%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP121^1 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:43 AM UTC 2026
% Result : Theorem 2.62s 1.88s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 483 ( 9 ~; 3 |; 0 &; 468 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 93 ( 90 usr; 14 con; 0-5 aty)
% Number of variables : 23 ( 0 ^; 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
set_a: $tType ).
thf(func_def_0,type,
set_a: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
thf(func_def_3,type,
condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
thf(func_def_4,type,
finite40241356em_a_a: ( a > a > a ) > $o ).
thf(func_def_5,type,
finite_finite_a: set_a > $o ).
thf(func_def_6,type,
abel_semigroup_a: ( a > a > a ) > $o ).
thf(func_def_7,type,
semigroup_a: ( a > a > a ) > $o ).
thf(func_def_8,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(func_def_9,type,
semilattice_a: ( a > a > a ) > $o ).
thf(func_def_10,type,
lattic247676691_fin_a: ( a > a > a ) > set_a > a ).
thf(func_def_11,type,
lattic1885654924_set_a: ( a > a > a ) > $o ).
thf(func_def_12,type,
lattic1781219155_fin_a: ( a > a > a ) > set_a > a ).
thf(func_def_13,type,
modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_14,type,
modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_15,type,
modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_16,type,
modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_17,type,
modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(func_def_18,type,
modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
thf(func_def_19,type,
bot_bot_set_a: set_a ).
thf(func_def_20,type,
least_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_21,type,
max_a: ( a > a > $o ) > a > a > a ).
thf(func_def_22,type,
min_a: ( a > a > $o ) > a > a > a ).
thf(func_def_23,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_24,type,
greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_25,type,
antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
thf(func_def_26,type,
mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
thf(func_def_27,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_28,type,
insert_a: a > set_a > set_a ).
thf(func_def_29,type,
set_atLeast_a: ( a > a > $o ) > a > set_a ).
thf(func_def_30,type,
set_atMost_a: ( a > a > $o ) > a > set_a ).
thf(func_def_31,type,
member_a: a > set_a > $o ).
thf(func_def_32,type,
a2: a ).
thf(func_def_33,type,
b: a ).
thf(func_def_34,type,
c: a ).
thf(func_def_35,type,
inf: a > a > a ).
thf(func_def_36,type,
less_eq: a > a > $o ).
thf(func_def_37,type,
sup: a > a > a ).
thf(func_def_52,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_53,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_55,type,
sK2: a ).
thf(func_def_56,type,
sK3: a ).
thf(func_def_57,type,
sK4: a ).
thf(func_def_58,type,
sK5: ( a > $o ) > a > a ).
thf(func_def_59,type,
sK6: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_60,type,
sK7: a > ( a > $o ) > a ).
thf(func_def_61,type,
sK8: set_a > a ).
thf(func_def_62,type,
sK9: set_a > a > a ).
thf(func_def_63,type,
sK10: set_a > set_a > a ).
thf(func_def_64,type,
sK11: a ).
thf(func_def_65,type,
sK12: a ).
thf(func_def_66,type,
sK13: set_a > a ).
thf(func_def_67,type,
sK14: set_a > a > a ).
thf(func_def_68,type,
sK15: set_a > a > a ).
thf(func_def_69,type,
sK16: set_a > a > a ).
thf(func_def_70,type,
sK17: a ).
thf(func_def_71,type,
sK18: a ).
thf(func_def_72,type,
sK19: a ).
thf(func_def_73,type,
sK20: a > ( a > $o ) > a ).
thf(func_def_74,type,
sK21: a > ( a > $o ) > a ).
thf(func_def_75,type,
sK22: ( a > set_a ) > a ).
thf(func_def_76,type,
sK23: ( a > set_a ) > a ).
thf(func_def_77,type,
sK24: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_78,type,
sK25: a > ( a > $o ) > a ).
thf(func_def_79,type,
sK26: a > ( a > $o ) > a ).
thf(func_def_80,type,
sK27: ( a > a > a ) > a ).
thf(func_def_81,type,
sK28: ( a > a > a ) > a ).
thf(func_def_82,type,
sK29: ( a > a > a ) > a ).
thf(func_def_83,type,
sK30: ( a > a > a ) > a ).
thf(func_def_84,type,
sK31: ( a > a > a ) > a ).
thf(func_def_85,type,
sK32: ( a > a > a ) > a ).
thf(func_def_86,type,
sK33: ( a > a > a ) > a ).
thf(func_def_87,type,
sK34: ( a > a > a ) > a ).
thf(func_def_88,type,
sK35: ( a > a > a ) > a ).
thf(func_def_89,type,
sK36: ( a > a > a ) > a ).
thf(func_def_90,type,
sK37: ( a > a > a ) > a ).
thf(func_def_91,type,
sK38: ( a > a > a ) > a ).
thf(func_def_92,type,
sK39: ( a > a > a ) > a ).
thf(func_def_93,type,
sK40: ( a > a > a ) > a ).
thf(func_def_94,type,
sK41: set_a > a ).
thf(func_def_95,type,
sK42: ( a > $o ) > a > a ).
thf(func_def_96,type,
sK43: a > set_a > a ).
thf(func_def_97,type,
sK44: set_a > a > a ).
thf(func_def_98,type,
sK45: ( a > set_a ) > a ).
thf(func_def_99,type,
sK46: ( a > set_a ) > a ).
thf(func_def_100,type,
sK47: ( a > a > a ) > a ).
thf(func_def_101,type,
sK48: ( a > a > a ) > a ).
thf(func_def_102,type,
sK49: ( a > a > a ) > a ).
thf(func_def_103,type,
sK50: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_104,type,
sK51: ( a > $o ) > a > a ).
thf(func_def_105,type,
sK52: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_107,type,
ph54:
!>[X0: $tType] : X0 ).
thf(f1513,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1467,f1264]) ).
thf(f1264,plain,
! [X0: a,X1: a] :
( ( less_eq @ ( inf @ X0 @ X1 ) @ X1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f599]) ).
thf(f599,plain,
! [X0: a,X1: a] :
( ( less_eq @ ( inf @ X0 @ X1 ) @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f598]) ).
thf(f598,plain,
! [X0: a,X1: a] : ( less_eq @ ( inf @ X0 @ X1 ) @ X1 ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,axiom,
! [X0: a,X1: a] : ( less_eq @ ( inf @ X0 @ X1 ) @ X1 ),
file('/export/starexec/sandbox2/tmp/tmp.eimr8lCgBt/DTF2THF_6676.p',fact_92_local_Oinf_Ocobounded2) ).
thf(f1467,plain,
( $true
!= ( less_eq @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1455]) ).
thf(f1455,plain,
( ( $true
!= ( less_eq @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) )
| ( ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) )
!= ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ) ),
inference(superposition,[status(thm)],[f1324,f1189]) ).
thf(f1189,plain,
! [X2: a,X0: a,X1: a] :
( ( ( sup @ X0 @ ( inf @ X1 @ X2 ) )
= ( inf @ X1 @ ( sup @ X0 @ X2 ) ) )
| ( ( less_eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f845]) ).
thf(f845,plain,
! [X0: a,X1: a,X2: a] :
( ( ( less_eq @ X0 @ X1 )
!= $true )
| ( ( sup @ X0 @ ( inf @ X1 @ X2 ) )
= ( inf @ X1 @ ( sup @ X0 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f529]) ).
thf(f529,plain,
! [X0: a,X1: a,X2: a] :
( ( ( less_eq @ X0 @ X1 )
= $true )
=> ( ( sup @ X0 @ ( inf @ X1 @ X2 ) )
= ( inf @ X1 @ ( sup @ X0 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f528]) ).
thf(f528,plain,
! [X0: a,X1: a,X2: a] :
( ( less_eq @ X0 @ X1 )
=> ( ( sup @ X0 @ ( inf @ X1 @ X2 ) )
= ( inf @ X1 @ ( sup @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f127]) ).
thf(f127,axiom,
! [X3: a,X4: a,X5: a] :
( ( less_eq @ X3 @ X4 )
=> ( ( sup @ X3 @ ( inf @ X4 @ X5 ) )
= ( inf @ X4 @ ( sup @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eimr8lCgBt/DTF2THF_6676.p',fact_126_local_Omodular) ).
thf(f1324,plain,
( ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) )
!= ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f759]) ).
thf(f759,plain,
( ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) )
!= ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ),
inference(flattening,[status(thm)],[f266]) ).
thf(f266,plain,
( ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) )
!= ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f256]) ).
thf(f256,negated_conjecture,
( ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) )
!= ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f255]) ).
thf(f255,conjecture,
( ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) )
= ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eimr8lCgBt/DTF2THF_6676.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP121^1 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:26:46 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP121^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer Modular_Distrib_Lattice problem prob_236__3262688_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : Modular_Distrib_Lattice/prob_236__3262688_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 293 ( 126 unt; 38 typ; 0 def)
% 0.30/0.46 % Number of atoms : 626 ( 202 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.30/0.46 % Number of connectives : 2164 ( 42 ~; 0 |; 24 &;1845 @)
% 0.30/0.46 % ( 0 <=>; 253 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 16 ( 6 avg)
% 0.30/0.46 % Number of types : 3 ( 2 usr)
% 0.30/0.46 % Number of type conns : 190 ( 190 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 37 ( 36 usr; 4 con; 0-5 aty)
% 0.30/0.46 % Number of variables : 603 ( 22 ^; 572 !; 9 ?; 603 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:44:30.144
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (2)
% 0.30/0.46 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 set_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (36)
% 0.30/0.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a,type,
% 0.30/0.46 condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a,type,
% 0.30/0.46 condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 0.30/0.46 finite40241356em_a_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
% 0.30/0.46 finite_finite_a: set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 0.30/0.46 abel_semigroup_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 0.30/0.46 semigroup_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 inf_inf_set_a: set_a > set_a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 0.30/0.46 semilattice_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin_001tf__a,type,
% 0.30/0.46 lattic247676691_fin_a: ( a > a > a ) > set_a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 0.30/0.46 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin_001tf__a,type,
% 0.30/0.46 lattic1781219155_fin_a: ( a > a > a ) > set_a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 0.30/0.46 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 0.30/0.46 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 0.30/0.46 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 0.30/0.46 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 0.30/0.46 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oincomp_001tf__a,type,
% 0.30/0.46 modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 bot_bot_set_a: set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord_OLeast_001tf__a,type,
% 0.30/0.46 least_a: ( a > a > $o ) > ( a > $o ) > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord_Omax_001tf__a,type,
% 0.30/0.46 max_a: ( a > a > $o ) > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord_Omin_001tf__a,type,
% 0.30/0.46 min_a: ( a > a > $o ) > a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder_OGreatest_001tf__a,type,
% 0.30/0.46 greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder_Oantimono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder_Omono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.30/0.46 collect_a: ( a > $o ) > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.30/0.46 insert_a: a > set_a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set__Interval_Oord_OatLeast_001tf__a,type,
% 0.30/0.46 set_atLeast_a: ( a > a > $o ) > a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set__Interval_Oord_OatMost_001tf__a,type,
% 0.30/0.46 set_atMost_a: ( a > a > $o ) > a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001tf__a,type,
% 0.30/0.46 member_a: a > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_a,type,
% 0.30/0.46 a2: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_b,type,
% 0.30/0.46 b: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_c,type,
% 0.30/0.46 c: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_inf,type,
% 0.30/0.46 inf: a > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_less__eq,type,
% 0.30/0.46 less_eq: a > a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_sup,type,
% 0.30/0.46 sup: a > a > a ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (254)
% 0.30/0.46 thf(fact_0_local_Oinf_Oassoc,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( inf @ ( inf @ A @ B ) @ C )
% 0.30/0.46 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.assoc
% 0.30/0.46 thf(fact_1_local_Oinf_Ocommute,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( inf @ A @ B )
% 0.30/0.46 = ( inf @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.commute
% 0.30/0.46 thf(fact_2_local_Oinf_Oleft__commute,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( inf @ B @ ( inf @ A @ C ) )
% 0.30/0.46 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.left_commute
% 0.30/0.46 thf(fact_3_local_Oinf__assoc,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ( inf @ ( inf @ X @ Y ) @ Z )
% 0.30/0.46 = ( inf @ X @ ( inf @ Y @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_assoc
% 0.30/0.46 thf(fact_4_local_Oinf__commute,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( inf @ X @ Y )
% 0.30/0.46 = ( inf @ Y @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_commute
% 0.30/0.46 thf(fact_5_local_Oinf__left__commute,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ( inf @ X @ ( inf @ Y @ Z ) )
% 0.30/0.46 = ( inf @ Y @ ( inf @ X @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_left_commute
% 0.30/0.46 thf(fact_6_local_Osup_Oassoc,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( sup @ ( sup @ A @ B ) @ C )
% 0.30/0.46 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.assoc
% 0.30/0.46 thf(fact_7_local_Osup_Ocommute,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( sup @ A @ B )
% 0.30/0.46 = ( sup @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.commute
% 0.30/0.46 thf(fact_8_local_Osup_Oleft__commute,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( sup @ B @ ( sup @ A @ C ) )
% 0.30/0.46 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.left_commute
% 0.30/0.46 thf(fact_9_local_Osup__assoc,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ( sup @ ( sup @ X @ Y ) @ Z )
% 0.30/0.46 = ( sup @ X @ ( sup @ Y @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_assoc
% 0.30/0.46 thf(fact_10_local_Osup__commute,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( sup @ X @ Y )
% 0.30/0.46 = ( sup @ Y @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_commute
% 0.30/0.46 thf(fact_11_local_Osup__left__commute,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ( sup @ X @ ( sup @ Y @ Z ) )
% 0.30/0.46 = ( sup @ Y @ ( sup @ X @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_left_commute
% 0.30/0.46 thf(fact_12_local_Odistrib__imp1,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ! [X2: a,Y2: a,Z2: a] :
% 0.30/0.46 ( ( inf @ X2 @ ( sup @ Y2 @ Z2 ) )
% 0.30/0.46 = ( sup @ ( inf @ X2 @ Y2 ) @ ( inf @ X2 @ Z2 ) ) )
% 0.30/0.46 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 0.30/0.46 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.distrib_imp1
% 0.30/0.46 thf(fact_13_local_Odistrib__imp2,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ! [X2: a,Y2: a,Z2: a] :
% 0.30/0.46 ( ( sup @ X2 @ ( inf @ Y2 @ Z2 ) )
% 0.30/0.46 = ( inf @ ( sup @ X2 @ Y2 ) @ ( sup @ X2 @ Z2 ) ) )
% 0.30/0.46 => ( ( inf @ X @ ( sup @ Y @ Z ) )
% 0.30/0.46 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.distrib_imp2
% 0.30/0.46 thf(fact_14_local_Oa__join__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.a_join_d
% 0.30/0.46 thf(fact_15_a__meet__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % a_meet_d
% 0.30/0.46 thf(fact_16_local_Ob__join__d,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.b_join_d
% 0.30/0.46 thf(fact_17_b__meet__d,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( inf @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ ( inf @ B @ C ) @ ( inf @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % b_meet_d
% 0.30/0.46 thf(fact_18_c__meet__d,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( inf @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( sup @ ( inf @ C @ A ) @ ( inf @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % c_meet_d
% 0.30/0.46 thf(fact_19_local_Od__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.d_aux_def
% 0.30/0.46 thf(fact_20_local_Od__b__c__a,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.d_b_c_a
% 0.30/0.46 thf(fact_21_local_Od__c__a__b,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.d_c_a_b
% 0.30/0.46 thf(fact_22_local_Oa__meet__e,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.a_meet_e
% 0.30/0.46 thf(fact_23_local_Ob__meet__e,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.b_meet_e
% 0.30/0.46 thf(fact_24_local_Oc__meet__e,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.c_meet_e
% 0.30/0.46 thf(fact_25_local_Oe__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.e_aux_def
% 0.30/0.46 thf(fact_26_local_Oe__b__c__a,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 0.30/0.46 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.e_b_c_a
% 0.30/0.46 thf(fact_27_local_Oe__c__a__b,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 0.30/0.46 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.e_c_a_b
% 0.30/0.46 thf(fact_28_local_Oinf_Oidem,axiom,
% 0.30/0.46 ! [A: a] :
% 0.30/0.46 ( ( inf @ A @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.idem
% 0.30/0.46 thf(fact_29_local_Oinf_Oleft__idem,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( inf @ A @ ( inf @ A @ B ) )
% 0.30/0.46 = ( inf @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.left_idem
% 0.30/0.46 thf(fact_30_local_Oinf_Oright__idem,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( inf @ ( inf @ A @ B ) @ B )
% 0.30/0.46 = ( inf @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.right_idem
% 0.30/0.46 thf(fact_31_local_Oinf__idem,axiom,
% 0.30/0.46 ! [X: a] :
% 0.30/0.46 ( ( inf @ X @ X )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_idem
% 0.30/0.46 thf(fact_32_local_Oinf__left__idem,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( inf @ X @ ( inf @ X @ Y ) )
% 0.30/0.46 = ( inf @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_left_idem
% 0.30/0.46 thf(fact_33_local_Oinf__right__idem,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 0.30/0.46 = ( inf @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_right_idem
% 0.30/0.46 thf(fact_34_local_Osup_Oidem,axiom,
% 0.30/0.46 ! [A: a] :
% 0.30/0.46 ( ( sup @ A @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.idem
% 0.30/0.46 thf(fact_35_local_Osup_Oleft__idem,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( sup @ A @ ( sup @ A @ B ) )
% 0.30/0.46 = ( sup @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.left_idem
% 0.30/0.46 thf(fact_36_local_Osup_Oright__idem,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( sup @ ( sup @ A @ B ) @ B )
% 0.30/0.46 = ( sup @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.right_idem
% 0.30/0.46 thf(fact_37_local_Osup__idem,axiom,
% 0.30/0.46 ! [X: a] :
% 0.30/0.46 ( ( sup @ X @ X )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_idem
% 0.30/0.46 thf(fact_38_local_Osup__left__idem,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( sup @ X @ ( sup @ X @ Y ) )
% 0.30/0.46 = ( sup @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_left_idem
% 0.30/0.46 thf(fact_39_calculation,axiom,
% 0.30/0.46 ( ( sup @ ( inf @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) )
% 0.30/0.46 = ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % calculation
% 0.30/0.46 thf(fact_40_local_Oinf__sup__absorb,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( inf @ X @ ( sup @ X @ Y ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_sup_absorb
% 0.30/0.46 thf(fact_41_local_Osup__inf__absorb,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( sup @ X @ ( inf @ X @ Y ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_inf_absorb
% 0.30/0.46 thf(fact_42_local_Ob__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.b_aux_def
% 0.30/0.46 thf(fact_43_local_Oc__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.c_aux_def
% 0.30/0.46 thf(fact_44_local_Oa__aux__def,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.a_aux_def
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: a,P: a > $o] :
% 0.30/0.46 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.30/0.46 = ( P @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( collect_a
% 0.30/0.46 @ ^ [X3: a] : ( member_a @ X3 @ A2 ) )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [P: a > $o,Q: a > $o] :
% 0.30/0.46 ( ! [X2: a] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 = ( Q @ X2 ) )
% 0.30/0.46 => ( ( collect_a @ P )
% 0.30/0.46 = ( collect_a @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_lattice_Od__aux_Ocong,axiom,
% 0.30/0.46 modula1936294176_aux_a = modula1936294176_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.d_aux.cong
% 0.30/0.46 thf(fact_49_lattice_Oe__aux_Ocong,axiom,
% 0.30/0.46 modula1144073633_aux_a = modula1144073633_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.e_aux.cong
% 0.30/0.46 thf(fact_50_d__less__e,axiom,
% 0.30/0.46 less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ).
% 0.30/0.46
% 0.30/0.46 % d_less_e
% 0.30/0.46 thf(fact_51_local_Ocomp__fun__idem__sup,axiom,
% 0.30/0.46 finite40241356em_a_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.comp_fun_idem_sup
% 0.30/0.46 thf(fact_52_local_Ocomp__fun__idem__inf,axiom,
% 0.30/0.46 finite40241356em_a_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.comp_fun_idem_inf
% 0.30/0.46 thf(fact_53_local_Osup_Osemigroup__axioms,axiom,
% 0.30/0.46 semigroup_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.sup.semigroup_axioms
% 0.30/0.46 thf(fact_54_local_Oinf_Osemigroup__axioms,axiom,
% 0.30/0.46 semigroup_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.inf.semigroup_axioms
% 0.30/0.46 thf(fact_55_local_Osup_Osemilattice__axioms,axiom,
% 0.30/0.46 semilattice_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.sup.semilattice_axioms
% 0.30/0.46 thf(fact_56_local_Oinf_Osemilattice__axioms,axiom,
% 0.30/0.46 semilattice_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.inf.semilattice_axioms
% 0.30/0.46 thf(fact_57_local_Osup_Oabel__semigroup__axioms,axiom,
% 0.30/0.46 abel_semigroup_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.sup.abel_semigroup_axioms
% 0.30/0.46 thf(fact_58_local_Oinf_Oabel__semigroup__axioms,axiom,
% 0.30/0.46 abel_semigroup_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.inf.abel_semigroup_axioms
% 0.30/0.46 thf(fact_59_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 0.30/0.46 lattic1885654924_set_a @ sup ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.semilattice_set_axioms
% 0.30/0.46 thf(fact_60_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 0.30/0.46 lattic1885654924_set_a @ inf ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.semilattice_set_axioms
% 0.30/0.46 thf(fact_61_local_Ob__a,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.b_a
% 0.30/0.46 thf(fact_62_local_Oantisym,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antisym
% 0.30/0.46 thf(fact_63_local_Oantisym__conv,axiom,
% 0.30/0.46 ! [Y: a,X: a] :
% 0.30/0.46 ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antisym_conv
% 0.30/0.46 thf(fact_64_local_Odual__order_Oantisym,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( less_eq @ A @ B )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.dual_order.antisym
% 0.30/0.46 thf(fact_65_local_Odual__order_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 0.30/0.46 = ( ^ [A3: a,B2: a] :
% 0.30/0.46 ( ( less_eq @ B2 @ A3 )
% 0.30/0.46 & ( less_eq @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.dual_order.eq_iff
% 0.30/0.46 thf(fact_66_local_Odual__order_Otrans,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( less_eq @ C @ B )
% 0.30/0.46 => ( less_eq @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.dual_order.trans
% 0.30/0.46 thf(fact_67_local_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 0.30/0.46 = ( ^ [X3: a,Y4: a] :
% 0.30/0.46 ( ( less_eq @ X3 @ Y4 )
% 0.30/0.46 & ( less_eq @ Y4 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.eq_iff
% 0.30/0.46 thf(fact_68_local_Oeq__refl,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( X = Y )
% 0.30/0.46 => ( less_eq @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.eq_refl
% 0.30/0.46 thf(fact_69_local_Oord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( less_eq @ B @ C )
% 0.30/0.46 => ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.ord_eq_le_trans
% 0.30/0.46 thf(fact_70_local_Oord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( B = C )
% 0.30/0.46 => ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.ord_le_eq_trans
% 0.30/0.46 thf(fact_71_local_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( less_eq @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.order.antisym
% 0.30/0.46 thf(fact_72_local_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 0.30/0.46 = ( ^ [A3: a,B2: a] :
% 0.30/0.46 ( ( less_eq @ A3 @ B2 )
% 0.30/0.46 & ( less_eq @ B2 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.order.eq_iff
% 0.30/0.46 thf(fact_73_local_Oorder_Otrans,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( less_eq @ B @ C )
% 0.30/0.46 => ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.order.trans
% 0.30/0.46 thf(fact_74_local_Oorder__trans,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( less_eq @ Y @ Z )
% 0.30/0.46 => ( less_eq @ X @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.order_trans
% 0.30/0.46 thf(fact_75_local_Ole__infI2,axiom,
% 0.30/0.46 ! [B: a,X: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ X )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_infI2
% 0.30/0.46 thf(fact_76_local_Ole__infI1,axiom,
% 0.30/0.46 ! [A: a,X: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ X )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_infI1
% 0.30/0.46 thf(fact_77_local_Ole__infI,axiom,
% 0.30/0.46 ! [X: a,A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ X @ A )
% 0.30/0.46 => ( ( less_eq @ X @ B )
% 0.30/0.46 => ( less_eq @ X @ ( inf @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_infI
% 0.30/0.46 thf(fact_78_local_Ole__infE,axiom,
% 0.30/0.46 ! [X: a,A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ X @ ( inf @ A @ B ) )
% 0.30/0.46 => ~ ( ( less_eq @ X @ A )
% 0.30/0.46 => ~ ( less_eq @ X @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_infE
% 0.30/0.46 thf(fact_79_local_Ole__iff__inf,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 = ( ( inf @ X @ Y )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_iff_inf
% 0.30/0.46 thf(fact_80_local_Oinf__unique,axiom,
% 0.30/0.46 ! [F: a > a > a,X: a,Y: a] :
% 0.30/0.46 ( ! [X2: a,Y2: a] : ( less_eq @ ( F @ X2 @ Y2 ) @ X2 )
% 0.30/0.46 => ( ! [X2: a,Y2: a] : ( less_eq @ ( F @ X2 @ Y2 ) @ Y2 )
% 0.30/0.46 => ( ! [X2: a,Y2: a,Z2: a] :
% 0.30/0.46 ( ( less_eq @ X2 @ Y2 )
% 0.30/0.46 => ( ( less_eq @ X2 @ Z2 )
% 0.30/0.46 => ( less_eq @ X2 @ ( F @ Y2 @ Z2 ) ) ) )
% 0.30/0.46 => ( ( inf @ X @ Y )
% 0.30/0.46 = ( F @ X @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_unique
% 0.30/0.46 thf(fact_81_local_Oinf__mono,axiom,
% 0.30/0.46 ! [A: a,C: a,B: a,D: a] :
% 0.30/0.46 ( ( less_eq @ A @ C )
% 0.30/0.46 => ( ( less_eq @ B @ D )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_mono
% 0.30/0.46 thf(fact_82_local_Oinf__le2,axiom,
% 0.30/0.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_le2
% 0.30/0.46 thf(fact_83_local_Oinf__le1,axiom,
% 0.30/0.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_le1
% 0.30/0.46 thf(fact_84_local_Oinf__greatest,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( less_eq @ X @ Z )
% 0.30/0.46 => ( less_eq @ X @ ( inf @ Y @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_greatest
% 0.30/0.46 thf(fact_85_local_Oinf__absorb2,axiom,
% 0.30/0.46 ! [Y: a,X: a] :
% 0.30/0.46 ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( ( inf @ X @ Y )
% 0.30/0.46 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_absorb2
% 0.30/0.46 thf(fact_86_local_Oinf__absorb1,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( inf @ X @ Y )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_absorb1
% 0.30/0.46 thf(fact_87_local_Oinf_Oorder__iff,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 = ( A
% 0.30/0.46 = ( inf @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.order_iff
% 0.30/0.46 thf(fact_88_local_Oinf_OorderI,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( inf @ A @ B ) )
% 0.30/0.46 => ( less_eq @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.orderI
% 0.30/0.46 thf(fact_89_local_Oinf_OorderE,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( A
% 0.30/0.46 = ( inf @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.orderE
% 0.30/0.46 thf(fact_90_local_Oinf_OcoboundedI2,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ C )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.coboundedI2
% 0.30/0.46 thf(fact_91_local_Oinf_OcoboundedI1,axiom,
% 0.30/0.46 ! [A: a,C: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ C )
% 0.30/0.46 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.coboundedI1
% 0.30/0.46 thf(fact_92_local_Oinf_Ocobounded2,axiom,
% 0.30/0.46 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.cobounded2
% 0.30/0.46 thf(fact_93_local_Oinf_Ocobounded1,axiom,
% 0.30/0.46 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.cobounded1
% 0.30/0.46 thf(fact_94_local_Oinf_OboundedI,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( less_eq @ A @ C )
% 0.30/0.46 => ( less_eq @ A @ ( inf @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.boundedI
% 0.30/0.46 thf(fact_95_local_Oinf_OboundedE,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 0.30/0.46 => ~ ( ( less_eq @ A @ B )
% 0.30/0.46 => ~ ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.boundedE
% 0.30/0.46 thf(fact_96_local_Oinf_Oabsorb__iff2,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 = ( ( inf @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.absorb_iff2
% 0.30/0.46 thf(fact_97_local_Oinf_Oabsorb__iff1,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 = ( ( inf @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.absorb_iff1
% 0.30/0.46 thf(fact_98_local_Oinf_Oabsorb2,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( inf @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.absorb2
% 0.30/0.46 thf(fact_99_local_Oinf_Oabsorb1,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( inf @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.absorb1
% 0.30/0.46 thf(fact_100_local_Osup__unique,axiom,
% 0.30/0.46 ! [F: a > a > a,X: a,Y: a] :
% 0.30/0.46 ( ! [X2: a,Y2: a] : ( less_eq @ X2 @ ( F @ X2 @ Y2 ) )
% 0.30/0.46 => ( ! [X2: a,Y2: a] : ( less_eq @ Y2 @ ( F @ X2 @ Y2 ) )
% 0.30/0.46 => ( ! [X2: a,Y2: a,Z2: a] :
% 0.30/0.46 ( ( less_eq @ Y2 @ X2 )
% 0.30/0.46 => ( ( less_eq @ Z2 @ X2 )
% 0.30/0.46 => ( less_eq @ ( F @ Y2 @ Z2 ) @ X2 ) ) )
% 0.30/0.46 => ( ( sup @ X @ Y )
% 0.30/0.46 = ( F @ X @ Y ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_unique
% 0.30/0.46 thf(fact_101_local_Osup__mono,axiom,
% 0.30/0.46 ! [A: a,C: a,B: a,D: a] :
% 0.30/0.46 ( ( less_eq @ A @ C )
% 0.30/0.46 => ( ( less_eq @ B @ D )
% 0.30/0.46 => ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_mono
% 0.30/0.46 thf(fact_102_local_Osup__least,axiom,
% 0.30/0.46 ! [Y: a,X: a,Z: a] :
% 0.30/0.46 ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( ( less_eq @ Z @ X )
% 0.30/0.46 => ( less_eq @ ( sup @ Y @ Z ) @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_least
% 0.30/0.46 thf(fact_103_local_Osup__ge2,axiom,
% 0.30/0.46 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_ge2
% 0.30/0.46 thf(fact_104_local_Osup__ge1,axiom,
% 0.30/0.46 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_ge1
% 0.30/0.46 thf(fact_105_local_Osup__absorb2,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( sup @ X @ Y )
% 0.30/0.46 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_absorb2
% 0.30/0.46 thf(fact_106_local_Osup__absorb1,axiom,
% 0.30/0.46 ! [Y: a,X: a] :
% 0.30/0.46 ( ( less_eq @ Y @ X )
% 0.30/0.46 => ( ( sup @ X @ Y )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_absorb1
% 0.30/0.46 thf(fact_107_local_Osup_Oorder__iff,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 = ( A
% 0.30/0.46 = ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.order_iff
% 0.30/0.46 thf(fact_108_local_Osup_OorderI,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( sup @ A @ B ) )
% 0.30/0.46 => ( less_eq @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.orderI
% 0.30/0.46 thf(fact_109_local_Osup_OorderE,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( A
% 0.30/0.46 = ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.orderE
% 0.30/0.46 thf(fact_110_local_Osup_Omono,axiom,
% 0.30/0.46 ! [C: a,A: a,D: a,B: a] :
% 0.30/0.46 ( ( less_eq @ C @ A )
% 0.30/0.46 => ( ( less_eq @ D @ B )
% 0.30/0.46 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.mono
% 0.30/0.46 thf(fact_111_local_Osup_OcoboundedI2,axiom,
% 0.30/0.46 ! [C: a,B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ C @ B )
% 0.30/0.46 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.coboundedI2
% 0.30/0.46 thf(fact_112_local_Osup_OcoboundedI1,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ C @ A )
% 0.30/0.46 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.coboundedI1
% 0.30/0.46 thf(fact_113_local_Osup_Ocobounded2,axiom,
% 0.30/0.46 ! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.cobounded2
% 0.30/0.46 thf(fact_114_local_Osup_Ocobounded1,axiom,
% 0.30/0.46 ! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.cobounded1
% 0.30/0.46 thf(fact_115_local_Osup_OboundedI,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( less_eq @ C @ A )
% 0.30/0.46 => ( less_eq @ ( sup @ B @ C ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.boundedI
% 0.30/0.46 thf(fact_116_local_Osup_OboundedE,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 0.30/0.46 => ~ ( ( less_eq @ B @ A )
% 0.30/0.46 => ~ ( less_eq @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.boundedE
% 0.30/0.46 thf(fact_117_local_Osup_Oabsorb__iff2,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 = ( ( sup @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.absorb_iff2
% 0.30/0.46 thf(fact_118_local_Osup_Oabsorb__iff1,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 = ( ( sup @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.absorb_iff1
% 0.30/0.46 thf(fact_119_local_Osup_Oabsorb2,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( sup @ A @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.absorb2
% 0.30/0.46 thf(fact_120_local_Osup_Oabsorb1,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ B @ A )
% 0.30/0.46 => ( ( sup @ A @ B )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.absorb1
% 0.30/0.46 thf(fact_121_local_Ole__supI2,axiom,
% 0.30/0.46 ! [X: a,B: a,A: a] :
% 0.30/0.46 ( ( less_eq @ X @ B )
% 0.30/0.46 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_supI2
% 0.30/0.46 thf(fact_122_local_Ole__supI1,axiom,
% 0.30/0.46 ! [X: a,A: a,B: a] :
% 0.30/0.46 ( ( less_eq @ X @ A )
% 0.30/0.46 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_supI1
% 0.30/0.46 thf(fact_123_local_Ole__supI,axiom,
% 0.30/0.46 ! [A: a,X: a,B: a] :
% 0.30/0.46 ( ( less_eq @ A @ X )
% 0.30/0.46 => ( ( less_eq @ B @ X )
% 0.30/0.46 => ( less_eq @ ( sup @ A @ B ) @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_supI
% 0.30/0.46 thf(fact_124_local_Ole__supE,axiom,
% 0.30/0.46 ! [A: a,B: a,X: a] :
% 0.30/0.46 ( ( less_eq @ ( sup @ A @ B ) @ X )
% 0.30/0.46 => ~ ( ( less_eq @ A @ X )
% 0.30/0.46 => ~ ( less_eq @ B @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_supE
% 0.30/0.46 thf(fact_125_local_Ole__iff__sup,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 = ( ( sup @ X @ Y )
% 0.30/0.46 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_iff_sup
% 0.30/0.46 thf(fact_126_local_Omodular,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 0.30/0.46 = ( inf @ Y @ ( sup @ X @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.modular
% 0.30/0.46 thf(fact_127_local_Odistrib__sup__le,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.distrib_sup_le
% 0.30/0.46 thf(fact_128_local_Odistrib__inf__le,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) @ ( inf @ X @ ( sup @ Y @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.distrib_inf_le
% 0.30/0.46 thf(fact_129_local_Oincomp__def,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( modula1727524044comp_a @ less_eq @ X @ Y )
% 0.30/0.46 = ( ~ ( less_eq @ X @ Y )
% 0.30/0.46 & ~ ( less_eq @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.incomp_def
% 0.30/0.46 thf(fact_130_local_Oc__a,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.c_a
% 0.30/0.46 thf(fact_131_local_Oorder_Orefl,axiom,
% 0.30/0.46 ! [A: a] : ( less_eq @ A @ A ) ).
% 0.30/0.46
% 0.30/0.46 % local.order.refl
% 0.30/0.46 thf(fact_132_local_Oorder__refl,axiom,
% 0.30/0.46 ! [X: a] : ( less_eq @ X @ X ) ).
% 0.30/0.46
% 0.30/0.46 % local.order_refl
% 0.30/0.46 thf(fact_133_local_OGreatestI2__order,axiom,
% 0.30/0.46 ! [P: a > $o,X: a,Q: a > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( less_eq @ Y2 @ X ) )
% 0.30/0.46 => ( ! [X2: a] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( ! [Y5: a] :
% 0.30/0.46 ( ( P @ Y5 )
% 0.30/0.46 => ( less_eq @ Y5 @ X2 ) )
% 0.30/0.46 => ( Q @ X2 ) ) )
% 0.30/0.46 => ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.GreatestI2_order
% 0.30/0.46 thf(fact_134_local_OGreatest__equality,axiom,
% 0.30/0.46 ! [P: a > $o,X: a] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( less_eq @ Y2 @ X ) )
% 0.30/0.46 => ( ( greatest_a @ less_eq @ P )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Greatest_equality
% 0.30/0.46 thf(fact_135_local_Omax__def,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( max_a @ less_eq @ A @ B )
% 0.30/0.46 = B ) )
% 0.30/0.46 & ( ~ ( less_eq @ A @ B )
% 0.30/0.46 => ( ( max_a @ less_eq @ A @ B )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.max_def
% 0.30/0.46 thf(fact_136_local_Omin__def,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ( less_eq @ A @ B )
% 0.30/0.46 => ( ( min_a @ less_eq @ A @ B )
% 0.30/0.46 = A ) )
% 0.30/0.46 & ( ~ ( less_eq @ A @ B )
% 0.30/0.46 => ( ( min_a @ less_eq @ A @ B )
% 0.30/0.46 = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.min_def
% 0.30/0.46 thf(fact_137_a__def__equiv,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( inf @ ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % a_def_equiv
% 0.30/0.46 thf(fact_138_c__def__equiv,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( inf @ ( sup @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % c_def_equiv
% 0.30/0.46 thf(fact_139_b__def__equiv,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 0.30/0.46 = ( inf @ ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % b_def_equiv
% 0.30/0.46 thf(fact_140_c__meet__a__eq__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( inf @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % c_meet_a_eq_d
% 0.30/0.46 thf(fact_141_a__meet__b__eq__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % a_meet_b_eq_d
% 0.30/0.46 thf(fact_142_b__meet__c__eq__d,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 => ( ( inf @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) )
% 0.30/0.46 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % b_meet_c_eq_d
% 0.30/0.46 thf(fact_143_local_Ole__inf__iff,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ( less_eq @ X @ ( inf @ Y @ Z ) )
% 0.30/0.46 = ( ( less_eq @ X @ Y )
% 0.30/0.46 & ( less_eq @ X @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_inf_iff
% 0.30/0.46 thf(fact_144_local_Oinf_Obounded__iff,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 0.30/0.46 = ( ( less_eq @ A @ B )
% 0.30/0.46 & ( less_eq @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf.bounded_iff
% 0.30/0.46 thf(fact_145_local_Osup_Obounded__iff,axiom,
% 0.30/0.46 ! [B: a,C: a,A: a] :
% 0.30/0.46 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 0.30/0.46 = ( ( less_eq @ B @ A )
% 0.30/0.46 & ( less_eq @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup.bounded_iff
% 0.30/0.46 thf(fact_146_local_Ole__sup__iff,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z: a] :
% 0.30/0.46 ( ( less_eq @ ( sup @ X @ Y ) @ Z )
% 0.30/0.46 = ( ( less_eq @ X @ Z )
% 0.30/0.46 & ( less_eq @ Y @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.le_sup_iff
% 0.30/0.46 thf(fact_147_local_OLeast1I,axiom,
% 0.30/0.46 ! [P: a > $o] :
% 0.30/0.46 ( ? [X4: a] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 & ! [Y2: a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( less_eq @ X4 @ Y2 ) )
% 0.30/0.46 & ! [Y2: a] :
% 0.30/0.46 ( ( ( P @ Y2 )
% 0.30/0.46 & ! [Ya: a] :
% 0.30/0.46 ( ( P @ Ya )
% 0.30/0.46 => ( less_eq @ Y2 @ Ya ) ) )
% 0.30/0.46 => ( Y2 = X4 ) ) )
% 0.30/0.46 => ( P @ ( least_a @ less_eq @ P ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Least1I
% 0.30/0.46 thf(fact_148_local_OLeast1__le,axiom,
% 0.30/0.46 ! [P: a > $o,Z: a] :
% 0.30/0.46 ( ? [X4: a] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 & ! [Y2: a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( less_eq @ X4 @ Y2 ) )
% 0.30/0.46 & ! [Y2: a] :
% 0.30/0.46 ( ( ( P @ Y2 )
% 0.30/0.46 & ! [Ya: a] :
% 0.30/0.46 ( ( P @ Ya )
% 0.30/0.46 => ( less_eq @ Y2 @ Ya ) ) )
% 0.30/0.46 => ( Y2 = X4 ) ) )
% 0.30/0.46 => ( ( P @ Z )
% 0.30/0.46 => ( less_eq @ ( least_a @ less_eq @ P ) @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Least1_le
% 0.30/0.46 thf(fact_149_local_OLeastI2__order,axiom,
% 0.30/0.46 ! [P: a > $o,X: a,Q: a > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( less_eq @ X @ Y2 ) )
% 0.30/0.46 => ( ! [X2: a] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( ! [Y5: a] :
% 0.30/0.46 ( ( P @ Y5 )
% 0.30/0.46 => ( less_eq @ X2 @ Y5 ) )
% 0.30/0.46 => ( Q @ X2 ) ) )
% 0.30/0.46 => ( Q @ ( least_a @ less_eq @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.LeastI2_order
% 0.30/0.46 thf(fact_150_local_OLeast__equality,axiom,
% 0.30/0.46 ! [P: a > $o,X: a] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( less_eq @ X @ Y2 ) )
% 0.30/0.46 => ( ( least_a @ less_eq @ P )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Least_equality
% 0.30/0.46 thf(fact_151_lattice_Oc__aux_Ocong,axiom,
% 0.30/0.46 modula581031071_aux_a = modula581031071_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.c_aux.cong
% 0.30/0.46 thf(fact_152_lattice_Ob__aux_Ocong,axiom,
% 0.30/0.46 modula1373251614_aux_a = modula1373251614_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.b_aux.cong
% 0.30/0.46 thf(fact_153_lattice_Oa__aux_Ocong,axiom,
% 0.30/0.46 modula17988509_aux_a = modula17988509_aux_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.a_aux.cong
% 0.30/0.46 thf(fact_154_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ( abel_semigroup_a @ F )
% 0.30/0.46 => ( semigroup_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % abel_semigroup.axioms(1)
% 0.30/0.46 thf(fact_155_semilattice__set__def,axiom,
% 0.30/0.46 lattic1885654924_set_a = semilattice_a ).
% 0.30/0.46
% 0.30/0.46 % semilattice_set_def
% 0.30/0.46 thf(fact_156_semilattice__set_Ointro,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( lattic1885654924_set_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_set.intro
% 0.30/0.46 thf(fact_157_semilattice__set_Oaxioms,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ( lattic1885654924_set_a @ F )
% 0.30/0.46 => ( semilattice_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice_set.axioms
% 0.30/0.46 thf(fact_158_semilattice_Oaxioms_I1_J,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( abel_semigroup_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice.axioms(1)
% 0.30/0.46 thf(fact_159_local_Obdd__above__def,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( condit1627435690bove_a @ less_eq @ A2 )
% 0.30/0.46 = ( ? [M: a] :
% 0.30/0.46 ! [X3: a] :
% 0.30/0.46 ( ( member_a @ X3 @ A2 )
% 0.30/0.46 => ( less_eq @ X3 @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_def
% 0.30/0.46 thf(fact_160_local_Obdd__below__def,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( condit1001553558elow_a @ less_eq @ A2 )
% 0.30/0.46 = ( ? [M2: a] :
% 0.30/0.46 ! [X3: a] :
% 0.30/0.46 ( ( member_a @ X3 @ A2 )
% 0.30/0.46 => ( less_eq @ M2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_def
% 0.30/0.46 thf(fact_161_local_Obdd__belowI,axiom,
% 0.30/0.46 ! [A2: set_a,M3: a] :
% 0.30/0.46 ( ! [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A2 )
% 0.30/0.46 => ( less_eq @ M3 @ X2 ) )
% 0.30/0.46 => ( condit1001553558elow_a @ less_eq @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_belowI
% 0.30/0.46 thf(fact_162_local_Obdd__aboveI,axiom,
% 0.30/0.46 ! [A2: set_a,M4: a] :
% 0.30/0.46 ( ! [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A2 )
% 0.30/0.46 => ( less_eq @ X2 @ M4 ) )
% 0.30/0.46 => ( condit1627435690bove_a @ less_eq @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_aboveI
% 0.30/0.46 thf(fact_163_lattice_Oincomp_Ocong,axiom,
% 0.30/0.46 modula1727524044comp_a = modula1727524044comp_a ).
% 0.30/0.46
% 0.30/0.46 % lattice.incomp.cong
% 0.30/0.46 thf(fact_164_abel__semigroup_Oleft__commute,axiom,
% 0.30/0.46 ! [F: a > a > a,B: a,A: a,C: a] :
% 0.30/0.46 ( ( abel_semigroup_a @ F )
% 0.30/0.46 => ( ( F @ B @ ( F @ A @ C ) )
% 0.30/0.46 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % abel_semigroup.left_commute
% 0.30/0.46 thf(fact_165_semilattice_Oright__idem,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a,B: a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( ( F @ ( F @ A @ B ) @ B )
% 0.30/0.46 = ( F @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice.right_idem
% 0.30/0.46 thf(fact_166_semilattice_Oleft__idem,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a,B: a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( ( F @ A @ ( F @ A @ B ) )
% 0.30/0.46 = ( F @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice.left_idem
% 0.30/0.46 thf(fact_167_abel__semigroup_Ocommute,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a,B: a] :
% 0.30/0.46 ( ( abel_semigroup_a @ F )
% 0.30/0.46 => ( ( F @ A @ B )
% 0.30/0.46 = ( F @ B @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % abel_semigroup.commute
% 0.30/0.46 thf(fact_168_semilattice_Oidem,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a] :
% 0.30/0.46 ( ( semilattice_a @ F )
% 0.30/0.46 => ( ( F @ A @ A )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % semilattice.idem
% 0.30/0.46 thf(fact_169_semigroup_Ointro,axiom,
% 0.30/0.46 ! [F: a > a > a] :
% 0.30/0.46 ( ! [A4: a,B3: a,C2: a] :
% 0.30/0.46 ( ( F @ ( F @ A4 @ B3 ) @ C2 )
% 0.30/0.46 = ( F @ A4 @ ( F @ B3 @ C2 ) ) )
% 0.30/0.46 => ( semigroup_a @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % semigroup.intro
% 0.30/0.46 thf(fact_170_semigroup_Oassoc,axiom,
% 0.30/0.46 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.30/0.46 ( ( semigroup_a @ F )
% 0.30/0.46 => ( ( F @ ( F @ A @ B ) @ C )
% 0.30/0.46 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semigroup.assoc
% 0.30/0.46 thf(fact_171_semigroup__def,axiom,
% 0.30/0.46 ( semigroup_a
% 0.30/0.46 = ( ^ [F2: a > a > a] :
% 0.30/0.46 ! [A3: a,B2: a,C3: a] :
% 0.30/0.46 ( ( F2 @ ( F2 @ A3 @ B2 ) @ C3 )
% 0.30/0.46 = ( F2 @ A3 @ ( F2 @ B2 @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % semigroup_def
% 0.30/0.46 thf(fact_172_local_Obdd__below__mono,axiom,
% 0.30/0.46 ! [B4: set_a,A2: set_a] :
% 0.30/0.46 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.46 => ( condit1001553558elow_a @ less_eq @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_mono
% 0.30/0.46 thf(fact_173_local_Obdd__above__mono,axiom,
% 0.30/0.46 ! [B4: set_a,A2: set_a] :
% 0.30/0.46 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.46 => ( condit1627435690bove_a @ less_eq @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_mono
% 0.30/0.46 thf(fact_174_local_Obdd__below__finite,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( condit1001553558elow_a @ less_eq @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_below_finite
% 0.30/0.46 thf(fact_175_local_Ofinite__has__maximal2,axiom,
% 0.30/0.46 ! [A2: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( member_a @ A @ A2 )
% 0.30/0.46 => ? [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A2 )
% 0.30/0.46 & ( less_eq @ A @ X2 )
% 0.30/0.46 & ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ A2 )
% 0.30/0.46 => ( ( less_eq @ X2 @ Xa )
% 0.30/0.46 => ( X2 = Xa ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.finite_has_maximal2
% 0.30/0.46 thf(fact_176_local_Ofinite__has__minimal2,axiom,
% 0.30/0.46 ! [A2: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( member_a @ A @ A2 )
% 0.30/0.46 => ? [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A2 )
% 0.30/0.46 & ( less_eq @ X2 @ A )
% 0.30/0.46 & ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ A2 )
% 0.30/0.46 => ( ( less_eq @ Xa @ X2 )
% 0.30/0.46 => ( X2 = Xa ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.finite_has_minimal2
% 0.30/0.46 thf(fact_177_local_Obdd__above__finite,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( condit1627435690bove_a @ less_eq @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.bdd_above_finite
% 0.30/0.46 thf(fact_178_local_OantimonoD,axiom,
% 0.30/0.46 ! [F: a > set_a,X: a,Y: a] :
% 0.30/0.46 ( ( antimono_a_set_a @ less_eq @ F )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antimonoD
% 0.30/0.46 thf(fact_179_local_OantimonoE,axiom,
% 0.30/0.46 ! [F: a > set_a,X: a,Y: a] :
% 0.30/0.46 ( ( antimono_a_set_a @ less_eq @ F )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antimonoE
% 0.30/0.46 thf(fact_180_local_OantimonoI,axiom,
% 0.30/0.46 ! [F: a > set_a] :
% 0.30/0.46 ( ! [X2: a,Y2: a] :
% 0.30/0.46 ( ( less_eq @ X2 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ Y2 ) @ ( F @ X2 ) ) )
% 0.30/0.46 => ( antimono_a_set_a @ less_eq @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antimonoI
% 0.30/0.46 thf(fact_181_local_Oantimono__def,axiom,
% 0.30/0.46 ! [F: a > set_a] :
% 0.30/0.46 ( ( antimono_a_set_a @ less_eq @ F )
% 0.30/0.46 = ( ! [X3: a,Y4: a] :
% 0.30/0.46 ( ( less_eq @ X3 @ Y4 )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ Y4 ) @ ( F @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.antimono_def
% 0.30/0.46 thf(fact_182_local_Omono__def,axiom,
% 0.30/0.46 ! [F: a > set_a] :
% 0.30/0.46 ( ( mono_a_set_a @ less_eq @ F )
% 0.30/0.46 = ( ! [X3: a,Y4: a] :
% 0.30/0.46 ( ( less_eq @ X3 @ Y4 )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.mono_def
% 0.30/0.46 thf(fact_183_local_OmonoI,axiom,
% 0.30/0.46 ! [F: a > set_a] :
% 0.30/0.46 ( ! [X2: a,Y2: a] :
% 0.30/0.46 ( ( less_eq @ X2 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( mono_a_set_a @ less_eq @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.monoI
% 0.30/0.46 thf(fact_184_local_OmonoE,axiom,
% 0.30/0.46 ! [F: a > set_a,X: a,Y: a] :
% 0.30/0.46 ( ( mono_a_set_a @ less_eq @ F )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.monoE
% 0.30/0.46 thf(fact_185_local_OmonoD,axiom,
% 0.30/0.46 ! [F: a > set_a,X: a,Y: a] :
% 0.30/0.46 ( ( mono_a_set_a @ less_eq @ F )
% 0.30/0.46 => ( ( less_eq @ X @ Y )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.monoD
% 0.30/0.46 thf(fact_186_local_OSup__fin_OcoboundedI,axiom,
% 0.30/0.46 ! [A2: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( member_a @ A @ A2 )
% 0.30/0.46 => ( less_eq @ A @ ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.coboundedI
% 0.30/0.46 thf(fact_187_local_OInf__fin_OcoboundedI,axiom,
% 0.30/0.46 ! [A2: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( member_a @ A @ A2 )
% 0.30/0.46 => ( less_eq @ ( lattic247676691_fin_a @ inf @ A2 ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.coboundedI
% 0.30/0.46 thf(fact_188_local_OSup__fin_Oin__idem,axiom,
% 0.30/0.46 ! [A2: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( member_a @ X @ A2 )
% 0.30/0.46 => ( ( sup @ X @ ( lattic1781219155_fin_a @ sup @ A2 ) )
% 0.30/0.46 = ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.in_idem
% 0.30/0.46 thf(fact_189_local_OInf__fin_Oin__idem,axiom,
% 0.30/0.46 ! [A2: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( member_a @ X @ A2 )
% 0.30/0.46 => ( ( inf @ X @ ( lattic247676691_fin_a @ inf @ A2 ) )
% 0.30/0.46 = ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.in_idem
% 0.30/0.46 thf(fact_190_local_Osup__Inf__absorb,axiom,
% 0.30/0.46 ! [A2: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( member_a @ A @ A2 )
% 0.30/0.46 => ( ( sup @ ( lattic247676691_fin_a @ inf @ A2 ) @ A )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.sup_Inf_absorb
% 0.30/0.46 thf(fact_191_local_Oinf__Sup__absorb,axiom,
% 0.30/0.46 ! [A2: set_a,A: a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( member_a @ A @ A2 )
% 0.30/0.46 => ( ( inf @ A @ ( lattic1781219155_fin_a @ sup @ A2 ) )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.inf_Sup_absorb
% 0.30/0.46 thf(fact_192_semilattice__inf_OInf__fin_Ocong,axiom,
% 0.30/0.46 lattic247676691_fin_a = lattic247676691_fin_a ).
% 0.30/0.46
% 0.30/0.46 % semilattice_inf.Inf_fin.cong
% 0.30/0.46 thf(fact_193_semilattice__sup_OSup__fin_Ocong,axiom,
% 0.30/0.46 lattic1781219155_fin_a = lattic1781219155_fin_a ).
% 0.30/0.46
% 0.30/0.46 % semilattice_sup.Sup_fin.cong
% 0.30/0.46 thf(fact_194_local_OInf__fin__le__Sup__fin,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( A2 != bot_bot_set_a )
% 0.30/0.46 => ( less_eq @ ( lattic247676691_fin_a @ inf @ A2 ) @ ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin_le_Sup_fin
% 0.30/0.46 thf(fact_195_local_OSup__fin_Osubset__imp,axiom,
% 0.30/0.46 ! [A2: set_a,B4: set_a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.46 => ( ( A2 != bot_bot_set_a )
% 0.30/0.46 => ( ( finite_finite_a @ B4 )
% 0.30/0.46 => ( less_eq @ ( lattic1781219155_fin_a @ sup @ A2 ) @ ( lattic1781219155_fin_a @ sup @ B4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.subset_imp
% 0.30/0.46 thf(fact_196_local_Ofinite__has__minimal,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( A2 != bot_bot_set_a )
% 0.30/0.46 => ? [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A2 )
% 0.30/0.46 & ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ A2 )
% 0.30/0.46 => ( ( less_eq @ Xa @ X2 )
% 0.30/0.46 => ( X2 = Xa ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.finite_has_minimal
% 0.30/0.46 thf(fact_197_local_Ofinite__has__maximal,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( A2 != bot_bot_set_a )
% 0.30/0.46 => ? [X2: a] :
% 0.30/0.46 ( ( member_a @ X2 @ A2 )
% 0.30/0.46 & ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ A2 )
% 0.30/0.46 => ( ( less_eq @ X2 @ Xa )
% 0.30/0.46 => ( X2 = Xa ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.finite_has_maximal
% 0.30/0.46 thf(fact_198_local_OInf__fin_Osubset,axiom,
% 0.30/0.46 ! [A2: set_a,B4: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( B4 != bot_bot_set_a )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ B4 @ A2 )
% 0.30/0.46 => ( ( inf @ ( lattic247676691_fin_a @ inf @ B4 ) @ ( lattic247676691_fin_a @ inf @ A2 ) )
% 0.30/0.46 = ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Inf_fin.subset
% 0.30/0.46 thf(fact_199_local_OSup__fin_Osubset,axiom,
% 0.30/0.46 ! [A2: set_a,B4: set_a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( B4 != bot_bot_set_a )
% 0.30/0.46 => ( ( ord_less_eq_set_a @ B4 @ A2 )
% 0.30/0.46 => ( ( sup @ ( lattic1781219155_fin_a @ sup @ B4 ) @ ( lattic1781219155_fin_a @ sup @ A2 ) )
% 0.30/0.46 = ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % local.Sup_fin.subset
% 0.30/0.46 thf(fact_200_local_OInf__fin_Obounded__iff,axiom,
% 0.30/0.46 ! [A2: set_a,X: a] :
% 0.30/0.46 ( ( finite_finite_a @ A2 )
% 0.30/0.46 => ( ( A2 != bot_bot_set_a )
% 0.30/0.46 => ( ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A2 ) )
% 0.30/0.47 = ( ! [X3: a] :
% 0.30/0.47 ( ( member_a @ X3 @ A2 )
% 0.30/0.47 => ( less_eq @ X @ X3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Inf_fin.bounded_iff
% 0.30/0.47 thf(fact_201_local_OInf__fin_OboundedI,axiom,
% 0.30/0.47 ! [A2: set_a,X: a] :
% 0.30/0.47 ( ( finite_finite_a @ A2 )
% 0.30/0.47 => ( ( A2 != bot_bot_set_a )
% 0.30/0.47 => ( ! [A4: a] :
% 0.30/0.47 ( ( member_a @ A4 @ A2 )
% 0.30/0.47 => ( less_eq @ X @ A4 ) )
% 0.30/0.47 => ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Inf_fin.boundedI
% 0.30/0.47 thf(fact_202_local_OInf__fin_OboundedE,axiom,
% 0.30/0.47 ! [A2: set_a,X: a] :
% 0.30/0.47 ( ( finite_finite_a @ A2 )
% 0.30/0.47 => ( ( A2 != bot_bot_set_a )
% 0.30/0.47 => ( ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A2 ) )
% 0.30/0.47 => ! [A5: a] :
% 0.30/0.47 ( ( member_a @ A5 @ A2 )
% 0.30/0.47 => ( less_eq @ X @ A5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Inf_fin.boundedE
% 0.30/0.47 thf(fact_203_local_OSup__fin_Obounded__iff,axiom,
% 0.30/0.47 ! [A2: set_a,X: a] :
% 0.30/0.47 ( ( finite_finite_a @ A2 )
% 0.30/0.47 => ( ( A2 != bot_bot_set_a )
% 0.30/0.47 => ( ( less_eq @ ( lattic1781219155_fin_a @ sup @ A2 ) @ X )
% 0.30/0.47 = ( ! [X3: a] :
% 0.30/0.47 ( ( member_a @ X3 @ A2 )
% 0.30/0.47 => ( less_eq @ X3 @ X ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Sup_fin.bounded_iff
% 0.30/0.47 thf(fact_204_local_OSup__fin_OboundedI,axiom,
% 0.30/0.47 ! [A2: set_a,X: a] :
% 0.30/0.47 ( ( finite_finite_a @ A2 )
% 0.30/0.47 => ( ( A2 != bot_bot_set_a )
% 0.30/0.47 => ( ! [A4: a] :
% 0.30/0.47 ( ( member_a @ A4 @ A2 )
% 0.30/0.47 => ( less_eq @ A4 @ X ) )
% 0.30/0.47 => ( less_eq @ ( lattic1781219155_fin_a @ sup @ A2 ) @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Sup_fin.boundedI
% 0.30/0.47 thf(fact_205_local_OSup__fin_OboundedE,axiom,
% 0.30/0.47 ! [A2: set_a,X: a] :
% 0.30/0.47 ( ( finite_finite_a @ A2 )
% 0.30/0.47 => ( ( A2 != bot_bot_set_a )
% 0.30/0.47 => ( ( less_eq @ ( lattic1781219155_fin_a @ sup @ A2 ) @ X )
% 0.30/0.47 => ! [A5: a] :
% 0.30/0.47 ( ( member_a @ A5 @ A2 )
% 0.30/0.47 => ( less_eq @ A5 @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Sup_fin.boundedE
% 0.30/0.47 thf(fact_206_local_OInf__fin_Osubset__imp,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.47 => ( ( A2 != bot_bot_set_a )
% 0.30/0.47 => ( ( finite_finite_a @ B4 )
% 0.30/0.47 => ( less_eq @ ( lattic247676691_fin_a @ inf @ B4 ) @ ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Inf_fin.subset_imp
% 0.30/0.47 thf(fact_207_local_Obdd__above__empty,axiom,
% 0.30/0.47 condit1627435690bove_a @ less_eq @ bot_bot_set_a ).
% 0.30/0.47
% 0.30/0.47 % local.bdd_above_empty
% 0.30/0.47 thf(fact_208_local_Obdd__below__empty,axiom,
% 0.30/0.47 condit1001553558elow_a @ less_eq @ bot_bot_set_a ).
% 0.30/0.47
% 0.30/0.47 % local.bdd_below_empty
% 0.30/0.47 thf(fact_209_local_Onot__empty__eq__Iic__eq__empty,axiom,
% 0.30/0.47 ! [H: a] :
% 0.30/0.47 ( bot_bot_set_a
% 0.30/0.47 != ( set_atMost_a @ less_eq @ H ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.not_empty_eq_Iic_eq_empty
% 0.30/0.47 thf(fact_210_local_Onot__empty__eq__Ici__eq__empty,axiom,
% 0.30/0.47 ! [L: a] :
% 0.30/0.47 ( bot_bot_set_a
% 0.30/0.47 != ( set_atLeast_a @ less_eq @ L ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.not_empty_eq_Ici_eq_empty
% 0.30/0.47 thf(fact_211_local_OatLeast__iff,axiom,
% 0.30/0.47 ! [I: a,K: a] :
% 0.30/0.47 ( ( member_a @ I @ ( set_atLeast_a @ less_eq @ K ) )
% 0.30/0.47 = ( less_eq @ K @ I ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.atLeast_iff
% 0.30/0.47 thf(fact_212_local_OatMost__iff,axiom,
% 0.30/0.47 ! [I: a,K: a] :
% 0.30/0.47 ( ( member_a @ I @ ( set_atMost_a @ less_eq @ K ) )
% 0.30/0.47 = ( less_eq @ I @ K ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.atMost_iff
% 0.30/0.47 thf(fact_213_local_Obdd__below__Ici,axiom,
% 0.30/0.47 ! [A: a] : ( condit1001553558elow_a @ less_eq @ ( set_atLeast_a @ less_eq @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.bdd_below_Ici
% 0.30/0.47 thf(fact_214_local_Obdd__above__Iic,axiom,
% 0.30/0.47 ! [B: a] : ( condit1627435690bove_a @ less_eq @ ( set_atMost_a @ less_eq @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.bdd_above_Iic
% 0.30/0.47 thf(fact_215_empty__subsetI,axiom,
% 0.30/0.47 ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) ).
% 0.30/0.47
% 0.30/0.47 % empty_subsetI
% 0.30/0.47 thf(fact_216_subset__empty,axiom,
% 0.30/0.47 ! [A2: set_a] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
% 0.30/0.47 = ( A2 = bot_bot_set_a ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_empty
% 0.30/0.47 thf(fact_217_empty__iff,axiom,
% 0.30/0.47 ! [C: a] :
% 0.30/0.47 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 0.30/0.47
% 0.30/0.47 % empty_iff
% 0.30/0.47 thf(fact_218_all__not__in__conv,axiom,
% 0.30/0.47 ! [A2: set_a] :
% 0.30/0.47 ( ( ! [X3: a] :
% 0.30/0.47 ~ ( member_a @ X3 @ A2 ) )
% 0.30/0.47 = ( A2 = bot_bot_set_a ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_not_in_conv
% 0.30/0.47 thf(fact_219_Collect__empty__eq,axiom,
% 0.30/0.47 ! [P: a > $o] :
% 0.30/0.47 ( ( ( collect_a @ P )
% 0.30/0.47 = bot_bot_set_a )
% 0.30/0.47 = ( ! [X3: a] :
% 0.30/0.47 ~ ( P @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_empty_eq
% 0.30/0.47 thf(fact_220_empty__Collect__eq,axiom,
% 0.30/0.47 ! [P: a > $o] :
% 0.30/0.47 ( ( bot_bot_set_a
% 0.30/0.47 = ( collect_a @ P ) )
% 0.30/0.47 = ( ! [X3: a] :
% 0.30/0.47 ~ ( P @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_Collect_eq
% 0.30/0.47 thf(fact_221_subsetI,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a] :
% 0.30/0.47 ( ! [X2: a] :
% 0.30/0.47 ( ( member_a @ X2 @ A2 )
% 0.30/0.47 => ( member_a @ X2 @ B4 ) )
% 0.30/0.47 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % subsetI
% 0.30/0.47 thf(fact_222_subset__antisym,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.47 => ( ( ord_less_eq_set_a @ B4 @ A2 )
% 0.30/0.47 => ( A2 = B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_antisym
% 0.30/0.47 thf(fact_223_emptyE,axiom,
% 0.30/0.47 ! [A: a] :
% 0.30/0.47 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 0.30/0.47
% 0.30/0.47 % emptyE
% 0.30/0.47 thf(fact_224_equals0D,axiom,
% 0.30/0.47 ! [A2: set_a,A: a] :
% 0.30/0.47 ( ( A2 = bot_bot_set_a )
% 0.30/0.47 => ~ ( member_a @ A @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equals0D
% 0.30/0.47 thf(fact_225_equals0I,axiom,
% 0.30/0.47 ! [A2: set_a] :
% 0.30/0.47 ( ! [Y2: a] :
% 0.30/0.47 ~ ( member_a @ Y2 @ A2 )
% 0.30/0.47 => ( A2 = bot_bot_set_a ) ) ).
% 0.30/0.47
% 0.30/0.47 % equals0I
% 0.30/0.47 thf(fact_226_ex__in__conv,axiom,
% 0.30/0.47 ! [A2: set_a] :
% 0.30/0.47 ( ( ? [X3: a] : ( member_a @ X3 @ A2 ) )
% 0.30/0.47 = ( A2 != bot_bot_set_a ) ) ).
% 0.30/0.47
% 0.30/0.47 % ex_in_conv
% 0.30/0.47 thf(fact_227_in__mono,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a,X: a] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.47 => ( ( member_a @ X @ A2 )
% 0.30/0.47 => ( member_a @ X @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_mono
% 0.30/0.47 thf(fact_228_subsetD,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a,C: a] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.47 => ( ( member_a @ C @ A2 )
% 0.30/0.47 => ( member_a @ C @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subsetD
% 0.30/0.47 thf(fact_229_equalityE,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a] :
% 0.30/0.47 ( ( A2 = B4 )
% 0.30/0.47 => ~ ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.47 => ~ ( ord_less_eq_set_a @ B4 @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % equalityE
% 0.30/0.47 thf(fact_230_subset__eq,axiom,
% 0.30/0.47 ( ord_less_eq_set_a
% 0.30/0.47 = ( ^ [A6: set_a,B5: set_a] :
% 0.30/0.47 ! [X3: a] :
% 0.30/0.47 ( ( member_a @ X3 @ A6 )
% 0.30/0.47 => ( member_a @ X3 @ B5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_eq
% 0.30/0.47 thf(fact_231_equalityD1,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a] :
% 0.30/0.47 ( ( A2 = B4 )
% 0.30/0.47 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equalityD1
% 0.30/0.47 thf(fact_232_equalityD2,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a] :
% 0.30/0.47 ( ( A2 = B4 )
% 0.30/0.47 => ( ord_less_eq_set_a @ B4 @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equalityD2
% 0.30/0.47 thf(fact_233_subset__iff,axiom,
% 0.30/0.47 ( ord_less_eq_set_a
% 0.30/0.47 = ( ^ [A6: set_a,B5: set_a] :
% 0.30/0.47 ! [T: a] :
% 0.30/0.47 ( ( member_a @ T @ A6 )
% 0.30/0.47 => ( member_a @ T @ B5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_iff
% 0.30/0.47 thf(fact_234_subset__refl,axiom,
% 0.30/0.47 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 0.30/0.47
% 0.30/0.47 % subset_refl
% 0.30/0.47 thf(fact_235_Collect__mono,axiom,
% 0.30/0.47 ! [P: a > $o,Q: a > $o] :
% 0.30/0.47 ( ! [X2: a] :
% 0.30/0.47 ( ( P @ X2 )
% 0.30/0.47 => ( Q @ X2 ) )
% 0.30/0.47 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mono
% 0.30/0.47 thf(fact_236_subset__trans,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a,C4: set_a] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.47 => ( ( ord_less_eq_set_a @ B4 @ C4 )
% 0.30/0.47 => ( ord_less_eq_set_a @ A2 @ C4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_trans
% 0.30/0.47 thf(fact_237_set__eq__subset,axiom,
% 0.30/0.47 ( ( ^ [Y3: set_a,Z3: set_a] : ( Y3 = Z3 ) )
% 0.30/0.47 = ( ^ [A6: set_a,B5: set_a] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ A6 @ B5 )
% 0.30/0.47 & ( ord_less_eq_set_a @ B5 @ A6 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % set_eq_subset
% 0.30/0.47 thf(fact_238_Collect__mono__iff,axiom,
% 0.30/0.47 ! [P: a > $o,Q: a > $o] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.30/0.47 = ( ! [X3: a] :
% 0.30/0.47 ( ( P @ X3 )
% 0.30/0.47 => ( Q @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mono_iff
% 0.30/0.47 thf(fact_239_local_Omono__inf,axiom,
% 0.30/0.47 ! [F: a > set_a,A2: a,B4: a] :
% 0.30/0.47 ( ( mono_a_set_a @ less_eq @ F )
% 0.30/0.47 => ( ord_less_eq_set_a @ ( F @ ( inf @ A2 @ B4 ) ) @ ( inf_inf_set_a @ ( F @ A2 ) @ ( F @ B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.mono_inf
% 0.30/0.47 thf(fact_240_local_OSup__fin_Oinsert__not__elem,axiom,
% 0.30/0.47 ! [A2: set_a,X: a] :
% 0.30/0.47 ( ( finite_finite_a @ A2 )
% 0.30/0.47 => ( ~ ( member_a @ X @ A2 )
% 0.30/0.47 => ( ( A2 != bot_bot_set_a )
% 0.30/0.47 => ( ( lattic1781219155_fin_a @ sup @ ( insert_a @ X @ A2 ) )
% 0.30/0.47 = ( sup @ X @ ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Sup_fin.insert_not_elem
% 0.30/0.47 thf(fact_241_local_Obdd__below__Int2,axiom,
% 0.30/0.47 ! [B4: set_a,A2: set_a] :
% 0.30/0.47 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 0.30/0.47 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.bdd_below_Int2
% 0.30/0.47 thf(fact_242_local_Obdd__below__Int1,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a] :
% 0.30/0.47 ( ( condit1001553558elow_a @ less_eq @ A2 )
% 0.30/0.47 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.bdd_below_Int1
% 0.30/0.47 thf(fact_243_local_Obdd__above__Int2,axiom,
% 0.30/0.47 ! [B4: set_a,A2: set_a] :
% 0.30/0.47 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 0.30/0.47 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.bdd_above_Int2
% 0.30/0.47 thf(fact_244_local_Obdd__above__Int1,axiom,
% 0.30/0.47 ! [A2: set_a,B4: set_a] :
% 0.30/0.47 ( ( condit1627435690bove_a @ less_eq @ A2 )
% 0.30/0.47 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.bdd_above_Int1
% 0.30/0.47 thf(fact_245_Int__subset__iff,axiom,
% 0.30/0.47 ! [C4: set_a,A2: set_a,B4: set_a] :
% 0.30/0.47 ( ( ord_less_eq_set_a @ C4 @ ( inf_inf_set_a @ A2 @ B4 ) )
% 0.30/0.47 = ( ( ord_less_eq_set_a @ C4 @ A2 )
% 0.30/0.47 & ( ord_less_eq_set_a @ C4 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Int_subset_iff
% 0.30/0.47 thf(fact_246_semilattice__inf__class_Oinf_Oidem,axiom,
% 0.30/0.47 ! [A: set_a] :
% 0.30/0.47 ( ( inf_inf_set_a @ A @ A )
% 0.30/0.47 = A ) ).
% 0.30/0.47
% 0.30/0.47 % semilattice_inf_class.inf.idem
% 0.30/0.47 thf(fact_247_semilattice__inf__class_Oinf__idem,axiom,
% 0.30/0.47 ! [X: set_a] :
% 0.30/0.47 ( ( inf_inf_set_a @ X @ X )
% 0.30/0.47 = X ) ).
% 0.30/0.47
% 0.30/0.47 % semilattice_inf_class.inf_idem
% 0.30/0.47 thf(fact_248_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 0.30/0.47 ! [A: set_a,B: set_a] :
% 0.30/0.47 ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
% 0.30/0.47 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 % semilattice_inf_class.inf.left_idem
% 0.30/0.47 thf(fact_249_semilattice__inf__class_Oinf__left__idem,axiom,
% 0.30/0.47 ! [X: set_a,Y: set_a] :
% 0.30/0.47 ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 0.30/0.47 = ( inf_inf_set_a @ X @ Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % semilattice_inf_class.inf_left_idem
% 0.30/0.47 thf(fact_250_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 0.30/0.47 ! [A: set_a,B: set_a] :
% 0.30/0.47 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
% 0.30/0.47 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.30/0.47
% 0.30/0.47 % semilattice_inf_class.inf.right_idem
% 0.30/0.47 thf(fact_251_semilattice__inf__class_Oinf__right__idem,axiom,
% 0.30/0.47 ! [X: set_a,Y: set_a] :
% 0.30/0.47 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Y )
% 0.30/0.47 = ( inf_inf_set_a @ X @ Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % semilattice_inf_class.inf_right_idem
% 0.30/0.47 thf(fact_252_local_OInf__fin_Oclosed,axiom,
% 0.30/0.47 ! [A2: set_a] :
% 0.30/0.47 ( ( finite_finite_a @ A2 )
% 0.30/0.47 => ( ( A2 != bot_bot_set_a )
% 0.30/0.47 => ( ! [X2: a,Y2: a] : ( member_a @ ( inf @ X2 @ Y2 ) @ ( insert_a @ X2 @ ( insert_a @ Y2 @ bot_bot_set_a ) ) )
% 0.30/0.47 => ( member_a @ ( lattic247676691_fin_a @ inf @ A2 ) @ A2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Inf_fin.closed
% 0.30/0.47 thf(fact_253_local_OInf__fin_Oinsert__not__elem,axiom,
% 0.30/0.47 ! [A2: set_a,X: a] :
% 0.30/0.47 ( ( finite_finite_a @ A2 )
% 0.30/0.47 => ( ~ ( member_a @ X @ A2 )
% 0.30/0.47 => ( ( A2 != bot_bot_set_a )
% 0.30/0.47 => ( ( lattic247676691_fin_a @ inf @ ( insert_a @ X @ A2 ) )
% 0.30/0.47 = ( inf @ X @ ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.Inf_fin.insert_not_elem
% 0.30/0.47
% 0.30/0.47 % Conjectures (1)
% 0.30/0.47 thf(conj_0,conjecture,
% 0.30/0.47 ( ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) )
% 0.30/0.47 = ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 2.37/1.46 ---- Embedded in THF ---
% 2.37/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.37/1.47 %%% Generated on Tue Feb 24 08:26:47 EST 2026
% 2.37/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 2.37/1.47 %%% Logic specification used:
% 2.37/1.47 %%% thf(spec, logic, $$dhol).
% 2.37/1.47
% 2.37/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.eimr8lCgBt/DTF2DTF6676.p
% See solution above
% 2.37/1.47 ------------------------
% 2.37/1.49 ---- Cleaned THF ---
% 2.37/1.49 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.37/1.49 set_a: $tType ).
% 2.37/1.49
% 2.37/1.49 thf(ty_n_tf__a,type,
% 2.37/1.49 a: $tType ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a,type,
% 2.37/1.49 condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a,type,
% 2.37/1.49 condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a,type,
% 2.37/1.49 finite40241356em_a_a: ( a > a > a ) > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
% 2.37/1.49 finite_finite_a: set_a > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Groups_Oabel__semigroup_001tf__a,type,
% 2.37/1.49 abel_semigroup_a: ( a > a > a ) > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Groups_Osemigroup_001tf__a,type,
% 2.37/1.49 semigroup_a: ( a > a > a ) > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
% 2.37/1.49 inf_inf_set_a: set_a > set_a > set_a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Lattices_Osemilattice_001tf__a,type,
% 2.37/1.49 semilattice_a: ( a > a > a ) > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin_001tf__a,type,
% 2.37/1.49 lattic247676691_fin_a: ( a > a > a ) > set_a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
% 2.37/1.49 lattic1885654924_set_a: ( a > a > a ) > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin_001tf__a,type,
% 2.37/1.49 lattic1781219155_fin_a: ( a > a > a ) > set_a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a,type,
% 2.37/1.49 modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a,type,
% 2.37/1.49 modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a,type,
% 2.37/1.49 modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a,type,
% 2.37/1.49 modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a,type,
% 2.37/1.49 modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oincomp_001tf__a,type,
% 2.37/1.49 modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 2.37/1.49 bot_bot_set_a: set_a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Orderings_Oord_OLeast_001tf__a,type,
% 2.37/1.49 least_a: ( a > a > $o ) > ( a > $o ) > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Orderings_Oord_Omax_001tf__a,type,
% 2.37/1.49 max_a: ( a > a > $o ) > a > a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Orderings_Oord_Omin_001tf__a,type,
% 2.37/1.49 min_a: ( a > a > $o ) > a > a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 2.37/1.49 ord_less_eq_set_a: set_a > set_a > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Orderings_Oorder_OGreatest_001tf__a,type,
% 2.37/1.49 greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Orderings_Oorder_Oantimono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 2.37/1.49 antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Orderings_Oorder_Omono_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 2.37/1.49 mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.37/1.49 collect_a: ( a > $o ) > set_a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Set_Oinsert_001tf__a,type,
% 2.37/1.49 insert_a: a > set_a > set_a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Set__Interval_Oord_OatLeast_001tf__a,type,
% 2.37/1.49 set_atLeast_a: ( a > a > $o ) > a > set_a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_Set__Interval_Oord_OatMost_001tf__a,type,
% 2.37/1.49 set_atMost_a: ( a > a > $o ) > a > set_a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_c_member_001tf__a,type,
% 2.37/1.49 member_a: a > set_a > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_v_a,type,
% 2.37/1.49 a2: a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_v_b,type,
% 2.37/1.49 b: a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_v_c,type,
% 2.37/1.49 c: a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_v_inf,type,
% 2.37/1.49 inf: a > a > a ).
% 2.37/1.49
% 2.37/1.49 thf(sy_v_less__eq,type,
% 2.37/1.49 less_eq: a > a > $o ).
% 2.37/1.49
% 2.37/1.49 thf(sy_v_sup,type,
% 2.37/1.49 sup: a > a > a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_0_local_Oinf_Oassoc,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( inf @ ( inf @ A @ B ) @ C )
% 2.37/1.49 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_1_local_Oinf_Ocommute,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( inf @ A @ B )
% 2.37/1.49 = ( inf @ B @ A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_2_local_Oinf_Oleft__commute,axiom,
% 2.37/1.49 ! [B: a,A: a,C: a] :
% 2.37/1.49 ( ( inf @ B @ ( inf @ A @ C ) )
% 2.37/1.49 = ( inf @ A @ ( inf @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_3_local_Oinf__assoc,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ( inf @ ( inf @ X @ Y ) @ Z )
% 2.37/1.49 = ( inf @ X @ ( inf @ Y @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_4_local_Oinf__commute,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( inf @ X @ Y )
% 2.37/1.49 = ( inf @ Y @ X ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_5_local_Oinf__left__commute,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ( inf @ X @ ( inf @ Y @ Z ) )
% 2.37/1.49 = ( inf @ Y @ ( inf @ X @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_6_local_Osup_Oassoc,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( sup @ ( sup @ A @ B ) @ C )
% 2.37/1.49 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_7_local_Osup_Ocommute,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( sup @ A @ B )
% 2.37/1.49 = ( sup @ B @ A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_8_local_Osup_Oleft__commute,axiom,
% 2.37/1.49 ! [B: a,A: a,C: a] :
% 2.37/1.49 ( ( sup @ B @ ( sup @ A @ C ) )
% 2.37/1.49 = ( sup @ A @ ( sup @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_9_local_Osup__assoc,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ( sup @ ( sup @ X @ Y ) @ Z )
% 2.37/1.49 = ( sup @ X @ ( sup @ Y @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_10_local_Osup__commute,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( sup @ X @ Y )
% 2.37/1.49 = ( sup @ Y @ X ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_11_local_Osup__left__commute,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ( sup @ X @ ( sup @ Y @ Z ) )
% 2.37/1.49 = ( sup @ Y @ ( sup @ X @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_12_local_Odistrib__imp1,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ! [X2: a,Y2: a,Z2: a] :
% 2.37/1.49 ( ( inf @ X2 @ ( sup @ Y2 @ Z2 ) )
% 2.37/1.49 = ( sup @ ( inf @ X2 @ Y2 ) @ ( inf @ X2 @ Z2 ) ) )
% 2.37/1.49 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 2.37/1.49 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_13_local_Odistrib__imp2,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ! [X2: a,Y2: a,Z2: a] :
% 2.37/1.49 ( ( sup @ X2 @ ( inf @ Y2 @ Z2 ) )
% 2.37/1.49 = ( inf @ ( sup @ X2 @ Y2 ) @ ( sup @ X2 @ Z2 ) ) )
% 2.37/1.49 => ( ( inf @ X @ ( sup @ Y @ Z ) )
% 2.37/1.49 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_14_local_Oa__join__d,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( sup @ A @ ( inf @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_15_a__meet__d,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_16_local_Ob__join__d,axiom,
% 2.37/1.49 ! [B: a,A: a,C: a] :
% 2.37/1.49 ( ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( sup @ B @ ( inf @ C @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_17_b__meet__d,axiom,
% 2.37/1.49 ! [B: a,A: a,C: a] :
% 2.37/1.49 ( ( inf @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( sup @ ( inf @ B @ C ) @ ( inf @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_18_c__meet__d,axiom,
% 2.37/1.49 ! [C: a,A: a,B: a] :
% 2.37/1.49 ( ( inf @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( sup @ ( inf @ C @ A ) @ ( inf @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_19_local_Od__aux__def,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_20_local_Od__b__c__a,axiom,
% 2.37/1.49 ! [B: a,C: a,A: a] :
% 2.37/1.49 ( ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A )
% 2.37/1.49 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_21_local_Od__c__a__b,axiom,
% 2.37/1.49 ! [C: a,A: a,B: a] :
% 2.37/1.49 ( ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B )
% 2.37/1.49 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_22_local_Oa__meet__e,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( inf @ A @ ( sup @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_23_local_Ob__meet__e,axiom,
% 2.37/1.49 ! [B: a,A: a,C: a] :
% 2.37/1.49 ( ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( inf @ B @ ( sup @ C @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_24_local_Oc__meet__e,axiom,
% 2.37/1.49 ! [C: a,A: a,B: a] :
% 2.37/1.49 ( ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( inf @ C @ ( sup @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_25_local_Oe__aux__def,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_26_local_Oe__b__c__a,axiom,
% 2.37/1.49 ! [B: a,C: a,A: a] :
% 2.37/1.49 ( ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A )
% 2.37/1.49 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_27_local_Oe__c__a__b,axiom,
% 2.37/1.49 ! [C: a,A: a,B: a] :
% 2.37/1.49 ( ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B )
% 2.37/1.49 = ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_28_local_Oinf_Oidem,axiom,
% 2.37/1.49 ! [A: a] :
% 2.37/1.49 ( ( inf @ A @ A )
% 2.37/1.49 = A ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_29_local_Oinf_Oleft__idem,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( inf @ A @ ( inf @ A @ B ) )
% 2.37/1.49 = ( inf @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_30_local_Oinf_Oright__idem,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( inf @ ( inf @ A @ B ) @ B )
% 2.37/1.49 = ( inf @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_31_local_Oinf__idem,axiom,
% 2.37/1.49 ! [X: a] :
% 2.37/1.49 ( ( inf @ X @ X )
% 2.37/1.49 = X ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_32_local_Oinf__left__idem,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( inf @ X @ ( inf @ X @ Y ) )
% 2.37/1.49 = ( inf @ X @ Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_33_local_Oinf__right__idem,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 2.37/1.49 = ( inf @ X @ Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_34_local_Osup_Oidem,axiom,
% 2.37/1.49 ! [A: a] :
% 2.37/1.49 ( ( sup @ A @ A )
% 2.37/1.49 = A ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_35_local_Osup_Oleft__idem,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( sup @ A @ ( sup @ A @ B ) )
% 2.37/1.49 = ( sup @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_36_local_Osup_Oright__idem,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( sup @ ( sup @ A @ B ) @ B )
% 2.37/1.49 = ( sup @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_37_local_Osup__idem,axiom,
% 2.37/1.49 ! [X: a] :
% 2.37/1.49 ( ( sup @ X @ X )
% 2.37/1.49 = X ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_38_local_Osup__left__idem,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( sup @ X @ ( sup @ X @ Y ) )
% 2.37/1.49 = ( sup @ X @ Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_39_calculation,axiom,
% 2.37/1.49 ( ( sup @ ( inf @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) )
% 2.37/1.49 = ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_40_local_Oinf__sup__absorb,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( inf @ X @ ( sup @ X @ Y ) )
% 2.37/1.49 = X ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_41_local_Osup__inf__absorb,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( sup @ X @ ( inf @ X @ Y ) )
% 2.37/1.49 = X ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_42_local_Ob__aux__def,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_43_local_Oc__aux__def,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_44_local_Oa__aux__def,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_45_mem__Collect__eq,axiom,
% 2.37/1.49 ! [A: a,P: a > $o] :
% 2.37/1.49 ( ( member_a @ A @ ( collect_a @ P ) )
% 2.37/1.49 = ( P @ A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_46_Collect__mem__eq,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( collect_a
% 2.37/1.49 @ ^ [X3: a] : ( member_a @ X3 @ A2 ) )
% 2.37/1.49 = A2 ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_47_Collect__cong,axiom,
% 2.37/1.49 ! [P: a > $o,Q: a > $o] :
% 2.37/1.49 ( ! [X2: a] :
% 2.37/1.49 ( ( P @ X2 )
% 2.37/1.49 = ( Q @ X2 ) )
% 2.37/1.49 => ( ( collect_a @ P )
% 2.37/1.49 = ( collect_a @ Q ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_48_lattice_Od__aux_Ocong,axiom,
% 2.37/1.49 modula1936294176_aux_a = modula1936294176_aux_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_49_lattice_Oe__aux_Ocong,axiom,
% 2.37/1.49 modula1144073633_aux_a = modula1144073633_aux_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_50_d__less__e,axiom,
% 2.37/1.49 less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_51_local_Ocomp__fun__idem__sup,axiom,
% 2.37/1.49 finite40241356em_a_a @ sup ).
% 2.37/1.49
% 2.37/1.49 thf(fact_52_local_Ocomp__fun__idem__inf,axiom,
% 2.37/1.49 finite40241356em_a_a @ inf ).
% 2.37/1.49
% 2.37/1.49 thf(fact_53_local_Osup_Osemigroup__axioms,axiom,
% 2.37/1.49 semigroup_a @ sup ).
% 2.37/1.49
% 2.37/1.49 thf(fact_54_local_Oinf_Osemigroup__axioms,axiom,
% 2.37/1.49 semigroup_a @ inf ).
% 2.37/1.49
% 2.37/1.49 thf(fact_55_local_Osup_Osemilattice__axioms,axiom,
% 2.37/1.49 semilattice_a @ sup ).
% 2.37/1.49
% 2.37/1.49 thf(fact_56_local_Oinf_Osemilattice__axioms,axiom,
% 2.37/1.49 semilattice_a @ inf ).
% 2.37/1.49
% 2.37/1.49 thf(fact_57_local_Osup_Oabel__semigroup__axioms,axiom,
% 2.37/1.49 abel_semigroup_a @ sup ).
% 2.37/1.49
% 2.37/1.49 thf(fact_58_local_Oinf_Oabel__semigroup__axioms,axiom,
% 2.37/1.49 abel_semigroup_a @ inf ).
% 2.37/1.49
% 2.37/1.49 thf(fact_59_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 2.37/1.49 lattic1885654924_set_a @ sup ).
% 2.37/1.49
% 2.37/1.49 thf(fact_60_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 2.37/1.49 lattic1885654924_set_a @ inf ).
% 2.37/1.49
% 2.37/1.49 thf(fact_61_local_Ob__a,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_62_local_Oantisym,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ( less_eq @ Y @ X )
% 2.37/1.49 => ( X = Y ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_63_local_Oantisym__conv,axiom,
% 2.37/1.49 ! [Y: a,X: a] :
% 2.37/1.49 ( ( less_eq @ Y @ X )
% 2.37/1.49 => ( ( less_eq @ X @ Y )
% 2.37/1.49 = ( X = Y ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_64_local_Odual__order_Oantisym,axiom,
% 2.37/1.49 ! [B: a,A: a] :
% 2.37/1.49 ( ( less_eq @ B @ A )
% 2.37/1.49 => ( ( less_eq @ A @ B )
% 2.37/1.49 => ( A = B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_65_local_Odual__order_Oeq__iff,axiom,
% 2.37/1.49 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 2.37/1.49 = ( ^ [A3: a,B2: a] :
% 2.37/1.49 ( ( less_eq @ B2 @ A3 )
% 2.37/1.49 & ( less_eq @ A3 @ B2 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_66_local_Odual__order_Otrans,axiom,
% 2.37/1.49 ! [B: a,A: a,C: a] :
% 2.37/1.49 ( ( less_eq @ B @ A )
% 2.37/1.49 => ( ( less_eq @ C @ B )
% 2.37/1.49 => ( less_eq @ C @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_67_local_Oeq__iff,axiom,
% 2.37/1.49 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 2.37/1.49 = ( ^ [X3: a,Y4: a] :
% 2.37/1.49 ( ( less_eq @ X3 @ Y4 )
% 2.37/1.49 & ( less_eq @ Y4 @ X3 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_68_local_Oeq__refl,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( X = Y )
% 2.37/1.49 => ( less_eq @ X @ Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_69_local_Oord__eq__le__trans,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( A = B )
% 2.37/1.49 => ( ( less_eq @ B @ C )
% 2.37/1.49 => ( less_eq @ A @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_70_local_Oord__le__eq__trans,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 => ( ( B = C )
% 2.37/1.49 => ( less_eq @ A @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_71_local_Oorder_Oantisym,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 => ( ( less_eq @ B @ A )
% 2.37/1.49 => ( A = B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_72_local_Oorder_Oeq__iff,axiom,
% 2.37/1.49 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 2.37/1.49 = ( ^ [A3: a,B2: a] :
% 2.37/1.49 ( ( less_eq @ A3 @ B2 )
% 2.37/1.49 & ( less_eq @ B2 @ A3 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_73_local_Oorder_Otrans,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 => ( ( less_eq @ B @ C )
% 2.37/1.49 => ( less_eq @ A @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_74_local_Oorder__trans,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ( less_eq @ Y @ Z )
% 2.37/1.49 => ( less_eq @ X @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_75_local_Ole__infI2,axiom,
% 2.37/1.49 ! [B: a,X: a,A: a] :
% 2.37/1.49 ( ( less_eq @ B @ X )
% 2.37/1.49 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_76_local_Ole__infI1,axiom,
% 2.37/1.49 ! [A: a,X: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ X )
% 2.37/1.49 => ( less_eq @ ( inf @ A @ B ) @ X ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_77_local_Ole__infI,axiom,
% 2.37/1.49 ! [X: a,A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ X @ A )
% 2.37/1.49 => ( ( less_eq @ X @ B )
% 2.37/1.49 => ( less_eq @ X @ ( inf @ A @ B ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_78_local_Ole__infE,axiom,
% 2.37/1.49 ! [X: a,A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ X @ ( inf @ A @ B ) )
% 2.37/1.49 => ~ ( ( less_eq @ X @ A )
% 2.37/1.49 => ~ ( less_eq @ X @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_79_local_Ole__iff__inf,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( less_eq @ X @ Y )
% 2.37/1.49 = ( ( inf @ X @ Y )
% 2.37/1.49 = X ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_80_local_Oinf__unique,axiom,
% 2.37/1.49 ! [F: a > a > a,X: a,Y: a] :
% 2.37/1.49 ( ! [X2: a,Y2: a] : ( less_eq @ ( F @ X2 @ Y2 ) @ X2 )
% 2.37/1.49 => ( ! [X2: a,Y2: a] : ( less_eq @ ( F @ X2 @ Y2 ) @ Y2 )
% 2.37/1.49 => ( ! [X2: a,Y2: a,Z2: a] :
% 2.37/1.49 ( ( less_eq @ X2 @ Y2 )
% 2.37/1.49 => ( ( less_eq @ X2 @ Z2 )
% 2.37/1.49 => ( less_eq @ X2 @ ( F @ Y2 @ Z2 ) ) ) )
% 2.37/1.49 => ( ( inf @ X @ Y )
% 2.37/1.49 = ( F @ X @ Y ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_81_local_Oinf__mono,axiom,
% 2.37/1.49 ! [A: a,C: a,B: a,D: a] :
% 2.37/1.49 ( ( less_eq @ A @ C )
% 2.37/1.49 => ( ( less_eq @ B @ D )
% 2.37/1.49 => ( less_eq @ ( inf @ A @ B ) @ ( inf @ C @ D ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_82_local_Oinf__le2,axiom,
% 2.37/1.49 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_83_local_Oinf__le1,axiom,
% 2.37/1.49 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_84_local_Oinf__greatest,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ( less_eq @ X @ Z )
% 2.37/1.49 => ( less_eq @ X @ ( inf @ Y @ Z ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_85_local_Oinf__absorb2,axiom,
% 2.37/1.49 ! [Y: a,X: a] :
% 2.37/1.49 ( ( less_eq @ Y @ X )
% 2.37/1.49 => ( ( inf @ X @ Y )
% 2.37/1.49 = Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_86_local_Oinf__absorb1,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ( inf @ X @ Y )
% 2.37/1.49 = X ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_87_local_Oinf_Oorder__iff,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 = ( A
% 2.37/1.49 = ( inf @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_88_local_Oinf_OorderI,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( A
% 2.37/1.49 = ( inf @ A @ B ) )
% 2.37/1.49 => ( less_eq @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_89_local_Oinf_OorderE,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 => ( A
% 2.37/1.49 = ( inf @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_90_local_Oinf_OcoboundedI2,axiom,
% 2.37/1.49 ! [B: a,C: a,A: a] :
% 2.37/1.49 ( ( less_eq @ B @ C )
% 2.37/1.49 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_91_local_Oinf_OcoboundedI1,axiom,
% 2.37/1.49 ! [A: a,C: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ C )
% 2.37/1.49 => ( less_eq @ ( inf @ A @ B ) @ C ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_92_local_Oinf_Ocobounded2,axiom,
% 2.37/1.49 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_93_local_Oinf_Ocobounded1,axiom,
% 2.37/1.49 ! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_94_local_Oinf_OboundedI,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 => ( ( less_eq @ A @ C )
% 2.37/1.49 => ( less_eq @ A @ ( inf @ B @ C ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_95_local_Oinf_OboundedE,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 2.37/1.49 => ~ ( ( less_eq @ A @ B )
% 2.37/1.49 => ~ ( less_eq @ A @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_96_local_Oinf_Oabsorb__iff2,axiom,
% 2.37/1.49 ! [B: a,A: a] :
% 2.37/1.49 ( ( less_eq @ B @ A )
% 2.37/1.49 = ( ( inf @ A @ B )
% 2.37/1.49 = B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_97_local_Oinf_Oabsorb__iff1,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 = ( ( inf @ A @ B )
% 2.37/1.49 = A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_98_local_Oinf_Oabsorb2,axiom,
% 2.37/1.49 ! [B: a,A: a] :
% 2.37/1.49 ( ( less_eq @ B @ A )
% 2.37/1.49 => ( ( inf @ A @ B )
% 2.37/1.49 = B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_99_local_Oinf_Oabsorb1,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 => ( ( inf @ A @ B )
% 2.37/1.49 = A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_100_local_Osup__unique,axiom,
% 2.37/1.49 ! [F: a > a > a,X: a,Y: a] :
% 2.37/1.49 ( ! [X2: a,Y2: a] : ( less_eq @ X2 @ ( F @ X2 @ Y2 ) )
% 2.37/1.49 => ( ! [X2: a,Y2: a] : ( less_eq @ Y2 @ ( F @ X2 @ Y2 ) )
% 2.37/1.49 => ( ! [X2: a,Y2: a,Z2: a] :
% 2.37/1.49 ( ( less_eq @ Y2 @ X2 )
% 2.37/1.49 => ( ( less_eq @ Z2 @ X2 )
% 2.37/1.49 => ( less_eq @ ( F @ Y2 @ Z2 ) @ X2 ) ) )
% 2.37/1.49 => ( ( sup @ X @ Y )
% 2.37/1.49 = ( F @ X @ Y ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_101_local_Osup__mono,axiom,
% 2.37/1.49 ! [A: a,C: a,B: a,D: a] :
% 2.37/1.49 ( ( less_eq @ A @ C )
% 2.37/1.49 => ( ( less_eq @ B @ D )
% 2.37/1.49 => ( less_eq @ ( sup @ A @ B ) @ ( sup @ C @ D ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_102_local_Osup__least,axiom,
% 2.37/1.49 ! [Y: a,X: a,Z: a] :
% 2.37/1.49 ( ( less_eq @ Y @ X )
% 2.37/1.49 => ( ( less_eq @ Z @ X )
% 2.37/1.49 => ( less_eq @ ( sup @ Y @ Z ) @ X ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_103_local_Osup__ge2,axiom,
% 2.37/1.49 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_104_local_Osup__ge1,axiom,
% 2.37/1.49 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_105_local_Osup__absorb2,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ( sup @ X @ Y )
% 2.37/1.49 = Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_106_local_Osup__absorb1,axiom,
% 2.37/1.49 ! [Y: a,X: a] :
% 2.37/1.49 ( ( less_eq @ Y @ X )
% 2.37/1.49 => ( ( sup @ X @ Y )
% 2.37/1.49 = X ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_107_local_Osup_Oorder__iff,axiom,
% 2.37/1.49 ! [B: a,A: a] :
% 2.37/1.49 ( ( less_eq @ B @ A )
% 2.37/1.49 = ( A
% 2.37/1.49 = ( sup @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_108_local_Osup_OorderI,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( A
% 2.37/1.49 = ( sup @ A @ B ) )
% 2.37/1.49 => ( less_eq @ B @ A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_109_local_Osup_OorderE,axiom,
% 2.37/1.49 ! [B: a,A: a] :
% 2.37/1.49 ( ( less_eq @ B @ A )
% 2.37/1.49 => ( A
% 2.37/1.49 = ( sup @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_110_local_Osup_Omono,axiom,
% 2.37/1.49 ! [C: a,A: a,D: a,B: a] :
% 2.37/1.49 ( ( less_eq @ C @ A )
% 2.37/1.49 => ( ( less_eq @ D @ B )
% 2.37/1.49 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A @ B ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_111_local_Osup_OcoboundedI2,axiom,
% 2.37/1.49 ! [C: a,B: a,A: a] :
% 2.37/1.49 ( ( less_eq @ C @ B )
% 2.37/1.49 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_112_local_Osup_OcoboundedI1,axiom,
% 2.37/1.49 ! [C: a,A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ C @ A )
% 2.37/1.49 => ( less_eq @ C @ ( sup @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_113_local_Osup_Ocobounded2,axiom,
% 2.37/1.49 ! [B: a,A: a] : ( less_eq @ B @ ( sup @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_114_local_Osup_Ocobounded1,axiom,
% 2.37/1.49 ! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_115_local_Osup_OboundedI,axiom,
% 2.37/1.49 ! [B: a,A: a,C: a] :
% 2.37/1.49 ( ( less_eq @ B @ A )
% 2.37/1.49 => ( ( less_eq @ C @ A )
% 2.37/1.49 => ( less_eq @ ( sup @ B @ C ) @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_116_local_Osup_OboundedE,axiom,
% 2.37/1.49 ! [B: a,C: a,A: a] :
% 2.37/1.49 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 2.37/1.49 => ~ ( ( less_eq @ B @ A )
% 2.37/1.49 => ~ ( less_eq @ C @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_117_local_Osup_Oabsorb__iff2,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 = ( ( sup @ A @ B )
% 2.37/1.49 = B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_118_local_Osup_Oabsorb__iff1,axiom,
% 2.37/1.49 ! [B: a,A: a] :
% 2.37/1.49 ( ( less_eq @ B @ A )
% 2.37/1.49 = ( ( sup @ A @ B )
% 2.37/1.49 = A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_119_local_Osup_Oabsorb2,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ B )
% 2.37/1.49 => ( ( sup @ A @ B )
% 2.37/1.49 = B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_120_local_Osup_Oabsorb1,axiom,
% 2.37/1.49 ! [B: a,A: a] :
% 2.37/1.49 ( ( less_eq @ B @ A )
% 2.37/1.49 => ( ( sup @ A @ B )
% 2.37/1.49 = A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_121_local_Ole__supI2,axiom,
% 2.37/1.49 ! [X: a,B: a,A: a] :
% 2.37/1.49 ( ( less_eq @ X @ B )
% 2.37/1.49 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_122_local_Ole__supI1,axiom,
% 2.37/1.49 ! [X: a,A: a,B: a] :
% 2.37/1.49 ( ( less_eq @ X @ A )
% 2.37/1.49 => ( less_eq @ X @ ( sup @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_123_local_Ole__supI,axiom,
% 2.37/1.49 ! [A: a,X: a,B: a] :
% 2.37/1.49 ( ( less_eq @ A @ X )
% 2.37/1.49 => ( ( less_eq @ B @ X )
% 2.37/1.49 => ( less_eq @ ( sup @ A @ B ) @ X ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_124_local_Ole__supE,axiom,
% 2.37/1.49 ! [A: a,B: a,X: a] :
% 2.37/1.49 ( ( less_eq @ ( sup @ A @ B ) @ X )
% 2.37/1.49 => ~ ( ( less_eq @ A @ X )
% 2.37/1.49 => ~ ( less_eq @ B @ X ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_125_local_Ole__iff__sup,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( less_eq @ X @ Y )
% 2.37/1.49 = ( ( sup @ X @ Y )
% 2.37/1.49 = Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_126_local_Omodular,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 2.37/1.49 = ( inf @ Y @ ( sup @ X @ Z ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_127_local_Odistrib__sup__le,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_128_local_Odistrib__inf__le,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) @ ( inf @ X @ ( sup @ Y @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_129_local_Oincomp__def,axiom,
% 2.37/1.49 ! [X: a,Y: a] :
% 2.37/1.49 ( ( modula1727524044comp_a @ less_eq @ X @ Y )
% 2.37/1.49 = ( ~ ( less_eq @ X @ Y )
% 2.37/1.49 & ~ ( less_eq @ Y @ X ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_130_local_Oc__a,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_131_local_Oorder_Orefl,axiom,
% 2.37/1.49 ! [A: a] : ( less_eq @ A @ A ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_132_local_Oorder__refl,axiom,
% 2.37/1.49 ! [X: a] : ( less_eq @ X @ X ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_133_local_OGreatestI2__order,axiom,
% 2.37/1.49 ! [P: a > $o,X: a,Q: a > $o] :
% 2.37/1.49 ( ( P @ X )
% 2.37/1.49 => ( ! [Y2: a] :
% 2.37/1.49 ( ( P @ Y2 )
% 2.37/1.49 => ( less_eq @ Y2 @ X ) )
% 2.37/1.49 => ( ! [X2: a] :
% 2.37/1.49 ( ( P @ X2 )
% 2.37/1.49 => ( ! [Y5: a] :
% 2.37/1.49 ( ( P @ Y5 )
% 2.37/1.49 => ( less_eq @ Y5 @ X2 ) )
% 2.37/1.49 => ( Q @ X2 ) ) )
% 2.37/1.49 => ( Q @ ( greatest_a @ less_eq @ P ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_134_local_OGreatest__equality,axiom,
% 2.37/1.49 ! [P: a > $o,X: a] :
% 2.37/1.49 ( ( P @ X )
% 2.37/1.49 => ( ! [Y2: a] :
% 2.37/1.49 ( ( P @ Y2 )
% 2.37/1.49 => ( less_eq @ Y2 @ X ) )
% 2.37/1.49 => ( ( greatest_a @ less_eq @ P )
% 2.37/1.49 = X ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_135_local_Omax__def,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( ( less_eq @ A @ B )
% 2.37/1.49 => ( ( max_a @ less_eq @ A @ B )
% 2.37/1.49 = B ) )
% 2.37/1.49 & ( ~ ( less_eq @ A @ B )
% 2.37/1.49 => ( ( max_a @ less_eq @ A @ B )
% 2.37/1.49 = A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_136_local_Omin__def,axiom,
% 2.37/1.49 ! [A: a,B: a] :
% 2.37/1.49 ( ( ( less_eq @ A @ B )
% 2.37/1.49 => ( ( min_a @ less_eq @ A @ B )
% 2.37/1.49 = A ) )
% 2.37/1.49 & ( ~ ( less_eq @ A @ B )
% 2.37/1.49 => ( ( min_a @ less_eq @ A @ B )
% 2.37/1.49 = B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_137_a__def__equiv,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 => ( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( inf @ ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_138_c__def__equiv,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 => ( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( inf @ ( sup @ C @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_139_b__def__equiv,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 => ( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
% 2.37/1.49 = ( inf @ ( sup @ B @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_140_c__meet__a__eq__d,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 => ( ( inf @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_141_a__meet__b__eq__d,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 => ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_142_b__meet__c__eq__d,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 => ( ( inf @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula581031071_aux_a @ inf @ sup @ A @ B @ C ) )
% 2.37/1.49 = ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_143_local_Ole__inf__iff,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ( less_eq @ X @ ( inf @ Y @ Z ) )
% 2.37/1.49 = ( ( less_eq @ X @ Y )
% 2.37/1.49 & ( less_eq @ X @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_144_local_Oinf_Obounded__iff,axiom,
% 2.37/1.49 ! [A: a,B: a,C: a] :
% 2.37/1.49 ( ( less_eq @ A @ ( inf @ B @ C ) )
% 2.37/1.49 = ( ( less_eq @ A @ B )
% 2.37/1.49 & ( less_eq @ A @ C ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_145_local_Osup_Obounded__iff,axiom,
% 2.37/1.49 ! [B: a,C: a,A: a] :
% 2.37/1.49 ( ( less_eq @ ( sup @ B @ C ) @ A )
% 2.37/1.49 = ( ( less_eq @ B @ A )
% 2.37/1.49 & ( less_eq @ C @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_146_local_Ole__sup__iff,axiom,
% 2.37/1.49 ! [X: a,Y: a,Z: a] :
% 2.37/1.49 ( ( less_eq @ ( sup @ X @ Y ) @ Z )
% 2.37/1.49 = ( ( less_eq @ X @ Z )
% 2.37/1.49 & ( less_eq @ Y @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_147_local_OLeast1I,axiom,
% 2.37/1.49 ! [P: a > $o] :
% 2.37/1.49 ( ? [X4: a] :
% 2.37/1.49 ( ( P @ X4 )
% 2.37/1.49 & ! [Y2: a] :
% 2.37/1.49 ( ( P @ Y2 )
% 2.37/1.49 => ( less_eq @ X4 @ Y2 ) )
% 2.37/1.49 & ! [Y2: a] :
% 2.37/1.49 ( ( ( P @ Y2 )
% 2.37/1.49 & ! [Ya: a] :
% 2.37/1.49 ( ( P @ Ya )
% 2.37/1.49 => ( less_eq @ Y2 @ Ya ) ) )
% 2.37/1.49 => ( Y2 = X4 ) ) )
% 2.37/1.49 => ( P @ ( least_a @ less_eq @ P ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_148_local_OLeast1__le,axiom,
% 2.37/1.49 ! [P: a > $o,Z: a] :
% 2.37/1.49 ( ? [X4: a] :
% 2.37/1.49 ( ( P @ X4 )
% 2.37/1.49 & ! [Y2: a] :
% 2.37/1.49 ( ( P @ Y2 )
% 2.37/1.49 => ( less_eq @ X4 @ Y2 ) )
% 2.37/1.49 & ! [Y2: a] :
% 2.37/1.49 ( ( ( P @ Y2 )
% 2.37/1.49 & ! [Ya: a] :
% 2.37/1.49 ( ( P @ Ya )
% 2.37/1.49 => ( less_eq @ Y2 @ Ya ) ) )
% 2.37/1.49 => ( Y2 = X4 ) ) )
% 2.37/1.49 => ( ( P @ Z )
% 2.37/1.49 => ( less_eq @ ( least_a @ less_eq @ P ) @ Z ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_149_local_OLeastI2__order,axiom,
% 2.37/1.49 ! [P: a > $o,X: a,Q: a > $o] :
% 2.37/1.49 ( ( P @ X )
% 2.37/1.49 => ( ! [Y2: a] :
% 2.37/1.49 ( ( P @ Y2 )
% 2.37/1.49 => ( less_eq @ X @ Y2 ) )
% 2.37/1.49 => ( ! [X2: a] :
% 2.37/1.49 ( ( P @ X2 )
% 2.37/1.49 => ( ! [Y5: a] :
% 2.37/1.49 ( ( P @ Y5 )
% 2.37/1.49 => ( less_eq @ X2 @ Y5 ) )
% 2.37/1.49 => ( Q @ X2 ) ) )
% 2.37/1.49 => ( Q @ ( least_a @ less_eq @ P ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_150_local_OLeast__equality,axiom,
% 2.37/1.49 ! [P: a > $o,X: a] :
% 2.37/1.49 ( ( P @ X )
% 2.37/1.49 => ( ! [Y2: a] :
% 2.37/1.49 ( ( P @ Y2 )
% 2.37/1.49 => ( less_eq @ X @ Y2 ) )
% 2.37/1.49 => ( ( least_a @ less_eq @ P )
% 2.37/1.49 = X ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_151_lattice_Oc__aux_Ocong,axiom,
% 2.37/1.49 modula581031071_aux_a = modula581031071_aux_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_152_lattice_Ob__aux_Ocong,axiom,
% 2.37/1.49 modula1373251614_aux_a = modula1373251614_aux_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_153_lattice_Oa__aux_Ocong,axiom,
% 2.37/1.49 modula17988509_aux_a = modula17988509_aux_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_154_abel__semigroup_Oaxioms_I1_J,axiom,
% 2.37/1.49 ! [F: a > a > a] :
% 2.37/1.49 ( ( abel_semigroup_a @ F )
% 2.37/1.49 => ( semigroup_a @ F ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_155_semilattice__set__def,axiom,
% 2.37/1.49 lattic1885654924_set_a = semilattice_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_156_semilattice__set_Ointro,axiom,
% 2.37/1.49 ! [F: a > a > a] :
% 2.37/1.49 ( ( semilattice_a @ F )
% 2.37/1.49 => ( lattic1885654924_set_a @ F ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_157_semilattice__set_Oaxioms,axiom,
% 2.37/1.49 ! [F: a > a > a] :
% 2.37/1.49 ( ( lattic1885654924_set_a @ F )
% 2.37/1.49 => ( semilattice_a @ F ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_158_semilattice_Oaxioms_I1_J,axiom,
% 2.37/1.49 ! [F: a > a > a] :
% 2.37/1.49 ( ( semilattice_a @ F )
% 2.37/1.49 => ( abel_semigroup_a @ F ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_159_local_Obdd__above__def,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( condit1627435690bove_a @ less_eq @ A2 )
% 2.37/1.49 = ( ? [M: a] :
% 2.37/1.49 ! [X3: a] :
% 2.37/1.49 ( ( member_a @ X3 @ A2 )
% 2.37/1.49 => ( less_eq @ X3 @ M ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_160_local_Obdd__below__def,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( condit1001553558elow_a @ less_eq @ A2 )
% 2.37/1.49 = ( ? [M2: a] :
% 2.37/1.49 ! [X3: a] :
% 2.37/1.49 ( ( member_a @ X3 @ A2 )
% 2.37/1.49 => ( less_eq @ M2 @ X3 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_161_local_Obdd__belowI,axiom,
% 2.37/1.49 ! [A2: set_a,M3: a] :
% 2.37/1.49 ( ! [X2: a] :
% 2.37/1.49 ( ( member_a @ X2 @ A2 )
% 2.37/1.49 => ( less_eq @ M3 @ X2 ) )
% 2.37/1.49 => ( condit1001553558elow_a @ less_eq @ A2 ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_162_local_Obdd__aboveI,axiom,
% 2.37/1.49 ! [A2: set_a,M4: a] :
% 2.37/1.49 ( ! [X2: a] :
% 2.37/1.49 ( ( member_a @ X2 @ A2 )
% 2.37/1.49 => ( less_eq @ X2 @ M4 ) )
% 2.37/1.49 => ( condit1627435690bove_a @ less_eq @ A2 ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_163_lattice_Oincomp_Ocong,axiom,
% 2.37/1.49 modula1727524044comp_a = modula1727524044comp_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_164_abel__semigroup_Oleft__commute,axiom,
% 2.37/1.49 ! [F: a > a > a,B: a,A: a,C: a] :
% 2.37/1.49 ( ( abel_semigroup_a @ F )
% 2.37/1.49 => ( ( F @ B @ ( F @ A @ C ) )
% 2.37/1.49 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_165_semilattice_Oright__idem,axiom,
% 2.37/1.49 ! [F: a > a > a,A: a,B: a] :
% 2.37/1.49 ( ( semilattice_a @ F )
% 2.37/1.49 => ( ( F @ ( F @ A @ B ) @ B )
% 2.37/1.49 = ( F @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_166_semilattice_Oleft__idem,axiom,
% 2.37/1.49 ! [F: a > a > a,A: a,B: a] :
% 2.37/1.49 ( ( semilattice_a @ F )
% 2.37/1.49 => ( ( F @ A @ ( F @ A @ B ) )
% 2.37/1.49 = ( F @ A @ B ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_167_abel__semigroup_Ocommute,axiom,
% 2.37/1.49 ! [F: a > a > a,A: a,B: a] :
% 2.37/1.49 ( ( abel_semigroup_a @ F )
% 2.37/1.49 => ( ( F @ A @ B )
% 2.37/1.49 = ( F @ B @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_168_semilattice_Oidem,axiom,
% 2.37/1.49 ! [F: a > a > a,A: a] :
% 2.37/1.49 ( ( semilattice_a @ F )
% 2.37/1.49 => ( ( F @ A @ A )
% 2.37/1.49 = A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_169_semigroup_Ointro,axiom,
% 2.37/1.49 ! [F: a > a > a] :
% 2.37/1.49 ( ! [A4: a,B3: a,C2: a] :
% 2.37/1.49 ( ( F @ ( F @ A4 @ B3 ) @ C2 )
% 2.37/1.49 = ( F @ A4 @ ( F @ B3 @ C2 ) ) )
% 2.37/1.49 => ( semigroup_a @ F ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_170_semigroup_Oassoc,axiom,
% 2.37/1.49 ! [F: a > a > a,A: a,B: a,C: a] :
% 2.37/1.49 ( ( semigroup_a @ F )
% 2.37/1.49 => ( ( F @ ( F @ A @ B ) @ C )
% 2.37/1.49 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_171_semigroup__def,axiom,
% 2.37/1.49 ( semigroup_a
% 2.37/1.49 = ( ^ [F2: a > a > a] :
% 2.37/1.49 ! [A3: a,B2: a,C3: a] :
% 2.37/1.49 ( ( F2 @ ( F2 @ A3 @ B2 ) @ C3 )
% 2.37/1.49 = ( F2 @ A3 @ ( F2 @ B2 @ C3 ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_172_local_Obdd__below__mono,axiom,
% 2.37/1.49 ! [B4: set_a,A2: set_a] :
% 2.37/1.49 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 2.37/1.49 => ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.37/1.49 => ( condit1001553558elow_a @ less_eq @ A2 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_173_local_Obdd__above__mono,axiom,
% 2.37/1.49 ! [B4: set_a,A2: set_a] :
% 2.37/1.49 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 2.37/1.49 => ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.37/1.49 => ( condit1627435690bove_a @ less_eq @ A2 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_174_local_Obdd__below__finite,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( condit1001553558elow_a @ less_eq @ A2 ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_175_local_Ofinite__has__maximal2,axiom,
% 2.37/1.49 ! [A2: set_a,A: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( member_a @ A @ A2 )
% 2.37/1.49 => ? [X2: a] :
% 2.37/1.49 ( ( member_a @ X2 @ A2 )
% 2.37/1.49 & ( less_eq @ A @ X2 )
% 2.37/1.49 & ! [Xa: a] :
% 2.37/1.49 ( ( member_a @ Xa @ A2 )
% 2.37/1.49 => ( ( less_eq @ X2 @ Xa )
% 2.37/1.49 => ( X2 = Xa ) ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_176_local_Ofinite__has__minimal2,axiom,
% 2.37/1.49 ! [A2: set_a,A: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( member_a @ A @ A2 )
% 2.37/1.49 => ? [X2: a] :
% 2.37/1.49 ( ( member_a @ X2 @ A2 )
% 2.37/1.49 & ( less_eq @ X2 @ A )
% 2.37/1.49 & ! [Xa: a] :
% 2.37/1.49 ( ( member_a @ Xa @ A2 )
% 2.37/1.49 => ( ( less_eq @ Xa @ X2 )
% 2.37/1.49 => ( X2 = Xa ) ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_177_local_Obdd__above__finite,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( condit1627435690bove_a @ less_eq @ A2 ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_178_local_OantimonoD,axiom,
% 2.37/1.49 ! [F: a > set_a,X: a,Y: a] :
% 2.37/1.49 ( ( antimono_a_set_a @ less_eq @ F )
% 2.37/1.49 => ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_179_local_OantimonoE,axiom,
% 2.37/1.49 ! [F: a > set_a,X: a,Y: a] :
% 2.37/1.49 ( ( antimono_a_set_a @ less_eq @ F )
% 2.37/1.49 => ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( F @ Y ) @ ( F @ X ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_180_local_OantimonoI,axiom,
% 2.37/1.49 ! [F: a > set_a] :
% 2.37/1.49 ( ! [X2: a,Y2: a] :
% 2.37/1.49 ( ( less_eq @ X2 @ Y2 )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( F @ Y2 ) @ ( F @ X2 ) ) )
% 2.37/1.49 => ( antimono_a_set_a @ less_eq @ F ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_181_local_Oantimono__def,axiom,
% 2.37/1.49 ! [F: a > set_a] :
% 2.37/1.49 ( ( antimono_a_set_a @ less_eq @ F )
% 2.37/1.49 = ( ! [X3: a,Y4: a] :
% 2.37/1.49 ( ( less_eq @ X3 @ Y4 )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( F @ Y4 ) @ ( F @ X3 ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_182_local_Omono__def,axiom,
% 2.37/1.49 ! [F: a > set_a] :
% 2.37/1.49 ( ( mono_a_set_a @ less_eq @ F )
% 2.37/1.49 = ( ! [X3: a,Y4: a] :
% 2.37/1.49 ( ( less_eq @ X3 @ Y4 )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_183_local_OmonoI,axiom,
% 2.37/1.49 ! [F: a > set_a] :
% 2.37/1.49 ( ! [X2: a,Y2: a] :
% 2.37/1.49 ( ( less_eq @ X2 @ Y2 )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.37/1.49 => ( mono_a_set_a @ less_eq @ F ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_184_local_OmonoE,axiom,
% 2.37/1.49 ! [F: a > set_a,X: a,Y: a] :
% 2.37/1.49 ( ( mono_a_set_a @ less_eq @ F )
% 2.37/1.49 => ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_185_local_OmonoD,axiom,
% 2.37/1.49 ! [F: a > set_a,X: a,Y: a] :
% 2.37/1.49 ( ( mono_a_set_a @ less_eq @ F )
% 2.37/1.49 => ( ( less_eq @ X @ Y )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_186_local_OSup__fin_OcoboundedI,axiom,
% 2.37/1.49 ! [A2: set_a,A: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( member_a @ A @ A2 )
% 2.37/1.49 => ( less_eq @ A @ ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_187_local_OInf__fin_OcoboundedI,axiom,
% 2.37/1.49 ! [A2: set_a,A: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( member_a @ A @ A2 )
% 2.37/1.49 => ( less_eq @ ( lattic247676691_fin_a @ inf @ A2 ) @ A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_188_local_OSup__fin_Oin__idem,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( member_a @ X @ A2 )
% 2.37/1.49 => ( ( sup @ X @ ( lattic1781219155_fin_a @ sup @ A2 ) )
% 2.37/1.49 = ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_189_local_OInf__fin_Oin__idem,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( member_a @ X @ A2 )
% 2.37/1.49 => ( ( inf @ X @ ( lattic247676691_fin_a @ inf @ A2 ) )
% 2.37/1.49 = ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_190_local_Osup__Inf__absorb,axiom,
% 2.37/1.49 ! [A2: set_a,A: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( member_a @ A @ A2 )
% 2.37/1.49 => ( ( sup @ ( lattic247676691_fin_a @ inf @ A2 ) @ A )
% 2.37/1.49 = A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_191_local_Oinf__Sup__absorb,axiom,
% 2.37/1.49 ! [A2: set_a,A: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( member_a @ A @ A2 )
% 2.37/1.49 => ( ( inf @ A @ ( lattic1781219155_fin_a @ sup @ A2 ) )
% 2.37/1.49 = A ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_192_semilattice__inf_OInf__fin_Ocong,axiom,
% 2.37/1.49 lattic247676691_fin_a = lattic247676691_fin_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_193_semilattice__sup_OSup__fin_Ocong,axiom,
% 2.37/1.49 lattic1781219155_fin_a = lattic1781219155_fin_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_194_local_OInf__fin__le__Sup__fin,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( less_eq @ ( lattic247676691_fin_a @ inf @ A2 ) @ ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_195_local_OSup__fin_Osubset__imp,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ( finite_finite_a @ B4 )
% 2.37/1.49 => ( less_eq @ ( lattic1781219155_fin_a @ sup @ A2 ) @ ( lattic1781219155_fin_a @ sup @ B4 ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_196_local_Ofinite__has__minimal,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ? [X2: a] :
% 2.37/1.49 ( ( member_a @ X2 @ A2 )
% 2.37/1.49 & ! [Xa: a] :
% 2.37/1.49 ( ( member_a @ Xa @ A2 )
% 2.37/1.49 => ( ( less_eq @ Xa @ X2 )
% 2.37/1.49 => ( X2 = Xa ) ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_197_local_Ofinite__has__maximal,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ? [X2: a] :
% 2.37/1.49 ( ( member_a @ X2 @ A2 )
% 2.37/1.49 & ! [Xa: a] :
% 2.37/1.49 ( ( member_a @ Xa @ A2 )
% 2.37/1.49 => ( ( less_eq @ X2 @ Xa )
% 2.37/1.49 => ( X2 = Xa ) ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_198_local_OInf__fin_Osubset,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( B4 != bot_bot_set_a )
% 2.37/1.49 => ( ( ord_less_eq_set_a @ B4 @ A2 )
% 2.37/1.49 => ( ( inf @ ( lattic247676691_fin_a @ inf @ B4 ) @ ( lattic247676691_fin_a @ inf @ A2 ) )
% 2.37/1.49 = ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_199_local_OSup__fin_Osubset,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( B4 != bot_bot_set_a )
% 2.37/1.49 => ( ( ord_less_eq_set_a @ B4 @ A2 )
% 2.37/1.49 => ( ( sup @ ( lattic1781219155_fin_a @ sup @ B4 ) @ ( lattic1781219155_fin_a @ sup @ A2 ) )
% 2.37/1.49 = ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_200_local_OInf__fin_Obounded__iff,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A2 ) )
% 2.37/1.49 = ( ! [X3: a] :
% 2.37/1.49 ( ( member_a @ X3 @ A2 )
% 2.37/1.49 => ( less_eq @ X @ X3 ) ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_201_local_OInf__fin_OboundedI,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ! [A4: a] :
% 2.37/1.49 ( ( member_a @ A4 @ A2 )
% 2.37/1.49 => ( less_eq @ X @ A4 ) )
% 2.37/1.49 => ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_202_local_OInf__fin_OboundedE,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ( less_eq @ X @ ( lattic247676691_fin_a @ inf @ A2 ) )
% 2.37/1.49 => ! [A5: a] :
% 2.37/1.49 ( ( member_a @ A5 @ A2 )
% 2.37/1.49 => ( less_eq @ X @ A5 ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_203_local_OSup__fin_Obounded__iff,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ( less_eq @ ( lattic1781219155_fin_a @ sup @ A2 ) @ X )
% 2.37/1.49 = ( ! [X3: a] :
% 2.37/1.49 ( ( member_a @ X3 @ A2 )
% 2.37/1.49 => ( less_eq @ X3 @ X ) ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_204_local_OSup__fin_OboundedI,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ! [A4: a] :
% 2.37/1.49 ( ( member_a @ A4 @ A2 )
% 2.37/1.49 => ( less_eq @ A4 @ X ) )
% 2.37/1.49 => ( less_eq @ ( lattic1781219155_fin_a @ sup @ A2 ) @ X ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_205_local_OSup__fin_OboundedE,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ( less_eq @ ( lattic1781219155_fin_a @ sup @ A2 ) @ X )
% 2.37/1.49 => ! [A5: a] :
% 2.37/1.49 ( ( member_a @ A5 @ A2 )
% 2.37/1.49 => ( less_eq @ A5 @ X ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_206_local_OInf__fin_Osubset__imp,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ( finite_finite_a @ B4 )
% 2.37/1.49 => ( less_eq @ ( lattic247676691_fin_a @ inf @ B4 ) @ ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_207_local_Obdd__above__empty,axiom,
% 2.37/1.49 condit1627435690bove_a @ less_eq @ bot_bot_set_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_208_local_Obdd__below__empty,axiom,
% 2.37/1.49 condit1001553558elow_a @ less_eq @ bot_bot_set_a ).
% 2.37/1.49
% 2.37/1.49 thf(fact_209_local_Onot__empty__eq__Iic__eq__empty,axiom,
% 2.37/1.49 ! [H: a] :
% 2.37/1.49 ( bot_bot_set_a
% 2.37/1.49 != ( set_atMost_a @ less_eq @ H ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_210_local_Onot__empty__eq__Ici__eq__empty,axiom,
% 2.37/1.49 ! [L: a] :
% 2.37/1.49 ( bot_bot_set_a
% 2.37/1.49 != ( set_atLeast_a @ less_eq @ L ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_211_local_OatLeast__iff,axiom,
% 2.37/1.49 ! [I: a,K: a] :
% 2.37/1.49 ( ( member_a @ I @ ( set_atLeast_a @ less_eq @ K ) )
% 2.37/1.49 = ( less_eq @ K @ I ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_212_local_OatMost__iff,axiom,
% 2.37/1.49 ! [I: a,K: a] :
% 2.37/1.49 ( ( member_a @ I @ ( set_atMost_a @ less_eq @ K ) )
% 2.37/1.49 = ( less_eq @ I @ K ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_213_local_Obdd__below__Ici,axiom,
% 2.37/1.49 ! [A: a] : ( condit1001553558elow_a @ less_eq @ ( set_atLeast_a @ less_eq @ A ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_214_local_Obdd__above__Iic,axiom,
% 2.37/1.49 ! [B: a] : ( condit1627435690bove_a @ less_eq @ ( set_atMost_a @ less_eq @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_215_empty__subsetI,axiom,
% 2.37/1.49 ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_216_subset__empty,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
% 2.37/1.49 = ( A2 = bot_bot_set_a ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_217_empty__iff,axiom,
% 2.37/1.49 ! [C: a] :
% 2.37/1.49 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_218_all__not__in__conv,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( ! [X3: a] :
% 2.37/1.49 ~ ( member_a @ X3 @ A2 ) )
% 2.37/1.49 = ( A2 = bot_bot_set_a ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_219_Collect__empty__eq,axiom,
% 2.37/1.49 ! [P: a > $o] :
% 2.37/1.49 ( ( ( collect_a @ P )
% 2.37/1.49 = bot_bot_set_a )
% 2.37/1.49 = ( ! [X3: a] :
% 2.37/1.49 ~ ( P @ X3 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_220_empty__Collect__eq,axiom,
% 2.37/1.49 ! [P: a > $o] :
% 2.37/1.49 ( ( bot_bot_set_a
% 2.37/1.49 = ( collect_a @ P ) )
% 2.37/1.49 = ( ! [X3: a] :
% 2.37/1.49 ~ ( P @ X3 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_221_subsetI,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ! [X2: a] :
% 2.37/1.49 ( ( member_a @ X2 @ A2 )
% 2.37/1.49 => ( member_a @ X2 @ B4 ) )
% 2.37/1.49 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_222_subset__antisym,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.37/1.49 => ( ( ord_less_eq_set_a @ B4 @ A2 )
% 2.37/1.49 => ( A2 = B4 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_223_emptyE,axiom,
% 2.37/1.49 ! [A: a] :
% 2.37/1.49 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_224_equals0D,axiom,
% 2.37/1.49 ! [A2: set_a,A: a] :
% 2.37/1.49 ( ( A2 = bot_bot_set_a )
% 2.37/1.49 => ~ ( member_a @ A @ A2 ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_225_equals0I,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ! [Y2: a] :
% 2.37/1.49 ~ ( member_a @ Y2 @ A2 )
% 2.37/1.49 => ( A2 = bot_bot_set_a ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_226_ex__in__conv,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( ? [X3: a] : ( member_a @ X3 @ A2 ) )
% 2.37/1.49 = ( A2 != bot_bot_set_a ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_227_in__mono,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a,X: a] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.37/1.49 => ( ( member_a @ X @ A2 )
% 2.37/1.49 => ( member_a @ X @ B4 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_228_subsetD,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a,C: a] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.37/1.49 => ( ( member_a @ C @ A2 )
% 2.37/1.49 => ( member_a @ C @ B4 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_229_equalityE,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( A2 = B4 )
% 2.37/1.49 => ~ ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.37/1.49 => ~ ( ord_less_eq_set_a @ B4 @ A2 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_230_subset__eq,axiom,
% 2.37/1.49 ( ord_less_eq_set_a
% 2.37/1.49 = ( ^ [A6: set_a,B5: set_a] :
% 2.37/1.49 ! [X3: a] :
% 2.37/1.49 ( ( member_a @ X3 @ A6 )
% 2.37/1.49 => ( member_a @ X3 @ B5 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_231_equalityD1,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( A2 = B4 )
% 2.37/1.49 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_232_equalityD2,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( A2 = B4 )
% 2.37/1.49 => ( ord_less_eq_set_a @ B4 @ A2 ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_233_subset__iff,axiom,
% 2.37/1.49 ( ord_less_eq_set_a
% 2.37/1.49 = ( ^ [A6: set_a,B5: set_a] :
% 2.37/1.49 ! [T: a] :
% 2.37/1.49 ( ( member_a @ T @ A6 )
% 2.37/1.49 => ( member_a @ T @ B5 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_234_subset__refl,axiom,
% 2.37/1.49 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_235_Collect__mono,axiom,
% 2.37/1.49 ! [P: a > $o,Q: a > $o] :
% 2.37/1.49 ( ! [X2: a] :
% 2.37/1.49 ( ( P @ X2 )
% 2.37/1.49 => ( Q @ X2 ) )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_236_subset__trans,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a,C4: set_a] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.37/1.49 => ( ( ord_less_eq_set_a @ B4 @ C4 )
% 2.37/1.49 => ( ord_less_eq_set_a @ A2 @ C4 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_237_set__eq__subset,axiom,
% 2.37/1.49 ( ( ^ [Y3: set_a,Z3: set_a] : ( Y3 = Z3 ) )
% 2.37/1.49 = ( ^ [A6: set_a,B5: set_a] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ A6 @ B5 )
% 2.37/1.49 & ( ord_less_eq_set_a @ B5 @ A6 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_238_Collect__mono__iff,axiom,
% 2.37/1.49 ! [P: a > $o,Q: a > $o] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 2.37/1.49 = ( ! [X3: a] :
% 2.37/1.49 ( ( P @ X3 )
% 2.37/1.49 => ( Q @ X3 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_239_local_Omono__inf,axiom,
% 2.37/1.49 ! [F: a > set_a,A2: a,B4: a] :
% 2.37/1.49 ( ( mono_a_set_a @ less_eq @ F )
% 2.37/1.49 => ( ord_less_eq_set_a @ ( F @ ( inf @ A2 @ B4 ) ) @ ( inf_inf_set_a @ ( F @ A2 ) @ ( F @ B4 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_240_local_OSup__fin_Oinsert__not__elem,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ~ ( member_a @ X @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ( lattic1781219155_fin_a @ sup @ ( insert_a @ X @ A2 ) )
% 2.37/1.49 = ( sup @ X @ ( lattic1781219155_fin_a @ sup @ A2 ) ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_241_local_Obdd__below__Int2,axiom,
% 2.37/1.49 ! [B4: set_a,A2: set_a] :
% 2.37/1.49 ( ( condit1001553558elow_a @ less_eq @ B4 )
% 2.37/1.49 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_242_local_Obdd__below__Int1,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( condit1001553558elow_a @ less_eq @ A2 )
% 2.37/1.49 => ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_243_local_Obdd__above__Int2,axiom,
% 2.37/1.49 ! [B4: set_a,A2: set_a] :
% 2.37/1.49 ( ( condit1627435690bove_a @ less_eq @ B4 )
% 2.37/1.49 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_244_local_Obdd__above__Int1,axiom,
% 2.37/1.49 ! [A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( condit1627435690bove_a @ less_eq @ A2 )
% 2.37/1.49 => ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_245_Int__subset__iff,axiom,
% 2.37/1.49 ! [C4: set_a,A2: set_a,B4: set_a] :
% 2.37/1.49 ( ( ord_less_eq_set_a @ C4 @ ( inf_inf_set_a @ A2 @ B4 ) )
% 2.37/1.49 = ( ( ord_less_eq_set_a @ C4 @ A2 )
% 2.37/1.49 & ( ord_less_eq_set_a @ C4 @ B4 ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_246_semilattice__inf__class_Oinf_Oidem,axiom,
% 2.37/1.49 ! [A: set_a] :
% 2.37/1.49 ( ( inf_inf_set_a @ A @ A )
% 2.37/1.49 = A ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_247_semilattice__inf__class_Oinf__idem,axiom,
% 2.37/1.49 ! [X: set_a] :
% 2.37/1.49 ( ( inf_inf_set_a @ X @ X )
% 2.37/1.49 = X ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_248_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 2.37/1.49 ! [A: set_a,B: set_a] :
% 2.37/1.49 ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
% 2.37/1.49 = ( inf_inf_set_a @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_249_semilattice__inf__class_Oinf__left__idem,axiom,
% 2.37/1.49 ! [X: set_a,Y: set_a] :
% 2.37/1.49 ( ( inf_inf_set_a @ X @ ( inf_inf_set_a @ X @ Y ) )
% 2.37/1.49 = ( inf_inf_set_a @ X @ Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_250_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 2.37/1.49 ! [A: set_a,B: set_a] :
% 2.37/1.49 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
% 2.37/1.49 = ( inf_inf_set_a @ A @ B ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_251_semilattice__inf__class_Oinf__right__idem,axiom,
% 2.37/1.49 ! [X: set_a,Y: set_a] :
% 2.37/1.49 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X @ Y ) @ Y )
% 2.37/1.49 = ( inf_inf_set_a @ X @ Y ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_252_local_OInf__fin_Oclosed,axiom,
% 2.37/1.49 ! [A2: set_a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ! [X2: a,Y2: a] : ( member_a @ ( inf @ X2 @ Y2 ) @ ( insert_a @ X2 @ ( insert_a @ Y2 @ bot_bot_set_a ) ) )
% 2.37/1.49 => ( member_a @ ( lattic247676691_fin_a @ inf @ A2 ) @ A2 ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(fact_253_local_OInf__fin_Oinsert__not__elem,axiom,
% 2.37/1.49 ! [A2: set_a,X: a] :
% 2.37/1.49 ( ( finite_finite_a @ A2 )
% 2.37/1.49 => ( ~ ( member_a @ X @ A2 )
% 2.37/1.49 => ( ( A2 != bot_bot_set_a )
% 2.37/1.49 => ( ( lattic247676691_fin_a @ inf @ ( insert_a @ X @ A2 ) )
% 2.37/1.49 = ( inf @ X @ ( lattic247676691_fin_a @ inf @ A2 ) ) ) ) ) ) ).
% 2.37/1.49
% 2.37/1.49 thf(conj_0,conjecture,
% 2.37/1.49 ( ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) )
% 2.37/1.49 = ( inf @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ) ) ).
% 2.37/1.49 ------------------------
% 2.62/1.51 % (6947)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/183Mi)
% 2.62/1.52 % (6951)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_6676 for (2999ds/2Mi)
% 2.62/1.52 % (6951)Instruction limit reached!
% 2.62/1.52 % (6951)------------------------------
% 2.62/1.52 % (6951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.52 % (6951)Termination reason: Unknown
% 2.62/1.52 % (6951)Termination phase: shuffling
% 2.62/1.52
% 2.62/1.52 % (6951)Memory used [KB]: 1151
% 2.62/1.52 % (6951)Time elapsed: 0.002 s
% 2.62/1.52 % (6951)Instructions burned: 2 (million)
% 2.62/1.52 % (6951)------------------------------
% 2.62/1.52 % (6951)------------------------------
% 2.62/1.52 % (6953)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/18Mi)
% 2.62/1.52 % (6953)Instruction limit reached!
% 2.62/1.52 % (6953)------------------------------
% 2.62/1.52 % (6953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.52 % (6953)Termination reason: Unknown
% 2.62/1.52 % (6953)Termination phase: Property scanning
% 2.62/1.52
% 2.62/1.52 % (6953)Memory used [KB]: 1407
% 2.62/1.52 % (6953)Time elapsed: 0.008 s
% 2.62/1.52 % (6953)Instructions burned: 21 (million)
% 2.62/1.52 % (6953)------------------------------
% 2.62/1.52 % (6953)------------------------------
% 2.62/1.52 % (6948)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_6676 for (2999ds/4Mi)
% 2.62/1.52 % (6949)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_6676 for (2999ds/27Mi)
% 2.62/1.52 % (6950)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/2Mi)
% 2.62/1.52 % (6952)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_6676 for (2999ds/275Mi)
% 2.62/1.52 % (6950)Instruction limit reached!
% 2.62/1.52 % (6950)------------------------------
% 2.62/1.52 % (6950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.52 % (6950)Termination reason: Unknown
% 2.62/1.52 % (6950)Termination phase: shuffling
% 2.62/1.52
% 2.62/1.52 % (6950)Memory used [KB]: 1279
% 2.62/1.52 % (6950)Time elapsed: 0.004 s
% 2.62/1.52 % (6950)Instructions burned: 3 (million)
% 2.62/1.52 % (6950)------------------------------
% 2.62/1.52 % (6950)------------------------------
% 2.62/1.53 % (6954)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/3Mi)
% 2.62/1.53 % (6948)Instruction limit reached!
% 2.62/1.53 % (6948)------------------------------
% 2.62/1.53 % (6948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.53 % (6948)Termination reason: Unknown
% 2.62/1.53 % (6948)Termination phase: shuffling
% 2.62/1.53
% 2.62/1.53 % (6948)Memory used [KB]: 1279
% 2.62/1.53 % (6948)Time elapsed: 0.005 s
% 2.62/1.53 % (6948)Instructions burned: 5 (million)
% 2.62/1.53 % (6948)------------------------------
% 2.62/1.53 % (6948)------------------------------
% 2.62/1.53 % (6954)Instruction limit reached!
% 2.62/1.53 % (6954)------------------------------
% 2.62/1.53 % (6954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.53 % (6954)Termination reason: Unknown
% 2.62/1.53 % (6954)Termination phase: shuffling
% 2.62/1.53
% 2.62/1.53 % (6954)Memory used [KB]: 1279
% 2.62/1.53 % (6954)Time elapsed: 0.002 s
% 2.62/1.53 % (6954)Instructions burned: 3 (million)
% 2.62/1.53 % (6954)------------------------------
% 2.62/1.53 % (6954)------------------------------
% 2.62/1.53 % (6955)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_6676 for (2999ds/37Mi)
% 2.62/1.54 % (6958)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_6676 for (2999ds/1041Mi)
% 2.62/1.54 % (6949)Instruction limit reached!
% 2.62/1.54 % (6949)------------------------------
% 2.62/1.54 % (6949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.54 % (6949)Termination reason: Unknown
% 2.62/1.54 % (6949)Termination phase: Property scanning
% 2.62/1.54
% 2.62/1.54 % (6949)Memory used [KB]: 1407
% 2.62/1.54 % (6949)Time elapsed: 0.018 s
% 2.62/1.54 % (6949)Instructions burned: 28 (million)
% 2.62/1.54 % (6949)------------------------------
% 2.62/1.54 % (6949)------------------------------
% 2.62/1.54 % (6956)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_6676 for (2999ds/15Mi)
% 2.62/1.54 % (6957)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_6676 for (2999ds/3Mi)
% 2.62/1.54 % (6955)Instruction limit reached!
% 2.62/1.54 % (6955)------------------------------
% 2.62/1.54 % (6955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.54 % (6955)Termination reason: Unknown
% 2.62/1.54 % (6955)Termination phase: Property scanning
% 2.62/1.54
% 2.62/1.54 % (6955)Memory used [KB]: 1791
% 2.62/1.54 % (6955)Time elapsed: 0.013 s
% 2.62/1.54 % (6955)Instructions burned: 40 (million)
% 2.62/1.54 % (6955)------------------------------
% 2.62/1.54 % (6955)------------------------------
% 2.62/1.54 % (6957)Instruction limit reached!
% 2.62/1.54 % (6957)------------------------------
% 2.62/1.54 % (6957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.54 % (6957)Termination reason: Unknown
% 2.62/1.54 % (6957)Termination phase: shuffling
% 2.62/1.54
% 2.62/1.54 % (6957)Memory used [KB]: 1279
% 2.62/1.54 % (6957)Time elapsed: 0.004 s
% 2.62/1.54 % (6957)Instructions burned: 3 (million)
% 2.62/1.54 % (6957)------------------------------
% 2.62/1.54 % (6957)------------------------------
% 2.62/1.55 % (6956)Instruction limit reached!
% 2.62/1.55 % (6956)------------------------------
% 2.62/1.55 % (6956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.55 % (6956)Termination reason: Unknown
% 2.62/1.55 % (6956)Termination phase: shuffling
% 2.62/1.55
% 2.62/1.55 % (6956)Memory used [KB]: 1407
% 2.62/1.55 % (6956)Time elapsed: 0.011 s
% 2.62/1.55 % (6956)Instructions burned: 15 (million)
% 2.62/1.55 % (6956)------------------------------
% 2.62/1.55 % (6956)------------------------------
% 2.62/1.55 % (6960)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/16Mi)
% 2.62/1.55 % (6959)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/7Mi)
% 2.62/1.56 % (6959)Instruction limit reached!
% 2.62/1.56 % (6959)------------------------------
% 2.62/1.56 % (6959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.56 % (6959)Termination reason: Unknown
% 2.62/1.56 % (6959)Termination phase: shuffling
% 2.62/1.56
% 2.62/1.56 % (6959)Memory used [KB]: 1407
% 2.62/1.56 % (6959)Time elapsed: 0.005 s
% 2.62/1.56 % (6959)Instructions burned: 9 (million)
% 2.62/1.56 % (6959)------------------------------
% 2.62/1.56 % (6959)------------------------------
% 2.62/1.56 % (6960)Instruction limit reached!
% 2.62/1.56 % (6960)------------------------------
% 2.62/1.56 % (6960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.56 % (6960)Termination reason: Unknown
% 2.62/1.56 % (6960)Termination phase: Property scanning
% 2.62/1.56
% 2.62/1.56 % (6960)Memory used [KB]: 1407
% 2.62/1.56 % (6960)Time elapsed: 0.008 s
% 2.62/1.56 % (6960)Instructions burned: 19 (million)
% 2.62/1.56 % (6960)------------------------------
% 2.62/1.56 % (6960)------------------------------
% 2.62/1.56 % (6961)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_6676 for (2999ds/3Mi)
% 2.62/1.56 % (6961)Instruction limit reached!
% 2.62/1.56 % (6961)------------------------------
% 2.62/1.56 % (6961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.56 % (6961)Termination reason: Unknown
% 2.62/1.56 % (6961)Termination phase: shuffling
% 2.62/1.56
% 2.62/1.56 % (6961)Memory used [KB]: 1279
% 2.62/1.56 % (6961)Time elapsed: 0.004 s
% 2.62/1.56 % (6961)Instructions burned: 3 (million)
% 2.62/1.56 % (6961)------------------------------
% 2.62/1.56 % (6961)------------------------------
% 2.62/1.57 % (6962)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_6676 for (2999ds/3Mi)
% 2.62/1.57 % (6962)Instruction limit reached!
% 2.62/1.57 % (6962)------------------------------
% 2.62/1.57 % (6962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.57 % (6962)Termination reason: Unknown
% 2.62/1.57 % (6962)Termination phase: shuffling
% 2.62/1.57
% 2.62/1.57 % (6962)Memory used [KB]: 1279
% 2.62/1.57 % (6962)Time elapsed: 0.003 s
% 2.62/1.57 % (6962)Instructions burned: 5 (million)
% 2.62/1.57 % (6962)------------------------------
% 2.62/1.57 % (6962)------------------------------
% 2.62/1.57 % (6963)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/7Mi)
% 2.62/1.57 % (6947)Instruction limit reached!
% 2.62/1.57 % (6947)------------------------------
% 2.62/1.57 % (6947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.57 % (6947)Termination reason: Unknown
% 2.62/1.57 % (6947)Termination phase: Saturation
% 2.62/1.57
% 2.62/1.57 % (6947)Memory used [KB]: 6780
% 2.62/1.57 % (6947)Time elapsed: 0.057 s
% 2.62/1.57 % (6947)Instructions burned: 184 (million)
% 2.62/1.57 % (6947)------------------------------
% 2.62/1.57 % (6947)------------------------------
% 2.62/1.57 % (6964)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/3Mi)
% 2.62/1.57 % (6963)Instruction limit reached!
% 2.62/1.57 % (6963)------------------------------
% 2.62/1.57 % (6963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.57 % (6963)Termination reason: Unknown
% 2.62/1.57 % (6963)Termination phase: shuffling
% 2.62/1.57
% 2.62/1.57 % (6963)Memory used [KB]: 1279
% 2.62/1.57 % (6963)Time elapsed: 0.004 s
% 2.62/1.57 % (6963)Instructions burned: 7 (million)
% 2.62/1.57 % (6963)------------------------------
% 2.62/1.57 % (6963)------------------------------
% 2.62/1.57 % (6964)Instruction limit reached!
% 2.62/1.57 % (6964)------------------------------
% 2.62/1.57 % (6964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.57 % (6964)Termination reason: Unknown
% 2.62/1.57 % (6964)Termination phase: shuffling
% 2.62/1.57
% 2.62/1.57 % (6964)Memory used [KB]: 1279
% 2.62/1.57 % (6964)Time elapsed: 0.003 s
% 2.62/1.57 % (6964)Instructions burned: 4 (million)
% 2.62/1.57 % (6964)------------------------------
% 2.62/1.57 % (6964)------------------------------
% 2.62/1.58 % (6966)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/18Mi)
% 2.62/1.58 % (6967)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/710Mi)
% 2.62/1.58 % (6968)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/6Mi)
% 2.62/1.58 % (6965)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/4Mi)
% 2.62/1.58 % (6969)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_6676 for (2999ds/902Mi)
% 2.62/1.58 % (6968)Instruction limit reached!
% 2.62/1.58 % (6968)------------------------------
% 2.62/1.58 % (6968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.58 % (6968)Termination reason: Unknown
% 2.62/1.58 % (6968)Termination phase: shuffling
% 2.62/1.58
% 2.62/1.58 % (6968)Memory used [KB]: 1279
% 2.62/1.58 % (6968)Time elapsed: 0.004 s
% 2.62/1.58 % (6968)Instructions burned: 7 (million)
% 2.62/1.58 % (6968)------------------------------
% 2.62/1.58 % (6968)------------------------------
% 2.62/1.58 % (6965)Instruction limit reached!
% 2.62/1.58 % (6965)------------------------------
% 2.62/1.58 % (6965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.58 % (6965)Termination reason: Unknown
% 2.62/1.58 % (6965)Termination phase: shuffling
% 2.62/1.58
% 2.62/1.58 % (6965)Memory used [KB]: 1279
% 2.62/1.58 % (6965)Time elapsed: 0.005 s
% 2.62/1.58 % (6965)Instructions burned: 5 (million)
% 2.62/1.58 % (6965)------------------------------
% 2.62/1.58 % (6965)------------------------------
% 2.62/1.59 % (6966)Instruction limit reached!
% 2.62/1.59 % (6966)------------------------------
% 2.62/1.59 % (6966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.59 % (6966)Termination reason: Unknown
% 2.62/1.59 % (6966)Termination phase: Property scanning
% 2.62/1.59
% 2.62/1.59 % (6966)Memory used [KB]: 1407
% 2.62/1.59 % (6966)Time elapsed: 0.008 s
% 2.62/1.59 % (6966)Instructions burned: 19 (million)
% 2.62/1.59 % (6966)------------------------------
% 2.62/1.59 % (6966)------------------------------
% 2.62/1.59 % (6970)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_6676 for (2999ds/21Mi)
% 2.62/1.60 % (6972)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_6676 for (2999ds/6Mi)
% 2.62/1.60 % (6972)Instruction limit reached!
% 2.62/1.60 % (6972)------------------------------
% 2.62/1.60 % (6972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.60 % (6972)Termination reason: Unknown
% 2.62/1.60 % (6972)Termination phase: shuffling
% 2.62/1.60
% 2.62/1.60 % (6972)Memory used [KB]: 1407
% 2.62/1.60 % (6972)Time elapsed: 0.004 s
% 2.62/1.60 % (6972)Instructions burned: 8 (million)
% 2.62/1.60 % (6972)------------------------------
% 2.62/1.60 % (6972)------------------------------
% 2.62/1.60 % (6970)Instruction limit reached!
% 2.62/1.60 % (6970)------------------------------
% 2.62/1.60 % (6970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.60 % (6970)Termination reason: Unknown
% 2.62/1.60 % (6970)Termination phase: shuffling
% 2.62/1.60
% 2.62/1.60 % (6970)Memory used [KB]: 1535
% 2.62/1.60 % (6970)Time elapsed: 0.009 s
% 2.62/1.60 % (6970)Instructions burned: 21 (million)
% 2.62/1.60 % (6970)------------------------------
% 2.62/1.60 % (6970)------------------------------
% 2.62/1.60 % (6971)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/5Mi)
% 2.62/1.61 % (6971)Instruction limit reached!
% 2.62/1.61 % (6971)------------------------------
% 2.62/1.61 % (6971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.61 % (6971)Termination reason: Unknown
% 2.62/1.61 % (6971)Termination phase: shuffling
% 2.62/1.61
% 2.62/1.61 % (6971)Memory used [KB]: 1279
% 2.62/1.61 % (6971)Time elapsed: 0.005 s
% 2.62/1.61 % (6971)Instructions burned: 6 (million)
% 2.62/1.61 % (6971)------------------------------
% 2.62/1.61 % (6971)------------------------------
% 2.62/1.61 % (6973)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6676 for (2999ds/377Mi)
% 2.62/1.61 % (6974)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_6676 for (2999ds/779Mi)
% 2.62/1.62 % (6975)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_6676 for (2998ds/19Mi)
% 2.62/1.62 % (6952)Instruction limit reached!
% 2.62/1.62 % (6952)------------------------------
% 2.62/1.62 % (6952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.62 % (6952)Termination reason: Unknown
% 2.62/1.62 % (6952)Termination phase: Saturation
% 2.62/1.62
% 2.62/1.62 % (6952)Memory used [KB]: 6396
% 2.62/1.62 % (6952)Time elapsed: 0.103 s
% 2.62/1.62 % (6952)Instructions burned: 278 (million)
% 2.62/1.62 % (6952)------------------------------
% 2.62/1.62 % (6952)------------------------------
% 2.62/1.63 % (6975)Instruction limit reached!
% 2.62/1.63 % (6975)------------------------------
% 2.62/1.63 % (6975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.63 % (6975)Termination reason: Unknown
% 2.62/1.63 % (6975)Termination phase: shuffling
% 2.62/1.63
% 2.62/1.63 % (6975)Memory used [KB]: 1663
% 2.62/1.63 % (6975)Time elapsed: 0.011 s
% 2.62/1.63 % (6975)Instructions burned: 19 (million)
% 2.62/1.63 % (6975)------------------------------
% 2.62/1.63 % (6975)------------------------------
% 2.62/1.63 % (6976)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6676 for (2998ds/879Mi)
% 2.62/1.64 % (6977)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6676 for (2998ds/17Mi)
% 2.62/1.65 % (6977)Instruction limit reached!
% 2.62/1.65 % (6977)------------------------------
% 2.62/1.65 % (6977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.65 % (6977)Termination reason: Unknown
% 2.62/1.65 % (6977)Termination phase: Property scanning
% 2.62/1.65
% 2.62/1.65 % (6977)Memory used [KB]: 1407
% 2.62/1.65 % (6977)Time elapsed: 0.008 s
% 2.62/1.65 % (6977)Instructions burned: 18 (million)
% 2.62/1.65 % (6977)------------------------------
% 2.62/1.65 % (6977)------------------------------
% 2.62/1.66 % (6978)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6676 for (2998ds/3Mi)
% 2.62/1.66 % (6978)Instruction limit reached!
% 2.62/1.66 % (6978)------------------------------
% 2.62/1.66 % (6978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.66 % (6978)Termination reason: Unknown
% 2.62/1.66 % (6978)Termination phase: shuffling
% 2.62/1.66
% 2.62/1.66 % (6978)Memory used [KB]: 1279
% 2.62/1.66 % (6978)Time elapsed: 0.003 s
% 2.62/1.66 % (6978)Instructions burned: 4 (million)
% 2.62/1.66 % (6978)------------------------------
% 2.62/1.66 % (6978)------------------------------
% 2.62/1.67 % (6979)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_6676 for (2998ds/30Mi)
% 2.62/1.68 % (6979)Instruction limit reached!
% 2.62/1.68 % (6979)------------------------------
% 2.62/1.68 % (6979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.68 % (6979)Termination reason: Unknown
% 2.62/1.68 % (6979)Termination phase: Property scanning
% 2.62/1.68
% 2.62/1.68 % (6979)Memory used [KB]: 1535
% 2.62/1.68 % (6979)Time elapsed: 0.012 s
% 2.62/1.68 % (6979)Instructions burned: 32 (million)
% 2.62/1.68 % (6979)------------------------------
% 2.62/1.68 % (6979)------------------------------
% 2.62/1.69 % (6980)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_6676 for (2998ds/127Mi)
% 2.62/1.73 % (6973)Instruction limit reached!
% 2.62/1.73 % (6973)------------------------------
% 2.62/1.73 % (6973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.73 % (6973)Termination reason: Unknown
% 2.62/1.73 % (6973)Termination phase: Saturation
% 2.62/1.73
% 2.62/1.73 % (6973)Memory used [KB]: 7291
% 2.62/1.73 % (6973)Time elapsed: 0.124 s
% 2.62/1.73 % (6973)Instructions burned: 379 (million)
% 2.62/1.73 % (6973)------------------------------
% 2.62/1.73 % (6973)------------------------------
% 2.62/1.73 % (6980)Instruction limit reached!
% 2.62/1.73 % (6980)------------------------------
% 2.62/1.73 % (6980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.73 % (6980)Termination reason: Unknown
% 2.62/1.73 % (6980)Termination phase: Saturation
% 2.62/1.73
% 2.62/1.73 % (6980)Memory used [KB]: 6524
% 2.62/1.73 % (6980)Time elapsed: 0.063 s
% 2.62/1.73 % (6980)Instructions burned: 129 (million)
% 2.62/1.73 % (6980)------------------------------
% 2.62/1.73 % (6980)------------------------------
% 2.62/1.74 % (6981)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_6676 for (2997ds/100Mi)
% 2.62/1.74 % (6982)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_6676 for (2997ds/3Mi)
% 2.62/1.74 % (6982)Instruction limit reached!
% 2.62/1.74 % (6982)------------------------------
% 2.62/1.74 % (6982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.74 % (6982)Termination reason: Unknown
% 2.62/1.74 % (6982)Termination phase: shuffling
% 2.62/1.74
% 2.62/1.74 % (6982)Memory used [KB]: 1279
% 2.62/1.74 % (6982)Time elapsed: 0.003 s
% 2.62/1.74 % (6982)Instructions burned: 4 (million)
% 2.62/1.74 % (6982)------------------------------
% 2.62/1.74 % (6982)------------------------------
% 2.62/1.75 % (6983)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_6676 for (2997ds/20Mi)
% 2.62/1.76 % (6983)Instruction limit reached!
% 2.62/1.76 % (6983)------------------------------
% 2.62/1.76 % (6983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.76 % (6983)Termination reason: Unknown
% 2.62/1.76 % (6983)Termination phase: Property scanning
% 2.62/1.76
% 2.62/1.76 % (6983)Memory used [KB]: 1407
% 2.62/1.76 % (6983)Time elapsed: 0.009 s
% 2.62/1.76 % (6983)Instructions burned: 22 (million)
% 2.62/1.76 % (6983)------------------------------
% 2.62/1.76 % (6983)------------------------------
% 2.62/1.77 % (6981)Instruction limit reached!
% 2.62/1.77 % (6981)------------------------------
% 2.62/1.77 % (6981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.77 % (6981)Termination reason: Unknown
% 2.62/1.77 % (6981)Termination phase: Property scanning
% 2.62/1.77
% 2.62/1.77 % (6981)Memory used [KB]: 1918
% 2.62/1.77 % (6981)Time elapsed: 0.029 s
% 2.62/1.77 % (6981)Instructions burned: 101 (million)
% 2.62/1.77 % (6981)------------------------------
% 2.62/1.77 % (6981)------------------------------
% 2.62/1.77 % (6984)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_6676 for (2997ds/86Mi)
% 2.62/1.78 % (6985)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_6676 for (2997ds/107Mi)
% 2.62/1.79 % (6967)Refutation not found, non-redundant clauses discarded% (6967)------------------------------
% 2.62/1.79 % (6967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.79 % (6967)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.62/1.79
% 2.62/1.79 % (6967)Memory used [KB]: 7036
% 2.62/1.79 % (6967)Time elapsed: 0.210 s
% 2.62/1.79 % (6967)Instructions burned: 703 (million)
% 2.62/1.79 % (6967)------------------------------
% 2.62/1.79 % (6967)------------------------------
% 2.62/1.80 % (6984)Instruction limit reached!
% 2.62/1.80 % (6984)------------------------------
% 2.62/1.80 % (6984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.80 % (6984)Termination reason: Unknown
% 2.62/1.80 % (6984)Termination phase: Saturation
% 2.62/1.80
% 2.62/1.80 % (6984)Memory used [KB]: 6396
% 2.62/1.80 % (6984)Time elapsed: 0.028 s
% 2.62/1.80 % (6984)Instructions burned: 87 (million)
% 2.62/1.80 % (6984)------------------------------
% 2.62/1.80 % (6984)------------------------------
% 2.62/1.80 % (6986)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_6676 for (2997ds/39Mi)
% 2.62/1.81 % (6987)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_6676 for (2996ds/448Mi)
% 2.62/1.81 % (6986)Instruction limit reached!
% 2.62/1.81 % (6986)------------------------------
% 2.62/1.81 % (6986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.81 % (6986)Termination reason: Unknown
% 2.62/1.81 % (6986)Termination phase: Property scanning
% 2.62/1.81
% 2.62/1.81 % (6986)Memory used [KB]: 1791
% 2.62/1.81 % (6986)Time elapsed: 0.011 s
% 2.62/1.81 % (6986)Instructions burned: 39 (million)
% 2.62/1.81 % (6986)------------------------------
% 2.62/1.81 % (6986)------------------------------
% 2.62/1.81 % (6985)Instruction limit reached!
% 2.62/1.81 % (6985)------------------------------
% 2.62/1.81 % (6985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.81 % (6985)Termination reason: Unknown
% 2.62/1.81 % (6985)Termination phase: Saturation
% 2.62/1.81
% 2.62/1.81 % (6985)Memory used [KB]: 6396
% 2.62/1.81 % (6985)Time elapsed: 0.036 s
% 2.62/1.81 % (6985)Instructions burned: 107 (million)
% 2.62/1.81 % (6985)------------------------------
% 2.62/1.81 % (6985)------------------------------
% 2.62/1.82 % (6988)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_6676 for (2996ds/46Mi)
% 2.62/1.82 % (6989)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_6676 for (2996ds/98Mi)
% 2.62/1.83 % (6969)Instruction limit reached!
% 2.62/1.83 % (6969)------------------------------
% 2.62/1.83 % (6969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.83 % (6969)Termination reason: Unknown
% 2.62/1.83 % (6969)Termination phase: Saturation
% 2.62/1.83
% 2.62/1.83 % (6969)Memory used [KB]: 7036
% 2.62/1.83 % (6969)Time elapsed: 0.252 s
% 2.62/1.83 % (6969)Instructions burned: 903 (million)
% 2.62/1.83 % (6969)------------------------------
% 2.62/1.83 % (6969)------------------------------
% 2.62/1.83 % (6988)Instruction limit reached!
% 2.62/1.83 % (6988)------------------------------
% 2.62/1.83 % (6988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.83 % (6988)Termination reason: Unknown
% 2.62/1.83 % (6988)Termination phase: Property scanning
% 2.62/1.83
% 2.62/1.83 % (6988)Memory used [KB]: 1535
% 2.62/1.83 % (6988)Time elapsed: 0.015 s
% 2.62/1.83 % (6988)Instructions burned: 48 (million)
% 2.62/1.83 % (6988)------------------------------
% 2.62/1.83 % (6988)------------------------------
% 2.62/1.84 % (6990)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_6676 for (2996ds/507Mi)
% 2.62/1.84 % (6991)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_6676 for (2996ds/149Mi)
% 2.62/1.85 % (6958)Instruction limit reached!
% 2.62/1.85 % (6958)------------------------------
% 2.62/1.85 % (6958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.85 % (6958)Termination reason: Unknown
% 2.62/1.85 % (6958)Termination phase: Saturation
% 2.62/1.85
% 2.62/1.85 % (6958)Memory used [KB]: 8059
% 2.62/1.85 % (6958)Time elapsed: 0.313 s
% 2.62/1.85 % (6958)Instructions burned: 1041 (million)
% 2.62/1.85 % (6958)------------------------------
% 2.62/1.85 % (6958)------------------------------
% 2.62/1.85 % (6989)Instruction limit reached!
% 2.62/1.85 % (6989)------------------------------
% 2.62/1.85 % (6989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.85 % (6989)Termination reason: Unknown
% 2.62/1.85 % (6989)Termination phase: Property scanning
% 2.62/1.85
% 2.62/1.85 % (6989)Memory used [KB]: 2046
% 2.62/1.85 % (6989)Time elapsed: 0.029 s
% 2.62/1.85 % (6989)Instructions burned: 101 (million)
% 2.62/1.85 % (6989)------------------------------
% 2.62/1.85 % (6989)------------------------------
% 2.62/1.86 % (6992)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_6676 for (2996ds/39Mi)
% 2.62/1.86 % (6974)Instruction limit reached!
% 2.62/1.86 % (6974)------------------------------
% 2.62/1.86 % (6974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.86 % (6974)Termination reason: Unknown
% 2.62/1.86 % (6974)Termination phase: Saturation
% 2.62/1.86
% 2.62/1.86 % (6974)Memory used [KB]: 7164
% 2.62/1.86 % (6974)Time elapsed: 0.249 s
% 2.62/1.86 % (6974)Instructions burned: 780 (million)
% 2.62/1.86 % (6974)------------------------------
% 2.62/1.86 % (6974)------------------------------
% 2.62/1.86 % (6993)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_6676 for (2996ds/6Mi)
% 2.62/1.86 % (6993)Instruction limit reached!
% 2.62/1.86 % (6993)------------------------------
% 2.62/1.86 % (6993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.86 % (6993)Termination reason: Unknown
% 2.62/1.86 % (6993)Termination phase: shuffling
% 2.62/1.86
% 2.62/1.86 % (6993)Memory used [KB]: 1407
% 2.62/1.86 % (6993)Time elapsed: 0.004 s
% 2.62/1.86 % (6993)Instructions burned: 8 (million)
% 2.62/1.86 % (6993)------------------------------
% 2.62/1.86 % (6993)------------------------------
% 2.62/1.87 % (6994)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_6676 for (2996ds/1087Mi)
% 2.62/1.87 % (6992)Instruction limit reached!
% 2.62/1.87 % (6992)------------------------------
% 2.62/1.87 % (6992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.87 % (6992)Termination reason: Unknown
% 2.62/1.87 % (6992)Termination phase: Property scanning
% 2.62/1.87
% 2.62/1.87 % (6992)Memory used [KB]: 1663
% 2.62/1.87 % (6992)Time elapsed: 0.013 s
% 2.62/1.87 % (6992)Instructions burned: 41 (million)
% 2.62/1.87 % (6992)------------------------------
% 2.62/1.87 % (6992)------------------------------
% 2.62/1.87 % (6995)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_6676 for (2996ds/47Mi)
% 2.62/1.88 % (6996)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_6676 for (2996ds/44Mi)
% 2.62/1.88 % (6990)First to succeed.
% 2.62/1.88 % (6990)Refutation found. Thanks to Tanya!
% 2.62/1.88 % SZS status Theorem for DTF2THF_6676
% 2.62/1.88 % SZS output start Proof for DTF2THF_6676
% 2.62/1.88 thf(type_def_5, type, a: $tType).
% 2.62/1.88 thf(type_def_7, type, set_a: $tType).
% 2.62/1.88 thf(func_def_0, type, set_a: $tType).
% 2.62/1.88 thf(func_def_1, type, a: $tType).
% 2.62/1.88 thf(func_def_2, type, condit1627435690bove_a: (a > a > $o) > set_a > $o).
% 2.62/1.88 thf(func_def_3, type, condit1001553558elow_a: (a > a > $o) > set_a > $o).
% 2.62/1.88 thf(func_def_4, type, finite40241356em_a_a: (a > a > a) > $o).
% 2.62/1.88 thf(func_def_5, type, finite_finite_a: set_a > $o).
% 2.62/1.88 thf(func_def_6, type, abel_semigroup_a: (a > a > a) > $o).
% 2.62/1.88 thf(func_def_7, type, semigroup_a: (a > a > a) > $o).
% 2.62/1.88 thf(func_def_8, type, inf_inf_set_a: set_a > set_a > set_a).
% 2.62/1.88 thf(func_def_9, type, semilattice_a: (a > a > a) > $o).
% 2.62/1.88 thf(func_def_10, type, lattic247676691_fin_a: (a > a > a) > set_a > a).
% 2.62/1.88 thf(func_def_11, type, lattic1885654924_set_a: (a > a > a) > $o).
% 2.62/1.88 thf(func_def_12, type, lattic1781219155_fin_a: (a > a > a) > set_a > a).
% 2.62/1.88 thf(func_def_13, type, modula17988509_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.62/1.88 thf(func_def_14, type, modula1373251614_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.62/1.88 thf(func_def_15, type, modula581031071_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.62/1.88 thf(func_def_16, type, modula1936294176_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.62/1.88 thf(func_def_17, type, modula1144073633_aux_a: (a > a > a) > (a > a > a) > a > a > a > a).
% 2.62/1.88 thf(func_def_18, type, modula1727524044comp_a: (a > a > $o) > a > a > $o).
% 2.62/1.88 thf(func_def_19, type, bot_bot_set_a: set_a).
% 2.62/1.88 thf(func_def_20, type, least_a: (a > a > $o) > (a > $o) > a).
% 2.62/1.88 thf(func_def_21, type, max_a: (a > a > $o) > a > a > a).
% 2.62/1.88 thf(func_def_22, type, min_a: (a > a > $o) > a > a > a).
% 2.62/1.88 thf(func_def_23, type, ord_less_eq_set_a: set_a > set_a > $o).
% 2.62/1.88 thf(func_def_24, type, greatest_a: (a > a > $o) > (a > $o) > a).
% 2.62/1.88 thf(func_def_25, type, antimono_a_set_a: (a > a > $o) > (a > set_a) > $o).
% 2.62/1.88 thf(func_def_26, type, mono_a_set_a: (a > a > $o) > (a > set_a) > $o).
% 2.62/1.88 thf(func_def_27, type, collect_a: (a > $o) > set_a).
% 2.62/1.88 thf(func_def_28, type, insert_a: a > set_a > set_a).
% 2.62/1.88 thf(func_def_29, type, set_atLeast_a: (a > a > $o) > a > set_a).
% 2.62/1.88 thf(func_def_30, type, set_atMost_a: (a > a > $o) > a > set_a).
% 2.62/1.88 thf(func_def_31, type, member_a: a > set_a > $o).
% 2.62/1.88 thf(func_def_32, type, a2: a).
% 2.62/1.88 thf(func_def_33, type, b: a).
% 2.62/1.88 thf(func_def_34, type, c: a).
% 2.62/1.88 thf(func_def_35, type, inf: a > a > a).
% 2.62/1.88 thf(func_def_36, type, less_eq: a > a > $o).
% 2.62/1.88 thf(func_def_37, type, sup: a > a > a).
% 2.62/1.88 thf(func_def_52, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.62/1.88 thf(func_def_53, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.62/1.88 thf(func_def_55, type, sK2: a).
% 2.62/1.88 thf(func_def_56, type, sK3: a).
% 2.62/1.88 thf(func_def_57, type, sK4: a).
% 2.62/1.88 thf(func_def_58, type, sK5: (a > $o) > a > a).
% 2.62/1.88 thf(func_def_59, type, sK6: (a > $o) > (a > $o) > a).
% 2.62/1.88 thf(func_def_60, type, sK7: a > (a > $o) > a).
% 2.62/1.88 thf(func_def_61, type, sK8: set_a > a).
% 2.62/1.88 thf(func_def_62, type, sK9: set_a > a > a).
% 2.62/1.88 thf(func_def_63, type, sK10: set_a > set_a > a).
% 2.62/1.88 thf(func_def_64, type, sK11: a).
% 2.62/1.88 thf(func_def_65, type, sK12: a).
% 2.62/1.88 thf(func_def_66, type, sK13: set_a > a).
% 2.62/1.88 thf(func_def_67, type, sK14: set_a > a > a).
% 2.62/1.88 thf(func_def_68, type, sK15: set_a > a > a).
% 2.62/1.88 thf(func_def_69, type, sK16: set_a > a > a).
% 2.62/1.88 thf(func_def_70, type, sK17: a).
% 2.62/1.88 thf(func_def_71, type, sK18: a).
% 2.62/1.88 thf(func_def_72, type, sK19: a).
% 2.62/1.88 thf(func_def_73, type, sK20: a > (a > $o) > a).
% 2.62/1.88 thf(func_def_74, type, sK21: a > (a > $o) > a).
% 2.62/1.88 thf(func_def_75, type, sK22: (a > set_a) > a).
% 2.62/1.88 thf(func_def_76, type, sK23: (a > set_a) > a).
% 2.62/1.88 thf(func_def_77, type, sK24: (a > $o) > (a > $o) > a).
% 2.62/1.88 thf(func_def_78, type, sK25: a > (a > $o) > a).
% 2.62/1.88 thf(func_def_79, type, sK26: a > (a > $o) > a).
% 2.62/1.88 thf(func_def_80, type, sK27: (a > a > a) > a).
% 2.62/1.88 thf(func_def_81, type, sK28: (a > a > a) > a).
% 2.62/1.88 thf(func_def_82, type, sK29: (a > a > a) > a).
% 2.62/1.88 thf(func_def_83, type, sK30: (a > a > a) > a).
% 2.62/1.88 thf(func_def_84, type, sK31: (a > a > a) > a).
% 2.62/1.88 thf(func_def_85, type, sK32: (a > a > a) > a).
% 2.62/1.88 thf(func_def_86, type, sK33: (a > a > a) > a).
% 2.62/1.88 thf(func_def_87, type, sK34: (a > a > a) > a).
% 2.62/1.88 thf(func_def_88, type, sK35: (a > a > a) > a).
% 2.62/1.88 thf(func_def_89, type, sK36: (a > a > a) > a).
% 2.62/1.88 thf(func_def_90, type, sK37: (a > a > a) > a).
% 2.62/1.88 thf(func_def_91, type, sK38: (a > a > a) > a).
% 2.62/1.88 thf(func_def_92, type, sK39: (a > a > a) > a).
% 2.62/1.88 thf(func_def_93, type, sK40: (a > a > a) > a).
% 2.62/1.88 thf(func_def_94, type, sK41: set_a > a).
% 2.62/1.88 thf(func_def_95, type, sK42: (a > $o) > a > a).
% 2.62/1.88 thf(func_def_96, type, sK43: a > set_a > a).
% 2.62/1.88 thf(func_def_97, type, sK44: set_a > a > a).
% 2.62/1.88 thf(func_def_98, type, sK45: (a > set_a) > a).
% 2.62/1.88 thf(func_def_99, type, sK46: (a > set_a) > a).
% 2.62/1.88 thf(func_def_100, type, sK47: (a > a > a) > a).
% 2.62/1.88 thf(func_def_101, type, sK48: (a > a > a) > a).
% 2.62/1.88 thf(func_def_102, type, sK49: (a > a > a) > a).
% 2.62/1.88 thf(func_def_103, type, sK50: (a > $o) > (a > $o) > a).
% 2.62/1.88 thf(func_def_104, type, sK51: (a > $o) > a > a).
% 2.62/1.88 thf(func_def_105, type, sK52: (a > $o) > (a > $o) > a).
% 2.62/1.88 thf(func_def_107, type, ph54: !>[X0: $tType]:(X0)).
% 2.62/1.88 thf(f1513,plain,(
% 2.62/1.88 $false),
% 2.62/1.88 inference(subsumption_resolution,[status(thm)],[f1467,f1264])).
% 2.62/1.88 thf(f1264,plain,(
% 2.62/1.88 ( ! [X0 : a,X1 : a] : (((less_eq @ (inf @ X0 @ X1) @ X1) = $true)) )),
% 2.62/1.88 inference(cnf_transformation,[status(thm)],[f599])).
% 2.62/1.88 thf(f599,plain,(
% 2.62/1.88 ! [X0 : a,X1 : a] : ((less_eq @ (inf @ X0 @ X1) @ X1) = $true)),
% 2.62/1.88 inference(fool_elimination,[status(thm)],[f598])).
% 2.62/1.88 thf(f598,plain,(
% 2.62/1.88 ! [X0 : a,X1 : a] : (less_eq @ (inf @ X0 @ X1) @ X1)),
% 2.62/1.88 inference(rectify,[status(thm)],[f93])).
% 2.62/1.88 thf(f93,axiom,(
% 2.62/1.88 ! [X0 : a,X1 : a] : (less_eq @ (inf @ X0 @ X1) @ X1)),
% 2.62/1.88 file('/export/starexec/sandbox2/tmp/tmp.eimr8lCgBt/DTF2THF_6676.p',fact_92_local_Oinf_Ocobounded2)).
% 2.62/1.88 thf(f1467,plain,(
% 2.62/1.88 ($true != (less_eq @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))),
% 2.62/1.88 inference(trivial_inequality_removal,[status(thm)],[f1455])).
% 2.62/1.88 thf(f1455,plain,(
% 2.62/1.88 ($true != (less_eq @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))) | ((inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))) != (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))))),
% 2.62/1.88 inference(superposition,[status(thm)],[f1324,f1189])).
% 2.62/1.88 thf(f1189,plain,(
% 2.62/1.88 ( ! [X2 : a,X0 : a,X1 : a] : (((sup @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (sup @ X0 @ X2))) | ((less_eq @ X0 @ X1) != $true)) )),
% 2.62/1.88 inference(cnf_transformation,[status(thm)],[f845])).
% 2.62/1.88 thf(f845,plain,(
% 2.62/1.88 ! [X0 : a,X1 : a,X2 : a] : (((less_eq @ X0 @ X1) != $true) | ((sup @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (sup @ X0 @ X2))))),
% 2.62/1.88 inference(ennf_transformation,[status(thm)],[f529])).
% 2.62/1.88 thf(f529,plain,(
% 2.62/1.88 ! [X0 : a,X1 : a,X2 : a] : (((less_eq @ X0 @ X1) = $true) => ((sup @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (sup @ X0 @ X2))))),
% 2.62/1.88 inference(fool_elimination,[status(thm)],[f528])).
% 2.62/1.88 thf(f528,plain,(
% 2.62/1.88 ! [X0 : a,X1 : a,X2 : a] : ((less_eq @ X0 @ X1) => ((sup @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (sup @ X0 @ X2))))),
% 2.62/1.88 inference(rectify,[status(thm)],[f127])).
% 2.62/1.88 thf(f127,axiom,(
% 2.62/1.88 ! [X3 : a,X4 : a,X5 : a] : ((less_eq @ X3 @ X4) => ((sup @ X3 @ (inf @ X4 @ X5)) = (inf @ X4 @ (sup @ X3 @ X5))))),
% 2.62/1.88 file('/export/starexec/sandbox2/tmp/tmp.eimr8lCgBt/DTF2THF_6676.p',fact_126_local_Omodular)).
% 2.62/1.88 thf(f1324,plain,(
% 2.62/1.88 ((sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))) != (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))))),
% 2.62/1.88 inference(cnf_transformation,[status(thm)],[f759])).
% 2.62/1.88 thf(f759,plain,(
% 2.62/1.88 ((sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))) != (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))))),
% 2.62/1.88 inference(flattening,[status(thm)],[f266])).
% 2.62/1.88 thf(f266,plain,(
% 2.62/1.88 ~((sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))) = (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))))),
% 2.62/1.88 inference(fool_elimination,[status(thm)],[f256])).
% 2.62/1.88 thf(f256,negated_conjecture,(
% 2.62/1.88 ~((sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))) = (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))))),
% 2.62/1.88 inference(negated_conjecture,[status(cth)],[f255])).
% 2.62/1.88 thf(f255,conjecture,(
% 2.62/1.88 ((sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))) = (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))))),
% 2.62/1.88 file('/export/starexec/sandbox2/tmp/tmp.eimr8lCgBt/DTF2THF_6676.p',conj_0)).
% 2.62/1.88 % SZS output end Proof for DTF2THF_6676
% 2.62/1.88 % (6990)------------------------------
% 2.62/1.88 % (6990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.88 % (6990)Termination reason: Refutation
% 2.62/1.88
% 2.62/1.88 % (6990)Memory used [KB]: 6780
% 2.62/1.88 % (6990)Time elapsed: 0.039 s
% 2.62/1.88 % (6990)Instructions burned: 127 (million)
% 2.62/1.88 % (6990)------------------------------
% 2.62/1.88 % (6990)------------------------------
% 2.62/1.88 % (6946)Success in time 0.386 s
%------------------------------------------------------------------------------