
thf(f875,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)],[f874,f793]) ).
thf(f874,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ c @ a2 ) @ ( sup @ b @ c ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f873,f792]) ).
thf(f792,plain,
! [X2: a,X0: a,X1: a] :
( ( inf @ X1 @ ( inf @ X2 @ X0 ) )
= ( inf @ X2 @ ( inf @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f624]) ).
thf(f624,plain,
! [X0: a,X1: a,X2: a] :
( ( inf @ X1 @ ( inf @ X2 @ X0 ) )
= ( inf @ X2 @ ( inf @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,axiom,
! [X11: a,X0: a,X1: a] :
( ( inf @ X0 @ ( inf @ X1 @ X11 ) )
= ( inf @ X1 @ ( inf @ X0 @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_18_local_Oinf__left__commute) ).
thf(f873,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( sup @ c @ a2 ) @ ( inf @ ( sup @ a2 @ b ) @ ( sup @ b @ c ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f872,f793]) ).
thf(f872,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)],[f871,f742]) ).
thf(f742,plain,
! [X2: a,X0: a,X1: a] :
( ( inf @ ( inf @ ( sup @ X1 @ X2 ) @ ( sup @ X2 @ X0 ) ) @ ( sup @ X0 @ X1 ) )
= ( modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f618]) ).
thf(f618,plain,
! [X0: a,X1: a,X2: a] :
( ( inf @ ( inf @ ( sup @ X1 @ X2 ) @ ( sup @ X2 @ X0 ) ) @ ( sup @ X0 @ X1 ) )
= ( modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X0 ) ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,axiom,
! [X8: a,X3: a,X2: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( inf @ ( inf @ ( sup @ X3 @ X2 ) @ ( sup @ X2 @ X8 ) ) @ ( sup @ X8 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_92_local_Oe__aux__def) ).
thf(f871,plain,
( $true
= ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(forward_demodulation,[status(thm)],[f870,f815]) ).
thf(f870,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ a2 @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f869,f793]) ).
thf(f869,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f868,f815]) ).
thf(f868,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ c @ a2 ) @ ( inf @ b @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f867,f768]) ).
thf(f768,plain,
! [X2: a,X0: a,X1: a] :
( ( sup @ X1 @ ( sup @ X2 @ X0 ) )
= ( sup @ X2 @ ( sup @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f639]) ).
thf(f639,plain,
! [X0: a,X1: a,X2: a] :
( ( sup @ X1 @ ( sup @ X2 @ X0 ) )
= ( sup @ X2 @ ( sup @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,axiom,
! [X8: a,X3: a,X2: a] :
( ( sup @ X3 @ ( sup @ X2 @ X8 ) )
= ( sup @ X2 @ ( sup @ X3 @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_21_local_Osup_Oleft__commute) ).
thf(f867,plain,
( ( less_eq @ ( sup @ ( inf @ c @ a2 ) @ ( sup @ ( inf @ a2 @ b ) @ ( inf @ b @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f866,f815]) ).
thf(f866,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)],[f737,f804]) ).
thf(f804,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)],[f603]) ).
thf(f603,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/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_86_local_Od__aux__def) ).
thf(f737,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)],[f433]) ).
thf(f433,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)],[f432]) ).
thf(f432,plain,
less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ),
inference(rectify,[status(thm)],[f249]) ).
thf(f249,axiom,
less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',conj_0) ).
thf(f913,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)],[f912,f793]) ).
thf(f912,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)],[f911,f815]) ).
thf(f911,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)],[f910,f793]) ).
thf(f910,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( sup @ a2 @ b ) @ ( inf @ ( sup @ c @ a2 ) @ ( sup @ b @ c ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f909,f792]) ).
thf(f909,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( inf @ ( sup @ c @ a2 ) @ ( inf @ ( sup @ a2 @ b ) @ ( sup @ b @ c ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f908,f793]) ).
thf(f908,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)],[f907,f742]) ).
thf(f907,plain,
( $true
!= ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(forward_demodulation,[status(thm)],[f906,f822]) ).
thf(f822,plain,
! [X2: a,X0: a,X1: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X0 )
= ( modula1144073633_aux_a @ inf @ sup @ X0 @ X1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f616]) ).
thf(f616,plain,
! [X0: a,X1: a,X2: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X0 )
= ( modula1144073633_aux_a @ inf @ sup @ X0 @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f94]) ).
thf(f94,axiom,
! [X3: a,X2: a,X8: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( modula1144073633_aux_a @ inf @ sup @ X2 @ X8 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_93_local_Oe__b__c__a) ).
thf(f906,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)],[f905,f815]) ).
thf(f905,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ a2 @ c ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f904,f793]) ).
thf(f904,plain,
( ( less_eq @ ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f903,f815]) ).
thf(f903,plain,
( ( less_eq @ ( sup @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) @ ( inf @ a2 @ b ) ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f902]) ).
thf(f902,plain,
( ( ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) )
!= ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) ) )
| ( ( less_eq @ ( sup @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) @ ( inf @ a2 @ b ) ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f901,f815]) ).
thf(f901,plain,
( ( ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) )
!= ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ a2 @ c ) ) ) )
| ( ( less_eq @ ( sup @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) @ ( inf @ a2 @ b ) ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f900,f793]) ).
thf(f900,plain,
( ( ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) )
!= ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) ) )
| ( ( less_eq @ ( sup @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) @ ( inf @ a2 @ b ) ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f899,f804]) ).
thf(f899,plain,
( ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true )
| ( ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) )
!= ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f898,f815]) ).
thf(f898,plain,
( ( ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) )
!= ( sup @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) @ ( inf @ a2 @ b ) ) )
| ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f897,f804]) ).
thf(f897,plain,
( ( ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) )
!= ( modula1936294176_aux_a @ inf @ sup @ b @ c @ a2 ) )
| ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f865,f891]) ).
thf(f891,plain,
! [X2: a,X0: a,X1: a] :
( ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ X0 @ X1 @ X2 ) @ ( modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X0 ) )
= ( modula1936294176_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)],[f762,f845]) ).
thf(f845,plain,
! [X2: a,X0: a,X1: a] :
( ( modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1 )
= ( modula1373251614_aux_a @ inf @ sup @ X1 @ X0 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f645]) ).
thf(f645,plain,
! [X0: a,X1: a,X2: a] :
( ( modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1 )
= ( modula1373251614_aux_a @ inf @ sup @ X1 @ X0 @ X2 ) ),
inference(rectify,[status(thm)],[f126]) ).
thf(f126,axiom,
! [X2: a,X3: a,X8: a] :
( ( modula1373251614_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( modula17988509_aux_a @ inf @ sup @ X2 @ X8 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_125_local_Ob__a) ).
thf(f762,plain,
! [X2: a,X0: a,X1: a] :
( ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) @ ( modula1373251614_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) )
= ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) )
| ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) @ ( modula1144073633_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f713]) ).
thf(f713,plain,
! [X0: a,X1: a,X2: a] :
( ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) @ ( modula1144073633_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) )
!= $true )
| ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) @ ( modula1373251614_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) )
= ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f356]) ).
thf(f356,plain,
! [X0: a,X1: a,X2: a] :
( ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) @ ( modula1144073633_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) )
= $true )
=> ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) @ ( modula1373251614_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) )
= ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f355]) ).
thf(f355,plain,
! [X0: a,X1: a,X2: a] :
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) @ ( modula1144073633_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) )
=> ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) @ ( modula1373251614_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) )
= ( modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f132]) ).
thf(f132,axiom,
! [X2: a,X8: a,X3: a] :
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8 ) @ ( modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8 ) )
=> ( ( modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( inf @ ( modula17988509_aux_a @ inf @ sup @ X3 @ X2 @ X8 ) @ ( modula1373251614_aux_a @ inf @ sup @ X3 @ X2 @ X8 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_131_a__meet__b__eq__d) ).
thf(f865,plain,
( ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ a2 @ c ) @ ( inf @ b @ c ) ) )
!= ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) ) ),
inference(forward_demodulation,[status(thm)],[f864,f815]) ).
thf(f864,plain,
( ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ a2 @ c ) ) ) ),
inference(forward_demodulation,[status(thm)],[f863,f793]) ).
thf(f863,plain,
( ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ b @ c ) @ ( inf @ c @ a2 ) ) )
!= ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) ) ),
inference(forward_demodulation,[status(thm)],[f862,f815]) ).
thf(f862,plain,
( ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= ( sup @ ( inf @ a2 @ b ) @ ( sup @ ( inf @ c @ a2 ) @ ( inf @ b @ c ) ) ) ),
inference(forward_demodulation,[status(thm)],[f861,f768]) ).
thf(f861,plain,
( ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) )
!= ( sup @ ( inf @ c @ a2 ) @ ( sup @ ( inf @ a2 @ b ) @ ( inf @ b @ c ) ) ) ),
inference(forward_demodulation,[status(thm)],[f860,f815]) ).
thf(f860,plain,
( ( sup @ ( sup @ ( inf @ a2 @ b ) @ ( inf @ b @ c ) ) @ ( inf @ c @ a2 ) )
!= ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) ) ),
inference(forward_demodulation,[status(thm)],[f859,f804]) ).
thf(f859,plain,
( ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) ) ),
inference(forward_demodulation,[status(thm)],[f767,f734]) ).
thf(f734,plain,
! [X2: a,X0: a,X1: a] :
( ( modula581031071_aux_a @ inf @ sup @ X1 @ X2 @ X0 )
= ( modula17988509_aux_a @ inf @ sup @ X0 @ X1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f646]) ).
thf(f646,plain,
! [X0: a,X1: a,X2: a] :
( ( modula581031071_aux_a @ inf @ sup @ X1 @ X2 @ X0 )
= ( modula17988509_aux_a @ inf @ sup @ X0 @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f113]) ).
thf(f113,axiom,
! [X8: a,X3: a,X2: a] :
( ( modula581031071_aux_a @ inf @ sup @ X3 @ X2 @ X8 )
= ( modula17988509_aux_a @ inf @ sup @ X8 @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_112_local_Oc__a) ).
thf(f767,plain,
( ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(cnf_transformation,[status(thm)],[f601]) ).
thf(f601,plain,
( ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(flattening,[status(thm)],[f251]) ).
thf(f251,negated_conjecture,
( ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(negated_conjecture,[status(cth)],[f250]) ).
thf(f250,conjecture,
( ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c )
= ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP120^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n008.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 08:26:54 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : ITP120^1 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.46 % Domain : Interactive Theorem Proving
% 0.27/0.46 % Problem : Sledgehammer Modular_Distrib_Lattice problem prob_203__3262370_1
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Des21]
% 0.27/0.46 % Names : Modular_Distrib_Lattice/prob_203__3262370_1 [Des21]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.44 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0
% 0.27/0.46 % Syntax : Number of formulae : 284 ( 138 unt; 34 typ; 0 def)
% 0.27/0.46 % Number of atoms : 592 ( 190 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.27/0.46 % Number of connectives : 1817 ( 14 ~; 1 |; 30 &;1556 @)
% 0.27/0.46 % ( 0 <=>; 216 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 16 ( 5 avg)
% 0.27/0.46 % Number of types : 3 ( 2 usr)
% 0.27/0.46 % Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 35 ( 32 usr; 5 con; 0-5 aty)
% 0.27/0.46 % Number of variables : 616 ( 40 ^; 570 !; 6 ?; 616 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:44:17.242
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % Could-be-implicit typings (2)
% 0.27/0.46 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.27/0.46 set_a: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_tf__a,type,
% 0.27/0.46 a: $tType ).
% 0.27/0.46
% 0.27/0.46 % Explicit typings (32)
% 0.27/0.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a,type,
% 0.27/0.46 condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a,type,
% 0.27/0.46 condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 0.27/0.46 finite40241356em_a_a: ( a > a > a ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
% 0.27/0.46 finite_finite_a: set_a > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 0.27/0.46 abel_semigroup_a: ( a > a > a ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 0.27/0.46 semigroup_a: ( a > a > a ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_If_001tf__a,type,
% 0.27/0.46 if_a: $o > a > a > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.46 inf_inf_set_a: set_a > set_a > set_a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 0.27/0.46 semilattice_a: ( a > a > a ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.46 sup_sup_set_a: set_a > set_a > set_a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 0.27/0.46 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 0.27/0.46 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 0.27/0.46 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 0.27/0.46 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 0.27/0.46 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 0.27/0.46 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oincomp_001tf__a,type,
% 0.27/0.46 modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oord_OLeast_001tf__a,type,
% 0.27/0.46 least_a: ( a > a > $o ) > ( a > $o ) > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oord_Omax_001tf__a,type,
% 0.27/0.46 max_a: ( a > a > $o ) > a > a > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oord_Omin_001tf__a,type,
% 0.27/0.46 min_a: ( a > a > $o ) > a > a > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.46 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oorder_OGreatest_001tf__a,type,
% 0.27/0.46 greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oorder_Oantimono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.46 antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oorder_Omono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.46 mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.27/0.46 collect_a: ( a > $o ) > set_a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_member_001tf__a,type,
% 0.27/0.46 member_a: a > set_a > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_a,type,
% 0.27/0.46 a2: a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_b,type,
% 0.27/0.46 b: a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_c,type,
% 0.27/0.46 c: a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_inf,type,
% 0.27/0.46 inf: a > a > a ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_less__eq,type,
% 0.27/0.46 less_eq: a > a > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_sup,type,
% 0.27/0.46 sup: a > a > a ).
% 0.27/0.46
% 0.27/0.46 % Relevant facts (245)
% 0.27/0.46 thf(fact_0_local_Oantisym,axiom,
% 0.27/0.46 ! [X: a,Y: a] :
% 0.27/0.46 ( ( less_eq @ X @ Y )
% 0.27/0.46 => ( ( less_eq @ Y @ X )
% 0.27/0.46 => ( X = Y ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.antisym
% 0.27/0.46 thf(fact_1_local_Oantisym__conv,axiom,
% 0.27/0.46 ! [Y: a,X: a] :
% 0.27/0.46 ( ( less_eq @ Y @ X )
% 0.27/0.46 => ( ( less_eq @ X @ Y )
% 0.27/0.46 = ( X = Y ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.antisym_conv
% 0.27/0.46 thf(fact_2_local_Odual__order_Oantisym,axiom,
% 0.27/0.46 ! [B: a,A: a] :
% 0.27/0.46 ( ( less_eq @ B @ A )
% 0.27/0.46 => ( ( less_eq @ A @ B )
% 0.27/0.46 => ( A = B ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.dual_order.antisym
% 0.27/0.46 thf(fact_3_local_Odual__order_Oeq__iff,axiom,
% 0.27/0.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.27/0.46 = ( ^ [A2: a,B2: a] :
% 0.27/0.46 ( ( less_eq @ B2 @ A2 )
% 0.27/0.46 & ( less_eq @ A2 @ B2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.dual_order.eq_iff
% 0.27/0.46 thf(fact_4_local_Odual__order_Otrans,axiom,
% 0.27/0.46 ! [B: a,A: a,C: a] :
% 0.27/0.46 ( ( less_eq @ B @ A )
% 0.27/0.46 => ( ( less_eq @ C @ B )
% 0.27/0.46 => ( less_eq @ C @ A ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.dual_order.trans
% 0.27/0.46 thf(fact_5_local_Oeq__iff,axiom,
% 0.27/0.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.27/0.46 = ( ^ [X2: a,Y3: a] :
% 0.27/0.46 ( ( less_eq @ X2 @ Y3 )
% 0.27/0.46 & ( less_eq @ Y3 @ X2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.eq_iff
% 0.27/0.46 thf(fact_6_local_Oeq__refl,axiom,
% 0.27/0.46 ! [X: a,Y: a] :
% 0.27/0.46 ( ( X = Y )
% 0.27/0.46 => ( less_eq @ X @ Y ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.eq_refl
% 0.27/0.46 thf(fact_7_local_Oord__eq__le__trans,axiom,
% 0.27/0.46 ! [A: a,B: a,C: a] :
% 0.27/0.46 ( ( A = B )
% 0.27/0.46 => ( ( less_eq @ B @ C )
% 0.27/0.46 => ( less_eq @ A @ C ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.ord_eq_le_trans
% 0.27/0.46 thf(fact_8_local_Oord__le__eq__trans,axiom,
% 0.27/0.46 ! [A: a,B: a,C: a] :
% 0.27/0.46 ( ( less_eq @ A @ B )
% 0.27/0.46 => ( ( B = C )
% 0.27/0.46 => ( less_eq @ A @ C ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.ord_le_eq_trans
% 0.27/0.46 thf(fact_9_local_Oorder_Oantisym,axiom,
% 0.27/0.46 ! [A: a,B: a] :
% 0.27/0.46 ( ( less_eq @ A @ B )
% 0.27/0.46 => ( ( less_eq @ B @ A )
% 0.27/0.46 => ( A = B ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.order.antisym
% 0.27/0.46 thf(fact_10_local_Oorder_Oeq__iff,axiom,
% 0.27/0.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.27/0.46 = ( ^ [A2: a,B2: a] :
% 0.27/0.46 ( ( less_eq @ A2 @ B2 )
% 0.27/0.46 & ( less_eq @ B2 @ A2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.order.eq_iff
% 0.27/0.46 thf(fact_11_local_Oorder_Otrans,axiom,
% 0.27/0.46 ! [A: a,B: a,C: a] :
% 0.27/0.46 ( ( less_eq @ A @ B )
% 0.27/0.46 => ( ( less_eq @ B @ C )
% 0.27/0.46 => ( less_eq @ A @ C ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.order.trans
% 0.27/0.46 thf(fact_12_local_Oorder__trans,axiom,
% 0.27/0.46 ! [X: a,Y: a,Z2: a] :
% 0.27/0.46 ( ( less_eq @ X @ Y )
% 0.27/0.46 => ( ( less_eq @ Y @ Z2 )
% 0.27/0.46 => ( less_eq @ X @ Z2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.order_trans
% 0.27/0.46 thf(fact_13_local_Oinf_Oassoc,axiom,
% 0.27/0.46 ! [A: a,B: a,C: a] :
% 0.27/0.46 ( ( inf @ ( inf @ A @ B ) @ C )
% 0.27/0.46 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.assoc
% 0.27/0.46 thf(fact_14_local_Oinf_Ocommute,axiom,
% 0.27/0.46 ! [A: a,B: a] :
% 0.27/0.46 ( ( inf @ A @ B )
% 0.27/0.46 = ( inf @ B @ A ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.commute
% 0.27/0.46 thf(fact_15_local_Oinf_Oleft__commute,axiom,
% 0.27/0.46 ! [B: a,A: a,C: a] :
% 0.27/0.46 ( ( inf @ B @ ( inf @ A @ C ) )
% 0.27/0.46 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.left_commute
% 0.27/0.46 thf(fact_16_local_Oinf__assoc,axiom,
% 0.27/0.46 ! [X: a,Y: a,Z2: a] :
% 0.27/0.46 ( ( inf @ ( inf @ X @ Y ) @ Z2 )
% 0.27/0.46 = ( inf @ X @ ( inf @ Y @ Z2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf_assoc
% 0.27/0.46 thf(fact_17_local_Oinf__commute,axiom,
% 0.27/0.46 ! [X: a,Y: a] :
% 0.27/0.46 ( ( inf @ X @ Y )
% 0.27/0.46 = ( inf @ Y @ X ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf_commute
% 0.27/0.46 thf(fact_18_local_Oinf__left__commute,axiom,
% 0.27/0.46 ! [X: a,Y: a,Z2: a] :
% 0.27/0.46 ( ( inf @ X @ ( inf @ Y @ Z2 ) )
% 0.27/0.46 = ( inf @ Y @ ( inf @ X @ Z2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf_left_commute
% 0.27/0.46 thf(fact_19_local_Osup_Oassoc,axiom,
% 0.27/0.46 ! [A: a,B: a,C: a] :
% 0.27/0.46 ( ( sup @ ( sup @ A @ B ) @ C )
% 0.27/0.46 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.sup.assoc
% 0.27/0.46 thf(fact_20_local_Osup_Ocommute,axiom,
% 0.27/0.46 ! [A: a,B: a] :
% 0.27/0.46 ( ( sup @ A @ B )
% 0.27/0.46 = ( sup @ B @ A ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.sup.commute
% 0.27/0.46 thf(fact_21_local_Osup_Oleft__commute,axiom,
% 0.27/0.46 ! [B: a,A: a,C: a] :
% 0.27/0.46 ( ( sup @ B @ ( sup @ A @ C ) )
% 0.27/0.46 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.sup.left_commute
% 0.27/0.46 thf(fact_22_local_Osup__assoc,axiom,
% 0.27/0.46 ! [X: a,Y: a,Z2: a] :
% 0.27/0.46 ( ( sup @ ( sup @ X @ Y ) @ Z2 )
% 0.27/0.46 = ( sup @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.sup_assoc
% 0.27/0.46 thf(fact_23_local_Osup__commute,axiom,
% 0.27/0.46 ! [X: a,Y: a] :
% 0.27/0.46 ( ( sup @ X @ Y )
% 0.27/0.46 = ( sup @ Y @ X ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.sup_commute
% 0.27/0.46 thf(fact_24_local_Osup__left__commute,axiom,
% 0.27/0.46 ! [X: a,Y: a,Z2: a] :
% 0.27/0.46 ( ( sup @ X @ ( sup @ Y @ Z2 ) )
% 0.27/0.46 = ( sup @ Y @ ( sup @ X @ Z2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.sup_left_commute
% 0.27/0.46 thf(fact_25_local_Oinf_Oabsorb1,axiom,
% 0.27/0.46 ! [A: a,B: a] :
% 0.27/0.46 ( ( less_eq @ A @ B )
% 0.27/0.46 => ( ( inf @ A @ B )
% 0.27/0.46 = A ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.absorb1
% 0.27/0.46 thf(fact_26_local_Oinf_Oabsorb2,axiom,
% 0.27/0.46 ! [B: a,A: a] :
% 0.27/0.46 ( ( less_eq @ B @ A )
% 0.27/0.46 => ( ( inf @ A @ B )
% 0.27/0.46 = B ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.absorb2
% 0.27/0.46 thf(fact_27_local_Oinf_Oabsorb__iff1,axiom,
% 0.27/0.46 ! [A: a,B: a] :
% 0.27/0.46 ( ( less_eq @ A @ B )
% 0.27/0.46 = ( ( inf @ A @ B )
% 0.27/0.46 = A ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.absorb_iff1
% 0.27/0.46 thf(fact_28_local_Oinf_Oabsorb__iff2,axiom,
% 0.27/0.46 ! [B: a,A: a] :
% 0.27/0.46 ( ( less_eq @ B @ A )
% 0.27/0.46 = ( ( inf @ A @ B )
% 0.27/0.46 = B ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.absorb_iff2
% 0.27/0.46 thf(fact_29_local_Oinf_OboundedE,axiom,
% 0.27/0.46 ! [A: a,B: a,C: a] :
% 0.27/0.46 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 0.27/0.46 => ~ ( ( less_eq @ A @ B )
% 0.27/0.46 => ~ ( less_eq @ A @ C ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.boundedE
% 0.27/0.46 thf(fact_30_local_Oinf_OboundedI,axiom,
% 0.27/0.46 ! [A: a,B: a,C: a] :
% 0.27/0.46 ( ( less_eq @ A @ B )
% 0.27/0.46 => ( ( less_eq @ A @ C )
% 0.27/0.46 => ( less_eq @ A @ ( inf @ B @ C ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.boundedI
% 0.27/0.46 thf(fact_31_local_Oinf_Ocobounded1,axiom,
% 0.27/0.46 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.cobounded1
% 0.27/0.46 thf(fact_32_local_Oinf_Ocobounded2,axiom,
% 0.27/0.46 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.cobounded2
% 0.27/0.46 thf(fact_33_local_Oinf_OcoboundedI1,axiom,
% 0.27/0.46 ! [A: a,C: a,B: a] :
% 0.27/0.46 ( ( less_eq @ A @ C )
% 0.27/0.46 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.coboundedI1
% 0.27/0.46 thf(fact_34_local_Oinf_OcoboundedI2,axiom,
% 0.27/0.46 ! [B: a,C: a,A: a] :
% 0.27/0.46 ( ( less_eq @ B @ C )
% 0.27/0.46 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.coboundedI2
% 0.27/0.46 thf(fact_35_local_Oinf_OorderE,axiom,
% 0.27/0.46 ! [A: a,B: a] :
% 0.27/0.46 ( ( less_eq @ A @ B )
% 0.27/0.46 => ( A
% 0.27/0.46 = ( inf @ A @ B ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.orderE
% 0.27/0.46 thf(fact_36_local_Oinf_OorderI,axiom,
% 0.27/0.46 ! [A: a,B: a] :
% 0.27/0.46 ( ( A
% 0.27/0.46 = ( inf @ A @ B ) )
% 0.27/0.46 => ( less_eq @ A @ B ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.orderI
% 0.27/0.46 thf(fact_37_local_Oinf_Oorder__iff,axiom,
% 0.27/0.46 ! [A: a,B: a] :
% 0.27/0.46 ( ( less_eq @ A @ B )
% 0.27/0.46 = ( A
% 0.27/0.46 = ( inf @ A @ B ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf.order_iff
% 0.27/0.46 thf(fact_38_local_Oinf__absorb1,axiom,
% 0.27/0.46 ! [X: a,Y: a] :
% 0.27/0.46 ( ( less_eq @ X @ Y )
% 0.27/0.46 => ( ( inf @ X @ Y )
% 0.27/0.46 = X ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf_absorb1
% 0.27/0.46 thf(fact_39_local_Oinf__absorb2,axiom,
% 0.27/0.46 ! [Y: a,X: a] :
% 0.27/0.46 ( ( less_eq @ Y @ X )
% 0.27/0.46 => ( ( inf @ X @ Y )
% 0.27/0.46 = Y ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf_absorb2
% 0.27/0.46 thf(fact_40_local_Oinf__greatest,axiom,
% 0.27/0.46 ! [X: a,Y: a,Z2: a] :
% 0.27/0.46 ( ( less_eq @ X @ Y )
% 0.27/0.46 => ( ( less_eq @ X @ Z2 )
% 0.27/0.46 => ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf_greatest
% 0.27/0.46 thf(fact_41_local_Oinf__le1,axiom,
% 0.27/0.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf_le1
% 0.27/0.46 thf(fact_42_local_Oinf__le2,axiom,
% 0.27/0.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf_le2
% 0.27/0.46 thf(fact_43_local_Oinf__mono,axiom,
% 0.27/0.46 ! [A: a,C: a,B: a,D: a] :
% 0.27/0.46 ( ( less_eq @ A @ C )
% 0.27/0.46 => ( ( less_eq @ B @ D )
% 0.27/0.46 => ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % local.inf_mono
% 0.27/0.46 thf(fact_44_local_Oinf__unique,axiom,
% 0.27/0.46 ! [F: a > a > a,X: a,Y: a] :
% 0.27/0.46 ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
% 0.27/0.46 => ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
% 0.27/0.47 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.27/0.47 ( ( less_eq @ X3 @ Y4 )
% 0.27/0.47 => ( ( less_eq @ X3 @ Z3 )
% 0.27/0.47 => ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 0.27/0.47 => ( ( inf @ X @ Y )
% 0.27/0.47 = ( F @ X @ Y ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.inf_unique
% 0.27/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A: a,P: a > $o] :
% 0.27/0.47 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.27/0.47 = ( P @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ( collect_a
% 0.27/0.47 @ ^ [X2: a] : ( member_a @ X2 @ A3 ) )
% 0.27/0.47 = A3 ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_47_Collect__cong,axiom,
% 0.27/0.47 ! [P: a > $o,Q: a > $o] :
% 0.27/0.47 ( ! [X3: a] :
% 0.27/0.47 ( ( P @ X3 )
% 0.27/0.47 = ( Q @ X3 ) )
% 0.27/0.47 => ( ( collect_a @ P )
% 0.27/0.47 = ( collect_a @ Q ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_cong
% 0.27/0.47 thf(fact_48_local_Ole__iff__inf,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( less_eq @ X @ Y )
% 0.27/0.47 = ( ( inf @ X @ Y )
% 0.27/0.47 = X ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_iff_inf
% 0.27/0.47 thf(fact_49_local_Ole__infE,axiom,
% 0.27/0.47 ! [X: a,A: a,B: a] :
% 0.27/0.47 ( ( less_eq @ X @ ( inf @ A @ B ) )
% 0.27/0.47 => ~ ( ( less_eq @ X @ A )
% 0.27/0.47 => ~ ( less_eq @ X @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_infE
% 0.27/0.47 thf(fact_50_local_Ole__infI,axiom,
% 0.27/0.47 ! [X: a,A: a,B: a] :
% 0.27/0.47 ( ( less_eq @ X @ A )
% 0.27/0.47 => ( ( less_eq @ X @ B )
% 0.27/0.47 => ( less_eq @ X @ ( inf @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_infI
% 0.27/0.47 thf(fact_51_local_Ole__infI1,axiom,
% 0.27/0.47 ! [A: a,X: a,B: a] :
% 0.27/0.47 ( ( less_eq @ A @ X )
% 0.27/0.47 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_infI1
% 0.27/0.47 thf(fact_52_local_Ole__infI2,axiom,
% 0.27/0.47 ! [B: a,X: a,A: a] :
% 0.27/0.47 ( ( less_eq @ B @ X )
% 0.27/0.47 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_infI2
% 0.27/0.47 thf(fact_53_local_Ole__iff__sup,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( less_eq @ X @ Y )
% 0.27/0.47 = ( ( sup @ X @ Y )
% 0.27/0.47 = Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_iff_sup
% 0.27/0.47 thf(fact_54_local_Ole__supE,axiom,
% 0.27/0.47 ! [A: a,B: a,X: a] :
% 0.27/0.47 ( ( less_eq @ ( sup @ A @ B ) @ X )
% 0.27/0.47 => ~ ( ( less_eq @ A @ X )
% 0.27/0.47 => ~ ( less_eq @ B @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_supE
% 0.27/0.47 thf(fact_55_local_Ole__supI,axiom,
% 0.27/0.47 ! [A: a,X: a,B: a] :
% 0.27/0.47 ( ( less_eq @ A @ X )
% 0.27/0.47 => ( ( less_eq @ B @ X )
% 0.27/0.47 => ( less_eq @ ( sup @ A @ B ) @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_supI
% 0.27/0.47 thf(fact_56_local_Ole__supI1,axiom,
% 0.27/0.47 ! [X: a,A: a,B: a] :
% 0.27/0.47 ( ( less_eq @ X @ A )
% 0.27/0.47 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_supI1
% 0.27/0.47 thf(fact_57_local_Ole__supI2,axiom,
% 0.27/0.47 ! [X: a,B: a,A: a] :
% 0.27/0.47 ( ( less_eq @ X @ B )
% 0.27/0.47 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_supI2
% 0.27/0.47 thf(fact_58_local_Osup_Oabsorb1,axiom,
% 0.27/0.47 ! [B: a,A: a] :
% 0.27/0.47 ( ( less_eq @ B @ A )
% 0.27/0.47 => ( ( sup @ A @ B )
% 0.27/0.47 = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.absorb1
% 0.27/0.47 thf(fact_59_local_Osup_Oabsorb2,axiom,
% 0.27/0.47 ! [A: a,B: a] :
% 0.27/0.47 ( ( less_eq @ A @ B )
% 0.27/0.47 => ( ( sup @ A @ B )
% 0.27/0.47 = B ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.absorb2
% 0.27/0.47 thf(fact_60_local_Osup_Oabsorb__iff1,axiom,
% 0.27/0.47 ! [B: a,A: a] :
% 0.27/0.47 ( ( less_eq @ B @ A )
% 0.27/0.47 = ( ( sup @ A @ B )
% 0.27/0.47 = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.absorb_iff1
% 0.27/0.47 thf(fact_61_local_Osup_Oabsorb__iff2,axiom,
% 0.27/0.47 ! [A: a,B: a] :
% 0.27/0.47 ( ( less_eq @ A @ B )
% 0.27/0.47 = ( ( sup @ A @ B )
% 0.27/0.47 = B ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.absorb_iff2
% 0.27/0.47 thf(fact_62_local_Osup_OboundedE,axiom,
% 0.27/0.47 ! [B: a,C: a,A: a] :
% 0.27/0.47 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 0.27/0.47 => ~ ( ( less_eq @ B @ A )
% 0.27/0.47 => ~ ( less_eq @ C @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.boundedE
% 0.27/0.47 thf(fact_63_local_Osup_OboundedI,axiom,
% 0.27/0.47 ! [B: a,A: a,C: a] :
% 0.27/0.47 ( ( less_eq @ B @ A )
% 0.27/0.47 => ( ( less_eq @ C @ A )
% 0.27/0.47 => ( less_eq @ ( sup @ B @ C ) @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.boundedI
% 0.27/0.47 thf(fact_64_local_Osup_Ocobounded1,axiom,
% 0.27/0.47 ! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.cobounded1
% 0.27/0.47 thf(fact_65_local_Osup_Ocobounded2,axiom,
% 0.27/0.47 ! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.cobounded2
% 0.27/0.47 thf(fact_66_local_Osup_OcoboundedI1,axiom,
% 0.27/0.47 ! [C: a,A: a,B: a] :
% 0.27/0.47 ( ( less_eq @ C @ A )
% 0.27/0.47 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.coboundedI1
% 0.27/0.47 thf(fact_67_local_Osup_OcoboundedI2,axiom,
% 0.27/0.47 ! [C: a,B: a,A: a] :
% 0.27/0.47 ( ( less_eq @ C @ B )
% 0.27/0.47 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.coboundedI2
% 0.27/0.47 thf(fact_68_local_Osup_Omono,axiom,
% 0.27/0.47 ! [C: a,A: a,D: a,B: a] :
% 0.27/0.47 ( ( less_eq @ C @ A )
% 0.27/0.47 => ( ( less_eq @ D @ B )
% 0.27/0.47 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.mono
% 0.27/0.47 thf(fact_69_local_Osup_OorderE,axiom,
% 0.27/0.47 ! [B: a,A: a] :
% 0.27/0.47 ( ( less_eq @ B @ A )
% 0.27/0.47 => ( A
% 0.27/0.47 = ( sup @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.orderE
% 0.27/0.47 thf(fact_70_local_Osup_OorderI,axiom,
% 0.27/0.47 ! [A: a,B: a] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( sup @ A @ B ) )
% 0.27/0.47 => ( less_eq @ B @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.orderI
% 0.27/0.47 thf(fact_71_local_Osup_Oorder__iff,axiom,
% 0.27/0.47 ! [B: a,A: a] :
% 0.27/0.47 ( ( less_eq @ B @ A )
% 0.27/0.47 = ( A
% 0.27/0.47 = ( sup @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.order_iff
% 0.27/0.47 thf(fact_72_local_Osup__absorb1,axiom,
% 0.27/0.47 ! [Y: a,X: a] :
% 0.27/0.47 ( ( less_eq @ Y @ X )
% 0.27/0.47 => ( ( sup @ X @ Y )
% 0.27/0.47 = X ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_absorb1
% 0.27/0.47 thf(fact_73_local_Osup__absorb2,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( less_eq @ X @ Y )
% 0.27/0.47 => ( ( sup @ X @ Y )
% 0.27/0.47 = Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_absorb2
% 0.27/0.47 thf(fact_74_local_Osup__ge1,axiom,
% 0.27/0.47 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_ge1
% 0.27/0.47 thf(fact_75_local_Osup__ge2,axiom,
% 0.27/0.47 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_ge2
% 0.27/0.47 thf(fact_76_local_Osup__least,axiom,
% 0.27/0.47 ! [Y: a,X: a,Z2: a] :
% 0.27/0.47 ( ( less_eq @ Y @ X )
% 0.27/0.47 => ( ( less_eq @ Z2 @ X )
% 0.27/0.47 => ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_least
% 0.27/0.47 thf(fact_77_local_Osup__mono,axiom,
% 0.27/0.47 ! [A: a,C: a,B: a,D: a] :
% 0.27/0.47 ( ( less_eq @ A @ C )
% 0.27/0.47 => ( ( less_eq @ B @ D )
% 0.27/0.47 => ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_mono
% 0.27/0.47 thf(fact_78_local_Osup__unique,axiom,
% 0.27/0.47 ! [F: a > a > a,X: a,Y: a] :
% 0.27/0.47 ( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
% 0.27/0.47 => ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
% 0.27/0.47 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.27/0.47 ( ( less_eq @ Y4 @ X3 )
% 0.27/0.47 => ( ( less_eq @ Z3 @ X3 )
% 0.27/0.47 => ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
% 0.27/0.47 => ( ( sup @ X @ Y )
% 0.27/0.47 = ( F @ X @ Y ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_unique
% 0.27/0.47 thf(fact_79_local_Odistrib__imp1,axiom,
% 0.27/0.47 ! [X: a,Y: a,Z2: a] :
% 0.27/0.47 ( ! [X3: a,Y4: a,Z3: a] :
% 0.27/0.47 ( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
% 0.27/0.47 = ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
% 0.27/0.47 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.27/0.47 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.distrib_imp1
% 0.27/0.47 thf(fact_80_local_Odistrib__imp2,axiom,
% 0.27/0.47 ! [X: a,Y: a,Z2: a] :
% 0.27/0.47 ( ! [X3: a,Y4: a,Z3: a] :
% 0.27/0.47 ( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
% 0.27/0.47 = ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
% 0.27/0.47 => ( ( inf @ X @ ( sup @ Y @ Z2 ) )
% 0.27/0.47 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.distrib_imp2
% 0.27/0.47 thf(fact_81_local_Oa__join__d,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.a_join_d
% 0.27/0.47 thf(fact_82_a__meet__d,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 = ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % a_meet_d
% 0.27/0.47 thf(fact_83_local_Ob__join__d,axiom,
% 0.27/0.47 ! [B: a,A: a,C: a] :
% 0.27/0.47 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.b_join_d
% 0.27/0.47 thf(fact_84_b__meet__d,axiom,
% 0.27/0.47 ! [B: a,A: a,C: a] :
% 0.27/0.47 ( ( inf @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 = ( sup @ ( inf @ B @ C ) @ ( inf @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % b_meet_d
% 0.27/0.47 thf(fact_85_c__meet__d,axiom,
% 0.27/0.47 ! [C: a,A: a,B: a] :
% 0.27/0.47 ( ( inf @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 = ( sup @ ( inf @ C @ A ) @ ( inf @ B @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % c_meet_d
% 0.27/0.47 thf(fact_86_local_Od__aux__def,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 0.27/0.47 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.d_aux_def
% 0.27/0.47 thf(fact_87_local_Od__b__c__a,axiom,
% 0.27/0.47 ! [B: a,C: a,A: a] :
% 0.27/0.47 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 0.27/0.47 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.d_b_c_a
% 0.27/0.47 thf(fact_88_local_Od__c__a__b,axiom,
% 0.27/0.47 ! [C: a,A: a,B: a] :
% 0.27/0.47 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 0.27/0.47 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.d_c_a_b
% 0.27/0.47 thf(fact_89_local_Oa__meet__e,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.a_meet_e
% 0.27/0.47 thf(fact_90_local_Ob__meet__e,axiom,
% 0.27/0.47 ! [B: a,A: a,C: a] :
% 0.27/0.47 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.b_meet_e
% 0.27/0.47 thf(fact_91_local_Oc__meet__e,axiom,
% 0.27/0.47 ! [C: a,A: a,B: a] :
% 0.27/0.47 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.c_meet_e
% 0.27/0.47 thf(fact_92_local_Oe__aux__def,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 0.27/0.47 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.e_aux_def
% 0.27/0.47 thf(fact_93_local_Oe__b__c__a,axiom,
% 0.27/0.47 ! [B: a,C: a,A: a] :
% 0.27/0.47 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 0.27/0.47 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.e_b_c_a
% 0.27/0.47 thf(fact_94_local_Oe__c__a__b,axiom,
% 0.27/0.47 ! [C: a,A: a,B: a] :
% 0.27/0.47 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 0.27/0.47 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.e_c_a_b
% 0.27/0.47 thf(fact_95_local_Odistrib__inf__le,axiom,
% 0.27/0.47 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.distrib_inf_le
% 0.27/0.47 thf(fact_96_local_Odistrib__sup__le,axiom,
% 0.27/0.47 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.distrib_sup_le
% 0.27/0.47 thf(fact_97_local_Omodular,axiom,
% 0.27/0.47 ! [X: a,Y: a,Z2: a] :
% 0.27/0.47 ( ( less_eq @ X @ Y )
% 0.27/0.47 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.27/0.47 = ( inf @ Y @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.modular
% 0.27/0.47 thf(fact_98_local_Oincomp__def,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( modula1727524044comp_a @ less_eq @ X @ Y )
% 0.27/0.47 = ( ~ ( less_eq @ X @ Y )
% 0.27/0.47 & ~ ( less_eq @ Y @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.incomp_def
% 0.27/0.47 thf(fact_99_local_Oorder_Orefl,axiom,
% 0.27/0.47 ! [A: a] : ( less_eq @ A @ A ) ).
% 0.27/0.47
% 0.27/0.47 % local.order.refl
% 0.27/0.47 thf(fact_100_local_Oorder__refl,axiom,
% 0.27/0.47 ! [X: a] : ( less_eq @ X @ X ) ).
% 0.27/0.47
% 0.27/0.47 % local.order_refl
% 0.27/0.47 thf(fact_101_local_Oinf_Oidem,axiom,
% 0.27/0.47 ! [A: a] :
% 0.27/0.47 ( ( inf @ A @ A )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % local.inf.idem
% 0.27/0.47 thf(fact_102_local_Oinf_Oleft__idem,axiom,
% 0.27/0.47 ! [A: a,B: a] :
% 0.27/0.47 ( ( inf @ A @ ( inf @ A @ B ) )
% 0.27/0.47 = ( inf @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.inf.left_idem
% 0.27/0.47 thf(fact_103_local_Oinf_Oright__idem,axiom,
% 0.27/0.47 ! [A: a,B: a] :
% 0.27/0.47 ( ( inf @ ( inf @ A @ B ) @ B )
% 0.27/0.47 = ( inf @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.inf.right_idem
% 0.27/0.47 thf(fact_104_local_Oinf__idem,axiom,
% 0.27/0.47 ! [X: a] :
% 0.27/0.47 ( ( inf @ X @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % local.inf_idem
% 0.27/0.47 thf(fact_105_local_Oinf__left__idem,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( inf @ X @ ( inf @ X @ Y ) )
% 0.27/0.47 = ( inf @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.inf_left_idem
% 0.27/0.47 thf(fact_106_local_Oinf__right__idem,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 0.27/0.47 = ( inf @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.inf_right_idem
% 0.27/0.47 thf(fact_107_local_Osup_Oidem,axiom,
% 0.27/0.47 ! [A: a] :
% 0.27/0.47 ( ( sup @ A @ A )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.idem
% 0.27/0.47 thf(fact_108_local_Osup_Oleft__idem,axiom,
% 0.27/0.47 ! [A: a,B: a] :
% 0.27/0.47 ( ( sup @ A @ ( sup @ A @ B ) )
% 0.27/0.47 = ( sup @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.left_idem
% 0.27/0.47 thf(fact_109_local_Osup_Oright__idem,axiom,
% 0.27/0.47 ! [A: a,B: a] :
% 0.27/0.47 ( ( sup @ ( sup @ A @ B ) @ B )
% 0.27/0.47 = ( sup @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.right_idem
% 0.27/0.47 thf(fact_110_local_Osup__idem,axiom,
% 0.27/0.47 ! [X: a] :
% 0.27/0.47 ( ( sup @ X @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_idem
% 0.27/0.47 thf(fact_111_local_Osup__left__idem,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( sup @ X @ ( sup @ X @ Y ) )
% 0.27/0.47 = ( sup @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_left_idem
% 0.27/0.47 thf(fact_112_local_Oc__a,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.27/0.47 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.c_a
% 0.27/0.47 thf(fact_113_local_OGreatestI2__order,axiom,
% 0.27/0.47 ! [P: a > $o,X: a,Q: a > $o] :
% 0.27/0.47 ( ( P @ X )
% 0.27/0.47 => ( ! [Y4: a] :
% 0.27/0.47 ( ( P @ Y4 )
% 0.27/0.47 => ( less_eq @ Y4 @ X ) )
% 0.27/0.47 => ( ! [X3: a] :
% 0.27/0.47 ( ( P @ X3 )
% 0.27/0.47 => ( ! [Y5: a] :
% 0.27/0.47 ( ( P @ Y5 )
% 0.27/0.47 => ( less_eq @ Y5 @ X3 ) )
% 0.27/0.47 => ( Q @ X3 ) ) )
% 0.27/0.47 => ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.GreatestI2_order
% 0.27/0.47 thf(fact_114_local_OGreatest__equality,axiom,
% 0.27/0.47 ! [P: a > $o,X: a] :
% 0.27/0.47 ( ( P @ X )
% 0.27/0.47 => ( ! [Y4: a] :
% 0.27/0.47 ( ( P @ Y4 )
% 0.27/0.47 => ( less_eq @ Y4 @ X ) )
% 0.27/0.47 => ( ( greatest_a @ less_eq @ P )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.Greatest_equality
% 0.27/0.47 thf(fact_115_local_Omax__def,axiom,
% 0.27/0.47 ! [A: a,B: a] :
% 0.27/0.47 ( ( ( less_eq @ A @ B )
% 0.27/0.47 => ( ( max_a @ less_eq @ A @ B )
% 0.27/0.47 = B ) )
% 0.27/0.47 & ( ~ ( less_eq @ A @ B )
% 0.27/0.47 => ( ( max_a @ less_eq @ A @ B )
% 0.27/0.47 = A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.max_def
% 0.27/0.47 thf(fact_116_local_Omin__def,axiom,
% 0.27/0.47 ! [A: a,B: a] :
% 0.27/0.47 ( ( ( less_eq @ A @ B )
% 0.27/0.47 => ( ( min_a @ less_eq @ A @ B )
% 0.27/0.47 = A ) )
% 0.27/0.47 & ( ~ ( less_eq @ A @ B )
% 0.27/0.47 => ( ( min_a @ less_eq @ A @ B )
% 0.27/0.47 = B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.min_def
% 0.27/0.47 thf(fact_117_local_Oa__aux__def,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 0.27/0.47 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.a_aux_def
% 0.27/0.47 thf(fact_118_local_Oc__aux__def,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.27/0.47 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.c_aux_def
% 0.27/0.47 thf(fact_119_local_Oinf_Obounded__iff,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 0.27/0.47 = ( ( less_eq @ A @ B )
% 0.27/0.47 & ( less_eq @ A @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.inf.bounded_iff
% 0.27/0.47 thf(fact_120_local_Ole__inf__iff,axiom,
% 0.27/0.47 ! [X: a,Y: a,Z2: a] :
% 0.27/0.47 ( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
% 0.27/0.47 = ( ( less_eq @ X @ Y )
% 0.27/0.47 & ( less_eq @ X @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_inf_iff
% 0.27/0.47 thf(fact_121_local_Ole__sup__iff,axiom,
% 0.27/0.47 ! [X: a,Y: a,Z2: a] :
% 0.27/0.47 ( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
% 0.27/0.47 = ( ( less_eq @ X @ Z2 )
% 0.27/0.47 & ( less_eq @ Y @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.le_sup_iff
% 0.27/0.47 thf(fact_122_local_Osup_Obounded__iff,axiom,
% 0.27/0.47 ! [B: a,C: a,A: a] :
% 0.27/0.47 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 0.27/0.47 = ( ( less_eq @ B @ A )
% 0.27/0.47 & ( less_eq @ C @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup.bounded_iff
% 0.27/0.47 thf(fact_123_local_Oinf__sup__absorb,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( inf @ X @ ( sup @ X @ Y ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % local.inf_sup_absorb
% 0.27/0.47 thf(fact_124_local_Osup__inf__absorb,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( sup @ X @ ( inf @ X @ Y ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % local.sup_inf_absorb
% 0.27/0.47 thf(fact_125_local_Ob__a,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.27/0.47 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.b_a
% 0.27/0.47 thf(fact_126_local_OLeast1I,axiom,
% 0.27/0.47 ! [P: a > $o] :
% 0.27/0.47 ( ? [X4: a] :
% 0.27/0.47 ( ( P @ X4 )
% 0.27/0.47 & ! [Y4: a] :
% 0.27/0.47 ( ( P @ Y4 )
% 0.27/0.47 => ( less_eq @ X4 @ Y4 ) )
% 0.27/0.47 & ! [Y4: a] :
% 0.27/0.47 ( ( ( P @ Y4 )
% 0.27/0.47 & ! [Ya: a] :
% 0.27/0.47 ( ( P @ Ya )
% 0.27/0.47 => ( less_eq @ Y4 @ Ya ) ) )
% 0.27/0.47 => ( Y4 = X4 ) ) )
% 0.27/0.47 => ( P @ ( least_a @ less_eq @ P ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.Least1I
% 0.27/0.47 thf(fact_127_local_OLeast1__le,axiom,
% 0.27/0.47 ! [P: a > $o,Z2: a] :
% 0.27/0.47 ( ? [X4: a] :
% 0.27/0.47 ( ( P @ X4 )
% 0.27/0.47 & ! [Y4: a] :
% 0.27/0.47 ( ( P @ Y4 )
% 0.27/0.47 => ( less_eq @ X4 @ Y4 ) )
% 0.27/0.47 & ! [Y4: a] :
% 0.27/0.47 ( ( ( P @ Y4 )
% 0.27/0.47 & ! [Ya: a] :
% 0.27/0.47 ( ( P @ Ya )
% 0.27/0.47 => ( less_eq @ Y4 @ Ya ) ) )
% 0.27/0.47 => ( Y4 = X4 ) ) )
% 0.27/0.47 => ( ( P @ Z2 )
% 0.27/0.47 => ( less_eq @ ( least_a @ less_eq @ P ) @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.Least1_le
% 0.27/0.47 thf(fact_128_local_OLeastI2__order,axiom,
% 0.27/0.47 ! [P: a > $o,X: a,Q: a > $o] :
% 0.27/0.47 ( ( P @ X )
% 0.27/0.47 => ( ! [Y4: a] :
% 0.27/0.47 ( ( P @ Y4 )
% 0.27/0.47 => ( less_eq @ X @ Y4 ) )
% 0.27/0.47 => ( ! [X3: a] :
% 0.27/0.47 ( ( P @ X3 )
% 0.27/0.47 => ( ! [Y5: a] :
% 0.27/0.47 ( ( P @ Y5 )
% 0.27/0.47 => ( less_eq @ X3 @ Y5 ) )
% 0.27/0.47 => ( Q @ X3 ) ) )
% 0.27/0.47 => ( Q @ ( least_a @ less_eq @ P ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.LeastI2_order
% 0.27/0.47 thf(fact_129_local_OLeast__equality,axiom,
% 0.27/0.47 ! [P: a > $o,X: a] :
% 0.27/0.47 ( ( P @ X )
% 0.27/0.47 => ( ! [Y4: a] :
% 0.27/0.47 ( ( P @ Y4 )
% 0.27/0.47 => ( less_eq @ X @ Y4 ) )
% 0.27/0.47 => ( ( least_a @ less_eq @ P )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.Least_equality
% 0.27/0.47 thf(fact_130_local_Ob__aux__def,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.27/0.47 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.b_aux_def
% 0.27/0.47 thf(fact_131_a__meet__b__eq__d,axiom,
% 0.27/0.47 ! [A: a,B: a,C: a] :
% 0.27/0.47 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 => ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.27/0.47 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % a_meet_b_eq_d
% 0.27/0.47 thf(fact_132_lattice_Oa__aux_Ocong,axiom,
% 0.27/0.47 modula17988509_aux_a = modula17988509_aux_a ).
% 0.27/0.47
% 0.27/0.47 % lattice.a_aux.cong
% 0.27/0.47 thf(fact_133_lattice_Oc__aux_Ocong,axiom,
% 0.27/0.47 modula581031071_aux_a = modula581031071_aux_a ).
% 0.27/0.47
% 0.27/0.47 % lattice.c_aux.cong
% 0.27/0.47 thf(fact_134_lattice_Od__aux_Ocong,axiom,
% 0.27/0.47 modula1936294176_aux_a = modula1936294176_aux_a ).
% 0.27/0.47
% 0.27/0.47 % lattice.d_aux.cong
% 0.27/0.47 thf(fact_135_lattice_Oe__aux_Ocong,axiom,
% 0.27/0.47 modula1144073633_aux_a = modula1144073633_aux_a ).
% 0.27/0.47
% 0.27/0.47 % lattice.e_aux.cong
% 0.27/0.47 thf(fact_136_local_Ocomp__fun__idem__sup,axiom,
% 0.27/0.47 finite40241356em_a_a @ sup ).
% 0.27/0.47
% 0.27/0.47 % local.comp_fun_idem_sup
% 0.27/0.47 thf(fact_137_local_Ocomp__fun__idem__inf,axiom,
% 0.27/0.47 finite40241356em_a_a @ inf ).
% 0.27/0.47
% 0.27/0.47 % local.comp_fun_idem_inf
% 0.27/0.47 thf(fact_138_local_Osup_Osemigroup__axioms,axiom,
% 0.27/0.47 semigroup_a @ sup ).
% 0.27/0.47
% 0.27/0.47 % local.sup.semigroup_axioms
% 0.27/0.47 thf(fact_139_local_Oinf_Osemigroup__axioms,axiom,
% 0.27/0.47 semigroup_a @ inf ).
% 0.27/0.47
% 0.27/0.47 % local.inf.semigroup_axioms
% 0.27/0.47 thf(fact_140_local_Osup_Osemilattice__axioms,axiom,
% 0.27/0.47 semilattice_a @ sup ).
% 0.27/0.47
% 0.27/0.47 % local.sup.semilattice_axioms
% 0.27/0.47 thf(fact_141_local_Oinf_Osemilattice__axioms,axiom,
% 0.27/0.47 semilattice_a @ inf ).
% 0.27/0.47
% 0.27/0.47 % local.inf.semilattice_axioms
% 0.27/0.47 thf(fact_142_local_Osup_Oabel__semigroup__axioms,axiom,
% 0.27/0.47 abel_semigroup_a @ sup ).
% 0.27/0.47
% 0.27/0.47 % local.sup.abel_semigroup_axioms
% 0.27/0.47 thf(fact_143_local_Oinf_Oabel__semigroup__axioms,axiom,
% 0.27/0.47 abel_semigroup_a @ inf ).
% 0.27/0.47
% 0.27/0.47 % local.inf.abel_semigroup_axioms
% 0.27/0.47 thf(fact_144_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 0.27/0.47 lattic1885654924_set_a @ sup ).
% 0.27/0.47
% 0.27/0.47 % local.Sup_fin.semilattice_set_axioms
% 0.27/0.47 thf(fact_145_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 0.27/0.47 lattic1885654924_set_a @ inf ).
% 0.27/0.47
% 0.27/0.47 % local.Inf_fin.semilattice_set_axioms
% 0.27/0.47 thf(fact_146_local_Obdd__above__def,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 0.27/0.47 = ( ? [M: a] :
% 0.27/0.47 ! [X2: a] :
% 0.27/0.47 ( ( member_a @ X2 @ A3 )
% 0.27/0.47 => ( less_eq @ X2 @ M ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_above_def
% 0.27/0.47 thf(fact_147_local_Obdd__below__def,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 0.27/0.47 = ( ? [M2: a] :
% 0.27/0.47 ! [X2: a] :
% 0.27/0.47 ( ( member_a @ X2 @ A3 )
% 0.27/0.47 => ( less_eq @ M2 @ X2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_below_def
% 0.27/0.47 thf(fact_148_local_Obdd__belowI,axiom,
% 0.27/0.47 ! [A3: set_a,M3: a] :
% 0.27/0.47 ( ! [X3: a] :
% 0.27/0.47 ( ( member_a @ X3 @ A3 )
% 0.27/0.47 => ( less_eq @ M3 @ X3 ) )
% 0.27/0.47 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_belowI
% 0.27/0.47 thf(fact_149_local_Obdd__aboveI,axiom,
% 0.27/0.47 ! [A3: set_a,M4: a] :
% 0.27/0.47 ( ! [X3: a] :
% 0.27/0.47 ( ( member_a @ X3 @ A3 )
% 0.27/0.47 => ( less_eq @ X3 @ M4 ) )
% 0.27/0.47 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_aboveI
% 0.27/0.47 thf(fact_150_lattice_Oincomp_Ocong,axiom,
% 0.27/0.47 modula1727524044comp_a = modula1727524044comp_a ).
% 0.27/0.47
% 0.27/0.47 % lattice.incomp.cong
% 0.27/0.47 thf(fact_151_lattice_Ob__aux_Ocong,axiom,
% 0.27/0.47 modula1373251614_aux_a = modula1373251614_aux_a ).
% 0.27/0.47
% 0.27/0.47 % lattice.b_aux.cong
% 0.27/0.47 thf(fact_152_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.27/0.47 ! [F: a > a > a] :
% 0.27/0.47 ( ( abel_semigroup_a @ F )
% 0.27/0.47 => ( semigroup_a @ F ) ) ).
% 0.27/0.47
% 0.27/0.47 % abel_semigroup.axioms(1)
% 0.27/0.47 thf(fact_153_semilattice__set__def,axiom,
% 0.27/0.47 lattic1885654924_set_a = semilattice_a ).
% 0.27/0.47
% 0.27/0.47 % semilattice_set_def
% 0.27/0.47 thf(fact_154_semilattice__set_Ointro,axiom,
% 0.27/0.47 ! [F: a > a > a] :
% 0.27/0.47 ( ( semilattice_a @ F )
% 0.27/0.47 => ( lattic1885654924_set_a @ F ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_set.intro
% 0.27/0.47 thf(fact_155_abel__semigroup_Oleft__commute,axiom,
% 0.27/0.47 ! [F: a > a > a,B: a,A: a,C: a] :
% 0.27/0.47 ( ( abel_semigroup_a @ F )
% 0.27/0.47 => ( ( F @ B @ ( F @ A @ C ) )
% 0.27/0.47 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % abel_semigroup.left_commute
% 0.27/0.47 thf(fact_156_abel__semigroup_Ocommute,axiom,
% 0.27/0.47 ! [F: a > a > a,A: a,B: a] :
% 0.27/0.47 ( ( abel_semigroup_a @ F )
% 0.27/0.47 => ( ( F @ A @ B )
% 0.27/0.47 = ( F @ B @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % abel_semigroup.commute
% 0.27/0.47 thf(fact_157_semigroup_Ointro,axiom,
% 0.27/0.47 ! [F: a > a > a] :
% 0.27/0.47 ( ! [A4: a,B3: a,C2: a] :
% 0.27/0.47 ( ( F @ ( F @ A4 @ B3 ) @ C2 )
% 0.27/0.47 = ( F @ A4 @ ( F @ B3 @ C2 ) ) )
% 0.27/0.47 => ( semigroup_a @ F ) ) ).
% 0.27/0.47
% 0.27/0.47 % semigroup.intro
% 0.27/0.47 thf(fact_158_semigroup_Oassoc,axiom,
% 0.27/0.47 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.27/0.47 ( ( semigroup_a @ F )
% 0.27/0.47 => ( ( F @ ( F @ A @ B ) @ C )
% 0.27/0.47 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % semigroup.assoc
% 0.27/0.47 thf(fact_159_semigroup__def,axiom,
% 0.27/0.47 ( semigroup_a
% 0.27/0.47 = ( ^ [F2: a > a > a] :
% 0.27/0.47 ! [A2: a,B2: a,C3: a] :
% 0.27/0.47 ( ( F2 @ ( F2 @ A2 @ B2 ) @ C3 )
% 0.27/0.47 = ( F2 @ A2 @ ( F2 @ B2 @ C3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % semigroup_def
% 0.27/0.47 thf(fact_160_semilattice__set_Oaxioms,axiom,
% 0.27/0.47 ! [F: a > a > a] :
% 0.27/0.47 ( ( lattic1885654924_set_a @ F )
% 0.27/0.47 => ( semilattice_a @ F ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_set.axioms
% 0.27/0.47 thf(fact_161_semilattice_Oaxioms_I1_J,axiom,
% 0.27/0.47 ! [F: a > a > a] :
% 0.27/0.47 ( ( semilattice_a @ F )
% 0.27/0.47 => ( abel_semigroup_a @ F ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice.axioms(1)
% 0.27/0.47 thf(fact_162_local_Obdd__above__mono,axiom,
% 0.27/0.47 ! [B4: set_a,A3: set_a] :
% 0.27/0.47 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.27/0.47 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_above_mono
% 0.27/0.47 thf(fact_163_local_Obdd__below__mono,axiom,
% 0.27/0.47 ! [B4: set_a,A3: set_a] :
% 0.27/0.47 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.27/0.47 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_below_mono
% 0.27/0.47 thf(fact_164_local_Oantimono__def,axiom,
% 0.27/0.47 ! [F: a > set_a] :
% 0.27/0.47 ( ( antimono_a_set_a @ less_eq @ F )
% 0.27/0.47 = ( ! [X2: a,Y3: a] :
% 0.27/0.47 ( ( less_eq @ X2 @ Y3 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.antimono_def
% 0.27/0.47 thf(fact_165_local_OantimonoI,axiom,
% 0.27/0.47 ! [F: a > set_a] :
% 0.27/0.47 ( ! [X3: a,Y4: a] :
% 0.27/0.47 ( ( less_eq @ X3 @ Y4 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.27/0.47 => ( antimono_a_set_a @ less_eq @ F ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.antimonoI
% 0.27/0.47 thf(fact_166_local_OantimonoE,axiom,
% 0.27/0.47 ! [F: a > set_a,X: a,Y: a] :
% 0.27/0.47 ( ( antimono_a_set_a @ less_eq @ F )
% 0.27/0.47 => ( ( less_eq @ X @ Y )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.antimonoE
% 0.27/0.47 thf(fact_167_local_OantimonoD,axiom,
% 0.27/0.47 ! [F: a > set_a,X: a,Y: a] :
% 0.27/0.47 ( ( antimono_a_set_a @ less_eq @ F )
% 0.27/0.47 => ( ( less_eq @ X @ Y )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.antimonoD
% 0.27/0.47 thf(fact_168_local_OmonoD,axiom,
% 0.27/0.47 ! [F: a > set_a,X: a,Y: a] :
% 0.27/0.47 ( ( mono_a_set_a @ less_eq @ F )
% 0.27/0.47 => ( ( less_eq @ X @ Y )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.monoD
% 0.27/0.47 thf(fact_169_local_OmonoE,axiom,
% 0.27/0.47 ! [F: a > set_a,X: a,Y: a] :
% 0.27/0.47 ( ( mono_a_set_a @ less_eq @ F )
% 0.27/0.47 => ( ( less_eq @ X @ Y )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.monoE
% 0.27/0.47 thf(fact_170_local_OmonoI,axiom,
% 0.27/0.47 ! [F: a > set_a] :
% 0.27/0.47 ( ! [X3: a,Y4: a] :
% 0.27/0.47 ( ( less_eq @ X3 @ Y4 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.47 => ( mono_a_set_a @ less_eq @ F ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.monoI
% 0.27/0.47 thf(fact_171_local_Omono__def,axiom,
% 0.27/0.47 ! [F: a > set_a] :
% 0.27/0.47 ( ( mono_a_set_a @ less_eq @ F )
% 0.27/0.47 = ( ! [X2: a,Y3: a] :
% 0.27/0.47 ( ( less_eq @ X2 @ Y3 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.mono_def
% 0.27/0.47 thf(fact_172_semilattice_Oidem,axiom,
% 0.27/0.47 ! [F: a > a > a,A: a] :
% 0.27/0.47 ( ( semilattice_a @ F )
% 0.27/0.47 => ( ( F @ A @ A )
% 0.27/0.47 = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice.idem
% 0.27/0.47 thf(fact_173_semilattice_Oleft__idem,axiom,
% 0.27/0.47 ! [F: a > a > a,A: a,B: a] :
% 0.27/0.47 ( ( semilattice_a @ F )
% 0.27/0.47 => ( ( F @ A @ ( F @ A @ B ) )
% 0.27/0.47 = ( F @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice.left_idem
% 0.27/0.47 thf(fact_174_semilattice_Oright__idem,axiom,
% 0.27/0.47 ! [F: a > a > a,A: a,B: a] :
% 0.27/0.47 ( ( semilattice_a @ F )
% 0.27/0.47 => ( ( F @ ( F @ A @ B ) @ B )
% 0.27/0.47 = ( F @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice.right_idem
% 0.27/0.47 thf(fact_175_subsetI,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a] :
% 0.27/0.47 ( ! [X3: a] :
% 0.27/0.47 ( ( member_a @ X3 @ A3 )
% 0.27/0.47 => ( member_a @ X3 @ B4 ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 0.27/0.47
% 0.27/0.47 % subsetI
% 0.27/0.47 thf(fact_176_subset__antisym,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 0.27/0.47 => ( A3 = B4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_antisym
% 0.27/0.47 thf(fact_177_preorder__class_Oorder__refl,axiom,
% 0.27/0.47 ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).
% 0.27/0.47
% 0.27/0.47 % preorder_class.order_refl
% 0.27/0.47 thf(fact_178_order_Oantimono_Ocong,axiom,
% 0.27/0.47 antimono_a_set_a = antimono_a_set_a ).
% 0.27/0.47
% 0.27/0.47 % order.antimono.cong
% 0.27/0.47 thf(fact_179_order_Omono_Ocong,axiom,
% 0.27/0.47 mono_a_set_a = mono_a_set_a ).
% 0.27/0.47
% 0.27/0.47 % order.mono.cong
% 0.27/0.47 thf(fact_180_order__class_Odual__order_Oantisym,axiom,
% 0.27/0.47 ! [B: set_a,A: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ B @ A )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.47 => ( A = B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.dual_order.antisym
% 0.27/0.47 thf(fact_181_order__class_Odual__order_Oeq__iff,axiom,
% 0.27/0.47 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.27/0.47 = ( ^ [A2: set_a,B2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.27/0.47 & ( ord_less_eq_set_a @ A2 @ B2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.dual_order.eq_iff
% 0.27/0.47 thf(fact_182_order__class_Odual__order_Otrans,axiom,
% 0.27/0.47 ! [B: set_a,A: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ B @ A )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ C @ B )
% 0.27/0.47 => ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.dual_order.trans
% 0.27/0.47 thf(fact_183_order__class_Odual__order_Orefl,axiom,
% 0.27/0.47 ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.dual_order.refl
% 0.27/0.47 thf(fact_184_preorder__class_Oorder__trans,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ Y @ Z2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % preorder_class.order_trans
% 0.27/0.47 thf(fact_185_order__class_Oorder_Oantisym,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B @ A )
% 0.27/0.47 => ( A = B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.order.antisym
% 0.27/0.47 thf(fact_186_ord__class_Oord__le__eq__trans,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.47 => ( ( B = C )
% 0.27/0.47 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_class.ord_le_eq_trans
% 0.27/0.47 thf(fact_187_ord__class_Oord__eq__le__trans,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a,C: set_a] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B @ C )
% 0.27/0.47 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_class.ord_eq_le_trans
% 0.27/0.47 thf(fact_188_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.47 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.27/0.47 = ( ^ [A2: set_a,B2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 & ( ord_less_eq_set_a @ B2 @ A2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.order.eq_iff
% 0.27/0.47 thf(fact_189_order__class_Oantisym__conv,axiom,
% 0.27/0.47 ! [Y: set_a,X: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ Y @ X )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.47 = ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.antisym_conv
% 0.27/0.47 thf(fact_190_order__class_Oorder_Otrans,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B @ C )
% 0.27/0.47 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.order.trans
% 0.27/0.47 thf(fact_191_preorder__class_Oeq__refl,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( X = Y )
% 0.27/0.47 => ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % preorder_class.eq_refl
% 0.27/0.47 thf(fact_192_order__class_Oantisym,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ Y @ X )
% 0.27/0.47 => ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.antisym
% 0.27/0.47 thf(fact_193_order__class_Oeq__iff,axiom,
% 0.27/0.47 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.27/0.47 = ( ^ [X2: set_a,Y3: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.27/0.47 & ( ord_less_eq_set_a @ Y3 @ X2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.eq_iff
% 0.27/0.47 thf(fact_194_ord__le__eq__subst,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.47 => ( ( ( F @ B )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X3: set_a,Y4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_le_eq_subst
% 0.27/0.47 thf(fact_195_ord__eq__le__subst,axiom,
% 0.27/0.47 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( F @ B ) )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B @ C )
% 0.27/0.47 => ( ! [X3: set_a,Y4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_le_subst
% 0.27/0.47 thf(fact_196_order__subst2,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 0.27/0.47 => ( ! [X3: set_a,Y4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst2
% 0.27/0.47 thf(fact_197_order__subst1,axiom,
% 0.27/0.47 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B @ C )
% 0.27/0.47 => ( ! [X3: set_a,Y4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst1
% 0.27/0.47 thf(fact_198_Collect__mono__iff,axiom,
% 0.27/0.47 ! [P: a > $o,Q: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.27/0.47 = ( ! [X2: a] :
% 0.27/0.47 ( ( P @ X2 )
% 0.27/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mono_iff
% 0.27/0.47 thf(fact_199_set__eq__subset,axiom,
% 0.27/0.47 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.27/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 0.27/0.47 & ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % set_eq_subset
% 0.27/0.47 thf(fact_200_subset__trans,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a,C4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B4 @ C4 )
% 0.27/0.47 => ( ord_less_eq_set_a @ A3 @ C4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_trans
% 0.27/0.47 thf(fact_201_Collect__mono,axiom,
% 0.27/0.47 ! [P: a > $o,Q: a > $o] :
% 0.27/0.47 ( ! [X3: a] :
% 0.27/0.47 ( ( P @ X3 )
% 0.27/0.47 => ( Q @ X3 ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mono
% 0.27/0.47 thf(fact_202_subset__refl,axiom,
% 0.27/0.47 ! [A3: set_a] : ( ord_less_eq_set_a @ A3 @ A3 ) ).
% 0.27/0.47
% 0.27/0.47 % subset_refl
% 0.27/0.47 thf(fact_203_subset__iff,axiom,
% 0.27/0.47 ( ord_less_eq_set_a
% 0.27/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.47 ! [T: a] :
% 0.27/0.47 ( ( member_a @ T @ A5 )
% 0.27/0.47 => ( member_a @ T @ B5 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_iff
% 0.27/0.47 thf(fact_204_equalityD2,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a] :
% 0.27/0.47 ( ( A3 = B4 )
% 0.27/0.47 => ( ord_less_eq_set_a @ B4 @ A3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % equalityD2
% 0.27/0.47 thf(fact_205_equalityD1,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a] :
% 0.27/0.47 ( ( A3 = B4 )
% 0.27/0.47 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 0.27/0.47
% 0.27/0.47 % equalityD1
% 0.27/0.47 thf(fact_206_subset__eq,axiom,
% 0.27/0.47 ( ord_less_eq_set_a
% 0.27/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.47 ! [X2: a] :
% 0.27/0.47 ( ( member_a @ X2 @ A5 )
% 0.27/0.47 => ( member_a @ X2 @ B5 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_eq
% 0.27/0.47 thf(fact_207_equalityE,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a] :
% 0.27/0.47 ( ( A3 = B4 )
% 0.27/0.47 => ~ ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.27/0.47 => ~ ( ord_less_eq_set_a @ B4 @ A3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % equalityE
% 0.27/0.47 thf(fact_208_subsetD,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a,C: a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.27/0.47 => ( ( member_a @ C @ A3 )
% 0.27/0.47 => ( member_a @ C @ B4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subsetD
% 0.27/0.47 thf(fact_209_in__mono,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a,X: a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.27/0.47 => ( ( member_a @ X @ A3 )
% 0.27/0.47 => ( member_a @ X @ B4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % in_mono
% 0.27/0.47 thf(fact_210_ord_OLeast_Ocong,axiom,
% 0.27/0.47 least_a = least_a ).
% 0.27/0.47
% 0.27/0.47 % ord.Least.cong
% 0.27/0.47 thf(fact_211_order_OGreatest_Ocong,axiom,
% 0.27/0.47 greatest_a = greatest_a ).
% 0.27/0.47
% 0.27/0.47 % order.Greatest.cong
% 0.27/0.47 thf(fact_212_ord_Omin_Ocong,axiom,
% 0.27/0.47 min_a = min_a ).
% 0.27/0.47
% 0.27/0.47 % ord.min.cong
% 0.27/0.47 thf(fact_213_ord_Omax_Ocong,axiom,
% 0.27/0.47 max_a = max_a ).
% 0.27/0.47
% 0.27/0.47 % ord.max.cong
% 0.27/0.47 thf(fact_214_ord_Omin__def,axiom,
% 0.27/0.47 ( min_a
% 0.27/0.47 = ( ^ [Less_eq: a > a > $o,A2: a,B2: a] : ( if_a @ ( Less_eq @ A2 @ B2 ) @ A2 @ B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord.min_def
% 0.27/0.47 thf(fact_215_ord_Omax__def,axiom,
% 0.27/0.47 ( max_a
% 0.27/0.47 = ( ^ [Less_eq: a > a > $o,A2: a,B2: a] : ( if_a @ ( Less_eq @ A2 @ B2 ) @ B2 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord.max_def
% 0.27/0.47 thf(fact_216_local_Omono__inf,axiom,
% 0.27/0.47 ! [F: a > set_a,A3: a,B4: a] :
% 0.27/0.47 ( ( mono_a_set_a @ less_eq @ F )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ ( inf @ A3 @ B4 ) ) @ ( inf_inf_set_a @ ( F @ A3 ) @ ( F @ B4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.mono_inf
% 0.27/0.47 thf(fact_217_local_Omono__sup,axiom,
% 0.27/0.47 ! [F: a > set_a,A3: a,B4: a] :
% 0.27/0.47 ( ( mono_a_set_a @ less_eq @ F )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( sup_sup_set_a @ ( F @ A3 ) @ ( F @ B4 ) ) @ ( F @ ( sup @ A3 @ B4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.mono_sup
% 0.27/0.47 thf(fact_218_local_Obdd__above__finite,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ( finite_finite_a @ A3 )
% 0.27/0.47 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_above_finite
% 0.27/0.47 thf(fact_219_local_Ofinite__has__minimal2,axiom,
% 0.27/0.47 ! [A3: set_a,A: a] :
% 0.27/0.47 ( ( finite_finite_a @ A3 )
% 0.27/0.47 => ( ( member_a @ A @ A3 )
% 0.27/0.47 => ? [X3: a] :
% 0.27/0.47 ( ( member_a @ X3 @ A3 )
% 0.27/0.47 & ( less_eq @ X3 @ A )
% 0.27/0.47 & ! [Xa: a] :
% 0.27/0.47 ( ( member_a @ Xa @ A3 )
% 0.27/0.47 => ( ( less_eq @ Xa @ X3 )
% 0.27/0.47 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.finite_has_minimal2
% 0.27/0.47 thf(fact_220_local_Ofinite__has__maximal2,axiom,
% 0.27/0.47 ! [A3: set_a,A: a] :
% 0.27/0.47 ( ( finite_finite_a @ A3 )
% 0.27/0.47 => ( ( member_a @ A @ A3 )
% 0.27/0.47 => ? [X3: a] :
% 0.27/0.47 ( ( member_a @ X3 @ A3 )
% 0.27/0.47 & ( less_eq @ A @ X3 )
% 0.27/0.47 & ! [Xa: a] :
% 0.27/0.47 ( ( member_a @ Xa @ A3 )
% 0.27/0.47 => ( ( less_eq @ X3 @ Xa )
% 0.27/0.47 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.finite_has_maximal2
% 0.27/0.47 thf(fact_221_local_Obdd__below__Int2,axiom,
% 0.27/0.47 ! [B4: set_a,A3: set_a] :
% 0.27/0.47 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 0.27/0.47 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_below_Int2
% 0.27/0.47 thf(fact_222_local_Obdd__below__Int1,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a] :
% 0.27/0.47 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 0.27/0.47 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_below_Int1
% 0.27/0.47 thf(fact_223_local_Obdd__above__Int2,axiom,
% 0.27/0.47 ! [B4: set_a,A3: set_a] :
% 0.27/0.47 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 0.27/0.47 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_above_Int2
% 0.27/0.47 thf(fact_224_local_Obdd__above__Int1,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a] :
% 0.27/0.47 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 0.27/0.47 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_above_Int1
% 0.27/0.47 thf(fact_225_local_Obdd__below__finite,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ( finite_finite_a @ A3 )
% 0.27/0.47 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % local.bdd_below_finite
% 0.27/0.47 thf(fact_226_Un__subset__iff,axiom,
% 0.27/0.47 ! [A3: set_a,B4: set_a,C4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A3 @ B4 ) @ C4 )
% 0.27/0.47 = ( ( ord_less_eq_set_a @ A3 @ C4 )
% 0.27/0.47 & ( ord_less_eq_set_a @ B4 @ C4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_subset_iff
% 0.27/0.47 thf(fact_227_Int__subset__iff,axiom,
% 0.27/0.47 ! [C4: set_a,A3: set_a,B4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ C4 @ ( inf_inf_set_a @ A3 @ B4 ) )
% 0.27/0.47 = ( ( ord_less_eq_set_a @ C4 @ A3 )
% 0.27/0.47 & ( ord_less_eq_set_a @ C4 @ B4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Int_subset_iff
% 0.27/0.47 thf(fact_228_semilattice__inf__class_Oinf__right__idem,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Y )
% 0.27/0.47 = ( inf_inf_set_a @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_inf_class.inf_right_idem
% 0.27/0.47 thf(fact_229_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a] :
% 0.27/0.47 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
% 0.27/0.47 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_inf_class.inf.right_idem
% 0.27/0.47 thf(fact_230_semilattice__inf__class_Oinf__left__idem,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 0.27/0.47 = ( inf_inf_set_a @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_inf_class.inf_left_idem
% 0.27/0.47 thf(fact_231_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a] :
% 0.27/0.47 ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
% 0.27/0.47 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_inf_class.inf.left_idem
% 0.27/0.47 thf(fact_232_semilattice__inf__class_Oinf__idem,axiom,
% 0.27/0.47 ! [X: set_a] :
% 0.27/0.47 ( ( inf_inf_set_a @ X @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_inf_class.inf_idem
% 0.27/0.47 thf(fact_233_semilattice__inf__class_Oinf_Oidem,axiom,
% 0.27/0.47 ! [A: set_a] :
% 0.27/0.47 ( ( inf_inf_set_a @ A @ A )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_inf_class.inf.idem
% 0.27/0.47 thf(fact_234_semilattice__sup__class_Osup_Oright__idem,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a] :
% 0.27/0.47 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
% 0.27/0.47 = ( sup_sup_set_a @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_sup_class.sup.right_idem
% 0.27/0.47 thf(fact_235_semilattice__sup__class_Osup__left__idem,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( sup_sup_set_a @ X @ ( sup_sup_set_a @ X @ Y ) )
% 0.27/0.47 = ( sup_sup_set_a @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_sup_class.sup_left_idem
% 0.27/0.47 thf(fact_236_semilattice__sup__class_Osup_Oleft__idem,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a] :
% 0.27/0.47 ( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
% 0.27/0.47 = ( sup_sup_set_a @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_sup_class.sup.left_idem
% 0.27/0.47 thf(fact_237_semilattice__sup__class_Osup__idem,axiom,
% 0.27/0.47 ! [X: set_a] :
% 0.27/0.47 ( ( sup_sup_set_a @ X @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_sup_class.sup_idem
% 0.27/0.47 thf(fact_238_semilattice__sup__class_Osup_Oidem,axiom,
% 0.27/0.47 ! [A: set_a] :
% 0.27/0.47 ( ( sup_sup_set_a @ A @ A )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_sup_class.sup.idem
% 0.27/0.47 thf(fact_239_semilattice__inf__class_Ole__inf__iff,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X @ ( inf_inf_set_a @ Y @ Z2 ) )
% 0.27/0.47 = ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.47 & ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_inf_class.le_inf_iff
% 0.27/0.47 thf(fact_240_semilattice__inf__class_Oinf_Obounded__iff,axiom,
% 0.27/0.47 ! [A: set_a,B: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 0.27/0.47 = ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.47 & ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_inf_class.inf.bounded_iff
% 0.27/0.47 thf(fact_241_semilattice__sup__class_Ole__sup__iff,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ X @ Y ) @ Z2 )
% 0.27/0.47 = ( ( ord_less_eq_set_a @ X @ Z2 )
% 0.27/0.47 & ( ord_less_eq_set_a @ Y @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_sup_class.le_sup_iff
% 0.27/0.47 thf(fact_242_semilattice__sup__class_Osup_Obounded__iff,axiom,
% 0.27/0.47 ! [B: set_a,C: set_a,A: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ B @ C ) @ A )
% 0.27/0.47 = ( ( ord_less_eq_set_a @ B @ A )
% 0.27/0.47 & ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % semilattice_sup_class.sup.bounded_iff
% 0.27/0.47 thf(fact_243_lattice__class_Osup__inf__absorb,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( sup_sup_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % lattice_class.sup_inf_absorb
% 0.27/0.47 thf(fact_244_lattice__class_Oinf__sup__absorb,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( inf_inf_set_a @ X @ ( sup_sup_set_a @ X @ Y ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % lattice_class.inf_sup_absorb
% 0.27/0.47
% 0.27/0.47 % Helper facts (3)
% 0.27/0.47 thf(help_If_3_1_If_001tf__a_T,axiom,
% 0.27/0.47 ! [P: $o] :
% 0.27/0.47 ( ( P = $true )
% 0.27/0.47 | ( P = $false ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_2_1_If_001tf__a_T,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( if_a @ $false @ X @ Y )
% 0.27/0.47 = Y ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_1_1_If_001tf__a_T,axiom,
% 0.27/0.47 ! [X: a,Y: a] :
% 0.27/0.47 ( ( if_a @ $true @ X @ Y )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % Conjectures (2)
% 0.27/0.47 thf(conj_0,hypothesis,
% 0.27/0.47 less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ).
% 0.27/0.47
% 0.27/0.47 thf(conj_1,conjecture,
% 0.27/0.47 ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) )
% 0.27/0.47 = ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 2.51/1.43 ---- Embedded in THF ---
% 2.51/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.51/1.43 %%% Generated on Tue Feb 24 08:26:55 EST 2026
% 2.51/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.51/1.43 %%% Logic specification used:
% 2.51/1.43 %%% thf(spec, logic, $$dhol).
% 2.51/1.43
% 2.51/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2DTF3946.p
% See solution above
% 2.51/1.44 ------------------------
% 2.51/1.46 ---- Cleaned THF ---
% 2.51/1.46 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.51/1.46 set_a: $tType ).
% 2.51/1.46
% 2.51/1.46 thf(ty_n_tf__a,type,
% 2.51/1.46 a: $tType ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a,type,
% 2.51/1.46 condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a,type,
% 2.51/1.46 condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 2.51/1.46 finite40241356em_a_a: ( a > a > a ) > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
% 2.51/1.46 finite_finite_a: set_a > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 2.51/1.46 abel_semigroup_a: ( a > a > a ) > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 2.51/1.46 semigroup_a: ( a > a > a ) > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_If_001tf__a,type,
% 2.51/1.46 if_a: $o > a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
% 2.51/1.46 inf_inf_set_a: set_a > set_a > set_a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 2.51/1.46 semilattice_a: ( a > a > a ) > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
% 2.51/1.46 sup_sup_set_a: set_a > set_a > set_a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 2.51/1.46 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 2.51/1.46 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 2.51/1.46 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 2.51/1.46 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 2.51/1.46 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 2.51/1.46 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oincomp_001tf__a,type,
% 2.51/1.46 modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Orderings_Oord_OLeast_001tf__a,type,
% 2.51/1.46 least_a: ( a > a > $o ) > ( a > $o ) > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Orderings_Oord_Omax_001tf__a,type,
% 2.51/1.46 max_a: ( a > a > $o ) > a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Orderings_Oord_Omin_001tf__a,type,
% 2.51/1.46 min_a: ( a > a > $o ) > a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 2.51/1.46 ord_less_eq_set_a: set_a > set_a > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Orderings_Oorder_OGreatest_001tf__a,type,
% 2.51/1.46 greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Orderings_Oorder_Oantimono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 2.51/1.46 antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Orderings_Oorder_Omono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 2.51/1.46 mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.51/1.46 collect_a: ( a > $o ) > set_a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_c_member_001tf__a,type,
% 2.51/1.46 member_a: a > set_a > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_v_a,type,
% 2.51/1.46 a2: a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_v_b,type,
% 2.51/1.46 b: a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_v_c,type,
% 2.51/1.46 c: a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_v_inf,type,
% 2.51/1.46 inf: a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(sy_v_less__eq,type,
% 2.51/1.46 less_eq: a > a > $o ).
% 2.51/1.46
% 2.51/1.46 thf(sy_v_sup,type,
% 2.51/1.46 sup: a > a > a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_0_local_Oantisym,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ( less_eq @ Y @ X )
% 2.51/1.46 => ( X = Y ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_1_local_Oantisym__conv,axiom,
% 2.51/1.46 ! [Y: a,X: a] :
% 2.51/1.46 ( ( less_eq @ Y @ X )
% 2.51/1.46 => ( ( less_eq @ X @ Y )
% 2.51/1.46 = ( X = Y ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_2_local_Odual__order_Oantisym,axiom,
% 2.51/1.46 ! [B: a,A: a] :
% 2.51/1.46 ( ( less_eq @ B @ A )
% 2.51/1.46 => ( ( less_eq @ A @ B )
% 2.51/1.46 => ( A = B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_3_local_Odual__order_Oeq__iff,axiom,
% 2.51/1.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.51/1.46 = ( ^ [A2: a,B2: a] :
% 2.51/1.46 ( ( less_eq @ B2 @ A2 )
% 2.51/1.46 & ( less_eq @ A2 @ B2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_4_local_Odual__order_Otrans,axiom,
% 2.51/1.46 ! [B: a,A: a,C: a] :
% 2.51/1.46 ( ( less_eq @ B @ A )
% 2.51/1.46 => ( ( less_eq @ C @ B )
% 2.51/1.46 => ( less_eq @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_5_local_Oeq__iff,axiom,
% 2.51/1.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.51/1.46 = ( ^ [X2: a,Y3: a] :
% 2.51/1.46 ( ( less_eq @ X2 @ Y3 )
% 2.51/1.46 & ( less_eq @ Y3 @ X2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_6_local_Oeq__refl,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( X = Y )
% 2.51/1.46 => ( less_eq @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_7_local_Oord__eq__le__trans,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( A = B )
% 2.51/1.46 => ( ( less_eq @ B @ C )
% 2.51/1.46 => ( less_eq @ A @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_8_local_Oord__le__eq__trans,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 => ( ( B = C )
% 2.51/1.46 => ( less_eq @ A @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_9_local_Oorder_Oantisym,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 => ( ( less_eq @ B @ A )
% 2.51/1.46 => ( A = B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_10_local_Oorder_Oeq__iff,axiom,
% 2.51/1.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.51/1.46 = ( ^ [A2: a,B2: a] :
% 2.51/1.46 ( ( less_eq @ A2 @ B2 )
% 2.51/1.46 & ( less_eq @ B2 @ A2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_11_local_Oorder_Otrans,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 => ( ( less_eq @ B @ C )
% 2.51/1.46 => ( less_eq @ A @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_12_local_Oorder__trans,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ( less_eq @ Y @ Z2 )
% 2.51/1.46 => ( less_eq @ X @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_13_local_Oinf_Oassoc,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( inf @ ( inf @ A @ B ) @ C )
% 2.51/1.46 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_14_local_Oinf_Ocommute,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( inf @ A @ B )
% 2.51/1.46 = ( inf @ B @ A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_15_local_Oinf_Oleft__commute,axiom,
% 2.51/1.46 ! [B: a,A: a,C: a] :
% 2.51/1.46 ( ( inf @ B @ ( inf @ A @ C ) )
% 2.51/1.46 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_16_local_Oinf__assoc,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ( inf @ ( inf @ X @ Y ) @ Z2 )
% 2.51/1.46 = ( inf @ X @ ( inf @ Y @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_17_local_Oinf__commute,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( inf @ X @ Y )
% 2.51/1.46 = ( inf @ Y @ X ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_18_local_Oinf__left__commute,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ( inf @ X @ ( inf @ Y @ Z2 ) )
% 2.51/1.46 = ( inf @ Y @ ( inf @ X @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_19_local_Osup_Oassoc,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( sup @ ( sup @ A @ B ) @ C )
% 2.51/1.46 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_20_local_Osup_Ocommute,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( sup @ A @ B )
% 2.51/1.46 = ( sup @ B @ A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_21_local_Osup_Oleft__commute,axiom,
% 2.51/1.46 ! [B: a,A: a,C: a] :
% 2.51/1.46 ( ( sup @ B @ ( sup @ A @ C ) )
% 2.51/1.46 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_22_local_Osup__assoc,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ( sup @ ( sup @ X @ Y ) @ Z2 )
% 2.51/1.46 = ( sup @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_23_local_Osup__commute,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( sup @ X @ Y )
% 2.51/1.46 = ( sup @ Y @ X ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_24_local_Osup__left__commute,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ( sup @ X @ ( sup @ Y @ Z2 ) )
% 2.51/1.46 = ( sup @ Y @ ( sup @ X @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_25_local_Oinf_Oabsorb1,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 => ( ( inf @ A @ B )
% 2.51/1.46 = A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_26_local_Oinf_Oabsorb2,axiom,
% 2.51/1.46 ! [B: a,A: a] :
% 2.51/1.46 ( ( less_eq @ B @ A )
% 2.51/1.46 => ( ( inf @ A @ B )
% 2.51/1.46 = B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_27_local_Oinf_Oabsorb__iff1,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 = ( ( inf @ A @ B )
% 2.51/1.46 = A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_28_local_Oinf_Oabsorb__iff2,axiom,
% 2.51/1.46 ! [B: a,A: a] :
% 2.51/1.46 ( ( less_eq @ B @ A )
% 2.51/1.46 = ( ( inf @ A @ B )
% 2.51/1.46 = B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_29_local_Oinf_OboundedE,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 2.51/1.46 => ~ ( ( less_eq @ A @ B )
% 2.51/1.46 => ~ ( less_eq @ A @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_30_local_Oinf_OboundedI,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 => ( ( less_eq @ A @ C )
% 2.51/1.46 => ( less_eq @ A @ ( inf @ B @ C ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_31_local_Oinf_Ocobounded1,axiom,
% 2.51/1.46 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_32_local_Oinf_Ocobounded2,axiom,
% 2.51/1.46 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_33_local_Oinf_OcoboundedI1,axiom,
% 2.51/1.46 ! [A: a,C: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ C )
% 2.51/1.46 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_34_local_Oinf_OcoboundedI2,axiom,
% 2.51/1.46 ! [B: a,C: a,A: a] :
% 2.51/1.46 ( ( less_eq @ B @ C )
% 2.51/1.46 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_35_local_Oinf_OorderE,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 => ( A
% 2.51/1.46 = ( inf @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_36_local_Oinf_OorderI,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( A
% 2.51/1.46 = ( inf @ A @ B ) )
% 2.51/1.46 => ( less_eq @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_37_local_Oinf_Oorder__iff,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 = ( A
% 2.51/1.46 = ( inf @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_38_local_Oinf__absorb1,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ( inf @ X @ Y )
% 2.51/1.46 = X ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_39_local_Oinf__absorb2,axiom,
% 2.51/1.46 ! [Y: a,X: a] :
% 2.51/1.46 ( ( less_eq @ Y @ X )
% 2.51/1.46 => ( ( inf @ X @ Y )
% 2.51/1.46 = Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_40_local_Oinf__greatest,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ( less_eq @ X @ Z2 )
% 2.51/1.46 => ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_41_local_Oinf__le1,axiom,
% 2.51/1.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_42_local_Oinf__le2,axiom,
% 2.51/1.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_43_local_Oinf__mono,axiom,
% 2.51/1.46 ! [A: a,C: a,B: a,D: a] :
% 2.51/1.46 ( ( less_eq @ A @ C )
% 2.51/1.46 => ( ( less_eq @ B @ D )
% 2.51/1.46 => ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_44_local_Oinf__unique,axiom,
% 2.51/1.46 ! [F: a > a > a,X: a,Y: a] :
% 2.51/1.46 ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
% 2.51/1.46 => ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
% 2.51/1.46 => ( ! [X3: a,Y4: a,Z3: a] :
% 2.51/1.46 ( ( less_eq @ X3 @ Y4 )
% 2.51/1.46 => ( ( less_eq @ X3 @ Z3 )
% 2.51/1.46 => ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 2.51/1.46 => ( ( inf @ X @ Y )
% 2.51/1.46 = ( F @ X @ Y ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_45_mem__Collect__eq,axiom,
% 2.51/1.46 ! [A: a,P: a > $o] :
% 2.51/1.46 ( ( member_a @ A @ ( collect_a @ P ) )
% 2.51/1.46 = ( P @ A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_46_Collect__mem__eq,axiom,
% 2.51/1.46 ! [A3: set_a] :
% 2.51/1.46 ( ( collect_a
% 2.51/1.46 @ ^ [X2: a] : ( member_a @ X2 @ A3 ) )
% 2.51/1.46 = A3 ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_47_Collect__cong,axiom,
% 2.51/1.46 ! [P: a > $o,Q: a > $o] :
% 2.51/1.46 ( ! [X3: a] :
% 2.51/1.46 ( ( P @ X3 )
% 2.51/1.46 = ( Q @ X3 ) )
% 2.51/1.46 => ( ( collect_a @ P )
% 2.51/1.46 = ( collect_a @ Q ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_48_local_Ole__iff__inf,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( less_eq @ X @ Y )
% 2.51/1.46 = ( ( inf @ X @ Y )
% 2.51/1.46 = X ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_49_local_Ole__infE,axiom,
% 2.51/1.46 ! [X: a,A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ X @ ( inf @ A @ B ) )
% 2.51/1.46 => ~ ( ( less_eq @ X @ A )
% 2.51/1.46 => ~ ( less_eq @ X @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_50_local_Ole__infI,axiom,
% 2.51/1.46 ! [X: a,A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ X @ A )
% 2.51/1.46 => ( ( less_eq @ X @ B )
% 2.51/1.46 => ( less_eq @ X @ ( inf @ A @ B ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_51_local_Ole__infI1,axiom,
% 2.51/1.46 ! [A: a,X: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ X )
% 2.51/1.46 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_52_local_Ole__infI2,axiom,
% 2.51/1.46 ! [B: a,X: a,A: a] :
% 2.51/1.46 ( ( less_eq @ B @ X )
% 2.51/1.46 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_53_local_Ole__iff__sup,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( less_eq @ X @ Y )
% 2.51/1.46 = ( ( sup @ X @ Y )
% 2.51/1.46 = Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_54_local_Ole__supE,axiom,
% 2.51/1.46 ! [A: a,B: a,X: a] :
% 2.51/1.46 ( ( less_eq @ ( sup @ A @ B ) @ X )
% 2.51/1.46 => ~ ( ( less_eq @ A @ X )
% 2.51/1.46 => ~ ( less_eq @ B @ X ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_55_local_Ole__supI,axiom,
% 2.51/1.46 ! [A: a,X: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ X )
% 2.51/1.46 => ( ( less_eq @ B @ X )
% 2.51/1.46 => ( less_eq @ ( sup @ A @ B ) @ X ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_56_local_Ole__supI1,axiom,
% 2.51/1.46 ! [X: a,A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ X @ A )
% 2.51/1.46 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_57_local_Ole__supI2,axiom,
% 2.51/1.46 ! [X: a,B: a,A: a] :
% 2.51/1.46 ( ( less_eq @ X @ B )
% 2.51/1.46 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_58_local_Osup_Oabsorb1,axiom,
% 2.51/1.46 ! [B: a,A: a] :
% 2.51/1.46 ( ( less_eq @ B @ A )
% 2.51/1.46 => ( ( sup @ A @ B )
% 2.51/1.46 = A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_59_local_Osup_Oabsorb2,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 => ( ( sup @ A @ B )
% 2.51/1.46 = B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_60_local_Osup_Oabsorb__iff1,axiom,
% 2.51/1.46 ! [B: a,A: a] :
% 2.51/1.46 ( ( less_eq @ B @ A )
% 2.51/1.46 = ( ( sup @ A @ B )
% 2.51/1.46 = A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_61_local_Osup_Oabsorb__iff2,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ A @ B )
% 2.51/1.46 = ( ( sup @ A @ B )
% 2.51/1.46 = B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_62_local_Osup_OboundedE,axiom,
% 2.51/1.46 ! [B: a,C: a,A: a] :
% 2.51/1.46 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 2.51/1.46 => ~ ( ( less_eq @ B @ A )
% 2.51/1.46 => ~ ( less_eq @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_63_local_Osup_OboundedI,axiom,
% 2.51/1.46 ! [B: a,A: a,C: a] :
% 2.51/1.46 ( ( less_eq @ B @ A )
% 2.51/1.46 => ( ( less_eq @ C @ A )
% 2.51/1.46 => ( less_eq @ ( sup @ B @ C ) @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_64_local_Osup_Ocobounded1,axiom,
% 2.51/1.46 ! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_65_local_Osup_Ocobounded2,axiom,
% 2.51/1.46 ! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_66_local_Osup_OcoboundedI1,axiom,
% 2.51/1.46 ! [C: a,A: a,B: a] :
% 2.51/1.46 ( ( less_eq @ C @ A )
% 2.51/1.46 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_67_local_Osup_OcoboundedI2,axiom,
% 2.51/1.46 ! [C: a,B: a,A: a] :
% 2.51/1.46 ( ( less_eq @ C @ B )
% 2.51/1.46 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_68_local_Osup_Omono,axiom,
% 2.51/1.46 ! [C: a,A: a,D: a,B: a] :
% 2.51/1.46 ( ( less_eq @ C @ A )
% 2.51/1.46 => ( ( less_eq @ D @ B )
% 2.51/1.46 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_69_local_Osup_OorderE,axiom,
% 2.51/1.46 ! [B: a,A: a] :
% 2.51/1.46 ( ( less_eq @ B @ A )
% 2.51/1.46 => ( A
% 2.51/1.46 = ( sup @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_70_local_Osup_OorderI,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( A
% 2.51/1.46 = ( sup @ A @ B ) )
% 2.51/1.46 => ( less_eq @ B @ A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_71_local_Osup_Oorder__iff,axiom,
% 2.51/1.46 ! [B: a,A: a] :
% 2.51/1.46 ( ( less_eq @ B @ A )
% 2.51/1.46 = ( A
% 2.51/1.46 = ( sup @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_72_local_Osup__absorb1,axiom,
% 2.51/1.46 ! [Y: a,X: a] :
% 2.51/1.46 ( ( less_eq @ Y @ X )
% 2.51/1.46 => ( ( sup @ X @ Y )
% 2.51/1.46 = X ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_73_local_Osup__absorb2,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ( sup @ X @ Y )
% 2.51/1.46 = Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_74_local_Osup__ge1,axiom,
% 2.51/1.46 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_75_local_Osup__ge2,axiom,
% 2.51/1.46 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_76_local_Osup__least,axiom,
% 2.51/1.46 ! [Y: a,X: a,Z2: a] :
% 2.51/1.46 ( ( less_eq @ Y @ X )
% 2.51/1.46 => ( ( less_eq @ Z2 @ X )
% 2.51/1.46 => ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_77_local_Osup__mono,axiom,
% 2.51/1.46 ! [A: a,C: a,B: a,D: a] :
% 2.51/1.46 ( ( less_eq @ A @ C )
% 2.51/1.46 => ( ( less_eq @ B @ D )
% 2.51/1.46 => ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_78_local_Osup__unique,axiom,
% 2.51/1.46 ! [F: a > a > a,X: a,Y: a] :
% 2.51/1.46 ( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
% 2.51/1.46 => ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
% 2.51/1.46 => ( ! [X3: a,Y4: a,Z3: a] :
% 2.51/1.46 ( ( less_eq @ Y4 @ X3 )
% 2.51/1.46 => ( ( less_eq @ Z3 @ X3 )
% 2.51/1.46 => ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
% 2.51/1.46 => ( ( sup @ X @ Y )
% 2.51/1.46 = ( F @ X @ Y ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_79_local_Odistrib__imp1,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ! [X3: a,Y4: a,Z3: a] :
% 2.51/1.46 ( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
% 2.51/1.46 = ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
% 2.51/1.46 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 2.51/1.46 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_80_local_Odistrib__imp2,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ! [X3: a,Y4: a,Z3: a] :
% 2.51/1.46 ( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
% 2.51/1.46 = ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
% 2.51/1.46 => ( ( inf @ X @ ( sup @ Y @ Z2 ) )
% 2.51/1.46 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_81_local_Oa__join__d,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_82_a__meet__d,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 = ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_83_local_Ob__join__d,axiom,
% 2.51/1.46 ! [B: a,A: a,C: a] :
% 2.51/1.46 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_84_b__meet__d,axiom,
% 2.51/1.46 ! [B: a,A: a,C: a] :
% 2.51/1.46 ( ( inf @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 = ( sup @ ( inf @ B @ C ) @ ( inf @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_85_c__meet__d,axiom,
% 2.51/1.46 ! [C: a,A: a,B: a] :
% 2.51/1.46 ( ( inf @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 = ( sup @ ( inf @ C @ A ) @ ( inf @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_86_local_Od__aux__def,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 2.51/1.46 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_87_local_Od__b__c__a,axiom,
% 2.51/1.46 ! [B: a,C: a,A: a] :
% 2.51/1.46 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 2.51/1.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_88_local_Od__c__a__b,axiom,
% 2.51/1.46 ! [C: a,A: a,B: a] :
% 2.51/1.46 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 2.51/1.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_89_local_Oa__meet__e,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_90_local_Ob__meet__e,axiom,
% 2.51/1.46 ! [B: a,A: a,C: a] :
% 2.51/1.46 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_91_local_Oc__meet__e,axiom,
% 2.51/1.46 ! [C: a,A: a,B: a] :
% 2.51/1.46 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_92_local_Oe__aux__def,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 2.51/1.46 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_93_local_Oe__b__c__a,axiom,
% 2.51/1.46 ! [B: a,C: a,A: a] :
% 2.51/1.46 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 2.51/1.46 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_94_local_Oe__c__a__b,axiom,
% 2.51/1.46 ! [C: a,A: a,B: a] :
% 2.51/1.46 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 2.51/1.46 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_95_local_Odistrib__inf__le,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_96_local_Odistrib__sup__le,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_97_local_Omodular,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 2.51/1.46 = ( inf @ Y @ ( sup @ X @ Z2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_98_local_Oincomp__def,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( modula1727524044comp_a @ less_eq @ X @ Y )
% 2.51/1.46 = ( ~ ( less_eq @ X @ Y )
% 2.51/1.46 & ~ ( less_eq @ Y @ X ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_99_local_Oorder_Orefl,axiom,
% 2.51/1.46 ! [A: a] : ( less_eq @ A @ A ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_100_local_Oorder__refl,axiom,
% 2.51/1.46 ! [X: a] : ( less_eq @ X @ X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_101_local_Oinf_Oidem,axiom,
% 2.51/1.46 ! [A: a] :
% 2.51/1.46 ( ( inf @ A @ A )
% 2.51/1.46 = A ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_102_local_Oinf_Oleft__idem,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( inf @ A @ ( inf @ A @ B ) )
% 2.51/1.46 = ( inf @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_103_local_Oinf_Oright__idem,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( inf @ ( inf @ A @ B ) @ B )
% 2.51/1.46 = ( inf @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_104_local_Oinf__idem,axiom,
% 2.51/1.46 ! [X: a] :
% 2.51/1.46 ( ( inf @ X @ X )
% 2.51/1.46 = X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_105_local_Oinf__left__idem,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( inf @ X @ ( inf @ X @ Y ) )
% 2.51/1.46 = ( inf @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_106_local_Oinf__right__idem,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 2.51/1.46 = ( inf @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_107_local_Osup_Oidem,axiom,
% 2.51/1.46 ! [A: a] :
% 2.51/1.46 ( ( sup @ A @ A )
% 2.51/1.46 = A ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_108_local_Osup_Oleft__idem,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( sup @ A @ ( sup @ A @ B ) )
% 2.51/1.46 = ( sup @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_109_local_Osup_Oright__idem,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( sup @ ( sup @ A @ B ) @ B )
% 2.51/1.46 = ( sup @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_110_local_Osup__idem,axiom,
% 2.51/1.46 ! [X: a] :
% 2.51/1.46 ( ( sup @ X @ X )
% 2.51/1.46 = X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_111_local_Osup__left__idem,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( sup @ X @ ( sup @ X @ Y ) )
% 2.51/1.46 = ( sup @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_112_local_Oc__a,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 2.51/1.46 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_113_local_OGreatestI2__order,axiom,
% 2.51/1.46 ! [P: a > $o,X: a,Q: a > $o] :
% 2.51/1.46 ( ( P @ X )
% 2.51/1.46 => ( ! [Y4: a] :
% 2.51/1.46 ( ( P @ Y4 )
% 2.51/1.46 => ( less_eq @ Y4 @ X ) )
% 2.51/1.46 => ( ! [X3: a] :
% 2.51/1.46 ( ( P @ X3 )
% 2.51/1.46 => ( ! [Y5: a] :
% 2.51/1.46 ( ( P @ Y5 )
% 2.51/1.46 => ( less_eq @ Y5 @ X3 ) )
% 2.51/1.46 => ( Q @ X3 ) ) )
% 2.51/1.46 => ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_114_local_OGreatest__equality,axiom,
% 2.51/1.46 ! [P: a > $o,X: a] :
% 2.51/1.46 ( ( P @ X )
% 2.51/1.46 => ( ! [Y4: a] :
% 2.51/1.46 ( ( P @ Y4 )
% 2.51/1.46 => ( less_eq @ Y4 @ X ) )
% 2.51/1.46 => ( ( greatest_a @ less_eq @ P )
% 2.51/1.46 = X ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_115_local_Omax__def,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( ( less_eq @ A @ B )
% 2.51/1.46 => ( ( max_a @ less_eq @ A @ B )
% 2.51/1.46 = B ) )
% 2.51/1.46 & ( ~ ( less_eq @ A @ B )
% 2.51/1.46 => ( ( max_a @ less_eq @ A @ B )
% 2.51/1.46 = A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_116_local_Omin__def,axiom,
% 2.51/1.46 ! [A: a,B: a] :
% 2.51/1.46 ( ( ( less_eq @ A @ B )
% 2.51/1.46 => ( ( min_a @ less_eq @ A @ B )
% 2.51/1.46 = A ) )
% 2.51/1.46 & ( ~ ( less_eq @ A @ B )
% 2.51/1.46 => ( ( min_a @ less_eq @ A @ B )
% 2.51/1.46 = B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_117_local_Oa__aux__def,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 2.51/1.46 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_118_local_Oc__aux__def,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 2.51/1.46 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_119_local_Oinf_Obounded__iff,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 2.51/1.46 = ( ( less_eq @ A @ B )
% 2.51/1.46 & ( less_eq @ A @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_120_local_Ole__inf__iff,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
% 2.51/1.46 = ( ( less_eq @ X @ Y )
% 2.51/1.46 & ( less_eq @ X @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_121_local_Ole__sup__iff,axiom,
% 2.51/1.46 ! [X: a,Y: a,Z2: a] :
% 2.51/1.46 ( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
% 2.51/1.46 = ( ( less_eq @ X @ Z2 )
% 2.51/1.46 & ( less_eq @ Y @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_122_local_Osup_Obounded__iff,axiom,
% 2.51/1.46 ! [B: a,C: a,A: a] :
% 2.51/1.46 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 2.51/1.46 = ( ( less_eq @ B @ A )
% 2.51/1.46 & ( less_eq @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_123_local_Oinf__sup__absorb,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( inf @ X @ ( sup @ X @ Y ) )
% 2.51/1.46 = X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_124_local_Osup__inf__absorb,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( sup @ X @ ( inf @ X @ Y ) )
% 2.51/1.46 = X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_125_local_Ob__a,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 2.51/1.46 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_126_local_OLeast1I,axiom,
% 2.51/1.46 ! [P: a > $o] :
% 2.51/1.46 ( ? [X4: a] :
% 2.51/1.46 ( ( P @ X4 )
% 2.51/1.46 & ! [Y4: a] :
% 2.51/1.46 ( ( P @ Y4 )
% 2.51/1.46 => ( less_eq @ X4 @ Y4 ) )
% 2.51/1.46 & ! [Y4: a] :
% 2.51/1.46 ( ( ( P @ Y4 )
% 2.51/1.46 & ! [Ya: a] :
% 2.51/1.46 ( ( P @ Ya )
% 2.51/1.46 => ( less_eq @ Y4 @ Ya ) ) )
% 2.51/1.46 => ( Y4 = X4 ) ) )
% 2.51/1.46 => ( P @ ( least_a @ less_eq @ P ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_127_local_OLeast1__le,axiom,
% 2.51/1.46 ! [P: a > $o,Z2: a] :
% 2.51/1.46 ( ? [X4: a] :
% 2.51/1.46 ( ( P @ X4 )
% 2.51/1.46 & ! [Y4: a] :
% 2.51/1.46 ( ( P @ Y4 )
% 2.51/1.46 => ( less_eq @ X4 @ Y4 ) )
% 2.51/1.46 & ! [Y4: a] :
% 2.51/1.46 ( ( ( P @ Y4 )
% 2.51/1.46 & ! [Ya: a] :
% 2.51/1.46 ( ( P @ Ya )
% 2.51/1.46 => ( less_eq @ Y4 @ Ya ) ) )
% 2.51/1.46 => ( Y4 = X4 ) ) )
% 2.51/1.46 => ( ( P @ Z2 )
% 2.51/1.46 => ( less_eq @ ( least_a @ less_eq @ P ) @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_128_local_OLeastI2__order,axiom,
% 2.51/1.46 ! [P: a > $o,X: a,Q: a > $o] :
% 2.51/1.46 ( ( P @ X )
% 2.51/1.46 => ( ! [Y4: a] :
% 2.51/1.46 ( ( P @ Y4 )
% 2.51/1.46 => ( less_eq @ X @ Y4 ) )
% 2.51/1.46 => ( ! [X3: a] :
% 2.51/1.46 ( ( P @ X3 )
% 2.51/1.46 => ( ! [Y5: a] :
% 2.51/1.46 ( ( P @ Y5 )
% 2.51/1.46 => ( less_eq @ X3 @ Y5 ) )
% 2.51/1.46 => ( Q @ X3 ) ) )
% 2.51/1.46 => ( Q @ ( least_a @ less_eq @ P ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_129_local_OLeast__equality,axiom,
% 2.51/1.46 ! [P: a > $o,X: a] :
% 2.51/1.46 ( ( P @ X )
% 2.51/1.46 => ( ! [Y4: a] :
% 2.51/1.46 ( ( P @ Y4 )
% 2.51/1.46 => ( less_eq @ X @ Y4 ) )
% 2.51/1.46 => ( ( least_a @ less_eq @ P )
% 2.51/1.46 = X ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_130_local_Ob__aux__def,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 2.51/1.46 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_131_a__meet__b__eq__d,axiom,
% 2.51/1.46 ! [A: a,B: a,C: a] :
% 2.51/1.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 => ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.51/1.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_132_lattice_Oa__aux_Ocong,axiom,
% 2.51/1.46 modula17988509_aux_a = modula17988509_aux_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_133_lattice_Oc__aux_Ocong,axiom,
% 2.51/1.46 modula581031071_aux_a = modula581031071_aux_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_134_lattice_Od__aux_Ocong,axiom,
% 2.51/1.46 modula1936294176_aux_a = modula1936294176_aux_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_135_lattice_Oe__aux_Ocong,axiom,
% 2.51/1.46 modula1144073633_aux_a = modula1144073633_aux_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_136_local_Ocomp__fun__idem__sup,axiom,
% 2.51/1.46 finite40241356em_a_a @ sup ).
% 2.51/1.46
% 2.51/1.46 thf(fact_137_local_Ocomp__fun__idem__inf,axiom,
% 2.51/1.46 finite40241356em_a_a @ inf ).
% 2.51/1.46
% 2.51/1.46 thf(fact_138_local_Osup_Osemigroup__axioms,axiom,
% 2.51/1.46 semigroup_a @ sup ).
% 2.51/1.46
% 2.51/1.46 thf(fact_139_local_Oinf_Osemigroup__axioms,axiom,
% 2.51/1.46 semigroup_a @ inf ).
% 2.51/1.46
% 2.51/1.46 thf(fact_140_local_Osup_Osemilattice__axioms,axiom,
% 2.51/1.46 semilattice_a @ sup ).
% 2.51/1.46
% 2.51/1.46 thf(fact_141_local_Oinf_Osemilattice__axioms,axiom,
% 2.51/1.46 semilattice_a @ inf ).
% 2.51/1.46
% 2.51/1.46 thf(fact_142_local_Osup_Oabel__semigroup__axioms,axiom,
% 2.51/1.46 abel_semigroup_a @ sup ).
% 2.51/1.46
% 2.51/1.46 thf(fact_143_local_Oinf_Oabel__semigroup__axioms,axiom,
% 2.51/1.46 abel_semigroup_a @ inf ).
% 2.51/1.46
% 2.51/1.46 thf(fact_144_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 2.51/1.46 lattic1885654924_set_a @ sup ).
% 2.51/1.46
% 2.51/1.46 thf(fact_145_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 2.51/1.46 lattic1885654924_set_a @ inf ).
% 2.51/1.46
% 2.51/1.46 thf(fact_146_local_Obdd__above__def,axiom,
% 2.51/1.46 ! [A3: set_a] :
% 2.51/1.46 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 2.51/1.46 = ( ? [M: a] :
% 2.51/1.46 ! [X2: a] :
% 2.51/1.46 ( ( member_a @ X2 @ A3 )
% 2.51/1.46 => ( less_eq @ X2 @ M ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_147_local_Obdd__below__def,axiom,
% 2.51/1.46 ! [A3: set_a] :
% 2.51/1.46 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 2.51/1.46 = ( ? [M2: a] :
% 2.51/1.46 ! [X2: a] :
% 2.51/1.46 ( ( member_a @ X2 @ A3 )
% 2.51/1.46 => ( less_eq @ M2 @ X2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_148_local_Obdd__belowI,axiom,
% 2.51/1.46 ! [A3: set_a,M3: a] :
% 2.51/1.46 ( ! [X3: a] :
% 2.51/1.46 ( ( member_a @ X3 @ A3 )
% 2.51/1.46 => ( less_eq @ M3 @ X3 ) )
% 2.51/1.46 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_149_local_Obdd__aboveI,axiom,
% 2.51/1.46 ! [A3: set_a,M4: a] :
% 2.51/1.46 ( ! [X3: a] :
% 2.51/1.46 ( ( member_a @ X3 @ A3 )
% 2.51/1.46 => ( less_eq @ X3 @ M4 ) )
% 2.51/1.46 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_150_lattice_Oincomp_Ocong,axiom,
% 2.51/1.46 modula1727524044comp_a = modula1727524044comp_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_151_lattice_Ob__aux_Ocong,axiom,
% 2.51/1.46 modula1373251614_aux_a = modula1373251614_aux_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_152_abel__semigroup_Oaxioms_I1_J,axiom,
% 2.51/1.46 ! [F: a > a > a] :
% 2.51/1.46 ( ( abel_semigroup_a @ F )
% 2.51/1.46 => ( semigroup_a @ F ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_153_semilattice__set__def,axiom,
% 2.51/1.46 lattic1885654924_set_a = semilattice_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_154_semilattice__set_Ointro,axiom,
% 2.51/1.46 ! [F: a > a > a] :
% 2.51/1.46 ( ( semilattice_a @ F )
% 2.51/1.46 => ( lattic1885654924_set_a @ F ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_155_abel__semigroup_Oleft__commute,axiom,
% 2.51/1.46 ! [F: a > a > a,B: a,A: a,C: a] :
% 2.51/1.46 ( ( abel_semigroup_a @ F )
% 2.51/1.46 => ( ( F @ B @ ( F @ A @ C ) )
% 2.51/1.46 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_156_abel__semigroup_Ocommute,axiom,
% 2.51/1.46 ! [F: a > a > a,A: a,B: a] :
% 2.51/1.46 ( ( abel_semigroup_a @ F )
% 2.51/1.46 => ( ( F @ A @ B )
% 2.51/1.46 = ( F @ B @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_157_semigroup_Ointro,axiom,
% 2.51/1.46 ! [F: a > a > a] :
% 2.51/1.46 ( ! [A4: a,B3: a,C2: a] :
% 2.51/1.46 ( ( F @ ( F @ A4 @ B3 ) @ C2 )
% 2.51/1.46 = ( F @ A4 @ ( F @ B3 @ C2 ) ) )
% 2.51/1.46 => ( semigroup_a @ F ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_158_semigroup_Oassoc,axiom,
% 2.51/1.46 ! [F: a > a > a,A: a,B: a,C: a] :
% 2.51/1.46 ( ( semigroup_a @ F )
% 2.51/1.46 => ( ( F @ ( F @ A @ B ) @ C )
% 2.51/1.46 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_159_semigroup__def,axiom,
% 2.51/1.46 ( semigroup_a
% 2.51/1.46 = ( ^ [F2: a > a > a] :
% 2.51/1.46 ! [A2: a,B2: a,C3: a] :
% 2.51/1.46 ( ( F2 @ ( F2 @ A2 @ B2 ) @ C3 )
% 2.51/1.46 = ( F2 @ A2 @ ( F2 @ B2 @ C3 ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_160_semilattice__set_Oaxioms,axiom,
% 2.51/1.46 ! [F: a > a > a] :
% 2.51/1.46 ( ( lattic1885654924_set_a @ F )
% 2.51/1.46 => ( semilattice_a @ F ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_161_semilattice_Oaxioms_I1_J,axiom,
% 2.51/1.46 ! [F: a > a > a] :
% 2.51/1.46 ( ( semilattice_a @ F )
% 2.51/1.46 => ( abel_semigroup_a @ F ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_162_local_Obdd__above__mono,axiom,
% 2.51/1.46 ! [B4: set_a,A3: set_a] :
% 2.51/1.46 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 2.51/1.46 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_163_local_Obdd__below__mono,axiom,
% 2.51/1.46 ! [B4: set_a,A3: set_a] :
% 2.51/1.46 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ A3 @ B4 )
% 2.51/1.46 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_164_local_Oantimono__def,axiom,
% 2.51/1.46 ! [F: a > set_a] :
% 2.51/1.46 ( ( antimono_a_set_a @ less_eq @ F )
% 2.51/1.46 = ( ! [X2: a,Y3: a] :
% 2.51/1.46 ( ( less_eq @ X2 @ Y3 )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_165_local_OantimonoI,axiom,
% 2.51/1.46 ! [F: a > set_a] :
% 2.51/1.46 ( ! [X3: a,Y4: a] :
% 2.51/1.46 ( ( less_eq @ X3 @ Y4 )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 2.51/1.46 => ( antimono_a_set_a @ less_eq @ F ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_166_local_OantimonoE,axiom,
% 2.51/1.46 ! [F: a > set_a,X: a,Y: a] :
% 2.51/1.46 ( ( antimono_a_set_a @ less_eq @ F )
% 2.51/1.46 => ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_167_local_OantimonoD,axiom,
% 2.51/1.46 ! [F: a > set_a,X: a,Y: a] :
% 2.51/1.46 ( ( antimono_a_set_a @ less_eq @ F )
% 2.51/1.46 => ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_168_local_OmonoD,axiom,
% 2.51/1.46 ! [F: a > set_a,X: a,Y: a] :
% 2.51/1.46 ( ( mono_a_set_a @ less_eq @ F )
% 2.51/1.46 => ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_169_local_OmonoE,axiom,
% 2.51/1.46 ! [F: a > set_a,X: a,Y: a] :
% 2.51/1.46 ( ( mono_a_set_a @ less_eq @ F )
% 2.51/1.46 => ( ( less_eq @ X @ Y )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_170_local_OmonoI,axiom,
% 2.51/1.46 ! [F: a > set_a] :
% 2.51/1.46 ( ! [X3: a,Y4: a] :
% 2.51/1.46 ( ( less_eq @ X3 @ Y4 )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.51/1.46 => ( mono_a_set_a @ less_eq @ F ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_171_local_Omono__def,axiom,
% 2.51/1.46 ! [F: a > set_a] :
% 2.51/1.46 ( ( mono_a_set_a @ less_eq @ F )
% 2.51/1.46 = ( ! [X2: a,Y3: a] :
% 2.51/1.46 ( ( less_eq @ X2 @ Y3 )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_172_semilattice_Oidem,axiom,
% 2.51/1.46 ! [F: a > a > a,A: a] :
% 2.51/1.46 ( ( semilattice_a @ F )
% 2.51/1.46 => ( ( F @ A @ A )
% 2.51/1.46 = A ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_173_semilattice_Oleft__idem,axiom,
% 2.51/1.46 ! [F: a > a > a,A: a,B: a] :
% 2.51/1.46 ( ( semilattice_a @ F )
% 2.51/1.46 => ( ( F @ A @ ( F @ A @ B ) )
% 2.51/1.46 = ( F @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_174_semilattice_Oright__idem,axiom,
% 2.51/1.46 ! [F: a > a > a,A: a,B: a] :
% 2.51/1.46 ( ( semilattice_a @ F )
% 2.51/1.46 => ( ( F @ ( F @ A @ B ) @ B )
% 2.51/1.46 = ( F @ A @ B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_175_subsetI,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a] :
% 2.51/1.46 ( ! [X3: a] :
% 2.51/1.46 ( ( member_a @ X3 @ A3 )
% 2.51/1.46 => ( member_a @ X3 @ B4 ) )
% 2.51/1.46 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_176_subset__antisym,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 2.51/1.46 => ( A3 = B4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_177_preorder__class_Oorder__refl,axiom,
% 2.51/1.46 ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_178_order_Oantimono_Ocong,axiom,
% 2.51/1.46 antimono_a_set_a = antimono_a_set_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_179_order_Omono_Ocong,axiom,
% 2.51/1.46 mono_a_set_a = mono_a_set_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_180_order__class_Odual__order_Oantisym,axiom,
% 2.51/1.46 ! [B: set_a,A: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ B @ A )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ A @ B )
% 2.51/1.46 => ( A = B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_181_order__class_Odual__order_Oeq__iff,axiom,
% 2.51/1.46 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 2.51/1.46 = ( ^ [A2: set_a,B2: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 2.51/1.46 & ( ord_less_eq_set_a @ A2 @ B2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_182_order__class_Odual__order_Otrans,axiom,
% 2.51/1.46 ! [B: set_a,A: set_a,C: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ B @ A )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ C @ B )
% 2.51/1.46 => ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_183_order__class_Odual__order_Orefl,axiom,
% 2.51/1.46 ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_184_preorder__class_Oorder__trans,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a,Z2: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ X @ Y )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ Y @ Z2 )
% 2.51/1.46 => ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_185_order__class_Oorder_Oantisym,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A @ B )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ B @ A )
% 2.51/1.46 => ( A = B ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_186_ord__class_Oord__le__eq__trans,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a,C: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A @ B )
% 2.51/1.46 => ( ( B = C )
% 2.51/1.46 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_187_ord__class_Oord__eq__le__trans,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a,C: set_a] :
% 2.51/1.46 ( ( A = B )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ B @ C )
% 2.51/1.46 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_188_order__class_Oorder_Oeq__iff,axiom,
% 2.51/1.46 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 2.51/1.46 = ( ^ [A2: set_a,B2: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.51/1.46 & ( ord_less_eq_set_a @ B2 @ A2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_189_order__class_Oantisym__conv,axiom,
% 2.51/1.46 ! [Y: set_a,X: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ Y @ X )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ X @ Y )
% 2.51/1.46 = ( X = Y ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_190_order__class_Oorder_Otrans,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a,C: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A @ B )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ B @ C )
% 2.51/1.46 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_191_preorder__class_Oeq__refl,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a] :
% 2.51/1.46 ( ( X = Y )
% 2.51/1.46 => ( ord_less_eq_set_a @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_192_order__class_Oantisym,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ X @ Y )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ Y @ X )
% 2.51/1.46 => ( X = Y ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_193_order__class_Oeq__iff,axiom,
% 2.51/1.46 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 2.51/1.46 = ( ^ [X2: set_a,Y3: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 2.51/1.46 & ( ord_less_eq_set_a @ Y3 @ X2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_194_ord__le__eq__subst,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A @ B )
% 2.51/1.46 => ( ( ( F @ B )
% 2.51/1.46 = C )
% 2.51/1.46 => ( ! [X3: set_a,Y4: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_195_ord__eq__le__subst,axiom,
% 2.51/1.46 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 2.51/1.46 ( ( A
% 2.51/1.46 = ( F @ B ) )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ B @ C )
% 2.51/1.46 => ( ! [X3: set_a,Y4: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.51/1.46 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_196_order__subst2,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A @ B )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 2.51/1.46 => ( ! [X3: set_a,Y4: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_197_order__subst1,axiom,
% 2.51/1.46 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ B @ C )
% 2.51/1.46 => ( ! [X3: set_a,Y4: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.51/1.46 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_198_Collect__mono__iff,axiom,
% 2.51/1.46 ! [P: a > $o,Q: a > $o] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 2.51/1.46 = ( ! [X2: a] :
% 2.51/1.46 ( ( P @ X2 )
% 2.51/1.46 => ( Q @ X2 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_199_set__eq__subset,axiom,
% 2.51/1.46 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 2.51/1.46 = ( ^ [A5: set_a,B5: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 2.51/1.46 & ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_200_subset__trans,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a,C4: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 2.51/1.46 => ( ( ord_less_eq_set_a @ B4 @ C4 )
% 2.51/1.46 => ( ord_less_eq_set_a @ A3 @ C4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_201_Collect__mono,axiom,
% 2.51/1.46 ! [P: a > $o,Q: a > $o] :
% 2.51/1.46 ( ! [X3: a] :
% 2.51/1.46 ( ( P @ X3 )
% 2.51/1.46 => ( Q @ X3 ) )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_202_subset__refl,axiom,
% 2.51/1.46 ! [A3: set_a] : ( ord_less_eq_set_a @ A3 @ A3 ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_203_subset__iff,axiom,
% 2.51/1.46 ( ord_less_eq_set_a
% 2.51/1.46 = ( ^ [A5: set_a,B5: set_a] :
% 2.51/1.46 ! [T: a] :
% 2.51/1.46 ( ( member_a @ T @ A5 )
% 2.51/1.46 => ( member_a @ T @ B5 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_204_equalityD2,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a] :
% 2.51/1.46 ( ( A3 = B4 )
% 2.51/1.46 => ( ord_less_eq_set_a @ B4 @ A3 ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_205_equalityD1,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a] :
% 2.51/1.46 ( ( A3 = B4 )
% 2.51/1.46 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_206_subset__eq,axiom,
% 2.51/1.46 ( ord_less_eq_set_a
% 2.51/1.46 = ( ^ [A5: set_a,B5: set_a] :
% 2.51/1.46 ! [X2: a] :
% 2.51/1.46 ( ( member_a @ X2 @ A5 )
% 2.51/1.46 => ( member_a @ X2 @ B5 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_207_equalityE,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a] :
% 2.51/1.46 ( ( A3 = B4 )
% 2.51/1.46 => ~ ( ( ord_less_eq_set_a @ A3 @ B4 )
% 2.51/1.46 => ~ ( ord_less_eq_set_a @ B4 @ A3 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_208_subsetD,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a,C: a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 2.51/1.46 => ( ( member_a @ C @ A3 )
% 2.51/1.46 => ( member_a @ C @ B4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_209_in__mono,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a,X: a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 2.51/1.46 => ( ( member_a @ X @ A3 )
% 2.51/1.46 => ( member_a @ X @ B4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_210_ord_OLeast_Ocong,axiom,
% 2.51/1.46 least_a = least_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_211_order_OGreatest_Ocong,axiom,
% 2.51/1.46 greatest_a = greatest_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_212_ord_Omin_Ocong,axiom,
% 2.51/1.46 min_a = min_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_213_ord_Omax_Ocong,axiom,
% 2.51/1.46 max_a = max_a ).
% 2.51/1.46
% 2.51/1.46 thf(fact_214_ord_Omin__def,axiom,
% 2.51/1.46 ( min_a
% 2.51/1.46 = ( ^ [Less_eq: a > a > $o,A2: a,B2: a] : ( if_a @ ( Less_eq @ A2 @ B2 ) @ A2 @ B2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_215_ord_Omax__def,axiom,
% 2.51/1.46 ( max_a
% 2.51/1.46 = ( ^ [Less_eq: a > a > $o,A2: a,B2: a] : ( if_a @ ( Less_eq @ A2 @ B2 ) @ B2 @ A2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_216_local_Omono__inf,axiom,
% 2.51/1.46 ! [F: a > set_a,A3: a,B4: a] :
% 2.51/1.46 ( ( mono_a_set_a @ less_eq @ F )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( F @ ( inf @ A3 @ B4 ) ) @ ( inf_inf_set_a @ ( F @ A3 ) @ ( F @ B4 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_217_local_Omono__sup,axiom,
% 2.51/1.46 ! [F: a > set_a,A3: a,B4: a] :
% 2.51/1.46 ( ( mono_a_set_a @ less_eq @ F )
% 2.51/1.46 => ( ord_less_eq_set_a @ ( sup_sup_set_a @ ( F @ A3 ) @ ( F @ B4 ) ) @ ( F @ ( sup @ A3 @ B4 ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_218_local_Obdd__above__finite,axiom,
% 2.51/1.46 ! [A3: set_a] :
% 2.51/1.46 ( ( finite_finite_a @ A3 )
% 2.51/1.46 => ( condit1627435690bove_a @ less_eq @ A3 ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_219_local_Ofinite__has__minimal2,axiom,
% 2.51/1.46 ! [A3: set_a,A: a] :
% 2.51/1.46 ( ( finite_finite_a @ A3 )
% 2.51/1.46 => ( ( member_a @ A @ A3 )
% 2.51/1.46 => ? [X3: a] :
% 2.51/1.46 ( ( member_a @ X3 @ A3 )
% 2.51/1.46 & ( less_eq @ X3 @ A )
% 2.51/1.46 & ! [Xa: a] :
% 2.51/1.46 ( ( member_a @ Xa @ A3 )
% 2.51/1.46 => ( ( less_eq @ Xa @ X3 )
% 2.51/1.46 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_220_local_Ofinite__has__maximal2,axiom,
% 2.51/1.46 ! [A3: set_a,A: a] :
% 2.51/1.46 ( ( finite_finite_a @ A3 )
% 2.51/1.46 => ( ( member_a @ A @ A3 )
% 2.51/1.46 => ? [X3: a] :
% 2.51/1.46 ( ( member_a @ X3 @ A3 )
% 2.51/1.46 & ( less_eq @ A @ X3 )
% 2.51/1.46 & ! [Xa: a] :
% 2.51/1.46 ( ( member_a @ Xa @ A3 )
% 2.51/1.46 => ( ( less_eq @ X3 @ Xa )
% 2.51/1.46 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_221_local_Obdd__below__Int2,axiom,
% 2.51/1.46 ! [B4: set_a,A3: set_a] :
% 2.51/1.46 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 2.51/1.46 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_222_local_Obdd__below__Int1,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a] :
% 2.51/1.46 ( ( condit1001553558elow_a @ less_eq @ A3 )
% 2.51/1.46 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_223_local_Obdd__above__Int2,axiom,
% 2.51/1.46 ! [B4: set_a,A3: set_a] :
% 2.51/1.46 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 2.51/1.46 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_224_local_Obdd__above__Int1,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a] :
% 2.51/1.46 ( ( condit1627435690bove_a @ less_eq @ A3 )
% 2.51/1.46 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A3 @ B4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_225_local_Obdd__below__finite,axiom,
% 2.51/1.46 ! [A3: set_a] :
% 2.51/1.46 ( ( finite_finite_a @ A3 )
% 2.51/1.46 => ( condit1001553558elow_a @ less_eq @ A3 ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_226_Un__subset__iff,axiom,
% 2.51/1.46 ! [A3: set_a,B4: set_a,C4: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A3 @ B4 ) @ C4 )
% 2.51/1.46 = ( ( ord_less_eq_set_a @ A3 @ C4 )
% 2.51/1.46 & ( ord_less_eq_set_a @ B4 @ C4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_227_Int__subset__iff,axiom,
% 2.51/1.46 ! [C4: set_a,A3: set_a,B4: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ C4 @ ( inf_inf_set_a @ A3 @ B4 ) )
% 2.51/1.46 = ( ( ord_less_eq_set_a @ C4 @ A3 )
% 2.51/1.46 & ( ord_less_eq_set_a @ C4 @ B4 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_228_semilattice__inf__class_Oinf__right__idem,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a] :
% 2.51/1.46 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Y )
% 2.51/1.46 = ( inf_inf_set_a @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_229_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a] :
% 2.51/1.46 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
% 2.51/1.46 = ( inf_inf_set_a @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_230_semilattice__inf__class_Oinf__left__idem,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a] :
% 2.51/1.46 ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 2.51/1.46 = ( inf_inf_set_a @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_231_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a] :
% 2.51/1.46 ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
% 2.51/1.46 = ( inf_inf_set_a @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_232_semilattice__inf__class_Oinf__idem,axiom,
% 2.51/1.46 ! [X: set_a] :
% 2.51/1.46 ( ( inf_inf_set_a @ X @ X )
% 2.51/1.46 = X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_233_semilattice__inf__class_Oinf_Oidem,axiom,
% 2.51/1.46 ! [A: set_a] :
% 2.51/1.46 ( ( inf_inf_set_a @ A @ A )
% 2.51/1.46 = A ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_234_semilattice__sup__class_Osup_Oright__idem,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a] :
% 2.51/1.46 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
% 2.51/1.46 = ( sup_sup_set_a @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_235_semilattice__sup__class_Osup__left__idem,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a] :
% 2.51/1.46 ( ( sup_sup_set_a @ X @ ( sup_sup_set_a @ X @ Y ) )
% 2.51/1.46 = ( sup_sup_set_a @ X @ Y ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_236_semilattice__sup__class_Osup_Oleft__idem,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a] :
% 2.51/1.46 ( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
% 2.51/1.46 = ( sup_sup_set_a @ A @ B ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_237_semilattice__sup__class_Osup__idem,axiom,
% 2.51/1.46 ! [X: set_a] :
% 2.51/1.46 ( ( sup_sup_set_a @ X @ X )
% 2.51/1.46 = X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_238_semilattice__sup__class_Osup_Oidem,axiom,
% 2.51/1.46 ! [A: set_a] :
% 2.51/1.46 ( ( sup_sup_set_a @ A @ A )
% 2.51/1.46 = A ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_239_semilattice__inf__class_Ole__inf__iff,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a,Z2: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ X @ ( inf_inf_set_a @ Y @ Z2 ) )
% 2.51/1.46 = ( ( ord_less_eq_set_a @ X @ Y )
% 2.51/1.46 & ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_240_semilattice__inf__class_Oinf_Obounded__iff,axiom,
% 2.51/1.46 ! [A: set_a,B: set_a,C: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 2.51/1.46 = ( ( ord_less_eq_set_a @ A @ B )
% 2.51/1.46 & ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_241_semilattice__sup__class_Ole__sup__iff,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a,Z2: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ X @ Y ) @ Z2 )
% 2.51/1.46 = ( ( ord_less_eq_set_a @ X @ Z2 )
% 2.51/1.46 & ( ord_less_eq_set_a @ Y @ Z2 ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_242_semilattice__sup__class_Osup_Obounded__iff,axiom,
% 2.51/1.46 ! [B: set_a,C: set_a,A: set_a] :
% 2.51/1.46 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ B @ C ) @ A )
% 2.51/1.46 = ( ( ord_less_eq_set_a @ B @ A )
% 2.51/1.46 & ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_243_lattice__class_Osup__inf__absorb,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a] :
% 2.51/1.46 ( ( sup_sup_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 2.51/1.46 = X ) ).
% 2.51/1.46
% 2.51/1.46 thf(fact_244_lattice__class_Oinf__sup__absorb,axiom,
% 2.51/1.46 ! [X: set_a,Y: set_a] :
% 2.51/1.46 ( ( inf_inf_set_a @ X @ ( sup_sup_set_a @ X @ Y ) )
% 2.51/1.46 = X ) ).
% 2.51/1.46
% 2.51/1.46 thf(help_If_3_1_If_001tf__a_T,axiom,
% 2.51/1.46 ! [P: $o] :
% 2.51/1.46 ( ( P = $true )
% 2.51/1.46 | ( P = $false ) ) ).
% 2.51/1.46
% 2.51/1.46 thf(help_If_2_1_If_001tf__a_T,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( if_a @ $false @ X @ Y )
% 2.51/1.46 = Y ) ).
% 2.51/1.46
% 2.51/1.46 thf(help_If_1_1_If_001tf__a_T,axiom,
% 2.51/1.46 ! [X: a,Y: a] :
% 2.51/1.46 ( ( if_a @ $true @ X @ Y )
% 2.51/1.46 = X ) ).
% 2.51/1.46
% 2.51/1.46 thf(conj_0,hypothesis,
% 2.51/1.46 less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ).
% 2.51/1.46
% 2.51/1.46 thf(conj_1,conjecture,
% 2.51/1.46 ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) )
% 2.51/1.46 = ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ).
% 2.51/1.46 ------------------------
% 2.51/1.48 % (4227)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_3946 for (2999ds/27Mi)
% 2.51/1.48 % (4225)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/183Mi)
% 2.51/1.48 % (4228)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/2Mi)
% 2.51/1.49 % (4228)Instruction limit reached!
% 2.51/1.49 % (4228)------------------------------
% 2.51/1.49 % (4228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.49 % (4228)Termination reason: Unknown
% 2.51/1.49 % (4228)Termination phase: shuffling
% 2.51/1.49
% 2.51/1.49 % (4228)Memory used [KB]: 1279
% 2.51/1.49 % (4228)Time elapsed: 0.002 s
% 2.51/1.49 % (4228)Instructions burned: 3 (million)
% 2.51/1.49 % (4228)------------------------------
% 2.51/1.49 % (4228)------------------------------
% 2.51/1.49 % (4226)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_3946 for (2999ds/4Mi)
% 2.51/1.49 % (4230)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_3946 for (2999ds/275Mi)
% 2.51/1.49 % (4229)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_3946 for (2999ds/2Mi)
% 2.51/1.49 % (4231)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/18Mi)
% 2.51/1.49 % (4227)Instruction limit reached!
% 2.51/1.49 % (4227)------------------------------
% 2.51/1.49 % (4227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.49 % (4227)Termination reason: Unknown
% 2.51/1.49 % (4227)Termination phase: Preprocessing 3
% 2.51/1.49
% 2.51/1.49 % (4227)Memory used [KB]: 1535
% 2.51/1.49 % (4227)Time elapsed: 0.010 s
% 2.51/1.49 % (4227)Instructions burned: 29 (million)
% 2.51/1.49 % (4227)------------------------------
% 2.51/1.49 % (4227)------------------------------
% 2.51/1.49 % (4229)Instruction limit reached!
% 2.51/1.49 % (4229)------------------------------
% 2.51/1.49 % (4229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.49 % (4229)Termination reason: Unknown
% 2.51/1.49 % (4229)Termination phase: shuffling
% 2.51/1.49
% 2.51/1.49 % (4229)Memory used [KB]: 1279
% 2.51/1.49 % (4229)Time elapsed: 0.004 s
% 2.51/1.49 % (4229)Instructions burned: 3 (million)
% 2.51/1.49 % (4229)------------------------------
% 2.51/1.49 % (4229)------------------------------
% 2.51/1.49 % (4226)Instruction limit reached!
% 2.51/1.49 % (4226)------------------------------
% 2.51/1.49 % (4226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.49 % (4226)Termination reason: Unknown
% 2.51/1.49 % (4226)Termination phase: shuffling
% 2.51/1.49
% 2.51/1.49 % (4226)Memory used [KB]: 1279
% 2.51/1.49 % (4226)Time elapsed: 0.005 s
% 2.51/1.49 % (4226)Instructions burned: 5 (million)
% 2.51/1.49 % (4226)------------------------------
% 2.51/1.49 % (4226)------------------------------
% 2.51/1.50 % (4232)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/3Mi)
% 2.60/1.50 % (4232)Instruction limit reached!
% 2.60/1.50 % (4232)------------------------------
% 2.60/1.50 % (4232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.50 % (4232)Termination reason: Unknown
% 2.60/1.50 % (4232)Termination phase: shuffling
% 2.60/1.50
% 2.60/1.50 % (4232)Memory used [KB]: 1279
% 2.60/1.50 % (4232)Time elapsed: 0.003 s
% 2.60/1.50 % (4232)Instructions burned: 3 (million)
% 2.60/1.50 % (4232)------------------------------
% 2.60/1.50 % (4232)------------------------------
% 2.60/1.50 % (4233)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_3946 for (2999ds/37Mi)
% 2.60/1.50 % (4231)Instruction limit reached!
% 2.60/1.50 % (4231)------------------------------
% 2.60/1.50 % (4231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.50 % (4231)Termination reason: Unknown
% 2.60/1.50 % (4231)Termination phase: Property scanning
% 2.60/1.50
% 2.60/1.50 % (4231)Memory used [KB]: 1407
% 2.60/1.50 % (4231)Time elapsed: 0.013 s
% 2.60/1.50 % (4231)Instructions burned: 18 (million)
% 2.60/1.50 % (4231)------------------------------
% 2.60/1.50 % (4231)------------------------------
% 2.60/1.51 % (4236)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_3946 for (2999ds/1041Mi)
% 2.60/1.51 % (4235)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_3946 for (2999ds/3Mi)
% 2.60/1.51 % (4234)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_3946 for (2999ds/15Mi)
% 2.60/1.51 % (4233)Instruction limit reached!
% 2.60/1.51 % (4233)------------------------------
% 2.60/1.51 % (4233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.51 % (4233)Termination reason: Unknown
% 2.60/1.51 % (4233)Termination phase: Property scanning
% 2.60/1.51
% 2.60/1.51 % (4233)Memory used [KB]: 1791
% 2.60/1.51 % (4233)Time elapsed: 0.011 s
% 2.60/1.51 % (4233)Instructions burned: 37 (million)
% 2.60/1.51 % (4233)------------------------------
% 2.60/1.51 % (4233)------------------------------
% 2.60/1.51 % (4235)Instruction limit reached!
% 2.60/1.51 % (4235)------------------------------
% 2.60/1.51 % (4235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.51 % (4235)Termination reason: Unknown
% 2.60/1.51 % (4235)Termination phase: shuffling
% 2.60/1.51
% 2.60/1.51 % (4235)Memory used [KB]: 1279
% 2.60/1.51 % (4235)Time elapsed: 0.004 s
% 2.60/1.51 % (4235)Instructions burned: 4 (million)
% 2.60/1.51 % (4235)------------------------------
% 2.60/1.51 % (4235)------------------------------
% 2.60/1.52 % (4237)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/7Mi)
% 2.60/1.52 % (4234)Instruction limit reached!
% 2.60/1.52 % (4234)------------------------------
% 2.60/1.52 % (4234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.52 % (4234)Termination reason: Unknown
% 2.60/1.52 % (4234)Termination phase: Property scanning
% 2.60/1.52
% 2.60/1.52 % (4234)Memory used [KB]: 1407
% 2.60/1.52 % (4234)Time elapsed: 0.012 s
% 2.60/1.52 % (4234)Instructions burned: 16 (million)
% 2.60/1.52 % (4234)------------------------------
% 2.60/1.52 % (4234)------------------------------
% 2.60/1.52 % (4238)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/16Mi)
% 2.60/1.52 % (4237)Instruction limit reached!
% 2.60/1.52 % (4237)------------------------------
% 2.60/1.52 % (4237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.52 % (4237)Termination reason: Unknown
% 2.60/1.52 % (4237)Termination phase: shuffling
% 2.60/1.52
% 2.60/1.52 % (4237)Memory used [KB]: 1279
% 2.60/1.52 % (4237)Time elapsed: 0.006 s
% 2.60/1.52 % (4237)Instructions burned: 7 (million)
% 2.60/1.52 % (4237)------------------------------
% 2.60/1.52 % (4237)------------------------------
% 2.60/1.52 % (4239)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_3946 for (2999ds/3Mi)
% 2.60/1.53 % (4239)Instruction limit reached!
% 2.60/1.53 % (4239)------------------------------
% 2.60/1.53 % (4239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.53 % (4239)Termination reason: Unknown
% 2.60/1.53 % (4239)Termination phase: shuffling
% 2.60/1.53
% 2.60/1.53 % (4239)Memory used [KB]: 1279
% 2.60/1.53 % (4239)Time elapsed: 0.002 s
% 2.60/1.53 % (4239)Instructions burned: 3 (million)
% 2.60/1.53 % (4239)------------------------------
% 2.60/1.53 % (4239)------------------------------
% 2.60/1.53 % (4238)Instruction limit reached!
% 2.60/1.53 % (4238)------------------------------
% 2.60/1.53 % (4238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.53 % (4238)Termination reason: Unknown
% 2.60/1.53 % (4238)Termination phase: Property scanning
% 2.60/1.53
% 2.60/1.53 % (4238)Memory used [KB]: 1407
% 2.60/1.53 % (4238)Time elapsed: 0.007 s
% 2.60/1.53 % (4238)Instructions burned: 19 (million)
% 2.60/1.53 % (4238)------------------------------
% 2.60/1.53 % (4238)------------------------------
% 2.60/1.54 % (4242)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/3Mi)
% 2.60/1.54 % (4242)Instruction limit reached!
% 2.60/1.54 % (4242)------------------------------
% 2.60/1.54 % (4242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.54 % (4242)Termination reason: Unknown
% 2.60/1.54 % (4242)Termination phase: shuffling
% 2.60/1.54
% 2.60/1.54 % (4242)Memory used [KB]: 1279
% 2.60/1.54 % (4242)Time elapsed: 0.003 s
% 2.60/1.54 % (4242)Instructions burned: 4 (million)
% 2.60/1.54 % (4242)------------------------------
% 2.60/1.54 % (4242)------------------------------
% 2.60/1.54 % (4243)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/4Mi)
% 2.60/1.54 % (4243)Instruction limit reached!
% 2.60/1.54 % (4243)------------------------------
% 2.60/1.54 % (4243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.54 % (4243)Termination reason: Unknown
% 2.60/1.54 % (4243)Termination phase: shuffling
% 2.60/1.54
% 2.60/1.54 % (4243)Memory used [KB]: 1279
% 2.60/1.54 % (4243)Time elapsed: 0.003 s
% 2.60/1.54 % (4243)Instructions burned: 6 (million)
% 2.60/1.54 % (4243)------------------------------
% 2.60/1.54 % (4243)------------------------------
% 2.60/1.54 % (4240)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_3946 for (2999ds/3Mi)
% 2.60/1.54 % (4240)Instruction limit reached!
% 2.60/1.54 % (4240)------------------------------
% 2.60/1.54 % (4240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.54 % (4240)Termination reason: Unknown
% 2.60/1.54 % (4240)Termination phase: shuffling
% 2.60/1.54
% 2.60/1.54 % (4240)Memory used [KB]: 1279
% 2.60/1.54 % (4240)Time elapsed: 0.004 s
% 2.60/1.54 % (4240)Instructions burned: 3 (million)
% 2.60/1.54 % (4240)------------------------------
% 2.60/1.54 % (4240)------------------------------
% 2.60/1.54 % (4241)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/7Mi)
% 2.60/1.54 % (4225)Instruction limit reached!
% 2.60/1.54 % (4225)------------------------------
% 2.60/1.54 % (4225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.54 % (4225)Termination reason: Unknown
% 2.60/1.54 % (4225)Termination phase: Saturation
% 2.60/1.54
% 2.60/1.54 % (4225)Memory used [KB]: 6908
% 2.60/1.54 % (4225)Time elapsed: 0.060 s
% 2.60/1.54 % (4225)Instructions burned: 185 (million)
% 2.60/1.54 % (4225)------------------------------
% 2.60/1.54 % (4225)------------------------------
% 2.60/1.55 % (4241)Instruction limit reached!
% 2.60/1.55 % (4241)------------------------------
% 2.60/1.55 % (4241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.55 % (4241)Termination reason: Unknown
% 2.60/1.55 % (4241)Termination phase: shuffling
% 2.60/1.55
% 2.60/1.55 % (4241)Memory used [KB]: 1279
% 2.60/1.55 % (4241)Time elapsed: 0.006 s
% 2.60/1.55 % (4241)Instructions burned: 7 (million)
% 2.60/1.55 % (4241)------------------------------
% 2.60/1.55 % (4241)------------------------------
% 2.60/1.55 % (4244)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/18Mi)
% 2.60/1.55 % (4245)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/710Mi)
% 2.60/1.55 % (4244)Instruction limit reached!
% 2.60/1.55 % (4244)------------------------------
% 2.60/1.55 % (4244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.55 % (4244)Termination reason: Unknown
% 2.60/1.55 % (4244)Termination phase: Property scanning
% 2.60/1.55
% 2.60/1.55 % (4244)Memory used [KB]: 1407
% 2.60/1.55 % (4244)Time elapsed: 0.008 s
% 2.60/1.55 % (4244)Instructions burned: 20 (million)
% 2.60/1.55 % (4244)------------------------------
% 2.60/1.55 % (4244)------------------------------
% 2.60/1.55 % (4247)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_3946 for (2999ds/902Mi)
% 2.60/1.56 % (4246)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/6Mi)
% 2.60/1.56 % (4246)Instruction limit reached!
% 2.60/1.56 % (4246)------------------------------
% 2.60/1.56 % (4246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.56 % (4246)Termination reason: Unknown
% 2.60/1.56 % (4246)Termination phase: shuffling
% 2.60/1.56
% 2.60/1.56 % (4246)Memory used [KB]: 1279
% 2.60/1.56 % (4246)Time elapsed: 0.006 s
% 2.60/1.56 % (4246)Instructions burned: 7 (million)
% 2.60/1.56 % (4246)------------------------------
% 2.60/1.56 % (4246)------------------------------
% 2.60/1.56 % (4249)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/5Mi)
% 2.60/1.56 % (4248)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_3946 for (2999ds/21Mi)
% 2.60/1.57 % (4249)Instruction limit reached!
% 2.60/1.57 % (4249)------------------------------
% 2.60/1.57 % (4249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.57 % (4249)Termination reason: Unknown
% 2.60/1.57 % (4249)Termination phase: shuffling
% 2.60/1.57
% 2.60/1.57 % (4249)Memory used [KB]: 1407
% 2.60/1.57 % (4249)Time elapsed: 0.004 s
% 2.60/1.57 % (4249)Instructions burned: 8 (million)
% 2.60/1.57 % (4249)------------------------------
% 2.60/1.57 % (4249)------------------------------
% 2.60/1.58 % (4250)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_3946 for (2999ds/6Mi)
% 2.60/1.58 % (4251)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3946 for (2999ds/377Mi)
% 2.60/1.58 % (4248)Instruction limit reached!
% 2.60/1.58 % (4248)------------------------------
% 2.60/1.58 % (4248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.58 % (4248)Termination reason: Unknown
% 2.60/1.58 % (4248)Termination phase: Property scanning
% 2.60/1.58
% 2.60/1.58 % (4248)Memory used [KB]: 1535
% 2.60/1.58 % (4248)Time elapsed: 0.015 s
% 2.60/1.58 % (4248)Instructions burned: 22 (million)
% 2.60/1.58 % (4248)------------------------------
% 2.60/1.58 % (4248)------------------------------
% 2.60/1.58 % (4250)Instruction limit reached!
% 2.60/1.58 % (4250)------------------------------
% 2.60/1.58 % (4250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.58 % (4250)Termination reason: Unknown
% 2.60/1.58 % (4250)Termination phase: shuffling
% 2.60/1.58
% 2.60/1.58 % (4250)Memory used [KB]: 1279
% 2.60/1.58 % (4250)Time elapsed: 0.004 s
% 2.60/1.58 % (4250)Instructions burned: 7 (million)
% 2.60/1.58 % (4250)------------------------------
% 2.60/1.58 % (4250)------------------------------
% 2.60/1.59 % (4253)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_3946 for (2998ds/19Mi)
% 2.60/1.59 % (4252)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_3946 for (2998ds/779Mi)
% 2.60/1.59 % (4253)Instruction limit reached!
% 2.60/1.59 % (4253)------------------------------
% 2.60/1.59 % (4253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.59 % (4253)Termination reason: Unknown
% 2.60/1.59 % (4253)Termination phase: shuffling
% 2.60/1.59
% 2.60/1.59 % (4253)Memory used [KB]: 1663
% 2.60/1.59 % (4253)Time elapsed: 0.008 s
% 2.60/1.59 % (4253)Instructions burned: 22 (million)
% 2.60/1.59 % (4253)------------------------------
% 2.60/1.59 % (4253)------------------------------
% 2.60/1.60 % (4254)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3946 for (2998ds/879Mi)
% 2.60/1.61 % (4230)Instruction limit reached!
% 2.60/1.61 % (4230)------------------------------
% 2.60/1.61 % (4230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.61 % (4230)Termination reason: Unknown
% 2.60/1.61 % (4230)Termination phase: Saturation
% 2.60/1.61
% 2.60/1.61 % (4230)Memory used [KB]: 6396
% 2.60/1.61 % (4230)Time elapsed: 0.119 s
% 2.60/1.61 % (4230)Instructions burned: 275 (million)
% 2.60/1.61 % (4230)------------------------------
% 2.60/1.61 % (4230)------------------------------
% 2.60/1.62 % (4255)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3946 for (2998ds/17Mi)
% 2.60/1.63 % (4255)Instruction limit reached!
% 2.60/1.63 % (4255)------------------------------
% 2.60/1.63 % (4255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.63 % (4255)Termination reason: Unknown
% 2.60/1.63 % (4255)Termination phase: Property scanning
% 2.60/1.63
% 2.60/1.63 % (4255)Memory used [KB]: 1407
% 2.60/1.63 % (4255)Time elapsed: 0.008 s
% 2.60/1.63 % (4255)Instructions burned: 19 (million)
% 2.60/1.63 % (4255)------------------------------
% 2.60/1.63 % (4255)------------------------------
% 2.60/1.64 % (4256)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3946 for (2998ds/3Mi)
% 2.60/1.64 % (4256)Instruction limit reached!
% 2.60/1.64 % (4256)------------------------------
% 2.60/1.64 % (4256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.64 % (4256)Termination reason: Unknown
% 2.60/1.64 % (4256)Termination phase: shuffling
% 2.60/1.64
% 2.60/1.64 % (4256)Memory used [KB]: 1279
% 2.60/1.64 % (4256)Time elapsed: 0.003 s
% 2.60/1.64 % (4256)Instructions burned: 4 (million)
% 2.60/1.64 % (4256)------------------------------
% 2.60/1.64 % (4256)------------------------------
% 2.60/1.65 % (4257)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3946 for (2998ds/30Mi)
% 2.60/1.66 % (4257)Instruction limit reached!
% 2.60/1.66 % (4257)------------------------------
% 2.60/1.66 % (4257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.66 % (4257)Termination reason: Unknown
% 2.60/1.66 % (4257)Termination phase: shuffling
% 2.60/1.66
% 2.60/1.66 % (4257)Memory used [KB]: 1535
% 2.60/1.66 % (4257)Time elapsed: 0.012 s
% 2.60/1.66 % (4257)Instructions burned: 32 (million)
% 2.60/1.66 % (4257)------------------------------
% 2.60/1.66 % (4257)------------------------------
% 2.60/1.67 % (4258)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3946 for (2998ds/127Mi)
% 2.60/1.70 % (4251)Instruction limit reached!
% 2.60/1.70 % (4251)------------------------------
% 2.60/1.70 % (4251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.70 % (4251)Termination reason: Unknown
% 2.60/1.70 % (4251)Termination phase: Saturation
% 2.60/1.70
% 2.60/1.70 % (4251)Memory used [KB]: 7419
% 2.60/1.70 % (4251)Time elapsed: 0.149 s
% 2.60/1.70 % (4251)Instructions burned: 380 (million)
% 2.60/1.70 % (4251)------------------------------
% 2.60/1.70 % (4251)------------------------------
% 2.60/1.71 % (4258)Instruction limit reached!
% 2.60/1.71 % (4258)------------------------------
% 2.60/1.71 % (4258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.71 % (4258)Termination reason: Unknown
% 2.60/1.71 % (4258)Termination phase: Saturation
% 2.60/1.71
% 2.60/1.71 % (4258)Memory used [KB]: 6780
% 2.60/1.71 % (4258)Time elapsed: 0.065 s
% 2.60/1.71 % (4258)Instructions burned: 127 (million)
% 2.60/1.71 % (4258)------------------------------
% 2.60/1.71 % (4258)------------------------------
% 2.60/1.71 % (4259)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3946 for (2997ds/100Mi)
% 2.60/1.72 % (4260)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_3946 for (2997ds/3Mi)
% 2.60/1.72 % (4260)Instruction limit reached!
% 2.60/1.72 % (4260)------------------------------
% 2.60/1.72 % (4260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.72 % (4260)Termination reason: Unknown
% 2.60/1.72 % (4260)Termination phase: shuffling
% 2.60/1.72
% 2.60/1.72 % (4260)Memory used [KB]: 1279
% 2.60/1.72 % (4260)Time elapsed: 0.003 s
% 2.60/1.72 % (4260)Instructions burned: 4 (million)
% 2.60/1.72 % (4260)------------------------------
% 2.60/1.72 % (4260)------------------------------
% 2.60/1.73 % (4261)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_3946 for (2997ds/20Mi)
% 2.60/1.73 % (4261)Instruction limit reached!
% 2.60/1.73 % (4261)------------------------------
% 2.60/1.73 % (4261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.73 % (4261)Termination reason: Unknown
% 2.60/1.73 % (4261)Termination phase: Property scanning
% 2.60/1.73
% 2.60/1.73 % (4261)Memory used [KB]: 1407
% 2.60/1.73 % (4261)Time elapsed: 0.009 s
% 2.60/1.73 % (4261)Instructions burned: 23 (million)
% 2.60/1.73 % (4261)------------------------------
% 2.60/1.73 % (4261)------------------------------
% 2.60/1.74 % (4259)Instruction limit reached!
% 2.60/1.74 % (4259)------------------------------
% 2.60/1.74 % (4259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.74 % (4259)Termination reason: Unknown
% 2.60/1.74 % (4259)Termination phase: Saturation
% 2.60/1.74
% 2.60/1.74 % (4259)Memory used [KB]: 1918
% 2.60/1.74 % (4259)Time elapsed: 0.029 s
% 2.60/1.74 % (4259)Instructions burned: 100 (million)
% 2.60/1.74 % (4259)------------------------------
% 2.60/1.74 % (4259)------------------------------
% 2.60/1.74 % (4262)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_3946 for (2997ds/86Mi)
% 2.60/1.75 % (4263)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_3946 for (2997ds/107Mi)
% 2.60/1.76 % (4245)Instruction limit reached!
% 2.60/1.76 % (4245)------------------------------
% 2.60/1.76 % (4245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.76 % (4245)Termination reason: Unknown
% 2.60/1.76 % (4245)Termination phase: Saturation
% 2.60/1.76
% 2.60/1.76 % (4245)Memory used [KB]: 7291
% 2.60/1.76 % (4245)Time elapsed: 0.215 s
% 2.60/1.76 % (4245)Instructions burned: 712 (million)
% 2.60/1.76 % (4245)------------------------------
% 2.60/1.76 % (4245)------------------------------
% 2.60/1.77 % (4262)Instruction limit reached!
% 2.60/1.77 % (4262)------------------------------
% 2.60/1.77 % (4262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.77 % (4262)Termination reason: Unknown
% 2.60/1.77 % (4262)Termination phase: Saturation
% 2.60/1.77
% 2.60/1.77 % (4262)Memory used [KB]: 6396
% 2.60/1.77 % (4262)Time elapsed: 0.028 s
% 2.60/1.77 % (4262)Instructions burned: 88 (million)
% 2.60/1.77 % (4262)------------------------------
% 2.60/1.77 % (4262)------------------------------
% 2.60/1.77 % (4264)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_3946 for (2996ds/39Mi)
% 2.60/1.78 % (4265)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_3946 for (2996ds/448Mi)
% 2.60/1.78 % (4264)Instruction limit reached!
% 2.60/1.78 % (4264)------------------------------
% 2.60/1.78 % (4264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.78 % (4264)Termination reason: Unknown
% 2.60/1.78 % (4264)Termination phase: Property scanning
% 2.60/1.78
% 2.60/1.78 % (4264)Memory used [KB]: 1791
% 2.60/1.78 % (4264)Time elapsed: 0.012 s
% 2.60/1.78 % (4264)Instructions burned: 41 (million)
% 2.60/1.78 % (4264)------------------------------
% 2.60/1.78 % (4264)------------------------------
% 2.60/1.78 % (4263)Instruction limit reached!
% 2.60/1.78 % (4263)------------------------------
% 2.60/1.78 % (4263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.78 % (4263)Termination reason: Unknown
% 2.60/1.78 % (4263)Termination phase: Saturation
% 2.60/1.78
% 2.60/1.78 % (4263)Memory used [KB]: 6396
% 2.60/1.78 % (4263)Time elapsed: 0.037 s
% 2.60/1.78 % (4263)Instructions burned: 109 (million)
% 2.60/1.78 % (4263)------------------------------
% 2.60/1.78 % (4263)------------------------------
% 2.60/1.79 % (4266)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_3946 for (2996ds/46Mi)
% 2.60/1.79 % (4267)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_3946 for (2996ds/98Mi)
% 2.60/1.80 % (4266)Instruction limit reached!
% 2.60/1.80 % (4266)------------------------------
% 2.60/1.80 % (4266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.80 % (4266)Termination reason: Unknown
% 2.60/1.80 % (4266)Termination phase: Property scanning
% 2.60/1.80
% 2.60/1.80 % (4266)Memory used [KB]: 1663
% 2.60/1.80 % (4266)Time elapsed: 0.014 s
% 2.60/1.80 % (4266)Instructions burned: 47 (million)
% 2.60/1.80 % (4266)------------------------------
% 2.60/1.80 % (4266)------------------------------
% 2.60/1.81 % (4268)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_3946 for (2996ds/507Mi)
% 2.60/1.82 % (4247)Instruction limit reached!
% 2.60/1.82 % (4247)------------------------------
% 2.60/1.82 % (4247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.82 % (4247)Termination reason: Unknown
% 2.60/1.82 % (4247)Termination phase: Saturation
% 2.60/1.82
% 2.60/1.82 % (4247)Memory used [KB]: 7419
% 2.60/1.82 % (4247)Time elapsed: 0.265 s
% 2.60/1.82 % (4247)Instructions burned: 902 (million)
% 2.60/1.82 % (4247)------------------------------
% 2.60/1.82 % (4247)------------------------------
% 2.60/1.82 % (4267)Instruction limit reached!
% 2.60/1.82 % (4267)------------------------------
% 2.60/1.82 % (4267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.82 % (4267)Termination reason: Unknown
% 2.60/1.82 % (4267)Termination phase: Property scanning
% 2.60/1.82
% 2.60/1.82 % (4267)Memory used [KB]: 2046
% 2.60/1.82 % (4267)Time elapsed: 0.029 s
% 2.60/1.82 % (4267)Instructions burned: 100 (million)
% 2.60/1.82 % (4267)------------------------------
% 2.60/1.82 % (4267)------------------------------
% 2.60/1.83 % (4269)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_3946 for (2996ds/149Mi)
% 2.60/1.83 % (4270)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3946 for (2996ds/39Mi)
% 2.60/1.83 % (4236)Instruction limit reached!
% 2.60/1.83 % (4236)------------------------------
% 2.60/1.83 % (4236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.83 % (4236)Termination reason: Unknown
% 2.60/1.83 % (4236)Termination phase: Saturation
% 2.60/1.83
% 2.60/1.83 % (4236)Memory used [KB]: 7931
% 2.60/1.83 % (4236)Time elapsed: 0.327 s
% 2.60/1.83 % (4236)Instructions burned: 1042 (million)
% 2.60/1.83 % (4236)------------------------------
% 2.60/1.83 % (4236)------------------------------
% 2.60/1.84 % (4270)Instruction limit reached!
% 2.60/1.84 % (4270)------------------------------
% 2.60/1.84 % (4270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.84 % (4270)Termination reason: Unknown
% 2.60/1.84 % (4270)Termination phase: Property scanning
% 2.60/1.84
% 2.60/1.84 % (4270)Memory used [KB]: 1663
% 2.60/1.84 % (4270)Time elapsed: 0.013 s
% 2.60/1.84 % (4270)Instructions burned: 40 (million)
% 2.60/1.84 % (4270)------------------------------
% 2.60/1.84 % (4270)------------------------------
% 2.60/1.84 % (4271)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_3946 for (2996ds/6Mi)
% 2.60/1.84 % (4271)Instruction limit reached!
% 2.60/1.84 % (4271)------------------------------
% 2.60/1.84 % (4271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.84 % (4271)Termination reason: Unknown
% 2.60/1.84 % (4271)Termination phase: shuffling
% 2.60/1.84
% 2.60/1.84 % (4271)Memory used [KB]: 1279
% 2.60/1.84 % (4271)Time elapsed: 0.003 s
% 2.60/1.84 % (4271)Instructions burned: 8 (million)
% 2.60/1.84 % (4271)------------------------------
% 2.60/1.84 % (4271)------------------------------
% 2.60/1.85 % (4272)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_3946 for (2996ds/1087Mi)
% 2.60/1.85 % (4273)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3946 for (2996ds/47Mi)
% 2.60/1.85 % (4252)Instruction limit reached!
% 2.60/1.85 % (4252)------------------------------
% 2.60/1.85 % (4252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.85 % (4252)Termination reason: Unknown
% 2.60/1.85 % (4252)Termination phase: Saturation
% 2.60/1.85
% 2.60/1.85 % (4252)Memory used [KB]: 7164
% 2.60/1.85 % (4252)Time elapsed: 0.285 s
% 2.60/1.85 % (4252)Instructions burned: 781 (million)
% 2.60/1.85 % (4252)------------------------------
% 2.60/1.85 % (4252)------------------------------
% 2.60/1.86 % (4274)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_3946 for (2996ds/44Mi)
% 2.60/1.87 % (4273)Instruction limit reached!
% 2.60/1.87 % (4273)------------------------------
% 2.60/1.87 % (4273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.87 % (4273)Termination reason: Unknown
% 2.60/1.87 % (4273)Termination phase: Property scanning
% 2.60/1.87
% 2.60/1.87 % (4273)Memory used [KB]: 1663
% 2.60/1.87 % (4273)Time elapsed: 0.015 s
% 2.60/1.87 % (4273)Instructions burned: 49 (million)
% 2.60/1.87 % (4273)------------------------------
% 2.60/1.87 % (4273)------------------------------
% 2.60/1.87 % (4269)Instruction limit reached!
% 2.60/1.87 % (4269)------------------------------
% 2.60/1.87 % (4269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.87 % (4269)Termination reason: Unknown
% 2.60/1.87 % (4269)Termination phase: Saturation
% 2.60/1.87
% 2.60/1.87 % (4269)Memory used [KB]: 6908
% 2.60/1.87 % (4269)Time elapsed: 0.047 s
% 2.60/1.87 % (4269)Instructions burned: 151 (million)
% 2.60/1.87 % (4269)------------------------------
% 2.60/1.87 % (4269)------------------------------
% 2.60/1.88 % (4274)Instruction limit reached!
% 2.60/1.88 % (4274)------------------------------
% 2.60/1.88 % (4274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.88 % (4274)Termination reason: Unknown
% 2.60/1.88 % (4274)Termination phase: Property scanning
% 2.60/1.88
% 2.60/1.88 % (4274)Memory used [KB]: 1791
% 2.60/1.88 % (4274)Time elapsed: 0.014 s
% 2.60/1.88 % (4274)Instructions burned: 44 (million)
% 2.60/1.88 % (4274)------------------------------
% 2.60/1.88 % (4274)------------------------------
% 2.60/1.88 % (4275)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_3946 for (2995ds/432Mi)
% 2.60/1.88 % (4276)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3946 for (2995ds/62Mi)
% 2.60/1.89 % (4254)Instruction limit reached!
% 2.60/1.89 % (4254)------------------------------
% 2.60/1.89 % (4254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.89 % (4254)Termination reason: Unknown
% 2.60/1.89 % (4254)Termination phase: Saturation
% 2.60/1.89
% 2.60/1.89 % (4254)Memory used [KB]: 7675
% 2.60/1.89 % (4254)Time elapsed: 0.314 s
% 2.60/1.89 % (4254)Instructions burned: 881 (million)
% 2.60/1.89 % (4254)------------------------------
% 2.60/1.89 % (4254)------------------------------
% 2.60/1.89 % (4277)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_3946 for (2995ds/31Mi)
% 2.60/1.90 % (4276)Instruction limit reached!
% 2.60/1.90 % (4276)------------------------------
% 2.60/1.90 % (4276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.90 % (4276)Termination reason: Unknown
% 2.60/1.90 % (4276)Termination phase: Property scanning
% 2.60/1.90
% 2.60/1.90 % (4276)Memory used [KB]: 1791
% 2.60/1.90 % (4276)Time elapsed: 0.017 s
% 2.60/1.90 % (4276)Instructions burned: 63 (million)
% 2.60/1.90 % (4276)------------------------------
% 2.60/1.90 % (4276)------------------------------
% 2.60/1.90 % (4278)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3946 for (2995ds/96Mi)
% 2.60/1.91 % (4279)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_3946 for (2995ds/453Mi)
% 2.60/1.91 % (4277)Instruction limit reached!
% 2.60/1.91 % (4277)------------------------------
% 2.60/1.91 % (4277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.91 % (4277)Termination reason: Unknown
% 2.60/1.91 % (4277)Termination phase: Clausification
% 2.60/1.91
% 2.60/1.91 % (4277)Memory used [KB]: 1663
% 2.60/1.91 % (4277)Time elapsed: 0.020 s
% 2.60/1.91 % (4277)Instructions burned: 32 (million)
% 2.60/1.91 % (4277)------------------------------
% 2.60/1.91 % (4277)------------------------------
% 2.60/1.93 % (4265)Instruction limit reached!
% 2.60/1.93 % (4265)------------------------------
% 2.60/1.93 % (4265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.93 % (4265)Termination reason: Unknown
% 2.60/1.93 % (4265)Termination phase: Saturation
% 2.60/1.93
% 2.60/1.93 % (4265)Memory used [KB]: 7164
% 2.60/1.93 % (4265)Time elapsed: 0.146 s
% 2.60/1.93 % (4265)Instructions burned: 448 (million)
% 2.60/1.93 % (4265)------------------------------
% 2.60/1.93 % (4265)------------------------------
% 2.60/1.93 % (4280)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_3946 for (2995ds/71Mi)
% 2.60/1.93 % (4278)Instruction limit reached!
% 2.60/1.93 % (4278)------------------------------
% 2.60/1.93 % (4278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.93 % (4278)Termination reason: Unknown
% 2.60/1.93 % (4278)Termination phase: Saturation
% 2.60/1.93
% 2.60/1.93 % (4278)Memory used [KB]: 6524
% 2.60/1.93 % (4278)Time elapsed: 0.031 s
% 2.60/1.93 % (4278)Instructions burned: 98 (million)
% 2.60/1.93 % (4278)------------------------------
% 2.60/1.93 % (4278)------------------------------
% 2.60/1.94 % (4281)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3946 for (2995ds/83Mi)
% 2.60/1.94 % (4282)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3946 for (2995ds/11Mi)
% 2.60/1.94 % (4282)Instruction limit reached!
% 2.60/1.94 % (4282)------------------------------
% 2.60/1.94 % (4282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.94 % (4282)Termination reason: Unknown
% 2.60/1.94 % (4282)Termination phase: shuffling
% 2.60/1.94
% 2.60/1.94 % (4282)Memory used [KB]: 1407
% 2.60/1.94 % (4282)Time elapsed: 0.004 s
% 2.60/1.94 % (4282)Instructions burned: 11 (million)
% 2.60/1.94 % (4282)------------------------------
% 2.60/1.94 % (4282)------------------------------
% 2.60/1.95 % (4283)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_3946 for (2995ds/41Mi)
% 2.60/1.96 % (4281)Instruction limit reached!
% 2.60/1.96 % (4281)------------------------------
% 2.60/1.96 % (4281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.96 % (4281)Termination reason: Unknown
% 2.60/1.96 % (4281)Termination phase: Saturation
% 2.60/1.96
% 2.60/1.96 % (4281)Memory used [KB]: 6140
% 2.60/1.96 % (4281)Time elapsed: 0.027 s
% 2.60/1.96 % (4281)Instructions burned: 84 (million)
% 2.60/1.96 % (4281)------------------------------
% 2.60/1.96 % (4281)------------------------------
% 2.60/1.96 % (4268)Instruction limit reached!
% 2.60/1.96 % (4268)------------------------------
% 2.60/1.96 % (4268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.96 % (4268)Termination reason: Unknown
% 2.60/1.96 % (4268)Termination phase: Saturation
% 2.60/1.96
% 2.60/1.96 % (4268)Memory used [KB]: 7291
% 2.60/1.96 % (4268)Time elapsed: 0.152 s
% 2.60/1.96 % (4268)Instructions burned: 509 (million)
% 2.60/1.96 % (4268)------------------------------
% 2.60/1.96 % (4268)------------------------------
% 2.60/1.97 % (4283)Instruction limit reached!
% 2.60/1.97 % (4283)------------------------------
% 2.60/1.97 % (4283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.97 % (4283)Termination reason: Unknown
% 2.60/1.97 % (4283)Termination phase: Property scanning
% 2.60/1.97
% 2.60/1.97 % (4283)Memory used [KB]: 1791
% 2.60/1.97 % (4283)Time elapsed: 0.013 s
% 2.60/1.97 % (4283)Instructions burned: 43 (million)
% 2.60/1.97 % (4283)------------------------------
% 2.60/1.97 % (4283)------------------------------
% 2.60/1.97 % (4280)Instruction limit reached!
% 2.60/1.97 % (4280)------------------------------
% 2.60/1.97 % (4280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.97 % (4280)Termination reason: Unknown
% 2.60/1.97 % (4280)Termination phase: Saturation
% 2.60/1.97
% 2.60/1.97 % (4280)Memory used [KB]: 6268
% 2.60/1.97 % (4280)Time elapsed: 0.039 s
% 2.60/1.97 % (4280)Instructions burned: 72 (million)
% 2.60/1.97 % (4280)------------------------------
% 2.60/1.97 % (4280)------------------------------
% 2.60/1.97 % (4284)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3946 for (2995ds/6Mi)
% 2.60/1.97 % (4284)Instruction limit reached!
% 2.60/1.97 % (4284)------------------------------
% 2.60/1.97 % (4284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.97 % (4284)Termination reason: Unknown
% 2.60/1.97 % (4284)Termination phase: shuffling
% 2.60/1.97
% 2.60/1.97 % (4284)Memory used [KB]: 1279
% 2.60/1.97 % (4284)Time elapsed: 0.003 s
% 2.60/1.97 % (4284)Instructions burned: 6 (million)
% 2.60/1.97 % (4284)------------------------------
% 2.60/1.97 % (4284)------------------------------
% 2.60/1.97 % (4286)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3946 for (2995ds/343Mi)
% 2.60/1.97 % (4285)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3946 for (2995ds/150Mi)
% 2.60/1.98 % (4287)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_3946 for (2995ds/109Mi)
% 2.60/1.98 % (4288)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_3946 for (2994ds/253Mi)
% 2.60/2.00 % (4275)Instruction limit reached!
% 2.60/2.00 % (4275)------------------------------
% 2.60/2.00 % (4275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/2.00 % (4275)Termination reason: Unknown
% 2.60/2.00 % (4275)Termination phase: Saturation
% 2.60/2.00
% 2.60/2.00 % (4275)Memory used [KB]: 3454
% 2.60/2.00 % (4275)Time elapsed: 0.128 s
% 2.60/2.00 % (4275)Instructions burned: 434 (million)
% 2.60/2.00 % (4275)------------------------------
% 2.60/2.00 % (4275)------------------------------
% 6.31/2.01 % (4287)Instruction limit reached!
% 6.31/2.01 % (4287)------------------------------
% 6.31/2.01 % (4287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.01 % (4287)Termination reason: Unknown
% 6.31/2.01 % (4287)Termination phase: Saturation
% 6.31/2.01
% 6.31/2.01 % (4287)Memory used [KB]: 6780
% 6.31/2.01 % (4287)Time elapsed: 0.035 s
% 6.31/2.01 % (4287)Instructions burned: 111 (million)
% 6.31/2.01 % (4287)------------------------------
% 6.31/2.01 % (4287)------------------------------
% 6.31/2.01 % (4289)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3946 for (2994ds/140Mi)
% 6.31/2.02 % (4285)Instruction limit reached!
% 6.31/2.02 % (4285)------------------------------
% 6.31/2.02 % (4285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.02 % (4285)Termination reason: Unknown
% 6.31/2.02 % (4285)Termination phase: Saturation
% 6.31/2.02
% 6.31/2.02 % (4285)Memory used [KB]: 6652
% 6.31/2.02 % (4285)Time elapsed: 0.047 s
% 6.31/2.02 % (4285)Instructions burned: 152 (million)
% 6.31/2.02 % (4285)------------------------------
% 6.31/2.02 % (4285)------------------------------
% 6.31/2.02 % (4290)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_3946 for (2994ds/614Mi)
% 6.31/2.03 % (4291)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_3946 for (2994ds/202Mi)
% 6.31/2.04 % (4279)Instruction limit reached!
% 6.31/2.04 % (4279)------------------------------
% 6.31/2.04 % (4279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.04 % (4279)Termination reason: Unknown
% 6.31/2.04 % (4279)Termination phase: Saturation
% 6.31/2.04
% 6.31/2.04 % (4279)Memory used [KB]: 7036
% 6.31/2.04 % (4279)Time elapsed: 0.134 s
% 6.31/2.04 % (4279)Instructions burned: 454 (million)
% 6.31/2.04 % (4279)------------------------------
% 6.31/2.04 % (4279)------------------------------
% 6.31/2.05 % (4292)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_3946 for (2994ds/339Mi)
% 6.31/2.05 % (4288)Instruction limit reached!
% 6.31/2.05 % (4288)------------------------------
% 6.31/2.05 % (4288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.05 % (4288)Termination reason: Unknown
% 6.31/2.05 % (4288)Termination phase: Saturation
% 6.31/2.05
% 6.31/2.05 % (4288)Memory used [KB]: 6524
% 6.31/2.05 % (4288)Time elapsed: 0.073 s
% 6.31/2.05 % (4288)Instructions burned: 254 (million)
% 6.31/2.05 % (4288)------------------------------
% 6.31/2.05 % (4288)------------------------------
% 6.31/2.06 % (4289)Instruction limit reached!
% 6.31/2.06 % (4289)------------------------------
% 6.31/2.06 % (4289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.06 % (4289)Termination reason: Unknown
% 6.31/2.06 % (4289)Termination phase: Saturation
% 6.31/2.06
% 6.31/2.06 % (4289)Memory used [KB]: 6396
% 6.31/2.06 % (4289)Time elapsed: 0.045 s
% 6.31/2.06 % (4289)Instructions burned: 142 (million)
% 6.31/2.06 % (4289)------------------------------
% 6.31/2.06 % (4289)------------------------------
% 6.31/2.06 % (4293)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_3946 for (2994ds/283Mi)
% 6.31/2.07 % (4294)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3946 for (2994ds/134Mi)
% 6.31/2.08 % (4286)Instruction limit reached!
% 6.31/2.08 % (4286)------------------------------
% 6.31/2.08 % (4286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.08 % (4286)Termination reason: Unknown
% 6.31/2.08 % (4286)Termination phase: Saturation
% 6.31/2.08
% 6.31/2.08 % (4286)Memory used [KB]: 6908
% 6.31/2.08 % (4286)Time elapsed: 0.107 s
% 6.31/2.08 % (4286)Instructions burned: 343 (million)
% 6.31/2.08 % (4286)------------------------------
% 6.31/2.08 % (4286)------------------------------
% 6.31/2.09 % (4291)Instruction limit reached!
% 6.31/2.09 % (4291)------------------------------
% 6.31/2.09 % (4291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.09 % (4291)Termination reason: Unknown
% 6.31/2.09 % (4291)Termination phase: Saturation
% 6.31/2.09
% 6.31/2.09 % (4291)Memory used [KB]: 6524
% 6.31/2.09 % (4291)Time elapsed: 0.059 s
% 6.31/2.09 % (4291)Instructions burned: 202 (million)
% 6.31/2.09 % (4291)------------------------------
% 6.31/2.09 % (4291)------------------------------
% 6.31/2.09 % (4295)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3946 for (2993ds/298Mi)
% 6.31/2.10 % (4296)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3946 for (2993ds/192Mi)
% 6.31/2.11 % (4294)Instruction limit reached!
% 6.31/2.11 % (4294)------------------------------
% 6.31/2.11 % (4294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.11 % (4294)Termination reason: Unknown
% 6.31/2.11 % (4294)Termination phase: Saturation
% 6.31/2.11
% 6.31/2.11 % (4294)Memory used [KB]: 6780
% 6.31/2.11 % (4294)Time elapsed: 0.062 s
% 6.31/2.11 % (4294)Instructions burned: 135 (million)
% 6.31/2.11 % (4294)------------------------------
% 6.31/2.11 % (4294)------------------------------
% 6.77/2.12 % (4297)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_3946 for (2993ds/258Mi)
% 6.77/2.15 % (4293)Instruction limit reached!
% 6.77/2.15 % (4293)------------------------------
% 6.77/2.15 % (4293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.15 % (4293)Termination reason: Unknown
% 6.77/2.15 % (4293)Termination phase: Saturation
% 6.77/2.15
% 6.77/2.15 % (4293)Memory used [KB]: 7036
% 6.77/2.15 % (4293)Time elapsed: 0.107 s
% 6.77/2.15 % (4293)Instructions burned: 284 (million)
% 6.77/2.15 % (4293)------------------------------
% 6.77/2.15 % (4293)------------------------------
% 6.77/2.15 % (4292)Instruction limit reached!
% 6.77/2.15 % (4292)------------------------------
% 6.77/2.15 % (4292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.15 % (4292)Termination reason: Unknown
% 6.77/2.15 % (4292)Termination phase: Saturation
% 6.77/2.15
% 6.77/2.15 % (4292)Memory used [KB]: 7931
% 6.77/2.15 % (4292)Time elapsed: 0.099 s
% 6.77/2.15 % (4292)Instructions burned: 339 (million)
% 6.77/2.15 % (4292)------------------------------
% 6.77/2.15 % (4292)------------------------------
% 6.77/2.15 % (4296)Instruction limit reached!
% 6.77/2.15 % (4296)------------------------------
% 6.77/2.15 % (4296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.15 % (4296)Termination reason: Unknown
% 6.77/2.15 % (4296)Termination phase: Saturation
% 6.77/2.15
% 6.77/2.15 % (4296)Memory used [KB]: 7164
% 6.77/2.15 % (4296)Time elapsed: 0.056 s
% 6.77/2.15 % (4296)Instructions burned: 192 (million)
% 6.77/2.15 % (4296)------------------------------
% 6.77/2.15 % (4296)------------------------------
% 6.77/2.16 % (4298)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_3946 for (2993ds/90Mi)
% 6.77/2.16 % (4299)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_3946 for (2993ds/231Mi)
% 6.77/2.16 % (4300)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_3946 for (2993ds/458Mi)
% 6.77/2.17 % (4295)Instruction limit reached!
% 6.77/2.17 % (4295)------------------------------
% 6.77/2.17 % (4295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.17 % (4295)Termination reason: Unknown
% 6.77/2.17 % (4295)Termination phase: Saturation
% 6.77/2.17
% 6.77/2.17 % (4295)Memory used [KB]: 7675
% 6.77/2.17 % (4295)Time elapsed: 0.084 s
% 6.77/2.17 % (4295)Instructions burned: 300 (million)
% 6.77/2.17 % (4295)------------------------------
% 6.77/2.17 % (4295)------------------------------
% 6.77/2.18 % (4298)Instruction limit reached!
% 6.77/2.18 % (4298)------------------------------
% 6.77/2.18 % (4298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.18 % (4298)Termination reason: Unknown
% 6.77/2.18 % (4298)Termination phase: Saturation
% 6.77/2.18
% 6.77/2.18 % (4298)Memory used [KB]: 6396
% 6.77/2.18 % (4298)Time elapsed: 0.026 s
% 6.77/2.18 % (4298)Instructions burned: 92 (million)
% 6.77/2.18 % (4298)------------------------------
% 6.77/2.18 % (4298)------------------------------
% 6.77/2.18 % (4272)Instruction limit reached!
% 6.77/2.18 % (4272)------------------------------
% 6.77/2.18 % (4272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.18 % (4272)Termination reason: Unknown
% 6.77/2.18 % (4272)Termination phase: Saturation
% 6.77/2.18
% 6.77/2.18 % (4272)Memory used [KB]: 7547
% 6.77/2.18 % (4272)Time elapsed: 0.333 s
% 6.77/2.18 % (4272)Instructions burned: 1089 (million)
% 6.77/2.18 % (4272)------------------------------
% 6.77/2.18 % (4272)------------------------------
% 6.77/2.18 % (4301)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_3946 for (2992ds/31Mi)
% 6.77/2.19 % (4297)Instruction limit reached!
% 6.77/2.19 % (4297)------------------------------
% 6.77/2.19 % (4297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.19 % (4297)Termination reason: Unknown
% 6.77/2.19 % (4297)Termination phase: Saturation
% 6.77/2.19
% 6.77/2.19 % (4297)Memory used [KB]: 6524
% 6.77/2.19 % (4297)Time elapsed: 0.075 s
% 6.77/2.19 % (4297)Instructions burned: 260 (million)
% 6.77/2.19 % (4297)------------------------------
% 6.77/2.19 % (4297)------------------------------
% 6.77/2.19 % (4302)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_3946 for (2992ds/297Mi)
% 6.77/2.19 % (4303)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_3946 for (2992ds/987Mi)
% 6.77/2.19 % (4301)Instruction limit reached!
% 6.77/2.19 % (4301)------------------------------
% 6.77/2.19 % (4301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.19 % (4301)Termination reason: Unknown
% 6.77/2.19 % (4301)Termination phase: Property scanning
% 6.77/2.19
% 6.77/2.19 % (4301)Memory used [KB]: 1663
% 6.77/2.19 % (4301)Time elapsed: 0.011 s
% 6.77/2.19 % (4301)Instructions burned: 34 (million)
% 6.77/2.19 % (4301)------------------------------
% 6.77/2.19 % (4301)------------------------------
% 7.34/2.20 % (4300)First to succeed.
% 7.34/2.20 % (4304)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_3946 for (2992ds/182Mi)
% 7.34/2.20 % (4300)Refutation found. Thanks to Tanya!
% 7.34/2.20 % SZS status Theorem for DTF2THF_3946
% 7.34/2.20 % SZS output start Proof for DTF2THF_3946
% 7.34/2.20 thf(type_def_5, type, a: $tType).
% 7.34/2.20 thf(type_def_7, type, set_a: $tType).
% 7.34/2.20 thf(func_def_0, type, set_a: $tType).
% 7.34/2.20 thf(func_def_1, type, a: $tType).
% 7.34/2.20 thf(func_def_2, type, condit1627435690bove_a: (a > a > $o) > set_a > $o).
% 7.34/2.20 thf(func_def_3, type, condit1001553558elow_a: (a > a > $o) > set_a > $o).
% 7.34/2.20 thf(func_def_4, type, finite40241356em_a_a: (a > a > a) > $o).
% 7.34/2.20 thf(func_def_5, type, finite_finite_a: set_a > $o).
% 7.34/2.20 thf(func_def_6, type, abel_semigroup_a: (a > a > a) > $o).
% 7.34/2.20 thf(func_def_7, type, semigroup_a: (a > a > a) > $o).
% 7.34/2.20 thf(func_def_8, type, if_a: $o > a > a > a).
% 7.34/2.20 thf(func_def_9, type, inf_inf_set_a: set_a > set_a > set_a).
% 7.34/2.20 thf(func_def_10, type, semilattice_a: (a > a > a) > $o).
% 7.34/2.20 thf(func_def_11, type, sup_sup_set_a: set_a > set_a > set_a).
% 7.34/2.20 thf(func_def_12, type, lattic1885654924_set_a: (a > a > a) > $o).
% 7.34/2.20 thf(func_def_13, type, modula17988509_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 7.34/2.20 thf(func_def_14, type, modula1373251614_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 7.34/2.20 thf(func_def_15, type, modula581031071_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 7.34/2.20 thf(func_def_16, type, modula1936294176_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 7.34/2.20 thf(func_def_17, type, modula1144073633_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 7.34/2.20 thf(func_def_18, type, modula1727524044comp_a: (a > a > $o) > a > a > $o).
% 7.34/2.20 thf(func_def_19, type, least_a: (a > a > $o) > (a > $o) > a).
% 7.34/2.20 thf(func_def_20, type, max_a: (a > a > $o) > a > a > a).
% 7.34/2.20 thf(func_def_21, type, min_a: (a > a > $o) > a > a > a).
% 7.34/2.20 thf(func_def_22, type, ord_less_eq_set_a: set_a > set_a > $o).
% 7.34/2.20 thf(func_def_23, type, greatest_a: (a > a > $o) > (a > $o) > a).
% 7.34/2.20 thf(func_def_24, type, antimono_a_set_a: (a > a > $o) > (a > set_a) > $o).
% 7.34/2.20 thf(func_def_25, type, mono_a_set_a: (a > a > $o) > (a > set_a) > $o).
% 7.34/2.20 thf(func_def_26, type, collect_a: (a > $o) > set_a).
% 7.34/2.20 thf(func_def_27, type, member_a: a > set_a > $o).
% 7.34/2.20 thf(func_def_28, type, a2: a).
% 7.34/2.20 thf(func_def_29, type, b: a).
% 7.34/2.20 thf(func_def_30, type, c: a).
% 7.34/2.20 thf(func_def_31, type, inf: a > a > a).
% 7.34/2.20 thf(func_def_32, type, less_eq: a > a > $o).
% 7.34/2.20 thf(func_def_33, type, sup: a > a > a).
% 7.34/2.20 thf(func_def_48, type, sK0: a).
% 7.34/2.20 thf(func_def_49, type, sK1: a).
% 7.34/2.20 thf(func_def_50, type, sK2: a).
% 7.34/2.20 thf(func_def_51, type, sK3: (a > a > a) > a).
% 7.34/2.20 thf(func_def_52, type, sK4: (a > a > a) > a).
% 7.34/2.20 thf(func_def_53, type, sK5: (a > a > a) > a).
% 7.34/2.20 thf(func_def_54, type, sK6: (a > a > a) > a).
% 7.34/2.20 thf(func_def_55, type, sK7: (a > a > a) > a).
% 7.34/2.20 thf(func_def_56, type, sK8: (a > a > a) > a).
% 7.34/2.20 thf(func_def_57, type, sK9: (a > a > a) > a).
% 7.34/2.20 thf(func_def_58, type, sK10: (a > a > a) > a).
% 7.34/2.20 thf(func_def_59, type, sK11: (a > a > a) > a).
% 7.34/2.20 thf(func_def_60, type, sK12: (a > a > a) > a).
% 7.34/2.20 thf(func_def_61, type, sK13: (a > a > a) > a).
% 7.34/2.20 thf(func_def_62, type, sK14: (a > a > a) > a).
% 7.34/2.20 thf(func_def_63, type, sK15: (a > a > a) > a).
% 7.34/2.20 thf(func_def_64, type, sK16: (a > a > a) > a).
% 7.34/2.20 thf(func_def_65, type, sK17: a).
% 7.34/2.20 thf(func_def_66, type, sK18: a).
% 7.34/2.20 thf(func_def_67, type, sK19: a).
% 7.34/2.20 thf(func_def_69, type, ph21: !>[X0: $tType]:(X0)).
% 7.34/2.20 thf(f914,plain,(
% 7.34/2.20 $false),
% 7.34/2.20 inference(subsumption_resolution,[status(thm)],[f913,f877])).
% 7.34/2.20 thf(f877,plain,(
% 7.34/2.20 ((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)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f876,f793])).
% 7.34/2.20 thf(f793,plain,(
% 7.34/2.20 ( ! [X0 : a,X1 : a] : (((inf @ X0 @ X1) = (inf @ X1 @ X0))) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f621])).
% 7.34/2.20 thf(f621,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a] : ((inf @ X0 @ X1) = (inf @ X1 @ X0))),
% 7.34/2.20 inference(rectify,[status(thm)],[f15])).
% 7.34/2.20 thf(f15,axiom,(
% 7.34/2.20 ! [X3 : a,X2 : a] : ((inf @ X3 @ X2) = (inf @ X2 @ X3))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_14_local_Oinf_Ocommute)).
% 7.34/2.20 thf(f876,plain,(
% 7.34/2.20 ((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)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f875,f815])).
% 7.34/2.20 thf(f815,plain,(
% 7.34/2.20 ( ! [X0 : a,X1 : a] : (((sup @ X0 @ X1) = (sup @ X1 @ X0))) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f24])).
% 7.34/2.20 thf(f24,axiom,(
% 7.34/2.20 ! [X0 : a,X1 : a] : ((sup @ X0 @ X1) = (sup @ X1 @ X0))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_23_local_Osup__commute)).
% 7.34/2.20 thf(f875,plain,(
% 7.34/2.20 ((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)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f874,f793])).
% 7.34/2.20 thf(f874,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ c @ a2) @ (sup @ b @ c)))) = $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f873,f792])).
% 7.34/2.20 thf(f792,plain,(
% 7.34/2.20 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ X1 @ (inf @ X2 @ X0)) = (inf @ X2 @ (inf @ X1 @ X0)))) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f624])).
% 7.34/2.20 thf(f624,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a,X2 : a] : ((inf @ X1 @ (inf @ X2 @ X0)) = (inf @ X2 @ (inf @ X1 @ X0)))),
% 7.34/2.20 inference(rectify,[status(thm)],[f19])).
% 7.34/2.20 thf(f19,axiom,(
% 7.34/2.20 ! [X11 : a,X0 : a,X1 : a] : ((inf @ X0 @ (inf @ X1 @ X11)) = (inf @ X1 @ (inf @ X0 @ X11)))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_18_local_Oinf__left__commute)).
% 7.34/2.20 thf(f873,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ c @ a2) @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)))) = $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f872,f793])).
% 7.34/2.20 thf(f872,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2))) = $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f871,f742])).
% 7.34/2.20 thf(f742,plain,(
% 7.34/2.20 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ (inf @ (sup @ X1 @ X2) @ (sup @ X2 @ X0)) @ (sup @ X0 @ X1)) = (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X0))) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f618])).
% 7.34/2.20 thf(f618,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a,X2 : a] : ((inf @ (inf @ (sup @ X1 @ X2) @ (sup @ X2 @ X0)) @ (sup @ X0 @ X1)) = (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X0))),
% 7.34/2.20 inference(rectify,[status(thm)],[f93])).
% 7.34/2.20 thf(f93,axiom,(
% 7.34/2.20 ! [X8 : a,X3 : a,X2 : a] : ((modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (inf @ (inf @ (sup @ X3 @ X2) @ (sup @ X2 @ X8)) @ (sup @ X8 @ X3)))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_92_local_Oe__aux__def)).
% 7.34/2.20 thf(f871,plain,(
% 7.34/2.20 ($true = (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f870,f815])).
% 7.34/2.20 thf(f870,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f869,f793])).
% 7.34/2.20 thf(f869,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f868,f815])).
% 7.34/2.20 thf(f868,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ c @ a2) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f867,f768])).
% 7.34/2.20 thf(f768,plain,(
% 7.34/2.20 ( ! [X2 : a,X0 : a,X1 : a] : (((sup @ X1 @ (sup @ X2 @ X0)) = (sup @ X2 @ (sup @ X1 @ X0)))) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f639])).
% 7.34/2.20 thf(f639,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a,X2 : a] : ((sup @ X1 @ (sup @ X2 @ X0)) = (sup @ X2 @ (sup @ X1 @ X0)))),
% 7.34/2.20 inference(rectify,[status(thm)],[f22])).
% 7.34/2.20 thf(f22,axiom,(
% 7.34/2.20 ! [X8 : a,X3 : a,X2 : a] : ((sup @ X3 @ (sup @ X2 @ X8)) = (sup @ X2 @ (sup @ X3 @ X8)))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_21_local_Osup_Oleft__commute)).
% 7.34/2.20 thf(f867,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f866,f815])).
% 7.34/2.20 thf(f866,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f737,f804])).
% 7.34/2.20 thf(f804,plain,(
% 7.34/2.20 ( ! [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)))) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f603])).
% 7.34/2.20 thf(f603,plain,(
% 7.34/2.20 ! [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)))),
% 7.34/2.20 inference(rectify,[status(thm)],[f87])).
% 7.34/2.20 thf(f87,axiom,(
% 7.34/2.20 ! [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)))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_86_local_Od__aux__def)).
% 7.34/2.20 thf(f737,plain,(
% 7.34/2.20 ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f433])).
% 7.34/2.20 thf(f433,plain,(
% 7.34/2.20 ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 7.34/2.20 inference(fool_elimination,[status(thm)],[f432])).
% 7.34/2.20 thf(f432,plain,(
% 7.34/2.20 (less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))),
% 7.34/2.20 inference(rectify,[status(thm)],[f249])).
% 7.34/2.20 thf(f249,axiom,(
% 7.34/2.20 (less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',conj_0)).
% 7.34/2.20 thf(f913,plain,(
% 7.34/2.20 ((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)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f912,f793])).
% 7.34/2.20 thf(f912,plain,(
% 7.34/2.20 ((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)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f911,f815])).
% 7.34/2.20 thf(f911,plain,(
% 7.34/2.20 ((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)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f910,f793])).
% 7.34/2.20 thf(f910,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ c @ a2) @ (sup @ b @ c)))) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f909,f792])).
% 7.34/2.20 thf(f909,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ c @ a2) @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)))) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f908,f793])).
% 7.34/2.20 thf(f908,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2))) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f907,f742])).
% 7.34/2.20 thf(f907,plain,(
% 7.34/2.20 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f906,f822])).
% 7.34/2.20 thf(f822,plain,(
% 7.34/2.20 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X0) = (modula1144073633_aux_a @ inf @ sup @ X0 @ X1 @ X2))) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f616])).
% 7.34/2.20 thf(f616,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a,X2 : a] : ((modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X0) = (modula1144073633_aux_a @ inf @ sup @ X0 @ X1 @ X2))),
% 7.34/2.20 inference(rectify,[status(thm)],[f94])).
% 7.34/2.20 thf(f94,axiom,(
% 7.34/2.20 ! [X3 : a,X2 : a,X8 : a] : ((modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (modula1144073633_aux_a @ inf @ sup @ X2 @ X8 @ X3))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_93_local_Oe__b__c__a)).
% 7.34/2.20 thf(f906,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f905,f815])).
% 7.34/2.20 thf(f905,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f904,f793])).
% 7.34/2.20 thf(f904,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f903,f815])).
% 7.34/2.20 thf(f903,plain,(
% 7.34/2.20 ((less_eq @ (sup @ (sup @ (inf @ b @ c) @ (inf @ c @ a2)) @ (inf @ a2 @ b)) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 7.34/2.20 inference(trivial_inequality_removal,[status(thm)],[f902])).
% 7.34/2.20 thf(f902,plain,(
% 7.34/2.20 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))) | ((less_eq @ (sup @ (sup @ (inf @ b @ c) @ (inf @ c @ a2)) @ (inf @ a2 @ b)) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f901,f815])).
% 7.34/2.20 thf(f901,plain,(
% 7.34/2.20 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c)))) | ((less_eq @ (sup @ (sup @ (inf @ b @ c) @ (inf @ c @ a2)) @ (inf @ a2 @ b)) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f900,f793])).
% 7.34/2.20 thf(f900,plain,(
% 7.34/2.20 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2)))) | ((less_eq @ (sup @ (sup @ (inf @ b @ c) @ (inf @ c @ a2)) @ (inf @ a2 @ b)) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f899,f804])).
% 7.34/2.20 thf(f899,plain,(
% 7.34/2.20 ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ b @ c @ a2) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true) | ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f898,f815])).
% 7.34/2.20 thf(f898,plain,(
% 7.34/2.20 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) != (sup @ (sup @ (inf @ b @ c) @ (inf @ c @ a2)) @ (inf @ a2 @ b))) | ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ b @ c @ a2) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f897,f804])).
% 7.34/2.20 thf(f897,plain,(
% 7.34/2.20 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) != (modula1936294176_aux_a @ inf @ sup @ b @ c @ a2)) | ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ b @ c @ a2) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ a2)) != $true)),
% 7.34/2.20 inference(superposition,[status(thm)],[f865,f891])).
% 7.34/2.20 thf(f891,plain,(
% 7.34/2.20 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ (modula17988509_aux_a @ inf @ sup @ X0 @ X1 @ X2) @ (modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X0)) = (modula1936294176_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)) )),
% 7.34/2.20 inference(superposition,[status(thm)],[f762,f845])).
% 7.34/2.20 thf(f845,plain,(
% 7.34/2.20 ( ! [X2 : a,X0 : a,X1 : a] : (((modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1) = (modula1373251614_aux_a @ inf @ sup @ X1 @ X0 @ X2))) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f645])).
% 7.34/2.20 thf(f645,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a,X2 : a] : ((modula17988509_aux_a @ inf @ sup @ X0 @ X2 @ X1) = (modula1373251614_aux_a @ inf @ sup @ X1 @ X0 @ X2))),
% 7.34/2.20 inference(rectify,[status(thm)],[f126])).
% 7.34/2.20 thf(f126,axiom,(
% 7.34/2.20 ! [X2 : a,X3 : a,X8 : a] : ((modula1373251614_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (modula17988509_aux_a @ inf @ sup @ X2 @ X8 @ X3))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_125_local_Ob__a)).
% 7.34/2.20 thf(f762,plain,(
% 7.34/2.20 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ (modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1) @ (modula1373251614_aux_a @ inf @ sup @ X2 @ X0 @ X1)) = (modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1)) | ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1) @ (modula1144073633_aux_a @ inf @ sup @ X2 @ X0 @ X1)) != $true)) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f713])).
% 7.34/2.20 thf(f713,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a,X2 : a] : (((less_eq @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1) @ (modula1144073633_aux_a @ inf @ sup @ X2 @ X0 @ X1)) != $true) | ((inf @ (modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1) @ (modula1373251614_aux_a @ inf @ sup @ X2 @ X0 @ X1)) = (modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1)))),
% 7.34/2.20 inference(ennf_transformation,[status(thm)],[f356])).
% 7.34/2.20 thf(f356,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a,X2 : a] : (((less_eq @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1) @ (modula1144073633_aux_a @ inf @ sup @ X2 @ X0 @ X1)) = $true) => ((inf @ (modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1) @ (modula1373251614_aux_a @ inf @ sup @ X2 @ X0 @ X1)) = (modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1)))),
% 7.34/2.20 inference(fool_elimination,[status(thm)],[f355])).
% 7.34/2.20 thf(f355,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a,X2 : a] : ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1) @ (modula1144073633_aux_a @ inf @ sup @ X2 @ X0 @ X1)) => ((inf @ (modula17988509_aux_a @ inf @ sup @ X2 @ X0 @ X1) @ (modula1373251614_aux_a @ inf @ sup @ X2 @ X0 @ X1)) = (modula1936294176_aux_a @ inf @ sup @ X2 @ X0 @ X1)))),
% 7.34/2.20 inference(rectify,[status(thm)],[f132])).
% 7.34/2.20 thf(f132,axiom,(
% 7.34/2.20 ! [X2 : a,X8 : a,X3 : a] : ((less_eq @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X2 @ X8)) => ((modula1936294176_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (inf @ (modula17988509_aux_a @ inf @ sup @ X3 @ X2 @ X8) @ (modula1373251614_aux_a @ inf @ sup @ X3 @ X2 @ X8))))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_131_a__meet__b__eq__d)).
% 7.34/2.20 thf(f865,plain,(
% 7.34/2.20 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) != (inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b)))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f864,f815])).
% 7.34/2.20 thf(f864,plain,(
% 7.34/2.20 ((inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b)) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f863,f793])).
% 7.34/2.20 thf(f863,plain,(
% 7.34/2.20 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) != (inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b)))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f862,f815])).
% 7.34/2.20 thf(f862,plain,(
% 7.34/2.20 ((inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b)) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ c @ a2) @ (inf @ b @ c))))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f861,f768])).
% 7.34/2.20 thf(f861,plain,(
% 7.34/2.20 ((inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b)) != (sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f860,f815])).
% 7.34/2.20 thf(f860,plain,(
% 7.34/2.20 ((sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) != (inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b)))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f859,f804])).
% 7.34/2.20 thf(f859,plain,(
% 7.34/2.20 ((modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) != (inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula17988509_aux_a @ inf @ sup @ c @ a2 @ b)))),
% 7.34/2.20 inference(forward_demodulation,[status(thm)],[f767,f734])).
% 7.34/2.20 thf(f734,plain,(
% 7.34/2.20 ( ! [X2 : a,X0 : a,X1 : a] : (((modula581031071_aux_a @ inf @ sup @ X1 @ X2 @ X0) = (modula17988509_aux_a @ inf @ sup @ X0 @ X1 @ X2))) )),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f646])).
% 7.34/2.20 thf(f646,plain,(
% 7.34/2.20 ! [X0 : a,X1 : a,X2 : a] : ((modula581031071_aux_a @ inf @ sup @ X1 @ X2 @ X0) = (modula17988509_aux_a @ inf @ sup @ X0 @ X1 @ X2))),
% 7.34/2.20 inference(rectify,[status(thm)],[f113])).
% 7.34/2.20 thf(f113,axiom,(
% 7.34/2.20 ! [X8 : a,X3 : a,X2 : a] : ((modula581031071_aux_a @ inf @ sup @ X3 @ X2 @ X8) = (modula17988509_aux_a @ inf @ sup @ X8 @ X3 @ X2))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',fact_112_local_Oc__a)).
% 7.34/2.20 thf(f767,plain,(
% 7.34/2.20 ((modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) != (inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula581031071_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 7.34/2.20 inference(cnf_transformation,[status(thm)],[f601])).
% 7.34/2.20 thf(f601,plain,(
% 7.34/2.20 ((modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) != (inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula581031071_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 7.34/2.20 inference(flattening,[status(thm)],[f251])).
% 7.34/2.20 thf(f251,negated_conjecture,(
% 7.34/2.20 ~((modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) = (inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula581031071_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 7.34/2.20 inference(negated_conjecture,[status(cth)],[f250])).
% 7.34/2.20 thf(f250,conjecture,(
% 7.34/2.20 ((modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) = (inf @ (modula17988509_aux_a @ inf @ sup @ b @ c @ a2) @ (modula581031071_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 7.34/2.20 file('/export/starexec/sandbox2/tmp/tmp.wpKMBFlRFX/DTF2THF_3946.p',conj_1)).
% 7.34/2.20 % SZS output end Proof for DTF2THF_3946
% 7.34/2.20 % (4300)------------------------------
% 7.34/2.20 % (4300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.20 % (4300)Termination reason: Refutation
% 7.34/2.20
% 7.34/2.20 % (4300)Memory used [KB]: 6396
% 7.34/2.20 % (4300)Time elapsed: 0.039 s
% 7.34/2.20 % (4300)Instructions burned: 121 (million)
% 7.34/2.20 % (4300)------------------------------
% 7.34/2.20 % (4300)------------------------------
% 7.34/2.20 % (4224)Success in time 0.745 s
%------------------------------------------------------------------------------