%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP121^2 : 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 : n017.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 2.52s 1.95s
% Output : Refutation 2.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ITP121^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n017.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 08:25:26 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.41 thf(spec,logic,$$dhol).
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % File : ITP121^2 : TPTP v9.2.1. Released v7.5.0.
% 0.15/0.41 % Domain : Interactive Theorem Proving
% 0.15/0.41 % Problem : Sledgehammer Modular_Distrib_Lattice problem prob_236__3262688_1
% 0.15/0.41 % Version : Especial.
% 0.15/0.41 % English :
% 0.15/0.41
% 0.15/0.41 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.15/0.41 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.15/0.41 % Source : [Des21]
% 0.15/0.41 % Names : Modular_Distrib_Lattice/prob_236__3262688_1 [Des21]
% 0.15/0.41
% 0.15/0.41 % Status : Theorem
% 0.15/0.41 % Rating : 0.67 v8.1.0, 0.25 v7.5.0
% 0.15/0.41 % Syntax : Number of formulae : 304 ( 122 unt; 41 typ; 0 def)
% 0.15/0.41 % Number of atoms : 653 ( 205 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 7 ( 2 avg)
% 0.15/0.41 % Number of connectives : 2771 ( 42 ~; 0 |; 24 &;2433 @)
% 0.15/0.41 % ( 0 <=>; 272 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 16 ( 6 avg)
% 0.15/0.41 % Number of types : 2 ( 1 usr)
% 0.15/0.41 % Number of type conns : 198 ( 198 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 41 ( 40 usr; 3 con; 0-6 aty)
% 0.15/0.41 % Number of variables : 719 ( 25 ^; 649 !; 9 ?; 719 :)
% 0.15/0.41 % ( 36 !>; 0 ?*; 0 @-; 0 @+)
% 0.15/0.41 % SPC : TH1_THM_EQU_NAR
% 0.15/0.41
% 0.15/0.41 % Comments : This file was generated by Sledgehammer 2021-02-23 16:29:41.514
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % Could-be-implicit typings (2)
% 0.15/0.41 thf(ty_t_Set_Oset,type,
% 0.15/0.41 set: $tType > $tType ).
% 0.15/0.41
% 0.15/0.41 thf(ty_tf_a,type,
% 0.15/0.41 a: $tType ).
% 0.15/0.41
% 0.15/0.41 % Explicit typings (39)
% 0.15/0.41 thf(sy_cl_HOL_Otype,type,
% 0.15/0.41 type:
% 0.15/0.41 !>[A: $tType] : $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_cl_Orderings_Oorder,type,
% 0.15/0.41 order:
% 0.15/0.41 !>[A: $tType] : $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.15/0.41 semilattice_inf:
% 0.15/0.41 !>[A: $tType] : $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above,type,
% 0.15/0.41 condit2040224947_above:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below,type,
% 0.15/0.41 condit1201339847_below:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Finite__Set_Ocomp__fun__idem,type,
% 0.15/0.41 finite_comp_fun_idem:
% 0.15/0.41 !>[A: $tType,B: $tType] : ( ( A > B > B ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Finite__Set_Ofinite,type,
% 0.15/0.41 finite_finite:
% 0.15/0.41 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Groups_Oabel__semigroup,type,
% 0.15/0.41 abel_semigroup:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Groups_Osemigroup,type,
% 0.15/0.41 semigroup:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.15/0.41 inf_inf:
% 0.15/0.41 !>[A: $tType] : ( A > A > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Lattices_Osemilattice,type,
% 0.15/0.41 semilattice:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin,type,
% 0.15/0.41 lattic1263571978nf_fin:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > ( set @ A ) > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Lattices__Big_Osemilattice__set,type,
% 0.15/0.41 lattic35693393ce_set:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin,type,
% 0.15/0.41 lattic1039401930up_fin:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > ( set @ A ) > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oa__aux,type,
% 0.15/0.41 modula105138637_a_aux:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Ob__aux,type,
% 0.15/0.41 modula477145868_b_aux:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oc__aux,type,
% 0.15/0.41 modula849153099_c_aux:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Od__aux,type,
% 0.15/0.41 modula1221160330_d_aux:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oe__aux,type,
% 0.15/0.41 modula1593167561_e_aux:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oincomp,type,
% 0.15/0.41 modula1937309406incomp:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.15/0.41 bot_bot:
% 0.15/0.41 !>[A: $tType] : A ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord_OLeast,type,
% 0.15/0.41 least:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord_Omax,type,
% 0.15/0.41 max:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord_Omin,type,
% 0.15/0.41 min:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.15/0.41 ord_less_eq:
% 0.15/0.41 !>[A: $tType] : ( A > A > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oorder_OGreatest,type,
% 0.15/0.41 greatest:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oorder_Oantimono,type,
% 0.15/0.41 antimono:
% 0.15/0.41 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oorder_Omono,type,
% 0.15/0.41 mono:
% 0.15/0.41 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Set_OCollect,type,
% 0.15/0.41 collect:
% 0.15/0.41 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Set_Oinsert,type,
% 0.15/0.41 insert:
% 0.15/0.41 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Set__Interval_Oord_OatLeast,type,
% 0.15/0.41 set_atLeast:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Set__Interval_Oord_OatMost,type,
% 0.15/0.41 set_atMost:
% 0.15/0.41 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_member,type,
% 0.15/0.41 member:
% 0.15/0.41 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_a,type,
% 0.15/0.41 a2: a ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_b,type,
% 0.15/0.41 b: a ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_c,type,
% 0.15/0.41 c: a ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_inf,type,
% 0.15/0.41 inf: a > a > a ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_less__eq,type,
% 0.15/0.41 less_eq: a > a > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_sup,type,
% 0.15/0.41 sup: a > a > a ).
% 0.15/0.41
% 0.15/0.41 % Relevant facts (256)
% 0.15/0.41 thf(fact_0_local_Oinf_Oassoc,axiom,
% 0.15/0.41 ! [A2: a,B2: a,C: a] :
% 0.15/0.41 ( ( inf @ ( inf @ A2 @ B2 ) @ C )
% 0.15/0.42 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.assoc
% 0.15/0.42 thf(fact_1_local_Oinf_Ocommute,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( inf @ A2 @ B2 )
% 0.15/0.42 = ( inf @ B2 @ A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.commute
% 0.15/0.42 thf(fact_2_local_Oinf_Oleft__commute,axiom,
% 0.15/0.42 ! [B2: a,A2: a,C: a] :
% 0.15/0.42 ( ( inf @ B2 @ ( inf @ A2 @ C ) )
% 0.15/0.42 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.left_commute
% 0.15/0.42 thf(fact_3_local_Oinf__assoc,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ( inf @ ( inf @ X @ Y ) @ Z )
% 0.15/0.42 = ( inf @ X @ ( inf @ Y @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_assoc
% 0.15/0.42 thf(fact_4_local_Oinf__commute,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( inf @ X @ Y )
% 0.15/0.42 = ( inf @ Y @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_commute
% 0.15/0.42 thf(fact_5_local_Oinf__left__commute,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ( inf @ X @ ( inf @ Y @ Z ) )
% 0.15/0.42 = ( inf @ Y @ ( inf @ X @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_left_commute
% 0.15/0.42 thf(fact_6_local_Osup_Oassoc,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( sup @ ( sup @ A2 @ B2 ) @ C )
% 0.15/0.42 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.assoc
% 0.15/0.42 thf(fact_7_local_Osup_Ocommute,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( sup @ A2 @ B2 )
% 0.15/0.42 = ( sup @ B2 @ A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.commute
% 0.15/0.42 thf(fact_8_local_Osup_Oleft__commute,axiom,
% 0.15/0.42 ! [B2: a,A2: a,C: a] :
% 0.15/0.42 ( ( sup @ B2 @ ( sup @ A2 @ C ) )
% 0.15/0.42 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.left_commute
% 0.15/0.42 thf(fact_9_local_Osup__assoc,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ( sup @ ( sup @ X @ Y ) @ Z )
% 0.15/0.42 = ( sup @ X @ ( sup @ Y @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_assoc
% 0.15/0.42 thf(fact_10_local_Osup__commute,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( sup @ X @ Y )
% 0.15/0.42 = ( sup @ Y @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_commute
% 0.15/0.42 thf(fact_11_local_Osup__left__commute,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ( sup @ X @ ( sup @ Y @ Z ) )
% 0.15/0.42 = ( sup @ Y @ ( sup @ X @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_left_commute
% 0.15/0.42 thf(fact_12_local_Odistrib__imp1,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ! [X2: a,Y2: a,Z2: a] :
% 0.15/0.42 ( ( inf @ X2 @ ( sup @ Y2 @ Z2 ) )
% 0.15/0.42 = ( sup @ ( inf @ X2 @ Y2 ) @ ( inf @ X2 @ Z2 ) ) )
% 0.15/0.42 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 0.15/0.42 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.distrib_imp1
% 0.15/0.42 thf(fact_13_local_Odistrib__imp2,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ! [X2: a,Y2: a,Z2: a] :
% 0.15/0.42 ( ( sup @ X2 @ ( inf @ Y2 @ Z2 ) )
% 0.15/0.42 = ( inf @ ( sup @ X2 @ Y2 ) @ ( sup @ X2 @ Z2 ) ) )
% 0.15/0.42 => ( ( inf @ X @ ( sup @ Y @ Z ) )
% 0.15/0.42 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.distrib_imp2
% 0.15/0.42 thf(fact_14_local_Oa__join__d,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( sup @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.a_join_d
% 0.15/0.42 thf(fact_15_a__meet__d,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( inf @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ C @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % a_meet_d
% 0.15/0.42 thf(fact_16_local_Ob__join__d,axiom,
% 0.15/0.42 ! [B2: a,A2: a,C: a] :
% 0.15/0.42 ( ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( sup @ B2 @ ( inf @ C @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.b_join_d
% 0.15/0.42 thf(fact_17_b__meet__d,axiom,
% 0.15/0.42 ! [B2: a,A2: a,C: a] :
% 0.15/0.42 ( ( inf @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( sup @ ( inf @ B2 @ C ) @ ( inf @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % b_meet_d
% 0.15/0.42 thf(fact_18_c__meet__d,axiom,
% 0.15/0.42 ! [C: a,A2: a,B2: a] :
% 0.15/0.42 ( ( inf @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( sup @ ( inf @ C @ A2 ) @ ( inf @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % c_meet_d
% 0.15/0.42 thf(fact_19_local_Od__aux__def,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( sup @ ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ B2 @ C ) ) @ ( inf @ C @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.d_aux_def
% 0.15/0.42 thf(fact_20_local_Od__b__c__a,axiom,
% 0.15/0.42 ! [B2: a,C: a,A2: a] :
% 0.15/0.42 ( ( modula1221160330_d_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 0.15/0.42 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.d_b_c_a
% 0.15/0.42 thf(fact_21_local_Od__c__a__b,axiom,
% 0.15/0.42 ! [C: a,A2: a,B2: a] :
% 0.15/0.42 ( ( modula1221160330_d_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 0.15/0.42 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.d_c_a_b
% 0.15/0.42 thf(fact_22_local_Oa__meet__e,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( inf @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.a_meet_e
% 0.15/0.42 thf(fact_23_local_Ob__meet__e,axiom,
% 0.15/0.42 ! [B2: a,A2: a,C: a] :
% 0.15/0.42 ( ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( inf @ B2 @ ( sup @ C @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.b_meet_e
% 0.15/0.42 thf(fact_24_local_Oc__meet__e,axiom,
% 0.15/0.42 ! [C: a,A2: a,B2: a] :
% 0.15/0.42 ( ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( inf @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.c_meet_e
% 0.15/0.42 thf(fact_25_local_Oe__aux__def,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( inf @ ( inf @ ( sup @ A2 @ B2 ) @ ( sup @ B2 @ C ) ) @ ( sup @ C @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.e_aux_def
% 0.15/0.42 thf(fact_26_local_Oe__b__c__a,axiom,
% 0.15/0.42 ! [B2: a,C: a,A2: a] :
% 0.15/0.42 ( ( modula1593167561_e_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 0.15/0.42 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.e_b_c_a
% 0.15/0.42 thf(fact_27_local_Oe__c__a__b,axiom,
% 0.15/0.42 ! [C: a,A2: a,B2: a] :
% 0.15/0.42 ( ( modula1593167561_e_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 0.15/0.42 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.e_c_a_b
% 0.15/0.42 thf(fact_28_local_Oinf_Oidem,axiom,
% 0.15/0.42 ! [A2: a] :
% 0.15/0.42 ( ( inf @ A2 @ A2 )
% 0.15/0.42 = A2 ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.idem
% 0.15/0.42 thf(fact_29_local_Oinf_Oleft__idem,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( inf @ A2 @ ( inf @ A2 @ B2 ) )
% 0.15/0.42 = ( inf @ A2 @ B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.left_idem
% 0.15/0.42 thf(fact_30_local_Oinf_Oright__idem,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( inf @ ( inf @ A2 @ B2 ) @ B2 )
% 0.15/0.42 = ( inf @ A2 @ B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.right_idem
% 0.15/0.42 thf(fact_31_local_Oinf__idem,axiom,
% 0.15/0.42 ! [X: a] :
% 0.15/0.42 ( ( inf @ X @ X )
% 0.15/0.42 = X ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_idem
% 0.15/0.42 thf(fact_32_local_Oinf__left__idem,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( inf @ X @ ( inf @ X @ Y ) )
% 0.15/0.42 = ( inf @ X @ Y ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_left_idem
% 0.15/0.42 thf(fact_33_local_Oinf__right__idem,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 0.15/0.42 = ( inf @ X @ Y ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_right_idem
% 0.15/0.42 thf(fact_34_local_Osup_Oidem,axiom,
% 0.15/0.42 ! [A2: a] :
% 0.15/0.42 ( ( sup @ A2 @ A2 )
% 0.15/0.42 = A2 ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.idem
% 0.15/0.42 thf(fact_35_local_Osup_Oleft__idem,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( sup @ A2 @ ( sup @ A2 @ B2 ) )
% 0.15/0.42 = ( sup @ A2 @ B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.left_idem
% 0.15/0.42 thf(fact_36_local_Osup_Oright__idem,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( sup @ ( sup @ A2 @ B2 ) @ B2 )
% 0.15/0.42 = ( sup @ A2 @ B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.right_idem
% 0.15/0.42 thf(fact_37_local_Osup__idem,axiom,
% 0.15/0.42 ! [X: a] :
% 0.15/0.42 ( ( sup @ X @ X )
% 0.15/0.42 = X ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_idem
% 0.15/0.42 thf(fact_38_local_Osup__left__idem,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( sup @ X @ ( sup @ X @ Y ) )
% 0.15/0.42 = ( sup @ X @ Y ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_left_idem
% 0.15/0.42 thf(fact_39_calculation,axiom,
% 0.15/0.42 ( ( sup @ ( inf @ ( sup @ a2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( sup @ b @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) )
% 0.15/0.42 = ( sup @ ( inf @ ( sup @ b @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % calculation
% 0.15/0.42 thf(fact_40_local_Oinf__sup__absorb,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( inf @ X @ ( sup @ X @ Y ) )
% 0.15/0.42 = X ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_sup_absorb
% 0.15/0.42 thf(fact_41_local_Osup__inf__absorb,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( sup @ X @ ( inf @ X @ Y ) )
% 0.15/0.42 = X ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_inf_absorb
% 0.15/0.42 thf(fact_42_local_Ob__aux__def,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( sup @ ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.b_aux_def
% 0.15/0.42 thf(fact_43_local_Oc__aux__def,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( sup @ ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.c_aux_def
% 0.15/0.42 thf(fact_44_local_Oa__aux__def,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( sup @ ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.a_aux_def
% 0.15/0.42 thf(fact_45_mem__Collect__eq,axiom,
% 0.15/0.42 ! [A: $tType,A2: A,P: A > $o] :
% 0.15/0.42 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.15/0.42 = ( P @ A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % mem_Collect_eq
% 0.15/0.42 thf(fact_46_Collect__mem__eq,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A] :
% 0.15/0.42 ( ( collect @ A
% 0.15/0.42 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 0.15/0.42 = A3 ) ).
% 0.15/0.42
% 0.15/0.42 % Collect_mem_eq
% 0.15/0.42 thf(fact_47_Collect__cong,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.15/0.42 ( ! [X2: A] :
% 0.15/0.42 ( ( P @ X2 )
% 0.15/0.42 = ( Q @ X2 ) )
% 0.15/0.42 => ( ( collect @ A @ P )
% 0.15/0.42 = ( collect @ A @ Q ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Collect_cong
% 0.15/0.42 thf(fact_48_ext,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.15/0.42 ( ! [X2: A] :
% 0.15/0.42 ( ( F @ X2 )
% 0.15/0.42 = ( G @ X2 ) )
% 0.15/0.42 => ( F = G ) ) ).
% 0.15/0.42
% 0.15/0.42 % ext
% 0.15/0.42 thf(fact_49_lattice_Od__aux_Ocong,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( modula1221160330_d_aux @ A )
% 0.15/0.42 = ( modula1221160330_d_aux @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lattice.d_aux.cong
% 0.15/0.42 thf(fact_50_lattice_Oe__aux_Ocong,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( modula1593167561_e_aux @ A )
% 0.15/0.42 = ( modula1593167561_e_aux @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lattice.e_aux.cong
% 0.15/0.42 thf(fact_51_d__less__e,axiom,
% 0.15/0.42 less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ).
% 0.15/0.42
% 0.15/0.42 % d_less_e
% 0.15/0.42 thf(fact_52_local_Ocomp__fun__idem__sup,axiom,
% 0.15/0.42 finite_comp_fun_idem @ a @ a @ sup ).
% 0.15/0.42
% 0.15/0.42 % local.comp_fun_idem_sup
% 0.15/0.42 thf(fact_53_local_Ocomp__fun__idem__inf,axiom,
% 0.15/0.42 finite_comp_fun_idem @ a @ a @ inf ).
% 0.15/0.42
% 0.15/0.42 % local.comp_fun_idem_inf
% 0.15/0.42 thf(fact_54_local_Osup_Osemigroup__axioms,axiom,
% 0.15/0.42 semigroup @ a @ sup ).
% 0.15/0.42
% 0.15/0.42 % local.sup.semigroup_axioms
% 0.15/0.42 thf(fact_55_local_Oinf_Osemigroup__axioms,axiom,
% 0.15/0.42 semigroup @ a @ inf ).
% 0.15/0.42
% 0.15/0.42 % local.inf.semigroup_axioms
% 0.15/0.42 thf(fact_56_local_Osup_Osemilattice__axioms,axiom,
% 0.15/0.42 semilattice @ a @ sup ).
% 0.15/0.42
% 0.15/0.42 % local.sup.semilattice_axioms
% 0.15/0.42 thf(fact_57_local_Oinf_Osemilattice__axioms,axiom,
% 0.15/0.42 semilattice @ a @ inf ).
% 0.15/0.42
% 0.15/0.42 % local.inf.semilattice_axioms
% 0.15/0.42 thf(fact_58_local_Osup_Oabel__semigroup__axioms,axiom,
% 0.15/0.42 abel_semigroup @ a @ sup ).
% 0.15/0.42
% 0.15/0.42 % local.sup.abel_semigroup_axioms
% 0.15/0.42 thf(fact_59_local_Oinf_Oabel__semigroup__axioms,axiom,
% 0.15/0.42 abel_semigroup @ a @ inf ).
% 0.15/0.42
% 0.15/0.42 % local.inf.abel_semigroup_axioms
% 0.15/0.42 thf(fact_60_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 0.15/0.42 lattic35693393ce_set @ a @ sup ).
% 0.15/0.42
% 0.15/0.42 % local.Sup_fin.semilattice_set_axioms
% 0.15/0.42 thf(fact_61_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 0.15/0.42 lattic35693393ce_set @ a @ inf ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.semilattice_set_axioms
% 0.15/0.42 thf(fact_62_local_Ob__a,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( modula105138637_a_aux @ a @ inf @ sup @ B2 @ C @ A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.b_a
% 0.15/0.42 thf(fact_63_local_Oantisym,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ( less_eq @ Y @ X )
% 0.15/0.42 => ( X = Y ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.antisym
% 0.15/0.42 thf(fact_64_local_Oantisym__conv,axiom,
% 0.15/0.42 ! [Y: a,X: a] :
% 0.15/0.42 ( ( less_eq @ Y @ X )
% 0.15/0.42 => ( ( less_eq @ X @ Y )
% 0.15/0.42 = ( X = Y ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.antisym_conv
% 0.15/0.42 thf(fact_65_local_Odual__order_Oantisym,axiom,
% 0.15/0.42 ! [B2: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 => ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( A2 = B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.dual_order.antisym
% 0.15/0.42 thf(fact_66_local_Odual__order_Oeq__iff,axiom,
% 0.15/0.42 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 0.15/0.42 = ( ^ [A4: a,B3: a] :
% 0.15/0.42 ( ( less_eq @ B3 @ A4 )
% 0.15/0.42 & ( less_eq @ A4 @ B3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.dual_order.eq_iff
% 0.15/0.42 thf(fact_67_local_Odual__order_Otrans,axiom,
% 0.15/0.42 ! [B2: a,A2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 => ( ( less_eq @ C @ B2 )
% 0.15/0.42 => ( less_eq @ C @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.dual_order.trans
% 0.15/0.42 thf(fact_68_local_Oeq__iff,axiom,
% 0.15/0.42 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 0.15/0.42 = ( ^ [X3: a,Y4: a] :
% 0.15/0.42 ( ( less_eq @ X3 @ Y4 )
% 0.15/0.42 & ( less_eq @ Y4 @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.eq_iff
% 0.15/0.42 thf(fact_69_local_Oeq__refl,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( X = Y )
% 0.15/0.42 => ( less_eq @ X @ Y ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.eq_refl
% 0.15/0.42 thf(fact_70_local_Oord__eq__le__trans,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( A2 = B2 )
% 0.15/0.42 => ( ( less_eq @ B2 @ C )
% 0.15/0.42 => ( less_eq @ A2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.ord_eq_le_trans
% 0.15/0.42 thf(fact_71_local_Oord__le__eq__trans,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( B2 = C )
% 0.15/0.42 => ( less_eq @ A2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.ord_le_eq_trans
% 0.15/0.42 thf(fact_72_local_Oorder_Oantisym,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 => ( A2 = B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.order.antisym
% 0.15/0.42 thf(fact_73_local_Oorder_Oeq__iff,axiom,
% 0.15/0.42 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 0.15/0.42 = ( ^ [A4: a,B3: a] :
% 0.15/0.42 ( ( less_eq @ A4 @ B3 )
% 0.15/0.42 & ( less_eq @ B3 @ A4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.order.eq_iff
% 0.15/0.42 thf(fact_74_local_Oorder_Otrans,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( less_eq @ B2 @ C )
% 0.15/0.42 => ( less_eq @ A2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.order.trans
% 0.15/0.42 thf(fact_75_local_Oorder__trans,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ( less_eq @ Y @ Z )
% 0.15/0.42 => ( less_eq @ X @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.order_trans
% 0.15/0.42 thf(fact_76_local_Ole__infI2,axiom,
% 0.15/0.42 ! [B2: a,X: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ X )
% 0.15/0.42 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_infI2
% 0.15/0.42 thf(fact_77_local_Ole__infI1,axiom,
% 0.15/0.42 ! [A2: a,X: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ X )
% 0.15/0.42 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_infI1
% 0.15/0.42 thf(fact_78_local_Ole__infI,axiom,
% 0.15/0.42 ! [X: a,A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ X @ A2 )
% 0.15/0.42 => ( ( less_eq @ X @ B2 )
% 0.15/0.42 => ( less_eq @ X @ ( inf @ A2 @ B2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_infI
% 0.15/0.42 thf(fact_79_local_Ole__infE,axiom,
% 0.15/0.42 ! [X: a,A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ X @ ( inf @ A2 @ B2 ) )
% 0.15/0.42 => ~ ( ( less_eq @ X @ A2 )
% 0.15/0.42 => ~ ( less_eq @ X @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_infE
% 0.15/0.42 thf(fact_80_local_Ole__iff__inf,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( less_eq @ X @ Y )
% 0.15/0.42 = ( ( inf @ X @ Y )
% 0.15/0.42 = X ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_iff_inf
% 0.15/0.42 thf(fact_81_local_Oinf__unique,axiom,
% 0.15/0.42 ! [F: a > a > a,X: a,Y: a] :
% 0.15/0.42 ( ! [X2: a,Y2: a] : ( less_eq @ ( F @ X2 @ Y2 ) @ X2 )
% 0.15/0.42 => ( ! [X2: a,Y2: a] : ( less_eq @ ( F @ X2 @ Y2 ) @ Y2 )
% 0.15/0.42 => ( ! [X2: a,Y2: a,Z2: a] :
% 0.15/0.42 ( ( less_eq @ X2 @ Y2 )
% 0.15/0.42 => ( ( less_eq @ X2 @ Z2 )
% 0.15/0.42 => ( less_eq @ X2 @ ( F @ Y2 @ Z2 ) ) ) )
% 0.15/0.42 => ( ( inf @ X @ Y )
% 0.15/0.42 = ( F @ X @ Y ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_unique
% 0.15/0.42 thf(fact_82_local_Oinf__mono,axiom,
% 0.15/0.42 ! [A2: a,C: a,B2: a,D: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ C )
% 0.15/0.42 => ( ( less_eq @ B2 @ D )
% 0.15/0.42 => ( less_eq @ ( inf @ A2 @ B2 ) @ ( inf @ C @ D ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_mono
% 0.15/0.42 thf(fact_83_local_Oinf__le2,axiom,
% 0.15/0.42 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_le2
% 0.15/0.42 thf(fact_84_local_Oinf__le1,axiom,
% 0.15/0.42 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_le1
% 0.15/0.42 thf(fact_85_local_Oinf__greatest,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ( less_eq @ X @ Z )
% 0.15/0.42 => ( less_eq @ X @ ( inf @ Y @ Z ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_greatest
% 0.15/0.42 thf(fact_86_local_Oinf__absorb2,axiom,
% 0.15/0.42 ! [Y: a,X: a] :
% 0.15/0.42 ( ( less_eq @ Y @ X )
% 0.15/0.42 => ( ( inf @ X @ Y )
% 0.15/0.42 = Y ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_absorb2
% 0.15/0.42 thf(fact_87_local_Oinf__absorb1,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ( inf @ X @ Y )
% 0.15/0.42 = X ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_absorb1
% 0.15/0.42 thf(fact_88_local_Oinf_Oorder__iff,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 = ( A2
% 0.15/0.42 = ( inf @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.order_iff
% 0.15/0.42 thf(fact_89_local_Oinf_OorderI,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( A2
% 0.15/0.42 = ( inf @ A2 @ B2 ) )
% 0.15/0.42 => ( less_eq @ A2 @ B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.orderI
% 0.15/0.42 thf(fact_90_local_Oinf_OorderE,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( A2
% 0.15/0.42 = ( inf @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.orderE
% 0.15/0.42 thf(fact_91_local_Oinf_OcoboundedI2,axiom,
% 0.15/0.42 ! [B2: a,C: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ C )
% 0.15/0.42 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.coboundedI2
% 0.15/0.42 thf(fact_92_local_Oinf_OcoboundedI1,axiom,
% 0.15/0.42 ! [A2: a,C: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ C )
% 0.15/0.42 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.coboundedI1
% 0.15/0.42 thf(fact_93_local_Oinf_Ocobounded2,axiom,
% 0.15/0.42 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ B2 ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.cobounded2
% 0.15/0.42 thf(fact_94_local_Oinf_Ocobounded1,axiom,
% 0.15/0.42 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ A2 ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.cobounded1
% 0.15/0.42 thf(fact_95_local_Oinf_OboundedI,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( less_eq @ A2 @ C )
% 0.15/0.42 => ( less_eq @ A2 @ ( inf @ B2 @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.boundedI
% 0.15/0.42 thf(fact_96_local_Oinf_OboundedE,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 0.15/0.42 => ~ ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ~ ( less_eq @ A2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.boundedE
% 0.15/0.42 thf(fact_97_local_Oinf_Oabsorb__iff2,axiom,
% 0.15/0.42 ! [B2: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 = ( ( inf @ A2 @ B2 )
% 0.15/0.42 = B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.absorb_iff2
% 0.15/0.42 thf(fact_98_local_Oinf_Oabsorb__iff1,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 = ( ( inf @ A2 @ B2 )
% 0.15/0.42 = A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.absorb_iff1
% 0.15/0.42 thf(fact_99_local_Oinf_Oabsorb2,axiom,
% 0.15/0.42 ! [B2: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 => ( ( inf @ A2 @ B2 )
% 0.15/0.42 = B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.absorb2
% 0.15/0.42 thf(fact_100_local_Oinf_Oabsorb1,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( inf @ A2 @ B2 )
% 0.15/0.42 = A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.absorb1
% 0.15/0.42 thf(fact_101_local_Osup__unique,axiom,
% 0.15/0.42 ! [F: a > a > a,X: a,Y: a] :
% 0.15/0.42 ( ! [X2: a,Y2: a] : ( less_eq @ X2 @ ( F @ X2 @ Y2 ) )
% 0.15/0.42 => ( ! [X2: a,Y2: a] : ( less_eq @ Y2 @ ( F @ X2 @ Y2 ) )
% 0.15/0.42 => ( ! [X2: a,Y2: a,Z2: a] :
% 0.15/0.42 ( ( less_eq @ Y2 @ X2 )
% 0.15/0.42 => ( ( less_eq @ Z2 @ X2 )
% 0.15/0.42 => ( less_eq @ ( F @ Y2 @ Z2 ) @ X2 ) ) )
% 0.15/0.42 => ( ( sup @ X @ Y )
% 0.15/0.42 = ( F @ X @ Y ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_unique
% 0.15/0.42 thf(fact_102_local_Osup__mono,axiom,
% 0.15/0.42 ! [A2: a,C: a,B2: a,D: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ C )
% 0.15/0.42 => ( ( less_eq @ B2 @ D )
% 0.15/0.42 => ( less_eq @ ( sup @ A2 @ B2 ) @ ( sup @ C @ D ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_mono
% 0.15/0.42 thf(fact_103_local_Osup__least,axiom,
% 0.15/0.42 ! [Y: a,X: a,Z: a] :
% 0.15/0.42 ( ( less_eq @ Y @ X )
% 0.15/0.42 => ( ( less_eq @ Z @ X )
% 0.15/0.42 => ( less_eq @ ( sup @ Y @ Z ) @ X ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_least
% 0.15/0.42 thf(fact_104_local_Osup__ge2,axiom,
% 0.15/0.42 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_ge2
% 0.15/0.42 thf(fact_105_local_Osup__ge1,axiom,
% 0.15/0.42 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_ge1
% 0.15/0.42 thf(fact_106_local_Osup__absorb2,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ( sup @ X @ Y )
% 0.15/0.42 = Y ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_absorb2
% 0.15/0.42 thf(fact_107_local_Osup__absorb1,axiom,
% 0.15/0.42 ! [Y: a,X: a] :
% 0.15/0.42 ( ( less_eq @ Y @ X )
% 0.15/0.42 => ( ( sup @ X @ Y )
% 0.15/0.42 = X ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_absorb1
% 0.15/0.42 thf(fact_108_local_Osup_Oorder__iff,axiom,
% 0.15/0.42 ! [B2: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 = ( A2
% 0.15/0.42 = ( sup @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.order_iff
% 0.15/0.42 thf(fact_109_local_Osup_OorderI,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( A2
% 0.15/0.42 = ( sup @ A2 @ B2 ) )
% 0.15/0.42 => ( less_eq @ B2 @ A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.orderI
% 0.15/0.42 thf(fact_110_local_Osup_OorderE,axiom,
% 0.15/0.42 ! [B2: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 => ( A2
% 0.15/0.42 = ( sup @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.orderE
% 0.15/0.42 thf(fact_111_local_Osup_Omono,axiom,
% 0.15/0.42 ! [C: a,A2: a,D: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ C @ A2 )
% 0.15/0.42 => ( ( less_eq @ D @ B2 )
% 0.15/0.42 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A2 @ B2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.mono
% 0.15/0.42 thf(fact_112_local_Osup_OcoboundedI2,axiom,
% 0.15/0.42 ! [C: a,B2: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ C @ B2 )
% 0.15/0.42 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.coboundedI2
% 0.15/0.42 thf(fact_113_local_Osup_OcoboundedI1,axiom,
% 0.15/0.42 ! [C: a,A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ C @ A2 )
% 0.15/0.42 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.coboundedI1
% 0.15/0.42 thf(fact_114_local_Osup_Ocobounded2,axiom,
% 0.15/0.42 ! [B2: a,A2: a] : ( less_eq @ B2 @ ( sup @ A2 @ B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.cobounded2
% 0.15/0.42 thf(fact_115_local_Osup_Ocobounded1,axiom,
% 0.15/0.42 ! [A2: a,B2: a] : ( less_eq @ A2 @ ( sup @ A2 @ B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.cobounded1
% 0.15/0.42 thf(fact_116_local_Osup_OboundedI,axiom,
% 0.15/0.42 ! [B2: a,A2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 => ( ( less_eq @ C @ A2 )
% 0.15/0.42 => ( less_eq @ ( sup @ B2 @ C ) @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.boundedI
% 0.15/0.42 thf(fact_117_local_Osup_OboundedE,axiom,
% 0.15/0.42 ! [B2: a,C: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 0.15/0.42 => ~ ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 => ~ ( less_eq @ C @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.boundedE
% 0.15/0.42 thf(fact_118_local_Osup_Oabsorb__iff2,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 = ( ( sup @ A2 @ B2 )
% 0.15/0.42 = B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.absorb_iff2
% 0.15/0.42 thf(fact_119_local_Osup_Oabsorb__iff1,axiom,
% 0.15/0.42 ! [B2: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 = ( ( sup @ A2 @ B2 )
% 0.15/0.42 = A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.absorb_iff1
% 0.15/0.42 thf(fact_120_local_Osup_Oabsorb2,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( sup @ A2 @ B2 )
% 0.15/0.42 = B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.absorb2
% 0.15/0.42 thf(fact_121_local_Osup_Oabsorb1,axiom,
% 0.15/0.42 ! [B2: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 => ( ( sup @ A2 @ B2 )
% 0.15/0.42 = A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.absorb1
% 0.15/0.42 thf(fact_122_local_Ole__supI2,axiom,
% 0.15/0.42 ! [X: a,B2: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ X @ B2 )
% 0.15/0.42 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_supI2
% 0.15/0.42 thf(fact_123_local_Ole__supI1,axiom,
% 0.15/0.42 ! [X: a,A2: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ X @ A2 )
% 0.15/0.42 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_supI1
% 0.15/0.42 thf(fact_124_local_Ole__supI,axiom,
% 0.15/0.42 ! [A2: a,X: a,B2: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ X )
% 0.15/0.42 => ( ( less_eq @ B2 @ X )
% 0.15/0.42 => ( less_eq @ ( sup @ A2 @ B2 ) @ X ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_supI
% 0.15/0.42 thf(fact_125_local_Ole__supE,axiom,
% 0.15/0.42 ! [A2: a,B2: a,X: a] :
% 0.15/0.42 ( ( less_eq @ ( sup @ A2 @ B2 ) @ X )
% 0.15/0.42 => ~ ( ( less_eq @ A2 @ X )
% 0.15/0.42 => ~ ( less_eq @ B2 @ X ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_supE
% 0.15/0.42 thf(fact_126_local_Ole__iff__sup,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( less_eq @ X @ Y )
% 0.15/0.42 = ( ( sup @ X @ Y )
% 0.15/0.42 = Y ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_iff_sup
% 0.15/0.42 thf(fact_127_local_Omodular,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 0.15/0.42 = ( inf @ Y @ ( sup @ X @ Z ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.modular
% 0.15/0.42 thf(fact_128_local_Odistrib__sup__le,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.distrib_sup_le
% 0.15/0.42 thf(fact_129_local_Odistrib__inf__le,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) @ ( inf @ X @ ( sup @ Y @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.distrib_inf_le
% 0.15/0.42 thf(fact_130_local_Oincomp__def,axiom,
% 0.15/0.42 ! [X: a,Y: a] :
% 0.15/0.42 ( ( modula1937309406incomp @ a @ less_eq @ X @ Y )
% 0.15/0.42 = ( ~ ( less_eq @ X @ Y )
% 0.15/0.42 & ~ ( less_eq @ Y @ X ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.incomp_def
% 0.15/0.42 thf(fact_131_local_Oc__a,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( modula105138637_a_aux @ a @ inf @ sup @ C @ A2 @ B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.c_a
% 0.15/0.42 thf(fact_132_local_Oorder_Orefl,axiom,
% 0.15/0.42 ! [A2: a] : ( less_eq @ A2 @ A2 ) ).
% 0.15/0.42
% 0.15/0.42 % local.order.refl
% 0.15/0.42 thf(fact_133_local_Oorder__refl,axiom,
% 0.15/0.42 ! [X: a] : ( less_eq @ X @ X ) ).
% 0.15/0.42
% 0.15/0.42 % local.order_refl
% 0.15/0.42 thf(fact_134_local_OGreatestI2__order,axiom,
% 0.15/0.42 ! [P: a > $o,X: a,Q: a > $o] :
% 0.15/0.42 ( ( P @ X )
% 0.15/0.42 => ( ! [Y2: a] :
% 0.15/0.42 ( ( P @ Y2 )
% 0.15/0.42 => ( less_eq @ Y2 @ X ) )
% 0.15/0.42 => ( ! [X2: a] :
% 0.15/0.42 ( ( P @ X2 )
% 0.15/0.42 => ( ! [Y5: a] :
% 0.15/0.42 ( ( P @ Y5 )
% 0.15/0.42 => ( less_eq @ Y5 @ X2 ) )
% 0.15/0.42 => ( Q @ X2 ) ) )
% 0.15/0.42 => ( Q @ ( greatest @ a @ less_eq @ P ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.GreatestI2_order
% 0.15/0.42 thf(fact_135_local_OGreatest__equality,axiom,
% 0.15/0.42 ! [P: a > $o,X: a] :
% 0.15/0.42 ( ( P @ X )
% 0.15/0.42 => ( ! [Y2: a] :
% 0.15/0.42 ( ( P @ Y2 )
% 0.15/0.42 => ( less_eq @ Y2 @ X ) )
% 0.15/0.42 => ( ( greatest @ a @ less_eq @ P )
% 0.15/0.42 = X ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Greatest_equality
% 0.15/0.42 thf(fact_136_local_Omax__def,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.15/0.42 = B2 ) )
% 0.15/0.42 & ( ~ ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.15/0.42 = A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.max_def
% 0.15/0.42 thf(fact_137_local_Omin__def,axiom,
% 0.15/0.42 ! [A2: a,B2: a] :
% 0.15/0.42 ( ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.15/0.42 = A2 ) )
% 0.15/0.42 & ( ~ ( less_eq @ A2 @ B2 )
% 0.15/0.42 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.15/0.42 = B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.min_def
% 0.15/0.42 thf(fact_138_a__def__equiv,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 => ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( inf @ ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % a_def_equiv
% 0.15/0.42 thf(fact_139_c__def__equiv,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 => ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( inf @ ( sup @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % c_def_equiv
% 0.15/0.42 thf(fact_140_b__def__equiv,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 => ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.15/0.42 = ( inf @ ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % b_def_equiv
% 0.15/0.42 thf(fact_141_c__meet__a__eq__d,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 => ( ( inf @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % c_meet_a_eq_d
% 0.15/0.42 thf(fact_142_a__meet__b__eq__d,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 => ( ( inf @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % a_meet_b_eq_d
% 0.15/0.42 thf(fact_143_b__meet__c__eq__d,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 => ( ( inf @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.15/0.42 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % b_meet_c_eq_d
% 0.15/0.42 thf(fact_144_local_Ole__inf__iff,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ( less_eq @ X @ ( inf @ Y @ Z ) )
% 0.15/0.42 = ( ( less_eq @ X @ Y )
% 0.15/0.42 & ( less_eq @ X @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_inf_iff
% 0.15/0.42 thf(fact_145_local_Oinf_Obounded__iff,axiom,
% 0.15/0.42 ! [A2: a,B2: a,C: a] :
% 0.15/0.42 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 0.15/0.42 = ( ( less_eq @ A2 @ B2 )
% 0.15/0.42 & ( less_eq @ A2 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf.bounded_iff
% 0.15/0.42 thf(fact_146_local_Osup_Obounded__iff,axiom,
% 0.15/0.42 ! [B2: a,C: a,A2: a] :
% 0.15/0.42 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 0.15/0.42 = ( ( less_eq @ B2 @ A2 )
% 0.15/0.42 & ( less_eq @ C @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup.bounded_iff
% 0.15/0.42 thf(fact_147_local_Ole__sup__iff,axiom,
% 0.15/0.42 ! [X: a,Y: a,Z: a] :
% 0.15/0.42 ( ( less_eq @ ( sup @ X @ Y ) @ Z )
% 0.15/0.42 = ( ( less_eq @ X @ Z )
% 0.15/0.42 & ( less_eq @ Y @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.le_sup_iff
% 0.15/0.42 thf(fact_148_local_OLeast1I,axiom,
% 0.15/0.42 ! [P: a > $o] :
% 0.15/0.42 ( ? [X4: a] :
% 0.15/0.42 ( ( P @ X4 )
% 0.15/0.42 & ! [Y2: a] :
% 0.15/0.42 ( ( P @ Y2 )
% 0.15/0.42 => ( less_eq @ X4 @ Y2 ) )
% 0.15/0.42 & ! [Y2: a] :
% 0.15/0.42 ( ( ( P @ Y2 )
% 0.15/0.42 & ! [Ya: a] :
% 0.15/0.42 ( ( P @ Ya )
% 0.15/0.42 => ( less_eq @ Y2 @ Ya ) ) )
% 0.15/0.42 => ( Y2 = X4 ) ) )
% 0.15/0.42 => ( P @ ( least @ a @ less_eq @ P ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Least1I
% 0.15/0.42 thf(fact_149_local_OLeast1__le,axiom,
% 0.15/0.42 ! [P: a > $o,Z: a] :
% 0.15/0.42 ( ? [X4: a] :
% 0.15/0.42 ( ( P @ X4 )
% 0.15/0.42 & ! [Y2: a] :
% 0.15/0.42 ( ( P @ Y2 )
% 0.15/0.42 => ( less_eq @ X4 @ Y2 ) )
% 0.15/0.42 & ! [Y2: a] :
% 0.15/0.42 ( ( ( P @ Y2 )
% 0.15/0.42 & ! [Ya: a] :
% 0.15/0.42 ( ( P @ Ya )
% 0.15/0.42 => ( less_eq @ Y2 @ Ya ) ) )
% 0.15/0.42 => ( Y2 = X4 ) ) )
% 0.15/0.42 => ( ( P @ Z )
% 0.15/0.42 => ( less_eq @ ( least @ a @ less_eq @ P ) @ Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Least1_le
% 0.15/0.42 thf(fact_150_local_OLeastI2__order,axiom,
% 0.15/0.42 ! [P: a > $o,X: a,Q: a > $o] :
% 0.15/0.42 ( ( P @ X )
% 0.15/0.42 => ( ! [Y2: a] :
% 0.15/0.42 ( ( P @ Y2 )
% 0.15/0.42 => ( less_eq @ X @ Y2 ) )
% 0.15/0.42 => ( ! [X2: a] :
% 0.15/0.42 ( ( P @ X2 )
% 0.15/0.42 => ( ! [Y5: a] :
% 0.15/0.42 ( ( P @ Y5 )
% 0.15/0.42 => ( less_eq @ X2 @ Y5 ) )
% 0.15/0.42 => ( Q @ X2 ) ) )
% 0.15/0.42 => ( Q @ ( least @ a @ less_eq @ P ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.LeastI2_order
% 0.15/0.42 thf(fact_151_local_OLeast__equality,axiom,
% 0.15/0.42 ! [P: a > $o,X: a] :
% 0.15/0.42 ( ( P @ X )
% 0.15/0.42 => ( ! [Y2: a] :
% 0.15/0.42 ( ( P @ Y2 )
% 0.15/0.42 => ( less_eq @ X @ Y2 ) )
% 0.15/0.42 => ( ( least @ a @ less_eq @ P )
% 0.15/0.42 = X ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Least_equality
% 0.15/0.42 thf(fact_152_lattice_Oc__aux_Ocong,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( modula849153099_c_aux @ A )
% 0.15/0.42 = ( modula849153099_c_aux @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lattice.c_aux.cong
% 0.15/0.42 thf(fact_153_lattice_Ob__aux_Ocong,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( modula477145868_b_aux @ A )
% 0.15/0.42 = ( modula477145868_b_aux @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lattice.b_aux.cong
% 0.15/0.42 thf(fact_154_lattice_Oa__aux_Ocong,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( modula105138637_a_aux @ A )
% 0.15/0.42 = ( modula105138637_a_aux @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lattice.a_aux.cong
% 0.15/0.42 thf(fact_155_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A] :
% 0.15/0.42 ( ( abel_semigroup @ A @ F )
% 0.15/0.42 => ( semigroup @ A @ F ) ) ).
% 0.15/0.42
% 0.15/0.42 % abel_semigroup.axioms(1)
% 0.15/0.42 thf(fact_156_semilattice__set__def,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( lattic35693393ce_set @ A )
% 0.15/0.42 = ( semilattice @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_set_def
% 0.15/0.42 thf(fact_157_semilattice__set_Ointro,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A] :
% 0.15/0.42 ( ( semilattice @ A @ F )
% 0.15/0.42 => ( lattic35693393ce_set @ A @ F ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_set.intro
% 0.15/0.42 thf(fact_158_semilattice__set_Oaxioms,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A] :
% 0.15/0.42 ( ( lattic35693393ce_set @ A @ F )
% 0.15/0.42 => ( semilattice @ A @ F ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_set.axioms
% 0.15/0.42 thf(fact_159_semilattice_Oaxioms_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A] :
% 0.15/0.42 ( ( semilattice @ A @ F )
% 0.15/0.42 => ( abel_semigroup @ A @ F ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice.axioms(1)
% 0.15/0.42 thf(fact_160_local_Obdd__above__def,axiom,
% 0.15/0.42 ! [A3: set @ a] :
% 0.15/0.42 ( ( condit2040224947_above @ a @ less_eq @ A3 )
% 0.15/0.42 = ( ? [M: a] :
% 0.15/0.42 ! [X3: a] :
% 0.15/0.42 ( ( member @ a @ X3 @ A3 )
% 0.15/0.42 => ( less_eq @ X3 @ M ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_above_def
% 0.15/0.42 thf(fact_161_local_Obdd__below__def,axiom,
% 0.15/0.42 ! [A3: set @ a] :
% 0.15/0.42 ( ( condit1201339847_below @ a @ less_eq @ A3 )
% 0.15/0.42 = ( ? [M2: a] :
% 0.15/0.42 ! [X3: a] :
% 0.15/0.42 ( ( member @ a @ X3 @ A3 )
% 0.15/0.42 => ( less_eq @ M2 @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_below_def
% 0.15/0.42 thf(fact_162_local_Obdd__belowI,axiom,
% 0.15/0.42 ! [A3: set @ a,M3: a] :
% 0.15/0.42 ( ! [X2: a] :
% 0.15/0.42 ( ( member @ a @ X2 @ A3 )
% 0.15/0.42 => ( less_eq @ M3 @ X2 ) )
% 0.15/0.42 => ( condit1201339847_below @ a @ less_eq @ A3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_belowI
% 0.15/0.42 thf(fact_163_local_Obdd__aboveI,axiom,
% 0.15/0.42 ! [A3: set @ a,M4: a] :
% 0.15/0.42 ( ! [X2: a] :
% 0.15/0.42 ( ( member @ a @ X2 @ A3 )
% 0.15/0.42 => ( less_eq @ X2 @ M4 ) )
% 0.15/0.42 => ( condit2040224947_above @ a @ less_eq @ A3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_aboveI
% 0.15/0.42 thf(fact_164_lattice_Oincomp_Ocong,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( modula1937309406incomp @ A )
% 0.15/0.42 = ( modula1937309406incomp @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lattice.incomp.cong
% 0.15/0.42 thf(fact_165_abel__semigroup_Oleft__commute,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A,B2: A,A2: A,C: A] :
% 0.15/0.42 ( ( abel_semigroup @ A @ F )
% 0.15/0.42 => ( ( F @ B2 @ ( F @ A2 @ C ) )
% 0.15/0.42 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % abel_semigroup.left_commute
% 0.15/0.42 thf(fact_166_semilattice_Oright__idem,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.15/0.42 ( ( semilattice @ A @ F )
% 0.15/0.42 => ( ( F @ ( F @ A2 @ B2 ) @ B2 )
% 0.15/0.42 = ( F @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice.right_idem
% 0.15/0.42 thf(fact_167_semilattice_Oleft__idem,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.15/0.42 ( ( semilattice @ A @ F )
% 0.15/0.42 => ( ( F @ A2 @ ( F @ A2 @ B2 ) )
% 0.15/0.42 = ( F @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice.left_idem
% 0.15/0.42 thf(fact_168_abel__semigroup_Ocommute,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.15/0.42 ( ( abel_semigroup @ A @ F )
% 0.15/0.42 => ( ( F @ A2 @ B2 )
% 0.15/0.42 = ( F @ B2 @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % abel_semigroup.commute
% 0.15/0.42 thf(fact_169_semilattice_Oidem,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A,A2: A] :
% 0.15/0.42 ( ( semilattice @ A @ F )
% 0.15/0.42 => ( ( F @ A2 @ A2 )
% 0.15/0.42 = A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice.idem
% 0.15/0.42 thf(fact_170_semigroup_Ointro,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A] :
% 0.15/0.42 ( ! [A5: A,B4: A,C2: A] :
% 0.15/0.42 ( ( F @ ( F @ A5 @ B4 ) @ C2 )
% 0.15/0.42 = ( F @ A5 @ ( F @ B4 @ C2 ) ) )
% 0.15/0.42 => ( semigroup @ A @ F ) ) ).
% 0.15/0.42
% 0.15/0.42 % semigroup.intro
% 0.15/0.42 thf(fact_171_semigroup_Oassoc,axiom,
% 0.15/0.42 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 0.15/0.42 ( ( semigroup @ A @ F )
% 0.15/0.42 => ( ( F @ ( F @ A2 @ B2 ) @ C )
% 0.15/0.42 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % semigroup.assoc
% 0.15/0.42 thf(fact_172_semigroup__def,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( semigroup @ A )
% 0.15/0.42 = ( ^ [F2: A > A > A] :
% 0.15/0.42 ! [A4: A,B3: A,C3: A] :
% 0.15/0.42 ( ( F2 @ ( F2 @ A4 @ B3 ) @ C3 )
% 0.15/0.42 = ( F2 @ A4 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % semigroup_def
% 0.15/0.42 thf(fact_173_local_Obdd__below__mono,axiom,
% 0.15/0.42 ! [B5: set @ a,A3: set @ a] :
% 0.15/0.42 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 0.15/0.42 => ( ( ord_less_eq @ ( set @ a ) @ A3 @ B5 )
% 0.15/0.42 => ( condit1201339847_below @ a @ less_eq @ A3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_below_mono
% 0.15/0.42 thf(fact_174_local_Obdd__above__mono,axiom,
% 0.15/0.42 ! [B5: set @ a,A3: set @ a] :
% 0.15/0.42 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 0.15/0.42 => ( ( ord_less_eq @ ( set @ a ) @ A3 @ B5 )
% 0.15/0.42 => ( condit2040224947_above @ a @ less_eq @ A3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_above_mono
% 0.15/0.42 thf(fact_175_local_Obdd__below__finite,axiom,
% 0.15/0.42 ! [A3: set @ a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( condit1201339847_below @ a @ less_eq @ A3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_below_finite
% 0.15/0.42 thf(fact_176_local_Ofinite__has__maximal2,axiom,
% 0.15/0.42 ! [A3: set @ a,A2: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( member @ a @ A2 @ A3 )
% 0.15/0.42 => ? [X2: a] :
% 0.15/0.42 ( ( member @ a @ X2 @ A3 )
% 0.15/0.42 & ( less_eq @ A2 @ X2 )
% 0.15/0.42 & ! [Xa: a] :
% 0.15/0.42 ( ( member @ a @ Xa @ A3 )
% 0.15/0.42 => ( ( less_eq @ X2 @ Xa )
% 0.15/0.42 => ( X2 = Xa ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.finite_has_maximal2
% 0.15/0.42 thf(fact_177_local_Ofinite__has__minimal2,axiom,
% 0.15/0.42 ! [A3: set @ a,A2: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( member @ a @ A2 @ A3 )
% 0.15/0.42 => ? [X2: a] :
% 0.15/0.42 ( ( member @ a @ X2 @ A3 )
% 0.15/0.42 & ( less_eq @ X2 @ A2 )
% 0.15/0.42 & ! [Xa: a] :
% 0.15/0.42 ( ( member @ a @ Xa @ A3 )
% 0.15/0.42 => ( ( less_eq @ Xa @ X2 )
% 0.15/0.42 => ( X2 = Xa ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.finite_has_minimal2
% 0.15/0.42 thf(fact_178_local_Obdd__above__finite,axiom,
% 0.15/0.42 ! [A3: set @ a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( condit2040224947_above @ a @ less_eq @ A3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_above_finite
% 0.15/0.42 thf(fact_179_local_OantimonoD,axiom,
% 0.15/0.42 ! [B: $tType] :
% 0.15/0.42 ( ( order @ B )
% 0.15/0.42 => ! [F: a > B,X: a,Y: a] :
% 0.15/0.42 ( ( antimono @ a @ B @ less_eq @ F )
% 0.15/0.42 => ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.antimonoD
% 0.15/0.42 thf(fact_180_local_OantimonoE,axiom,
% 0.15/0.42 ! [B: $tType] :
% 0.15/0.42 ( ( order @ B )
% 0.15/0.42 => ! [F: a > B,X: a,Y: a] :
% 0.15/0.42 ( ( antimono @ a @ B @ less_eq @ F )
% 0.15/0.42 => ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.antimonoE
% 0.15/0.42 thf(fact_181_local_OantimonoI,axiom,
% 0.15/0.42 ! [B: $tType] :
% 0.15/0.42 ( ( order @ B )
% 0.15/0.42 => ! [F: a > B] :
% 0.15/0.42 ( ! [X2: a,Y2: a] :
% 0.15/0.42 ( ( less_eq @ X2 @ Y2 )
% 0.15/0.42 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X2 ) ) )
% 0.15/0.42 => ( antimono @ a @ B @ less_eq @ F ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.antimonoI
% 0.15/0.42 thf(fact_182_local_Oantimono__def,axiom,
% 0.15/0.42 ! [B: $tType] :
% 0.15/0.42 ( ( order @ B )
% 0.15/0.42 => ! [F: a > B] :
% 0.15/0.42 ( ( antimono @ a @ B @ less_eq @ F )
% 0.15/0.42 = ( ! [X3: a,Y4: a] :
% 0.15/0.42 ( ( less_eq @ X3 @ Y4 )
% 0.15/0.42 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X3 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.antimono_def
% 0.15/0.42 thf(fact_183_local_Omono__def,axiom,
% 0.15/0.42 ! [B: $tType] :
% 0.15/0.42 ( ( order @ B )
% 0.15/0.42 => ! [F: a > B] :
% 0.15/0.42 ( ( mono @ a @ B @ less_eq @ F )
% 0.15/0.42 = ( ! [X3: a,Y4: a] :
% 0.15/0.42 ( ( less_eq @ X3 @ Y4 )
% 0.15/0.42 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.mono_def
% 0.15/0.42 thf(fact_184_local_OmonoI,axiom,
% 0.15/0.42 ! [B: $tType] :
% 0.15/0.42 ( ( order @ B )
% 0.15/0.42 => ! [F: a > B] :
% 0.15/0.42 ( ! [X2: a,Y2: a] :
% 0.15/0.42 ( ( less_eq @ X2 @ Y2 )
% 0.15/0.42 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.15/0.42 => ( mono @ a @ B @ less_eq @ F ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.monoI
% 0.15/0.42 thf(fact_185_local_OmonoE,axiom,
% 0.15/0.42 ! [B: $tType] :
% 0.15/0.42 ( ( order @ B )
% 0.15/0.42 => ! [F: a > B,X: a,Y: a] :
% 0.15/0.42 ( ( mono @ a @ B @ less_eq @ F )
% 0.15/0.42 => ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.monoE
% 0.15/0.42 thf(fact_186_local_OmonoD,axiom,
% 0.15/0.42 ! [B: $tType] :
% 0.15/0.42 ( ( order @ B )
% 0.15/0.42 => ! [F: a > B,X: a,Y: a] :
% 0.15/0.42 ( ( mono @ a @ B @ less_eq @ F )
% 0.15/0.42 => ( ( less_eq @ X @ Y )
% 0.15/0.42 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.monoD
% 0.15/0.42 thf(fact_187_local_OSup__fin_OcoboundedI,axiom,
% 0.15/0.42 ! [A3: set @ a,A2: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( member @ a @ A2 @ A3 )
% 0.15/0.42 => ( less_eq @ A2 @ ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Sup_fin.coboundedI
% 0.15/0.42 thf(fact_188_local_OInf__fin_OcoboundedI,axiom,
% 0.15/0.42 ! [A3: set @ a,A2: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( member @ a @ A2 @ A3 )
% 0.15/0.42 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) @ A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.coboundedI
% 0.15/0.42 thf(fact_189_local_OSup__fin_Oin__idem,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( member @ a @ X @ A3 )
% 0.15/0.42 => ( ( sup @ X @ ( lattic1039401930up_fin @ a @ sup @ A3 ) )
% 0.15/0.42 = ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Sup_fin.in_idem
% 0.15/0.42 thf(fact_190_local_OInf__fin_Oin__idem,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( member @ a @ X @ A3 )
% 0.15/0.42 => ( ( inf @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) )
% 0.15/0.42 = ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.in_idem
% 0.15/0.42 thf(fact_191_local_Osup__Inf__absorb,axiom,
% 0.15/0.42 ! [A3: set @ a,A2: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( member @ a @ A2 @ A3 )
% 0.15/0.42 => ( ( sup @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) @ A2 )
% 0.15/0.42 = A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.sup_Inf_absorb
% 0.15/0.42 thf(fact_192_local_Oinf__Sup__absorb,axiom,
% 0.15/0.42 ! [A3: set @ a,A2: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( member @ a @ A2 @ A3 )
% 0.15/0.42 => ( ( inf @ A2 @ ( lattic1039401930up_fin @ a @ sup @ A3 ) )
% 0.15/0.42 = A2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.inf_Sup_absorb
% 0.15/0.42 thf(fact_193_semilattice__inf_OInf__fin_Ocong,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( lattic1263571978nf_fin @ A )
% 0.15/0.42 = ( lattic1263571978nf_fin @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_inf.Inf_fin.cong
% 0.15/0.42 thf(fact_194_semilattice__sup_OSup__fin_Ocong,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( lattic1039401930up_fin @ A )
% 0.15/0.42 = ( lattic1039401930up_fin @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_sup.Sup_fin.cong
% 0.15/0.42 thf(fact_195_local_OInf__fin__le__Sup__fin,axiom,
% 0.15/0.42 ! [A3: set @ a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) @ ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin_le_Sup_fin
% 0.15/0.42 thf(fact_196_local_OSup__fin_Osubset__imp,axiom,
% 0.15/0.42 ! [A3: set @ a,B5: set @ a] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ a ) @ A3 @ B5 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( finite_finite @ a @ B5 )
% 0.15/0.42 => ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A3 ) @ ( lattic1039401930up_fin @ a @ sup @ B5 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Sup_fin.subset_imp
% 0.15/0.42 thf(fact_197_local_Ofinite__has__minimal,axiom,
% 0.15/0.42 ! [A3: set @ a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ? [X2: a] :
% 0.15/0.42 ( ( member @ a @ X2 @ A3 )
% 0.15/0.42 & ! [Xa: a] :
% 0.15/0.42 ( ( member @ a @ Xa @ A3 )
% 0.15/0.42 => ( ( less_eq @ Xa @ X2 )
% 0.15/0.42 => ( X2 = Xa ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.finite_has_minimal
% 0.15/0.42 thf(fact_198_local_Ofinite__has__maximal,axiom,
% 0.15/0.42 ! [A3: set @ a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ? [X2: a] :
% 0.15/0.42 ( ( member @ a @ X2 @ A3 )
% 0.15/0.42 & ! [Xa: a] :
% 0.15/0.42 ( ( member @ a @ Xa @ A3 )
% 0.15/0.42 => ( ( less_eq @ X2 @ Xa )
% 0.15/0.42 => ( X2 = Xa ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.finite_has_maximal
% 0.15/0.42 thf(fact_199_local_OInf__fin_Osubset,axiom,
% 0.15/0.42 ! [A3: set @ a,B5: set @ a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( B5
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( ord_less_eq @ ( set @ a ) @ B5 @ A3 )
% 0.15/0.42 => ( ( inf @ ( lattic1263571978nf_fin @ a @ inf @ B5 ) @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) )
% 0.15/0.42 = ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.subset
% 0.15/0.42 thf(fact_200_local_OSup__fin_Osubset,axiom,
% 0.15/0.42 ! [A3: set @ a,B5: set @ a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( B5
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( ord_less_eq @ ( set @ a ) @ B5 @ A3 )
% 0.15/0.42 => ( ( sup @ ( lattic1039401930up_fin @ a @ sup @ B5 ) @ ( lattic1039401930up_fin @ a @ sup @ A3 ) )
% 0.15/0.42 = ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Sup_fin.subset
% 0.15/0.42 thf(fact_201_local_OInf__fin_Obounded__iff,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) )
% 0.15/0.42 = ( ! [X3: a] :
% 0.15/0.42 ( ( member @ a @ X3 @ A3 )
% 0.15/0.42 => ( less_eq @ X @ X3 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.bounded_iff
% 0.15/0.42 thf(fact_202_local_OInf__fin_OboundedI,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ! [A5: a] :
% 0.15/0.42 ( ( member @ a @ A5 @ A3 )
% 0.15/0.42 => ( less_eq @ X @ A5 ) )
% 0.15/0.42 => ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.boundedI
% 0.15/0.42 thf(fact_203_local_OInf__fin_OboundedE,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) )
% 0.15/0.42 => ! [A6: a] :
% 0.15/0.42 ( ( member @ a @ A6 @ A3 )
% 0.15/0.42 => ( less_eq @ X @ A6 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.boundedE
% 0.15/0.42 thf(fact_204_local_OSup__fin_Obounded__iff,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A3 ) @ X )
% 0.15/0.42 = ( ! [X3: a] :
% 0.15/0.42 ( ( member @ a @ X3 @ A3 )
% 0.15/0.42 => ( less_eq @ X3 @ X ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Sup_fin.bounded_iff
% 0.15/0.42 thf(fact_205_local_OSup__fin_OboundedI,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ! [A5: a] :
% 0.15/0.42 ( ( member @ a @ A5 @ A3 )
% 0.15/0.42 => ( less_eq @ A5 @ X ) )
% 0.15/0.42 => ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A3 ) @ X ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Sup_fin.boundedI
% 0.15/0.42 thf(fact_206_local_OSup__fin_OboundedE,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A3 ) @ X )
% 0.15/0.42 => ! [A6: a] :
% 0.15/0.42 ( ( member @ a @ A6 @ A3 )
% 0.15/0.42 => ( less_eq @ A6 @ X ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Sup_fin.boundedE
% 0.15/0.42 thf(fact_207_local_OInf__fin_Osubset__imp,axiom,
% 0.15/0.42 ! [A3: set @ a,B5: set @ a] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ a ) @ A3 @ B5 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( finite_finite @ a @ B5 )
% 0.15/0.42 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ B5 ) @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.subset_imp
% 0.15/0.42 thf(fact_208_local_Obdd__above__empty,axiom,
% 0.15/0.42 condit2040224947_above @ a @ less_eq @ ( bot_bot @ ( set @ a ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_above_empty
% 0.15/0.42 thf(fact_209_local_Obdd__below__empty,axiom,
% 0.15/0.42 condit1201339847_below @ a @ less_eq @ ( bot_bot @ ( set @ a ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_below_empty
% 0.15/0.42 thf(fact_210_local_Onot__empty__eq__Iic__eq__empty,axiom,
% 0.15/0.42 ! [H: a] :
% 0.15/0.42 ( ( bot_bot @ ( set @ a ) )
% 0.15/0.42 != ( set_atMost @ a @ less_eq @ H ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.not_empty_eq_Iic_eq_empty
% 0.15/0.42 thf(fact_211_local_Onot__empty__eq__Ici__eq__empty,axiom,
% 0.15/0.42 ! [L: a] :
% 0.15/0.42 ( ( bot_bot @ ( set @ a ) )
% 0.15/0.42 != ( set_atLeast @ a @ less_eq @ L ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.not_empty_eq_Ici_eq_empty
% 0.15/0.42 thf(fact_212_local_OatLeast__iff,axiom,
% 0.15/0.42 ! [I: a,K: a] :
% 0.15/0.42 ( ( member @ a @ I @ ( set_atLeast @ a @ less_eq @ K ) )
% 0.15/0.42 = ( less_eq @ K @ I ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.atLeast_iff
% 0.15/0.42 thf(fact_213_local_OatMost__iff,axiom,
% 0.15/0.42 ! [I: a,K: a] :
% 0.15/0.42 ( ( member @ a @ I @ ( set_atMost @ a @ less_eq @ K ) )
% 0.15/0.42 = ( less_eq @ I @ K ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.atMost_iff
% 0.15/0.42 thf(fact_214_local_Obdd__below__Ici,axiom,
% 0.15/0.42 ! [A2: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeast @ a @ less_eq @ A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_below_Ici
% 0.15/0.42 thf(fact_215_local_Obdd__above__Iic,axiom,
% 0.15/0.42 ! [B2: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atMost @ a @ less_eq @ B2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_above_Iic
% 0.15/0.42 thf(fact_216_empty__subsetI,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 0.15/0.42
% 0.15/0.42 % empty_subsetI
% 0.15/0.42 thf(fact_217_subset__empty,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.15/0.42 = ( A3
% 0.15/0.42 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % subset_empty
% 0.15/0.42 thf(fact_218_empty__iff,axiom,
% 0.15/0.42 ! [A: $tType,C: A] :
% 0.15/0.42 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % empty_iff
% 0.15/0.42 thf(fact_219_all__not__in__conv,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A] :
% 0.15/0.42 ( ( ! [X3: A] :
% 0.15/0.42 ~ ( member @ A @ X3 @ A3 ) )
% 0.15/0.42 = ( A3
% 0.15/0.42 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % all_not_in_conv
% 0.15/0.42 thf(fact_220_Collect__empty__eq,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o] :
% 0.15/0.42 ( ( ( collect @ A @ P )
% 0.15/0.42 = ( bot_bot @ ( set @ A ) ) )
% 0.15/0.42 = ( ! [X3: A] :
% 0.15/0.42 ~ ( P @ X3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Collect_empty_eq
% 0.15/0.42 thf(fact_221_empty__Collect__eq,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o] :
% 0.15/0.42 ( ( ( bot_bot @ ( set @ A ) )
% 0.15/0.42 = ( collect @ A @ P ) )
% 0.15/0.42 = ( ! [X3: A] :
% 0.15/0.42 ~ ( P @ X3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % empty_Collect_eq
% 0.15/0.42 thf(fact_222_subsetI,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 0.15/0.42 ( ! [X2: A] :
% 0.15/0.42 ( ( member @ A @ X2 @ A3 )
% 0.15/0.42 => ( member @ A @ X2 @ B5 ) )
% 0.15/0.42 => ( ord_less_eq @ ( set @ A ) @ A3 @ B5 ) ) ).
% 0.15/0.42
% 0.15/0.42 % subsetI
% 0.15/0.42 thf(fact_223_subset__antisym,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 0.15/0.42 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A3 )
% 0.15/0.42 => ( A3 = B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % subset_antisym
% 0.15/0.42 thf(fact_224_emptyE,axiom,
% 0.15/0.42 ! [A: $tType,A2: A] :
% 0.15/0.42 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % emptyE
% 0.15/0.42 thf(fact_225_equals0D,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A,A2: A] :
% 0.15/0.42 ( ( A3
% 0.15/0.42 = ( bot_bot @ ( set @ A ) ) )
% 0.15/0.42 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % equals0D
% 0.15/0.42 thf(fact_226_equals0I,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A] :
% 0.15/0.42 ( ! [Y2: A] :
% 0.15/0.42 ~ ( member @ A @ Y2 @ A3 )
% 0.15/0.42 => ( A3
% 0.15/0.42 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % equals0I
% 0.15/0.42 thf(fact_227_ex__in__conv,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A] :
% 0.15/0.42 ( ( ? [X3: A] : ( member @ A @ X3 @ A3 ) )
% 0.15/0.42 = ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % ex_in_conv
% 0.15/0.42 thf(fact_228_in__mono,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A,B5: set @ A,X: A] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 0.15/0.42 => ( ( member @ A @ X @ A3 )
% 0.15/0.42 => ( member @ A @ X @ B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % in_mono
% 0.15/0.42 thf(fact_229_subsetD,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A,B5: set @ A,C: A] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 0.15/0.42 => ( ( member @ A @ C @ A3 )
% 0.15/0.42 => ( member @ A @ C @ B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % subsetD
% 0.15/0.42 thf(fact_230_equalityE,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 0.15/0.42 ( ( A3 = B5 )
% 0.15/0.42 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 0.15/0.42 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % equalityE
% 0.15/0.42 thf(fact_231_subset__eq,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) )
% 0.15/0.42 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.15/0.42 ! [X3: A] :
% 0.15/0.42 ( ( member @ A @ X3 @ A7 )
% 0.15/0.42 => ( member @ A @ X3 @ B6 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % subset_eq
% 0.15/0.42 thf(fact_232_equalityD1,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 0.15/0.42 ( ( A3 = B5 )
% 0.15/0.42 => ( ord_less_eq @ ( set @ A ) @ A3 @ B5 ) ) ).
% 0.15/0.42
% 0.15/0.42 % equalityD1
% 0.15/0.42 thf(fact_233_equalityD2,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 0.15/0.42 ( ( A3 = B5 )
% 0.15/0.42 => ( ord_less_eq @ ( set @ A ) @ B5 @ A3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % equalityD2
% 0.15/0.42 thf(fact_234_subset__iff,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) )
% 0.15/0.42 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.15/0.42 ! [T: A] :
% 0.15/0.42 ( ( member @ A @ T @ A7 )
% 0.15/0.42 => ( member @ A @ T @ B6 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % subset_iff
% 0.15/0.42 thf(fact_235_subset__refl,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.15/0.42
% 0.15/0.42 % subset_refl
% 0.15/0.42 thf(fact_236_Collect__mono,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.15/0.42 ( ! [X2: A] :
% 0.15/0.42 ( ( P @ X2 )
% 0.15/0.42 => ( Q @ X2 ) )
% 0.15/0.42 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Collect_mono
% 0.15/0.42 thf(fact_237_subset__trans,axiom,
% 0.15/0.42 ! [A: $tType,A3: set @ A,B5: set @ A,C4: set @ A] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 0.15/0.42 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 0.15/0.42 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % subset_trans
% 0.15/0.42 thf(fact_238_set__eq__subset,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( ^ [Y3: set @ A,Z3: set @ A] : ( Y3 = Z3 ) )
% 0.15/0.42 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B6 )
% 0.15/0.42 & ( ord_less_eq @ ( set @ A ) @ B6 @ A7 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % set_eq_subset
% 0.15/0.42 thf(fact_239_Collect__mono__iff,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.15/0.42 = ( ! [X3: A] :
% 0.15/0.42 ( ( P @ X3 )
% 0.15/0.42 => ( Q @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Collect_mono_iff
% 0.15/0.42 thf(fact_240_local_Omono__inf,axiom,
% 0.15/0.42 ! [B: $tType] :
% 0.15/0.42 ( ( semilattice_inf @ B )
% 0.15/0.42 => ! [F: a > B,A3: a,B5: a] :
% 0.15/0.42 ( ( mono @ a @ B @ less_eq @ F )
% 0.15/0.42 => ( ord_less_eq @ B @ ( F @ ( inf @ A3 @ B5 ) ) @ ( inf_inf @ B @ ( F @ A3 ) @ ( F @ B5 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.mono_inf
% 0.15/0.42 thf(fact_241_local_OSup__fin_Oinsert__not__elem,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ~ ( member @ a @ X @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ X @ A3 ) )
% 0.15/0.42 = ( sup @ X @ ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Sup_fin.insert_not_elem
% 0.15/0.42 thf(fact_242_local_Obdd__below__Int2,axiom,
% 0.15/0.42 ! [B5: set @ a,A3: set @ a] :
% 0.15/0.42 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 0.15/0.42 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A3 @ B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_below_Int2
% 0.15/0.42 thf(fact_243_local_Obdd__below__Int1,axiom,
% 0.15/0.42 ! [A3: set @ a,B5: set @ a] :
% 0.15/0.42 ( ( condit1201339847_below @ a @ less_eq @ A3 )
% 0.15/0.42 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A3 @ B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_below_Int1
% 0.15/0.42 thf(fact_244_local_Obdd__above__Int2,axiom,
% 0.15/0.42 ! [B5: set @ a,A3: set @ a] :
% 0.15/0.42 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 0.15/0.42 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A3 @ B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_above_Int2
% 0.15/0.42 thf(fact_245_local_Obdd__above__Int1,axiom,
% 0.15/0.42 ! [A3: set @ a,B5: set @ a] :
% 0.15/0.42 ( ( condit2040224947_above @ a @ less_eq @ A3 )
% 0.15/0.42 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A3 @ B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.bdd_above_Int1
% 0.15/0.42 thf(fact_246_Int__subset__iff,axiom,
% 0.15/0.42 ! [A: $tType,C4: set @ A,A3: set @ A,B5: set @ A] :
% 0.15/0.42 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A3 @ B5 ) )
% 0.15/0.42 = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A3 )
% 0.15/0.42 & ( ord_less_eq @ ( set @ A ) @ C4 @ B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Int_subset_iff
% 0.15/0.42 thf(fact_247_inf__apply,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType] :
% 0.15/0.42 ( ( semilattice_inf @ B )
% 0.15/0.42 => ( ( inf_inf @ ( A > B ) )
% 0.15/0.42 = ( ^ [F2: A > B,G2: A > B,X3: A] : ( inf_inf @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % inf_apply
% 0.15/0.42 thf(fact_248_semilattice__inf__class_Oinf_Oidem,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( semilattice_inf @ A )
% 0.15/0.42 => ! [A2: A] :
% 0.15/0.42 ( ( inf_inf @ A @ A2 @ A2 )
% 0.15/0.42 = A2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_inf_class.inf.idem
% 0.15/0.42 thf(fact_249_semilattice__inf__class_Oinf__idem,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( semilattice_inf @ A )
% 0.15/0.42 => ! [X: A] :
% 0.15/0.42 ( ( inf_inf @ A @ X @ X )
% 0.15/0.42 = X ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_inf_class.inf_idem
% 0.15/0.42 thf(fact_250_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( semilattice_inf @ A )
% 0.15/0.42 => ! [A2: A,B2: A] :
% 0.15/0.42 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.15/0.42 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_inf_class.inf.left_idem
% 0.15/0.42 thf(fact_251_semilattice__inf__class_Oinf__left__idem,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( semilattice_inf @ A )
% 0.15/0.42 => ! [X: A,Y: A] :
% 0.15/0.42 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.15/0.42 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_inf_class.inf_left_idem
% 0.15/0.42 thf(fact_252_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( semilattice_inf @ A )
% 0.15/0.42 => ! [A2: A,B2: A] :
% 0.15/0.42 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.15/0.42 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_inf_class.inf.right_idem
% 0.15/0.42 thf(fact_253_semilattice__inf__class_Oinf__right__idem,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( semilattice_inf @ A )
% 0.15/0.42 => ! [X: A,Y: A] :
% 0.15/0.42 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 0.15/0.42 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % semilattice_inf_class.inf_right_idem
% 0.15/0.42 thf(fact_254_local_OInf__fin_Oclosed,axiom,
% 0.15/0.42 ! [A3: set @ a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ! [X2: a,Y2: a] : ( member @ a @ ( inf @ X2 @ Y2 ) @ ( insert @ a @ X2 @ ( insert @ a @ Y2 @ ( bot_bot @ ( set @ a ) ) ) ) )
% 0.15/0.42 => ( member @ a @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) @ A3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.closed
% 0.15/0.42 thf(fact_255_local_OInf__fin_Oinsert__not__elem,axiom,
% 0.15/0.42 ! [A3: set @ a,X: a] :
% 0.15/0.42 ( ( finite_finite @ a @ A3 )
% 0.15/0.42 => ( ~ ( member @ a @ X @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( bot_bot @ ( set @ a ) ) )
% 0.15/0.42 => ( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ X @ A3 ) )
% 0.15/0.42 = ( inf @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.Inf_fin.insert_not_elem
% 0.15/0.42
% 0.15/0.42 % Type constructors (6)
% 0.15/0.42 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.15/0.42 ! [A8: $tType,A9: $tType] :
% 0.15/0.42 ( ( semilattice_inf @ A9 )
% 0.15/0.42 => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.15/0.42 ! [A8: $tType,A9: $tType] :
% 0.15/0.42 ( ( order @ A9 )
% 0.15/0.42 => ( order @ ( A8 > A9 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_1,axiom,
% 0.15/0.42 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 0.15/0.42 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_3,axiom,
% 0.15/0.42 semilattice_inf @ $o ).
% 0.15/0.42
% 0.15/0.42 thf(tcon_HOL_Obool___Orderings_Oorder_4,axiom,
% 0.15/0.42 order @ $o ).
% 0.15/0.42
% 0.15/0.42 % Conjectures (1)
% 0.15/0.42 thf(conj_0,conjecture,
% 0.15/0.42 ( ( sup @ ( inf @ ( sup @ b @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ) )
% 0.15/0.42 = ( inf @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 2.20/1.39 ---- Embedded in THF ---
% 2.20/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.20/1.39 %%% Generated on Tue Feb 24 08:25:27 EST 2026
% 2.20/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 2.20/1.39 %%% Logic specification used:
% 2.20/1.39 %%% thf(spec, logic, $$dhol).
% 2.20/1.39
% 2.20/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.mcq7CuGXAr/DTF2DTF13195.p
% 2.20/1.39 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.20/1.39 thf(ty_tf_a, type, a: $tType).
% 2.20/1.39 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.20/1.39 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.20/1.39 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 2.20/1.39 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above, type, condit2040224947_above: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.20/1.39 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below, type, condit1201339847_below: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.20/1.39 thf(sy_c_Finite__Set_Ocomp__fun__idem, type, finite_comp_fun_idem: (!> [A:$tType,B:$tType]: (((A > (B > B)) > $o)))).
% 2.20/1.39 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.20/1.39 thf(sy_c_Groups_Oabel__semigroup, type, abel_semigroup: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.20/1.39 thf(sy_c_Groups_Osemigroup, type, semigroup: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.20/1.39 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.20/1.39 thf(sy_c_Lattices_Osemilattice, type, semilattice: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.20/1.39 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin, type, lattic1263571978nf_fin: (!> [A:$tType]: (((A > (A > A)) > ((set @ A) > A))))).
% 2.20/1.39 thf(sy_c_Lattices__Big_Osemilattice__set, type, lattic35693393ce_set: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.20/1.39 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin, type, lattic1039401930up_fin: (!> [A:$tType]: (((A > (A > A)) > ((set @ A) > A))))).
% 2.20/1.39 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oa__aux, type, modula105138637_a_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.20/1.39 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Ob__aux, type, modula477145868_b_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.20/1.39 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oc__aux, type, modula849153099_c_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.20/1.39 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Od__aux, type, modula1221160330_d_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.20/1.39 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oe__aux, type, modula1593167561_e_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.20/1.39 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oincomp, type, modula1937309406incomp: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > $o)))))).
% 2.20/1.39 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.20/1.39 thf(sy_c_Orderings_Oord_OLeast, type, least: (!> [A:$tType]: (((A > (A > $o)) > ((A > $o) > A))))).
% 2.20/1.39 thf(sy_c_Orderings_Oord_Omax, type, max: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > A)))))).
% 2.20/1.39 thf(sy_c_Orderings_Oord_Omin, type, min: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > A)))))).
% 2.20/1.39 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.20/1.39 thf(sy_c_Orderings_Oorder_OGreatest, type, greatest: (!> [A:$tType]: (((A > (A > $o)) > ((A > $o) > A))))).
% 2.20/1.39 thf(sy_c_Orderings_Oorder_Oantimono, type, antimono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.20/1.39 thf(sy_c_Orderings_Oorder_Omono, type, mono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.20/1.39 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.20/1.39 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.20/1.39 thf(sy_c_Set__Interval_Oord_OatLeast, type, set_atLeast: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.20/1.39 thf(sy_c_Set__Interval_Oord_OatMost, type, set_atMost: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.20/1.39 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.20/1.39 thf(sy_v_a, type, a2: a).
% 2.20/1.39 thf(sy_v_b, type, b: a).
% 2.20/1.39 thf(sy_v_c, type, c: a).
% 2.20/1.39 thf(sy_v_inf, type, inf: (a > (a > a))).
% 2.20/1.39 thf(sy_v_less__eq, type, less_eq: (a > (a > $o))).
% 2.20/1.39 thf(sy_v_sup, type, sup: (a > (a > a))).
% 2.20/1.39 thf(fact_0_local_Oinf_Oassoc, axiom, (! [A2:a,B2:a,C:a]: ((((inf @ ((inf @ A2) @ B2)) @ C) = ((inf @ A2) @ ((inf @ B2) @ C)))))).
% 2.20/1.39 thf(fact_1_local_Oinf_Ocommute, axiom, (! [A2:a,B2:a]: ((((inf @ A2) @ B2) = ((inf @ B2) @ A2))))).
% 2.20/1.39 thf(fact_2_local_Oinf_Oleft__commute, axiom, (! [B2:a,A2:a,C:a]: ((((inf @ B2) @ ((inf @ A2) @ C)) = ((inf @ A2) @ ((inf @ B2) @ C)))))).
% 2.20/1.39 thf(fact_3_local_Oinf__assoc, axiom, (! [X:a,Y:a,Z:a]: ((((inf @ ((inf @ X) @ Y)) @ Z) = ((inf @ X) @ ((inf @ Y) @ Z)))))).
% 2.20/1.39 thf(fact_4_local_Oinf__commute, axiom, (! [X:a,Y:a]: ((((inf @ X) @ Y) = ((inf @ Y) @ X))))).
% 2.20/1.39 thf(fact_5_local_Oinf__left__commute, axiom, (! [X:a,Y:a,Z:a]: ((((inf @ X) @ ((inf @ Y) @ Z)) = ((inf @ Y) @ ((inf @ X) @ Z)))))).
% 2.20/1.39 thf(fact_6_local_Osup_Oassoc, axiom, (! [A2:a,B2:a,C:a]: ((((sup @ ((sup @ A2) @ B2)) @ C) = ((sup @ A2) @ ((sup @ B2) @ C)))))).
% 2.20/1.39 thf(fact_7_local_Osup_Ocommute, axiom, (! [A2:a,B2:a]: ((((sup @ A2) @ B2) = ((sup @ B2) @ A2))))).
% 2.20/1.39 thf(fact_8_local_Osup_Oleft__commute, axiom, (! [B2:a,A2:a,C:a]: ((((sup @ B2) @ ((sup @ A2) @ C)) = ((sup @ A2) @ ((sup @ B2) @ C)))))).
% 2.20/1.39 thf(fact_9_local_Osup__assoc, axiom, (! [X:a,Y:a,Z:a]: ((((sup @ ((sup @ X) @ Y)) @ Z) = ((sup @ X) @ ((sup @ Y) @ Z)))))).
% 2.20/1.39 thf(fact_10_local_Osup__commute, axiom, (! [X:a,Y:a]: ((((sup @ X) @ Y) = ((sup @ Y) @ X))))).
% 2.20/1.39 thf(fact_11_local_Osup__left__commute, axiom, (! [X:a,Y:a,Z:a]: ((((sup @ X) @ ((sup @ Y) @ Z)) = ((sup @ Y) @ ((sup @ X) @ Z)))))).
% 2.20/1.39 thf(fact_12_local_Odistrib__imp1, axiom, (! [X:a,Y:a,Z:a]: (((! [X2:a,Y2:a,Z2:a]: ((((inf @ X2) @ ((sup @ Y2) @ Z2)) = ((sup @ ((inf @ X2) @ Y2)) @ ((inf @ X2) @ Z2))))) => (((sup @ X) @ ((inf @ Y) @ Z)) = ((inf @ ((sup @ X) @ Y)) @ ((sup @ X) @ Z))))))).
% 2.20/1.39 thf(fact_13_local_Odistrib__imp2, axiom, (! [X:a,Y:a,Z:a]: (((! [X2:a,Y2:a,Z2:a]: ((((sup @ X2) @ ((inf @ Y2) @ Z2)) = ((inf @ ((sup @ X2) @ Y2)) @ ((sup @ X2) @ Z2))))) => (((inf @ X) @ ((sup @ Y) @ Z)) = ((sup @ ((inf @ X) @ Y)) @ ((inf @ X) @ Z))))))).
% 2.20/1.39 thf(fact_14_local_Oa__join__d, axiom, (! [A2:a,B2:a,C:a]: ((((sup @ A2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((sup @ A2) @ ((inf @ B2) @ C)))))).
% 2.20/1.39 thf(fact_15_a__meet__d, axiom, (! [A2:a,B2:a,C:a]: ((((inf @ A2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((sup @ ((inf @ A2) @ B2)) @ ((inf @ C) @ A2)))))).
% 2.20/1.39 thf(fact_16_local_Ob__join__d, axiom, (! [B2:a,A2:a,C:a]: ((((sup @ B2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((sup @ B2) @ ((inf @ C) @ A2)))))).
% 2.20/1.39 thf(fact_17_b__meet__d, axiom, (! [B2:a,A2:a,C:a]: ((((inf @ B2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((sup @ ((inf @ B2) @ C)) @ ((inf @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_18_c__meet__d, axiom, (! [C:a,A2:a,B2:a]: ((((inf @ C) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((sup @ ((inf @ C) @ A2)) @ ((inf @ B2) @ C)))))).
% 2.20/1.39 thf(fact_19_local_Od__aux__def, axiom, (! [A2:a,B2:a,C:a]: ((((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((sup @ ((sup @ ((inf @ A2) @ B2)) @ ((inf @ B2) @ C))) @ ((inf @ C) @ A2)))))).
% 2.20/1.39 thf(fact_20_local_Od__b__c__a, axiom, (! [B2:a,C:a,A2:a]: ((((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ B2) @ C) @ A2) = ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))))).
% 2.20/1.39 thf(fact_21_local_Od__c__a__b, axiom, (! [C:a,A2:a,B2:a]: ((((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ C) @ A2) @ B2) = ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))))).
% 2.20/1.39 thf(fact_22_local_Oa__meet__e, axiom, (! [A2:a,B2:a,C:a]: ((((inf @ A2) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((inf @ A2) @ ((sup @ B2) @ C)))))).
% 2.20/1.39 thf(fact_23_local_Ob__meet__e, axiom, (! [B2:a,A2:a,C:a]: ((((inf @ B2) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((inf @ B2) @ ((sup @ C) @ A2)))))).
% 2.20/1.39 thf(fact_24_local_Oc__meet__e, axiom, (! [C:a,A2:a,B2:a]: ((((inf @ C) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((inf @ C) @ ((sup @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_25_local_Oe__aux__def, axiom, (! [A2:a,B2:a,C:a]: ((((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((inf @ ((inf @ ((sup @ A2) @ B2)) @ ((sup @ B2) @ C))) @ ((sup @ C) @ A2)))))).
% 2.20/1.39 thf(fact_26_local_Oe__b__c__a, axiom, (! [B2:a,C:a,A2:a]: ((((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ B2) @ C) @ A2) = ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))))).
% 2.20/1.39 thf(fact_27_local_Oe__c__a__b, axiom, (! [C:a,A2:a,B2:a]: ((((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ C) @ A2) @ B2) = ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))))).
% 2.20/1.39 thf(fact_28_local_Oinf_Oidem, axiom, (! [A2:a]: ((((inf @ A2) @ A2) = A2)))).
% 2.20/1.39 thf(fact_29_local_Oinf_Oleft__idem, axiom, (! [A2:a,B2:a]: ((((inf @ A2) @ ((inf @ A2) @ B2)) = ((inf @ A2) @ B2))))).
% 2.20/1.39 thf(fact_30_local_Oinf_Oright__idem, axiom, (! [A2:a,B2:a]: ((((inf @ ((inf @ A2) @ B2)) @ B2) = ((inf @ A2) @ B2))))).
% 2.20/1.39 thf(fact_31_local_Oinf__idem, axiom, (! [X:a]: ((((inf @ X) @ X) = X)))).
% 2.20/1.39 thf(fact_32_local_Oinf__left__idem, axiom, (! [X:a,Y:a]: ((((inf @ X) @ ((inf @ X) @ Y)) = ((inf @ X) @ Y))))).
% 2.20/1.39 thf(fact_33_local_Oinf__right__idem, axiom, (! [X:a,Y:a]: ((((inf @ ((inf @ X) @ Y)) @ Y) = ((inf @ X) @ Y))))).
% 2.20/1.39 thf(fact_34_local_Osup_Oidem, axiom, (! [A2:a]: ((((sup @ A2) @ A2) = A2)))).
% 2.20/1.39 thf(fact_35_local_Osup_Oleft__idem, axiom, (! [A2:a,B2:a]: ((((sup @ A2) @ ((sup @ A2) @ B2)) = ((sup @ A2) @ B2))))).
% 2.20/1.39 thf(fact_36_local_Osup_Oright__idem, axiom, (! [A2:a,B2:a]: ((((sup @ ((sup @ A2) @ B2)) @ B2) = ((sup @ A2) @ B2))))).
% 2.20/1.39 thf(fact_37_local_Osup__idem, axiom, (! [X:a]: ((((sup @ X) @ X) = X)))).
% 2.20/1.39 thf(fact_38_local_Osup__left__idem, axiom, (! [X:a,Y:a]: ((((sup @ X) @ ((sup @ X) @ Y)) = ((sup @ X) @ Y))))).
% 2.20/1.39 thf(fact_39_calculation, axiom, (((sup @ ((inf @ ((sup @ a2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) @ ((inf @ ((sup @ b) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) = ((sup @ ((inf @ ((sup @ b) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) @ ((inf @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)) @ ((sup @ a2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)))))).
% 2.20/1.39 thf(fact_40_local_Oinf__sup__absorb, axiom, (! [X:a,Y:a]: ((((inf @ X) @ ((sup @ X) @ Y)) = X)))).
% 2.20/1.39 thf(fact_41_local_Osup__inf__absorb, axiom, (! [X:a,Y:a]: ((((sup @ X) @ ((inf @ X) @ Y)) = X)))).
% 2.20/1.39 thf(fact_42_local_Ob__aux__def, axiom, (! [A2:a,B2:a,C:a]: ((((((((modula477145868_b_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((sup @ ((inf @ B2) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.20/1.39 thf(fact_43_local_Oc__aux__def, axiom, (! [A2:a,B2:a,C:a]: ((((((((modula849153099_c_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((sup @ ((inf @ C) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.20/1.39 thf(fact_44_local_Oa__aux__def, axiom, (! [A2:a,B2:a,C:a]: ((((((((modula105138637_a_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((sup @ ((inf @ A2) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.20/1.39 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.20/1.39 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A3)))) = A3)))).
% 2.20/1.39 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.20/1.39 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 2.20/1.39 thf(fact_49_lattice_Od__aux_Ocong, axiom, (! [A:$tType]: (((modula1221160330_d_aux @ A) = (modula1221160330_d_aux @ A))))).
% 2.20/1.39 thf(fact_50_lattice_Oe__aux_Ocong, axiom, (! [A:$tType]: (((modula1593167561_e_aux @ A) = (modula1593167561_e_aux @ A))))).
% 2.20/1.39 thf(fact_51_d__less__e, axiom, ((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))).
% 2.20/1.39 thf(fact_52_local_Ocomp__fun__idem__sup, axiom, (((finite_comp_fun_idem @ a) @ a) @ sup)).
% 2.20/1.39 thf(fact_53_local_Ocomp__fun__idem__inf, axiom, (((finite_comp_fun_idem @ a) @ a) @ inf)).
% 2.20/1.39 thf(fact_54_local_Osup_Osemigroup__axioms, axiom, ((semigroup @ a) @ sup)).
% 2.20/1.39 thf(fact_55_local_Oinf_Osemigroup__axioms, axiom, ((semigroup @ a) @ inf)).
% 2.20/1.39 thf(fact_56_local_Osup_Osemilattice__axioms, axiom, ((semilattice @ a) @ sup)).
% 2.20/1.39 thf(fact_57_local_Oinf_Osemilattice__axioms, axiom, ((semilattice @ a) @ inf)).
% 2.20/1.39 thf(fact_58_local_Osup_Oabel__semigroup__axioms, axiom, ((abel_semigroup @ a) @ sup)).
% 2.20/1.39 thf(fact_59_local_Oinf_Oabel__semigroup__axioms, axiom, ((abel_semigroup @ a) @ inf)).
% 2.20/1.39 thf(fact_60_local_OSup__fin_Osemilattice__set__axioms, axiom, ((lattic35693393ce_set @ a) @ sup)).
% 2.20/1.39 thf(fact_61_local_OInf__fin_Osemilattice__set__axioms, axiom, ((lattic35693393ce_set @ a) @ inf)).
% 2.20/1.39 thf(fact_62_local_Ob__a, axiom, (! [A2:a,B2:a,C:a]: ((((((((modula477145868_b_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((((((modula105138637_a_aux @ a) @ inf) @ sup) @ B2) @ C) @ A2))))).
% 2.20/1.39 thf(fact_63_local_Oantisym, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) => (((less_eq @ Y) @ X) => (X = Y)))))).
% 2.20/1.39 thf(fact_64_local_Oantisym__conv, axiom, (! [Y:a,X:a]: ((((less_eq @ Y) @ X) => (((less_eq @ X) @ Y) = (X = Y)))))).
% 2.20/1.39 thf(fact_65_local_Odual__order_Oantisym, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (((less_eq @ A2) @ B2) => (A2 = B2)))))).
% 2.20/1.39 thf(fact_66_local_Odual__order_Oeq__iff, axiom, ((^ [Y3:a,Z3:a]: ((Y3 = Z3))) = (^ [A4:a,B3:a]: ((((less_eq @ B3) @ A4) & ((less_eq @ A4) @ B3)))))).
% 2.20/1.39 thf(fact_67_local_Odual__order_Otrans, axiom, (! [B2:a,A2:a,C:a]: ((((less_eq @ B2) @ A2) => (((less_eq @ C) @ B2) => ((less_eq @ C) @ A2)))))).
% 2.20/1.39 thf(fact_68_local_Oeq__iff, axiom, ((^ [Y3:a,Z3:a]: ((Y3 = Z3))) = (^ [X3:a,Y4:a]: ((((less_eq @ X3) @ Y4) & ((less_eq @ Y4) @ X3)))))).
% 2.20/1.39 thf(fact_69_local_Oeq__refl, axiom, (! [X:a,Y:a]: (((X = Y) => ((less_eq @ X) @ Y))))).
% 2.20/1.39 thf(fact_70_local_Oord__eq__le__trans, axiom, (! [A2:a,B2:a,C:a]: (((A2 = B2) => (((less_eq @ B2) @ C) => ((less_eq @ A2) @ C)))))).
% 2.20/1.39 thf(fact_71_local_Oord__le__eq__trans, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ B2) => ((B2 = C) => ((less_eq @ A2) @ C)))))).
% 2.20/1.39 thf(fact_72_local_Oorder_Oantisym, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (((less_eq @ B2) @ A2) => (A2 = B2)))))).
% 2.20/1.39 thf(fact_73_local_Oorder_Oeq__iff, axiom, ((^ [Y3:a,Z3:a]: ((Y3 = Z3))) = (^ [A4:a,B3:a]: ((((less_eq @ A4) @ B3) & ((less_eq @ B3) @ A4)))))).
% 2.20/1.39 thf(fact_74_local_Oorder_Otrans, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ B2) => (((less_eq @ B2) @ C) => ((less_eq @ A2) @ C)))))).
% 2.20/1.39 thf(fact_75_local_Oorder__trans, axiom, (! [X:a,Y:a,Z:a]: ((((less_eq @ X) @ Y) => (((less_eq @ Y) @ Z) => ((less_eq @ X) @ Z)))))).
% 2.20/1.39 thf(fact_76_local_Ole__infI2, axiom, (! [B2:a,X:a,A2:a]: ((((less_eq @ B2) @ X) => ((less_eq @ ((inf @ A2) @ B2)) @ X))))).
% 2.20/1.39 thf(fact_77_local_Ole__infI1, axiom, (! [A2:a,X:a,B2:a]: ((((less_eq @ A2) @ X) => ((less_eq @ ((inf @ A2) @ B2)) @ X))))).
% 2.20/1.39 thf(fact_78_local_Ole__infI, axiom, (! [X:a,A2:a,B2:a]: ((((less_eq @ X) @ A2) => (((less_eq @ X) @ B2) => ((less_eq @ X) @ ((inf @ A2) @ B2))))))).
% 2.20/1.39 thf(fact_79_local_Ole__infE, axiom, (! [X:a,A2:a,B2:a]: ((((less_eq @ X) @ ((inf @ A2) @ B2)) => (~ ((((less_eq @ X) @ A2) => (~ (((less_eq @ X) @ B2)))))))))).
% 2.20/1.39 thf(fact_80_local_Ole__iff__inf, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) = (((inf @ X) @ Y) = X))))).
% 2.20/1.39 thf(fact_81_local_Oinf__unique, axiom, (! [F:(a > (a > a)),X:a,Y:a]: (((! [X2:a,Y2:a]: (((less_eq @ ((F @ X2) @ Y2)) @ X2))) => ((! [X2:a,Y2:a]: (((less_eq @ ((F @ X2) @ Y2)) @ Y2))) => ((! [X2:a,Y2:a,Z2:a]: ((((less_eq @ X2) @ Y2) => (((less_eq @ X2) @ Z2) => ((less_eq @ X2) @ ((F @ Y2) @ Z2)))))) => (((inf @ X) @ Y) = ((F @ X) @ Y)))))))).
% 2.20/1.39 thf(fact_82_local_Oinf__mono, axiom, (! [A2:a,C:a,B2:a,D:a]: ((((less_eq @ A2) @ C) => (((less_eq @ B2) @ D) => ((less_eq @ ((inf @ A2) @ B2)) @ ((inf @ C) @ D))))))).
% 2.20/1.39 thf(fact_83_local_Oinf__le2, axiom, (! [X:a,Y:a]: (((less_eq @ ((inf @ X) @ Y)) @ Y)))).
% 2.20/1.39 thf(fact_84_local_Oinf__le1, axiom, (! [X:a,Y:a]: (((less_eq @ ((inf @ X) @ Y)) @ X)))).
% 2.20/1.39 thf(fact_85_local_Oinf__greatest, axiom, (! [X:a,Y:a,Z:a]: ((((less_eq @ X) @ Y) => (((less_eq @ X) @ Z) => ((less_eq @ X) @ ((inf @ Y) @ Z))))))).
% 2.20/1.39 thf(fact_86_local_Oinf__absorb2, axiom, (! [Y:a,X:a]: ((((less_eq @ Y) @ X) => (((inf @ X) @ Y) = Y))))).
% 2.20/1.39 thf(fact_87_local_Oinf__absorb1, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) => (((inf @ X) @ Y) = X))))).
% 2.20/1.39 thf(fact_88_local_Oinf_Oorder__iff, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) = (A2 = ((inf @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_89_local_Oinf_OorderI, axiom, (! [A2:a,B2:a]: (((A2 = ((inf @ A2) @ B2)) => ((less_eq @ A2) @ B2))))).
% 2.20/1.39 thf(fact_90_local_Oinf_OorderE, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (A2 = ((inf @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_91_local_Oinf_OcoboundedI2, axiom, (! [B2:a,C:a,A2:a]: ((((less_eq @ B2) @ C) => ((less_eq @ ((inf @ A2) @ B2)) @ C))))).
% 2.20/1.39 thf(fact_92_local_Oinf_OcoboundedI1, axiom, (! [A2:a,C:a,B2:a]: ((((less_eq @ A2) @ C) => ((less_eq @ ((inf @ A2) @ B2)) @ C))))).
% 2.20/1.39 thf(fact_93_local_Oinf_Ocobounded2, axiom, (! [A2:a,B2:a]: (((less_eq @ ((inf @ A2) @ B2)) @ B2)))).
% 2.20/1.39 thf(fact_94_local_Oinf_Ocobounded1, axiom, (! [A2:a,B2:a]: (((less_eq @ ((inf @ A2) @ B2)) @ A2)))).
% 2.20/1.39 thf(fact_95_local_Oinf_OboundedI, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ B2) => (((less_eq @ A2) @ C) => ((less_eq @ A2) @ ((inf @ B2) @ C))))))).
% 2.20/1.39 thf(fact_96_local_Oinf_OboundedE, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ ((inf @ B2) @ C)) => (~ ((((less_eq @ A2) @ B2) => (~ (((less_eq @ A2) @ C)))))))))).
% 2.20/1.39 thf(fact_97_local_Oinf_Oabsorb__iff2, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) = (((inf @ A2) @ B2) = B2))))).
% 2.20/1.39 thf(fact_98_local_Oinf_Oabsorb__iff1, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) = (((inf @ A2) @ B2) = A2))))).
% 2.20/1.39 thf(fact_99_local_Oinf_Oabsorb2, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (((inf @ A2) @ B2) = B2))))).
% 2.20/1.39 thf(fact_100_local_Oinf_Oabsorb1, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (((inf @ A2) @ B2) = A2))))).
% 2.20/1.39 thf(fact_101_local_Osup__unique, axiom, (! [F:(a > (a > a)),X:a,Y:a]: (((! [X2:a,Y2:a]: (((less_eq @ X2) @ ((F @ X2) @ Y2)))) => ((! [X2:a,Y2:a]: (((less_eq @ Y2) @ ((F @ X2) @ Y2)))) => ((! [X2:a,Y2:a,Z2:a]: ((((less_eq @ Y2) @ X2) => (((less_eq @ Z2) @ X2) => ((less_eq @ ((F @ Y2) @ Z2)) @ X2))))) => (((sup @ X) @ Y) = ((F @ X) @ Y)))))))).
% 2.20/1.39 thf(fact_102_local_Osup__mono, axiom, (! [A2:a,C:a,B2:a,D:a]: ((((less_eq @ A2) @ C) => (((less_eq @ B2) @ D) => ((less_eq @ ((sup @ A2) @ B2)) @ ((sup @ C) @ D))))))).
% 2.20/1.39 thf(fact_103_local_Osup__least, axiom, (! [Y:a,X:a,Z:a]: ((((less_eq @ Y) @ X) => (((less_eq @ Z) @ X) => ((less_eq @ ((sup @ Y) @ Z)) @ X)))))).
% 2.20/1.39 thf(fact_104_local_Osup__ge2, axiom, (! [Y:a,X:a]: (((less_eq @ Y) @ ((sup @ X) @ Y))))).
% 2.20/1.39 thf(fact_105_local_Osup__ge1, axiom, (! [X:a,Y:a]: (((less_eq @ X) @ ((sup @ X) @ Y))))).
% 2.20/1.39 thf(fact_106_local_Osup__absorb2, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) => (((sup @ X) @ Y) = Y))))).
% 2.20/1.39 thf(fact_107_local_Osup__absorb1, axiom, (! [Y:a,X:a]: ((((less_eq @ Y) @ X) => (((sup @ X) @ Y) = X))))).
% 2.20/1.39 thf(fact_108_local_Osup_Oorder__iff, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) = (A2 = ((sup @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_109_local_Osup_OorderI, axiom, (! [A2:a,B2:a]: (((A2 = ((sup @ A2) @ B2)) => ((less_eq @ B2) @ A2))))).
% 2.20/1.39 thf(fact_110_local_Osup_OorderE, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (A2 = ((sup @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_111_local_Osup_Omono, axiom, (! [C:a,A2:a,D:a,B2:a]: ((((less_eq @ C) @ A2) => (((less_eq @ D) @ B2) => ((less_eq @ ((sup @ C) @ D)) @ ((sup @ A2) @ B2))))))).
% 2.20/1.39 thf(fact_112_local_Osup_OcoboundedI2, axiom, (! [C:a,B2:a,A2:a]: ((((less_eq @ C) @ B2) => ((less_eq @ C) @ ((sup @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_113_local_Osup_OcoboundedI1, axiom, (! [C:a,A2:a,B2:a]: ((((less_eq @ C) @ A2) => ((less_eq @ C) @ ((sup @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_114_local_Osup_Ocobounded2, axiom, (! [B2:a,A2:a]: (((less_eq @ B2) @ ((sup @ A2) @ B2))))).
% 2.20/1.39 thf(fact_115_local_Osup_Ocobounded1, axiom, (! [A2:a,B2:a]: (((less_eq @ A2) @ ((sup @ A2) @ B2))))).
% 2.20/1.39 thf(fact_116_local_Osup_OboundedI, axiom, (! [B2:a,A2:a,C:a]: ((((less_eq @ B2) @ A2) => (((less_eq @ C) @ A2) => ((less_eq @ ((sup @ B2) @ C)) @ A2)))))).
% 2.20/1.39 thf(fact_117_local_Osup_OboundedE, axiom, (! [B2:a,C:a,A2:a]: ((((less_eq @ ((sup @ B2) @ C)) @ A2) => (~ ((((less_eq @ B2) @ A2) => (~ (((less_eq @ C) @ A2)))))))))).
% 2.20/1.39 thf(fact_118_local_Osup_Oabsorb__iff2, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) = (((sup @ A2) @ B2) = B2))))).
% 2.20/1.39 thf(fact_119_local_Osup_Oabsorb__iff1, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) = (((sup @ A2) @ B2) = A2))))).
% 2.20/1.39 thf(fact_120_local_Osup_Oabsorb2, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (((sup @ A2) @ B2) = B2))))).
% 2.20/1.39 thf(fact_121_local_Osup_Oabsorb1, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (((sup @ A2) @ B2) = A2))))).
% 2.20/1.39 thf(fact_122_local_Ole__supI2, axiom, (! [X:a,B2:a,A2:a]: ((((less_eq @ X) @ B2) => ((less_eq @ X) @ ((sup @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_123_local_Ole__supI1, axiom, (! [X:a,A2:a,B2:a]: ((((less_eq @ X) @ A2) => ((less_eq @ X) @ ((sup @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_124_local_Ole__supI, axiom, (! [A2:a,X:a,B2:a]: ((((less_eq @ A2) @ X) => (((less_eq @ B2) @ X) => ((less_eq @ ((sup @ A2) @ B2)) @ X)))))).
% 2.20/1.39 thf(fact_125_local_Ole__supE, axiom, (! [A2:a,B2:a,X:a]: ((((less_eq @ ((sup @ A2) @ B2)) @ X) => (~ ((((less_eq @ A2) @ X) => (~ (((less_eq @ B2) @ X)))))))))).
% 2.20/1.39 thf(fact_126_local_Ole__iff__sup, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) = (((sup @ X) @ Y) = Y))))).
% 2.20/1.39 thf(fact_127_local_Omodular, axiom, (! [X:a,Y:a,Z:a]: ((((less_eq @ X) @ Y) => (((sup @ X) @ ((inf @ Y) @ Z)) = ((inf @ Y) @ ((sup @ X) @ Z))))))).
% 2.20/1.39 thf(fact_128_local_Odistrib__sup__le, axiom, (! [X:a,Y:a,Z:a]: (((less_eq @ ((sup @ X) @ ((inf @ Y) @ Z))) @ ((inf @ ((sup @ X) @ Y)) @ ((sup @ X) @ Z)))))).
% 2.20/1.39 thf(fact_129_local_Odistrib__inf__le, axiom, (! [X:a,Y:a,Z:a]: (((less_eq @ ((sup @ ((inf @ X) @ Y)) @ ((inf @ X) @ Z))) @ ((inf @ X) @ ((sup @ Y) @ Z)))))).
% 2.20/1.39 thf(fact_130_local_Oincomp__def, axiom, (! [X:a,Y:a]: ((((((modula1937309406incomp @ a) @ less_eq) @ X) @ Y) = ((~ (((less_eq @ X) @ Y))) & (~ (((less_eq @ Y) @ X)))))))).
% 2.20/1.39 thf(fact_131_local_Oc__a, axiom, (! [A2:a,B2:a,C:a]: ((((((((modula849153099_c_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((((((modula105138637_a_aux @ a) @ inf) @ sup) @ C) @ A2) @ B2))))).
% 2.20/1.39 thf(fact_132_local_Oorder_Orefl, axiom, (! [A2:a]: (((less_eq @ A2) @ A2)))).
% 2.20/1.39 thf(fact_133_local_Oorder__refl, axiom, (! [X:a]: (((less_eq @ X) @ X)))).
% 2.20/1.39 thf(fact_134_local_OGreatestI2__order, axiom, (! [P:(a > $o),X:a,Q:(a > $o)]: (((P @ X) => ((! [Y2:a]: (((P @ Y2) => ((less_eq @ Y2) @ X)))) => ((! [X2:a]: (((P @ X2) => ((! [Y5:a]: (((P @ Y5) => ((less_eq @ Y5) @ X2)))) => (Q @ X2))))) => (Q @ (((greatest @ a) @ less_eq) @ P)))))))).
% 2.20/1.39 thf(fact_135_local_OGreatest__equality, axiom, (! [P:(a > $o),X:a]: (((P @ X) => ((! [Y2:a]: (((P @ Y2) => ((less_eq @ Y2) @ X)))) => ((((greatest @ a) @ less_eq) @ P) = X)))))).
% 2.20/1.39 thf(fact_136_local_Omax__def, axiom, (! [A2:a,B2:a]: (((((less_eq @ A2) @ B2) => (((((max @ a) @ less_eq) @ A2) @ B2) = B2)) & ((~ (((less_eq @ A2) @ B2))) => (((((max @ a) @ less_eq) @ A2) @ B2) = A2)))))).
% 2.20/1.39 thf(fact_137_local_Omin__def, axiom, (! [A2:a,B2:a]: (((((less_eq @ A2) @ B2) => (((((min @ a) @ less_eq) @ A2) @ B2) = A2)) & ((~ (((less_eq @ A2) @ B2))) => (((((min @ a) @ less_eq) @ A2) @ B2) = B2)))))).
% 2.20/1.39 thf(fact_138_a__def__equiv, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) => (((((((modula105138637_a_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((inf @ ((sup @ A2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))))))).
% 2.20/1.39 thf(fact_139_c__def__equiv, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) => (((((((modula849153099_c_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((inf @ ((sup @ C) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))))))).
% 2.20/1.39 thf(fact_140_b__def__equiv, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) => (((((((modula477145868_b_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((inf @ ((sup @ B2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))))))).
% 2.20/1.39 thf(fact_141_c__meet__a__eq__d, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) => (((inf @ ((((((modula849153099_c_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula105138637_a_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.20/1.39 thf(fact_142_a__meet__b__eq__d, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) => (((inf @ ((((((modula105138637_a_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula477145868_b_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.20/1.39 thf(fact_143_b__meet__c__eq__d, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) => (((inf @ ((((((modula477145868_b_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula849153099_c_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.20/1.39 thf(fact_144_local_Ole__inf__iff, axiom, (! [X:a,Y:a,Z:a]: ((((less_eq @ X) @ ((inf @ Y) @ Z)) = (((less_eq @ X) @ Y) & ((less_eq @ X) @ Z)))))).
% 2.20/1.39 thf(fact_145_local_Oinf_Obounded__iff, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ ((inf @ B2) @ C)) = (((less_eq @ A2) @ B2) & ((less_eq @ A2) @ C)))))).
% 2.20/1.39 thf(fact_146_local_Osup_Obounded__iff, axiom, (! [B2:a,C:a,A2:a]: ((((less_eq @ ((sup @ B2) @ C)) @ A2) = (((less_eq @ B2) @ A2) & ((less_eq @ C) @ A2)))))).
% 2.20/1.39 thf(fact_147_local_Ole__sup__iff, axiom, (! [X:a,Y:a,Z:a]: ((((less_eq @ ((sup @ X) @ Y)) @ Z) = (((less_eq @ X) @ Z) & ((less_eq @ Y) @ Z)))))).
% 2.20/1.39 thf(fact_148_local_OLeast1I, axiom, (! [P:(a > $o)]: (((? [X4:a]: (((P @ X4) & ((! [Y2:a]: (((P @ Y2) => ((less_eq @ X4) @ Y2)))) & (! [Y2:a]: ((((P @ Y2) & (! [Ya:a]: (((P @ Ya) => ((less_eq @ Y2) @ Ya))))) => (Y2 = X4)))))))) => (P @ (((least @ a) @ less_eq) @ P)))))).
% 2.20/1.39 thf(fact_149_local_OLeast1__le, axiom, (! [P:(a > $o),Z:a]: (((? [X4:a]: (((P @ X4) & ((! [Y2:a]: (((P @ Y2) => ((less_eq @ X4) @ Y2)))) & (! [Y2:a]: ((((P @ Y2) & (! [Ya:a]: (((P @ Ya) => ((less_eq @ Y2) @ Ya))))) => (Y2 = X4)))))))) => ((P @ Z) => ((less_eq @ (((least @ a) @ less_eq) @ P)) @ Z)))))).
% 2.20/1.39 thf(fact_150_local_OLeastI2__order, axiom, (! [P:(a > $o),X:a,Q:(a > $o)]: (((P @ X) => ((! [Y2:a]: (((P @ Y2) => ((less_eq @ X) @ Y2)))) => ((! [X2:a]: (((P @ X2) => ((! [Y5:a]: (((P @ Y5) => ((less_eq @ X2) @ Y5)))) => (Q @ X2))))) => (Q @ (((least @ a) @ less_eq) @ P)))))))).
% 2.20/1.39 thf(fact_151_local_OLeast__equality, axiom, (! [P:(a > $o),X:a]: (((P @ X) => ((! [Y2:a]: (((P @ Y2) => ((less_eq @ X) @ Y2)))) => ((((least @ a) @ less_eq) @ P) = X)))))).
% 2.20/1.39 thf(fact_152_lattice_Oc__aux_Ocong, axiom, (! [A:$tType]: (((modula849153099_c_aux @ A) = (modula849153099_c_aux @ A))))).
% 2.20/1.39 thf(fact_153_lattice_Ob__aux_Ocong, axiom, (! [A:$tType]: (((modula477145868_b_aux @ A) = (modula477145868_b_aux @ A))))).
% 2.20/1.39 thf(fact_154_lattice_Oa__aux_Ocong, axiom, (! [A:$tType]: (((modula105138637_a_aux @ A) = (modula105138637_a_aux @ A))))).
% 2.20/1.39 thf(fact_155_abel__semigroup_Oaxioms_I1_J, axiom, (! [A:$tType,F:(A > (A > A))]: ((((abel_semigroup @ A) @ F) => ((semigroup @ A) @ F))))).
% 2.20/1.39 thf(fact_156_semilattice__set__def, axiom, (! [A:$tType]: (((lattic35693393ce_set @ A) = (semilattice @ A))))).
% 2.20/1.39 thf(fact_157_semilattice__set_Ointro, axiom, (! [A:$tType,F:(A > (A > A))]: ((((semilattice @ A) @ F) => ((lattic35693393ce_set @ A) @ F))))).
% 2.20/1.39 thf(fact_158_semilattice__set_Oaxioms, axiom, (! [A:$tType,F:(A > (A > A))]: ((((lattic35693393ce_set @ A) @ F) => ((semilattice @ A) @ F))))).
% 2.20/1.39 thf(fact_159_semilattice_Oaxioms_I1_J, axiom, (! [A:$tType,F:(A > (A > A))]: ((((semilattice @ A) @ F) => ((abel_semigroup @ A) @ F))))).
% 2.20/1.39 thf(fact_160_local_Obdd__above__def, axiom, (! [A3:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ A3) = (? [M:a]: ((! [X3:a]: (((((member @ a) @ X3) @ A3) => ((less_eq @ X3) @ M)))))))))).
% 2.20/1.39 thf(fact_161_local_Obdd__below__def, axiom, (! [A3:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ A3) = (? [M2:a]: ((! [X3:a]: (((((member @ a) @ X3) @ A3) => ((less_eq @ M2) @ X3)))))))))).
% 2.20/1.39 thf(fact_162_local_Obdd__belowI, axiom, (! [A3:(set @ a),M3:a]: (((! [X2:a]: (((((member @ a) @ X2) @ A3) => ((less_eq @ M3) @ X2)))) => (((condit1201339847_below @ a) @ less_eq) @ A3))))).
% 2.20/1.39 thf(fact_163_local_Obdd__aboveI, axiom, (! [A3:(set @ a),M4:a]: (((! [X2:a]: (((((member @ a) @ X2) @ A3) => ((less_eq @ X2) @ M4)))) => (((condit2040224947_above @ a) @ less_eq) @ A3))))).
% 2.20/1.39 thf(fact_164_lattice_Oincomp_Ocong, axiom, (! [A:$tType]: (((modula1937309406incomp @ A) = (modula1937309406incomp @ A))))).
% 2.20/1.39 thf(fact_165_abel__semigroup_Oleft__commute, axiom, (! [A:$tType,F:(A > (A > A)),B2:A,A2:A,C:A]: ((((abel_semigroup @ A) @ F) => (((F @ B2) @ ((F @ A2) @ C)) = ((F @ A2) @ ((F @ B2) @ C))))))).
% 2.20/1.39 thf(fact_166_semilattice_Oright__idem, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A]: ((((semilattice @ A) @ F) => (((F @ ((F @ A2) @ B2)) @ B2) = ((F @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_167_semilattice_Oleft__idem, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A]: ((((semilattice @ A) @ F) => (((F @ A2) @ ((F @ A2) @ B2)) = ((F @ A2) @ B2)))))).
% 2.20/1.39 thf(fact_168_abel__semigroup_Ocommute, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A]: ((((abel_semigroup @ A) @ F) => (((F @ A2) @ B2) = ((F @ B2) @ A2)))))).
% 2.20/1.39 thf(fact_169_semilattice_Oidem, axiom, (! [A:$tType,F:(A > (A > A)),A2:A]: ((((semilattice @ A) @ F) => (((F @ A2) @ A2) = A2))))).
% 2.20/1.39 thf(fact_170_semigroup_Ointro, axiom, (! [A:$tType,F:(A > (A > A))]: (((! [A5:A,B4:A,C2:A]: ((((F @ ((F @ A5) @ B4)) @ C2) = ((F @ A5) @ ((F @ B4) @ C2))))) => ((semigroup @ A) @ F))))).
% 2.20/1.39 thf(fact_171_semigroup_Oassoc, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A,C:A]: ((((semigroup @ A) @ F) => (((F @ ((F @ A2) @ B2)) @ C) = ((F @ A2) @ ((F @ B2) @ C))))))).
% 2.20/1.39 thf(fact_172_semigroup__def, axiom, (! [A:$tType]: (((semigroup @ A) = (^ [F2:(A > (A > A))]: ((! [A4:A,B3:A,C3:A]: ((((F2 @ ((F2 @ A4) @ B3)) @ C3) = ((F2 @ A4) @ ((F2 @ B3) @ C3))))))))))).
% 2.20/1.39 thf(fact_173_local_Obdd__below__mono, axiom, (! [B5:(set @ a),A3:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ B5) => ((((ord_less_eq @ (set @ a)) @ A3) @ B5) => (((condit1201339847_below @ a) @ less_eq) @ A3)))))).
% 2.20/1.39 thf(fact_174_local_Obdd__above__mono, axiom, (! [B5:(set @ a),A3:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ B5) => ((((ord_less_eq @ (set @ a)) @ A3) @ B5) => (((condit2040224947_above @ a) @ less_eq) @ A3)))))).
% 2.20/1.39 thf(fact_175_local_Obdd__below__finite, axiom, (! [A3:(set @ a)]: ((((finite_finite @ a) @ A3) => (((condit1201339847_below @ a) @ less_eq) @ A3))))).
% 2.20/1.39 thf(fact_176_local_Ofinite__has__maximal2, axiom, (! [A3:(set @ a),A2:a]: ((((finite_finite @ a) @ A3) => ((((member @ a) @ A2) @ A3) => (? [X2:a]: (((((member @ a) @ X2) @ A3) & (((less_eq @ A2) @ X2) & (! [Xa:a]: (((((member @ a) @ Xa) @ A3) => (((less_eq @ X2) @ Xa) => (X2 = Xa)))))))))))))).
% 2.20/1.39 thf(fact_177_local_Ofinite__has__minimal2, axiom, (! [A3:(set @ a),A2:a]: ((((finite_finite @ a) @ A3) => ((((member @ a) @ A2) @ A3) => (? [X2:a]: (((((member @ a) @ X2) @ A3) & (((less_eq @ X2) @ A2) & (! [Xa:a]: (((((member @ a) @ Xa) @ A3) => (((less_eq @ Xa) @ X2) => (X2 = Xa)))))))))))))).
% 2.20/1.39 thf(fact_178_local_Obdd__above__finite, axiom, (! [A3:(set @ a)]: ((((finite_finite @ a) @ A3) => (((condit2040224947_above @ a) @ less_eq) @ A3))))).
% 2.20/1.39 thf(fact_179_local_OantimonoD, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B),X:a,Y:a]: ((((((antimono @ a) @ B) @ less_eq) @ F) => (((less_eq @ X) @ Y) => (((ord_less_eq @ B) @ (F @ Y)) @ (F @ X)))))))))).
% 2.20/1.39 thf(fact_180_local_OantimonoE, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B),X:a,Y:a]: ((((((antimono @ a) @ B) @ less_eq) @ F) => (((less_eq @ X) @ Y) => (((ord_less_eq @ B) @ (F @ Y)) @ (F @ X)))))))))).
% 2.20/1.39 thf(fact_181_local_OantimonoI, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: (((! [X2:a,Y2:a]: ((((less_eq @ X2) @ Y2) => (((ord_less_eq @ B) @ (F @ Y2)) @ (F @ X2))))) => ((((antimono @ a) @ B) @ less_eq) @ F)))))))).
% 2.20/1.39 thf(fact_182_local_Oantimono__def, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: ((((((antimono @ a) @ B) @ less_eq) @ F) = (! [X3:a,Y4:a]: ((((less_eq @ X3) @ Y4) => (((ord_less_eq @ B) @ (F @ Y4)) @ (F @ X3)))))))))))).
% 2.20/1.39 thf(fact_183_local_Omono__def, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: ((((((mono @ a) @ B) @ less_eq) @ F) = (! [X3:a,Y4:a]: ((((less_eq @ X3) @ Y4) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y4)))))))))))).
% 2.20/1.39 thf(fact_184_local_OmonoI, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: (((! [X2:a,Y2:a]: ((((less_eq @ X2) @ Y2) => (((ord_less_eq @ B) @ (F @ X2)) @ (F @ Y2))))) => ((((mono @ a) @ B) @ less_eq) @ F)))))))).
% 2.20/1.39 thf(fact_185_local_OmonoE, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B),X:a,Y:a]: ((((((mono @ a) @ B) @ less_eq) @ F) => (((less_eq @ X) @ Y) => (((ord_less_eq @ B) @ (F @ X)) @ (F @ Y)))))))))).
% 2.20/1.39 thf(fact_186_local_OmonoD, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B),X:a,Y:a]: ((((((mono @ a) @ B) @ less_eq) @ F) => (((less_eq @ X) @ Y) => (((ord_less_eq @ B) @ (F @ X)) @ (F @ Y)))))))))).
% 2.20/1.39 thf(fact_187_local_OSup__fin_OcoboundedI, axiom, (! [A3:(set @ a),A2:a]: ((((finite_finite @ a) @ A3) => ((((member @ a) @ A2) @ A3) => ((less_eq @ A2) @ (((lattic1039401930up_fin @ a) @ sup) @ A3))))))).
% 2.20/1.39 thf(fact_188_local_OInf__fin_OcoboundedI, axiom, (! [A3:(set @ a),A2:a]: ((((finite_finite @ a) @ A3) => ((((member @ a) @ A2) @ A3) => ((less_eq @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)) @ A2)))))).
% 2.20/1.39 thf(fact_189_local_OSup__fin_Oin__idem, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((((member @ a) @ X) @ A3) => (((sup @ X) @ (((lattic1039401930up_fin @ a) @ sup) @ A3)) = (((lattic1039401930up_fin @ a) @ sup) @ A3))))))).
% 2.20/1.39 thf(fact_190_local_OInf__fin_Oin__idem, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((((member @ a) @ X) @ A3) => (((inf @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)) = (((lattic1263571978nf_fin @ a) @ inf) @ A3))))))).
% 2.20/1.39 thf(fact_191_local_Osup__Inf__absorb, axiom, (! [A3:(set @ a),A2:a]: ((((finite_finite @ a) @ A3) => ((((member @ a) @ A2) @ A3) => (((sup @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)) @ A2) = A2)))))).
% 2.20/1.39 thf(fact_192_local_Oinf__Sup__absorb, axiom, (! [A3:(set @ a),A2:a]: ((((finite_finite @ a) @ A3) => ((((member @ a) @ A2) @ A3) => (((inf @ A2) @ (((lattic1039401930up_fin @ a) @ sup) @ A3)) = A2)))))).
% 2.20/1.39 thf(fact_193_semilattice__inf_OInf__fin_Ocong, axiom, (! [A:$tType]: (((lattic1263571978nf_fin @ A) = (lattic1263571978nf_fin @ A))))).
% 2.20/1.39 thf(fact_194_semilattice__sup_OSup__fin_Ocong, axiom, (! [A:$tType]: (((lattic1039401930up_fin @ A) = (lattic1039401930up_fin @ A))))).
% 2.20/1.39 thf(fact_195_local_OInf__fin__le__Sup__fin, axiom, (! [A3:(set @ a)]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => ((less_eq @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)) @ (((lattic1039401930up_fin @ a) @ sup) @ A3))))))).
% 2.20/1.39 thf(fact_196_local_OSup__fin_Osubset__imp, axiom, (! [A3:(set @ a),B5:(set @ a)]: (((((ord_less_eq @ (set @ a)) @ A3) @ B5) => ((A3 != (bot_bot @ (set @ a))) => (((finite_finite @ a) @ B5) => ((less_eq @ (((lattic1039401930up_fin @ a) @ sup) @ A3)) @ (((lattic1039401930up_fin @ a) @ sup) @ B5)))))))).
% 2.20/1.39 thf(fact_197_local_Ofinite__has__minimal, axiom, (! [A3:(set @ a)]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => (? [X2:a]: (((((member @ a) @ X2) @ A3) & (! [Xa:a]: (((((member @ a) @ Xa) @ A3) => (((less_eq @ Xa) @ X2) => (X2 = Xa))))))))))))).
% 2.20/1.39 thf(fact_198_local_Ofinite__has__maximal, axiom, (! [A3:(set @ a)]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => (? [X2:a]: (((((member @ a) @ X2) @ A3) & (! [Xa:a]: (((((member @ a) @ Xa) @ A3) => (((less_eq @ X2) @ Xa) => (X2 = Xa))))))))))))).
% 2.20/1.39 thf(fact_199_local_OInf__fin_Osubset, axiom, (! [A3:(set @ a),B5:(set @ a)]: ((((finite_finite @ a) @ A3) => ((B5 != (bot_bot @ (set @ a))) => ((((ord_less_eq @ (set @ a)) @ B5) @ A3) => (((inf @ (((lattic1263571978nf_fin @ a) @ inf) @ B5)) @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)) = (((lattic1263571978nf_fin @ a) @ inf) @ A3)))))))).
% 2.20/1.39 thf(fact_200_local_OSup__fin_Osubset, axiom, (! [A3:(set @ a),B5:(set @ a)]: ((((finite_finite @ a) @ A3) => ((B5 != (bot_bot @ (set @ a))) => ((((ord_less_eq @ (set @ a)) @ B5) @ A3) => (((sup @ (((lattic1039401930up_fin @ a) @ sup) @ B5)) @ (((lattic1039401930up_fin @ a) @ sup) @ A3)) = (((lattic1039401930up_fin @ a) @ sup) @ A3)))))))).
% 2.20/1.39 thf(fact_201_local_OInf__fin_Obounded__iff, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => (((less_eq @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)) = (! [X3:a]: (((((member @ a) @ X3) @ A3) => ((less_eq @ X) @ X3)))))))))).
% 2.20/1.39 thf(fact_202_local_OInf__fin_OboundedI, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => ((! [A5:a]: (((((member @ a) @ A5) @ A3) => ((less_eq @ X) @ A5)))) => ((less_eq @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)))))))).
% 2.20/1.39 thf(fact_203_local_OInf__fin_OboundedE, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => (((less_eq @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)) => (! [A6:a]: (((((member @ a) @ A6) @ A3) => ((less_eq @ X) @ A6)))))))))).
% 2.20/1.39 thf(fact_204_local_OSup__fin_Obounded__iff, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => (((less_eq @ (((lattic1039401930up_fin @ a) @ sup) @ A3)) @ X) = (! [X3:a]: (((((member @ a) @ X3) @ A3) => ((less_eq @ X3) @ X)))))))))).
% 2.20/1.39 thf(fact_205_local_OSup__fin_OboundedI, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => ((! [A5:a]: (((((member @ a) @ A5) @ A3) => ((less_eq @ A5) @ X)))) => ((less_eq @ (((lattic1039401930up_fin @ a) @ sup) @ A3)) @ X))))))).
% 2.20/1.39 thf(fact_206_local_OSup__fin_OboundedE, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => (((less_eq @ (((lattic1039401930up_fin @ a) @ sup) @ A3)) @ X) => (! [A6:a]: (((((member @ a) @ A6) @ A3) => ((less_eq @ A6) @ X)))))))))).
% 2.20/1.39 thf(fact_207_local_OInf__fin_Osubset__imp, axiom, (! [A3:(set @ a),B5:(set @ a)]: (((((ord_less_eq @ (set @ a)) @ A3) @ B5) => ((A3 != (bot_bot @ (set @ a))) => (((finite_finite @ a) @ B5) => ((less_eq @ (((lattic1263571978nf_fin @ a) @ inf) @ B5)) @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)))))))).
% 2.20/1.39 thf(fact_208_local_Obdd__above__empty, axiom, (((condit2040224947_above @ a) @ less_eq) @ (bot_bot @ (set @ a)))).
% 2.20/1.39 thf(fact_209_local_Obdd__below__empty, axiom, (((condit1201339847_below @ a) @ less_eq) @ (bot_bot @ (set @ a)))).
% 2.20/1.39 thf(fact_210_local_Onot__empty__eq__Iic__eq__empty, axiom, (! [H:a]: (((bot_bot @ (set @ a)) != (((set_atMost @ a) @ less_eq) @ H))))).
% 2.20/1.39 thf(fact_211_local_Onot__empty__eq__Ici__eq__empty, axiom, (! [L:a]: (((bot_bot @ (set @ a)) != (((set_atLeast @ a) @ less_eq) @ L))))).
% 2.20/1.39 thf(fact_212_local_OatLeast__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_atLeast @ a) @ less_eq) @ K)) = ((less_eq @ K) @ I))))).
% 2.20/1.39 thf(fact_213_local_OatMost__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_atMost @ a) @ less_eq) @ K)) = ((less_eq @ I) @ K))))).
% 2.20/1.39 thf(fact_214_local_Obdd__below__Ici, axiom, (! [A2:a]: ((((condit1201339847_below @ a) @ less_eq) @ (((set_atLeast @ a) @ less_eq) @ A2))))).
% 2.20/1.39 thf(fact_215_local_Obdd__above__Iic, axiom, (! [B2:a]: ((((condit2040224947_above @ a) @ less_eq) @ (((set_atMost @ a) @ less_eq) @ B2))))).
% 2.20/1.39 thf(fact_216_empty__subsetI, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A3)))).
% 2.20/1.39 thf(fact_217_subset__empty, axiom, (! [A:$tType,A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = (A3 = (bot_bot @ (set @ A))))))).
% 2.20/1.39 thf(fact_218_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 2.20/1.39 thf(fact_219_all__not__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X3:A]: ((~ ((((member @ A) @ X3) @ A3))))) = (A3 = (bot_bot @ (set @ A))))))).
% 2.20/1.39 thf(fact_220_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X3:A]: ((~ ((P @ X3))))))))).
% 2.20/1.39 thf(fact_221_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X3:A]: ((~ ((P @ X3))))))))).
% 2.20/1.39 thf(fact_222_subsetI, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A3) => (((member @ A) @ X2) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B5))))).
% 2.20/1.39 thf(fact_223_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A3) => (A3 = B5)))))).
% 2.20/1.39 thf(fact_224_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.20/1.39 thf(fact_225_equals0D, axiom, (! [A:$tType,A3:(set @ A),A2:A]: (((A3 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A3))))))).
% 2.20/1.39 thf(fact_226_equals0I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [Y2:A]: ((~ ((((member @ A) @ Y2) @ A3))))) => (A3 = (bot_bot @ (set @ A))))))).
% 2.20/1.39 thf(fact_227_ex__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((? [X3:A]: ((((member @ A) @ X3) @ A3))) = (A3 != (bot_bot @ (set @ A))))))).
% 2.20/1.39 thf(fact_228_in__mono, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B5) => ((((member @ A) @ X) @ A3) => (((member @ A) @ X) @ B5)))))).
% 2.20/1.39 thf(fact_229_subsetD, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B5) => ((((member @ A) @ C) @ A3) => (((member @ A) @ C) @ B5)))))).
% 2.20/1.39 thf(fact_230_equalityE, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A)]: (((A3 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A3)))))))))).
% 2.20/1.39 thf(fact_231_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B6:(set @ A)]: ((! [X3:A]: (((((member @ A) @ X3) @ A7) => (((member @ A) @ X3) @ B6)))))))))).
% 2.20/1.39 thf(fact_232_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A)]: (((A3 = B5) => (((ord_less_eq @ (set @ A)) @ A3) @ B5))))).
% 2.20/1.39 thf(fact_233_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A)]: (((A3 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A3))))).
% 2.20/1.39 thf(fact_234_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B6:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A7) => (((member @ A) @ T) @ B6)))))))))).
% 2.20/1.39 thf(fact_235_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 2.20/1.39 thf(fact_236_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) => (Q @ X2)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.20/1.39 thf(fact_237_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B5:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C4) => (((ord_less_eq @ (set @ A)) @ A3) @ C4)))))).
% 2.20/1.39 thf(fact_238_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y3:(set @ A),Z3:(set @ A)]: ((Y3 = Z3))) = (^ [A7:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A7)))))))).
% 2.20/1.39 thf(fact_239_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X3:A]: (((P @ X3) => (Q @ X3)))))))).
% 2.20/1.39 thf(fact_240_local_Omono__inf, axiom, (! [B:$tType]: (((semilattice_inf @ B) => (! [F:(a > B),A3:a,B5:a]: ((((((mono @ a) @ B) @ less_eq) @ F) => (((ord_less_eq @ B) @ (F @ ((inf @ A3) @ B5))) @ (((inf_inf @ B) @ (F @ A3)) @ (F @ B5)))))))))).
% 2.20/1.39 thf(fact_241_local_OSup__fin_Oinsert__not__elem, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((~ ((((member @ a) @ X) @ A3))) => ((A3 != (bot_bot @ (set @ a))) => ((((lattic1039401930up_fin @ a) @ sup) @ (((insert @ a) @ X) @ A3)) = ((sup @ X) @ (((lattic1039401930up_fin @ a) @ sup) @ A3))))))))).
% 2.20/1.39 thf(fact_242_local_Obdd__below__Int2, axiom, (! [B5:(set @ a),A3:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ B5) => (((condit1201339847_below @ a) @ less_eq) @ (((inf_inf @ (set @ a)) @ A3) @ B5)))))).
% 2.20/1.39 thf(fact_243_local_Obdd__below__Int1, axiom, (! [A3:(set @ a),B5:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ A3) => (((condit1201339847_below @ a) @ less_eq) @ (((inf_inf @ (set @ a)) @ A3) @ B5)))))).
% 2.20/1.39 thf(fact_244_local_Obdd__above__Int2, axiom, (! [B5:(set @ a),A3:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ B5) => (((condit2040224947_above @ a) @ less_eq) @ (((inf_inf @ (set @ a)) @ A3) @ B5)))))).
% 2.20/1.39 thf(fact_245_local_Obdd__above__Int1, axiom, (! [A3:(set @ a),B5:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ A3) => (((condit2040224947_above @ a) @ less_eq) @ (((inf_inf @ (set @ a)) @ A3) @ B5)))))).
% 2.20/1.39 thf(fact_246_Int__subset__iff, axiom, (! [A:$tType,C4:(set @ A),A3:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((inf_inf @ (set @ A)) @ A3) @ B5)) = ((((ord_less_eq @ (set @ A)) @ C4) @ A3) & (((ord_less_eq @ (set @ A)) @ C4) @ B5)))))).
% 2.20/1.39 thf(fact_247_inf__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X3:A]: ((((inf_inf @ B) @ (F2 @ X3)) @ (G2 @ X3))))))))).
% 2.20/1.39 thf(fact_248_semilattice__inf__class_Oinf_Oidem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 2.20/1.39 thf(fact_249_semilattice__inf__class_Oinf__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A]: (((((inf_inf @ A) @ X) @ X) = X))))))).
% 2.20/1.39 thf(fact_250_semilattice__inf__class_Oinf_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B2)) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.20/1.39 thf(fact_251_semilattice__inf__class_Oinf__left__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = (((inf_inf @ A) @ X) @ Y)))))))).
% 2.20/1.39 thf(fact_252_semilattice__inf__class_Oinf_Oright__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.20/1.39 thf(fact_253_semilattice__inf__class_Oinf__right__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Y) = (((inf_inf @ A) @ X) @ Y)))))))).
% 2.20/1.39 thf(fact_254_local_OInf__fin_Oclosed, axiom, (! [A3:(set @ a)]: ((((finite_finite @ a) @ A3) => ((A3 != (bot_bot @ (set @ a))) => ((! [X2:a,Y2:a]: ((((member @ a) @ ((inf @ X2) @ Y2)) @ (((insert @ a) @ X2) @ (((insert @ a) @ Y2) @ (bot_bot @ (set @ a))))))) => (((member @ a) @ (((lattic1263571978nf_fin @ a) @ inf) @ A3)) @ A3))))))).
% 2.20/1.39 thf(fact_255_local_OInf__fin_Oinsert__not__elem, axiom, (! [A3:(set @ a),X:a]: ((((finite_finite @ a) @ A3) => ((~ ((((member @ a) @ X) @ A3))) => ((A3 != (bot_bot @ (set @ a))) => ((((lattic1263571978nf_fin @ a) @ inf) @ (((insert @ a) @ X) @ A3)) = ((inf @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A3))))))))).
% 2.20/1.39 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A8:$tType,A9:$tType]: (((semilattice_inf @ A9) => (semilattice_inf @ (A8 > A9)))))).
% 2.20/1.39 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 2.20/1.39 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_1, axiom, (! [A8:$tType]: ((semilattice_inf @ (set @ A8))))).
% 2.20/1.39 thf(tcon_Set_Oset___Orderings_Oorder_2, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 2.20/1.39 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_3, axiom, (semilattice_inf @ $o)).
% 2.20/1.39 thf(tcon_HOL_Obool___Orderings_Oorder_4, axiom, (order @ $o)).
% 2.20/1.39 thf(conj_0, conjecture, (((sup @ ((inf @ ((sup @ b) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) @ ((inf @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)) @ ((sup @ a2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)))) = ((inf @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)) @ ((sup @ ((inf @ ((sup @ b) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))) @ ((sup @ a2) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)))))).
% 2.20/1.39 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.mcq7CuGXAr/DTF2DTF13195.p
% 2.20/1.39 ------------------------
% 2.48/1.43 ---- Cleaned THF ---
% 2.48/1.43 thf(ty_t_Set_Oset,type,
% 2.48/1.43 set: $tType > $tType ).
% 2.48/1.43
% 2.48/1.43 thf(ty_tf_a,type,
% 2.48/1.43 a: $tType ).
% 2.48/1.43
% 2.48/1.43 thf(sy_cl_HOL_Otype,type,
% 2.48/1.43 type:
% 2.48/1.43 !>[A: $tType] : $o ).
% 2.48/1.43
% 2.48/1.43 thf(sy_cl_Orderings_Oorder,type,
% 2.48/1.43 order:
% 2.48/1.43 !>[A: $tType] : $o ).
% 2.48/1.43
% 2.48/1.43 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 2.48/1.43 semilattice_inf:
% 2.48/1.43 !>[A: $tType] : $o ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above,type,
% 2.48/1.43 condit2040224947_above:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below,type,
% 2.48/1.43 condit1201339847_below:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Finite__Set_Ocomp__fun__idem,type,
% 2.48/1.43 finite_comp_fun_idem:
% 2.48/1.43 !>[A: $tType,B: $tType] : ( ( A > B > B ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Finite__Set_Ofinite,type,
% 2.48/1.43 finite_finite:
% 2.48/1.43 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Groups_Oabel__semigroup,type,
% 2.48/1.43 abel_semigroup:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Groups_Osemigroup,type,
% 2.48/1.43 semigroup:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 2.48/1.43 inf_inf:
% 2.48/1.43 !>[A: $tType] : ( A > A > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Lattices_Osemilattice,type,
% 2.48/1.43 semilattice:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin,type,
% 2.48/1.43 lattic1263571978nf_fin:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > ( set @ A ) > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Lattices__Big_Osemilattice__set,type,
% 2.48/1.43 lattic35693393ce_set:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin,type,
% 2.48/1.43 lattic1039401930up_fin:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > ( set @ A ) > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oa__aux,type,
% 2.48/1.43 modula105138637_a_aux:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Ob__aux,type,
% 2.48/1.43 modula477145868_b_aux:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oc__aux,type,
% 2.48/1.43 modula849153099_c_aux:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Od__aux,type,
% 2.48/1.43 modula1221160330_d_aux:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oe__aux,type,
% 2.48/1.43 modula1593167561_e_aux:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oincomp,type,
% 2.48/1.43 modula1937309406incomp:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.48/1.43 bot_bot:
% 2.48/1.43 !>[A: $tType] : A ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Orderings_Oord_OLeast,type,
% 2.48/1.43 least:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Orderings_Oord_Omax,type,
% 2.48/1.43 max:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Orderings_Oord_Omin,type,
% 2.48/1.43 min:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.48/1.43 ord_less_eq:
% 2.48/1.43 !>[A: $tType] : ( A > A > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Orderings_Oorder_OGreatest,type,
% 2.48/1.43 greatest:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Orderings_Oorder_Oantimono,type,
% 2.48/1.43 antimono:
% 2.48/1.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Orderings_Oorder_Omono,type,
% 2.48/1.43 mono:
% 2.48/1.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Set_OCollect,type,
% 2.48/1.43 collect:
% 2.48/1.43 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Set_Oinsert,type,
% 2.48/1.43 insert:
% 2.48/1.43 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Set__Interval_Oord_OatLeast,type,
% 2.48/1.43 set_atLeast:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_Set__Interval_Oord_OatMost,type,
% 2.48/1.43 set_atMost:
% 2.48/1.43 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_c_member,type,
% 2.48/1.43 member:
% 2.48/1.43 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.48/1.43
% 2.48/1.43 thf(sy_v_a,type,
% 2.48/1.43 a2: a ).
% 2.48/1.43
% 2.48/1.43 thf(sy_v_b,type,
% 2.48/1.43 b: a ).
% 2.48/1.43
% 2.48/1.43 thf(sy_v_c,type,
% 2.48/1.43 c: a ).
% 2.48/1.43
% 2.48/1.43 thf(sy_v_inf,type,
% 2.48/1.43 inf: a > a > a ).
% 2.48/1.43
% 2.48/1.43 thf(sy_v_less__eq,type,
% 2.48/1.43 less_eq: a > a > $o ).
% 2.48/1.43
% 2.48/1.43 thf(sy_v_sup,type,
% 2.48/1.43 sup: a > a > a ).
% 2.48/1.43
% 2.48/1.43 thf(fact_0_local_Oinf_Oassoc,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( inf @ ( inf @ A2 @ B2 ) @ C )
% 2.48/1.43 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_1_local_Oinf_Ocommute,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( inf @ A2 @ B2 )
% 2.48/1.43 = ( inf @ B2 @ A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_2_local_Oinf_Oleft__commute,axiom,
% 2.48/1.43 ! [B2: a,A2: a,C: a] :
% 2.48/1.43 ( ( inf @ B2 @ ( inf @ A2 @ C ) )
% 2.48/1.43 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_3_local_Oinf__assoc,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ( inf @ ( inf @ X @ Y ) @ Z )
% 2.48/1.43 = ( inf @ X @ ( inf @ Y @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_4_local_Oinf__commute,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( inf @ X @ Y )
% 2.48/1.43 = ( inf @ Y @ X ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_5_local_Oinf__left__commute,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ( inf @ X @ ( inf @ Y @ Z ) )
% 2.48/1.43 = ( inf @ Y @ ( inf @ X @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_6_local_Osup_Oassoc,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( sup @ ( sup @ A2 @ B2 ) @ C )
% 2.48/1.43 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_7_local_Osup_Ocommute,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( sup @ A2 @ B2 )
% 2.48/1.43 = ( sup @ B2 @ A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_8_local_Osup_Oleft__commute,axiom,
% 2.48/1.43 ! [B2: a,A2: a,C: a] :
% 2.48/1.43 ( ( sup @ B2 @ ( sup @ A2 @ C ) )
% 2.48/1.43 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_9_local_Osup__assoc,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ( sup @ ( sup @ X @ Y ) @ Z )
% 2.48/1.43 = ( sup @ X @ ( sup @ Y @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_10_local_Osup__commute,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( sup @ X @ Y )
% 2.48/1.43 = ( sup @ Y @ X ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_11_local_Osup__left__commute,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ( sup @ X @ ( sup @ Y @ Z ) )
% 2.48/1.43 = ( sup @ Y @ ( sup @ X @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_12_local_Odistrib__imp1,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ! [X2: a,Y2: a,Z2: a] :
% 2.48/1.43 ( ( inf @ X2 @ ( sup @ Y2 @ Z2 ) )
% 2.48/1.43 = ( sup @ ( inf @ X2 @ Y2 ) @ ( inf @ X2 @ Z2 ) ) )
% 2.48/1.43 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 2.48/1.43 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_13_local_Odistrib__imp2,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ! [X2: a,Y2: a,Z2: a] :
% 2.48/1.43 ( ( sup @ X2 @ ( inf @ Y2 @ Z2 ) )
% 2.48/1.43 = ( inf @ ( sup @ X2 @ Y2 ) @ ( sup @ X2 @ Z2 ) ) )
% 2.48/1.43 => ( ( inf @ X @ ( sup @ Y @ Z ) )
% 2.48/1.43 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_14_local_Oa__join__d,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( sup @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_15_a__meet__d,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( inf @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ C @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_16_local_Ob__join__d,axiom,
% 2.48/1.43 ! [B2: a,A2: a,C: a] :
% 2.48/1.43 ( ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( sup @ B2 @ ( inf @ C @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_17_b__meet__d,axiom,
% 2.48/1.43 ! [B2: a,A2: a,C: a] :
% 2.48/1.43 ( ( inf @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( sup @ ( inf @ B2 @ C ) @ ( inf @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_18_c__meet__d,axiom,
% 2.48/1.43 ! [C: a,A2: a,B2: a] :
% 2.48/1.43 ( ( inf @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( sup @ ( inf @ C @ A2 ) @ ( inf @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_19_local_Od__aux__def,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( sup @ ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ B2 @ C ) ) @ ( inf @ C @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_20_local_Od__b__c__a,axiom,
% 2.48/1.43 ! [B2: a,C: a,A2: a] :
% 2.48/1.43 ( ( modula1221160330_d_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 2.48/1.43 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_21_local_Od__c__a__b,axiom,
% 2.48/1.43 ! [C: a,A2: a,B2: a] :
% 2.48/1.43 ( ( modula1221160330_d_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 2.48/1.43 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_22_local_Oa__meet__e,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( inf @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_23_local_Ob__meet__e,axiom,
% 2.48/1.43 ! [B2: a,A2: a,C: a] :
% 2.48/1.43 ( ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( inf @ B2 @ ( sup @ C @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_24_local_Oc__meet__e,axiom,
% 2.48/1.43 ! [C: a,A2: a,B2: a] :
% 2.48/1.43 ( ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( inf @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_25_local_Oe__aux__def,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( inf @ ( inf @ ( sup @ A2 @ B2 ) @ ( sup @ B2 @ C ) ) @ ( sup @ C @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_26_local_Oe__b__c__a,axiom,
% 2.48/1.43 ! [B2: a,C: a,A2: a] :
% 2.48/1.43 ( ( modula1593167561_e_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 2.48/1.43 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_27_local_Oe__c__a__b,axiom,
% 2.48/1.43 ! [C: a,A2: a,B2: a] :
% 2.48/1.43 ( ( modula1593167561_e_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 2.48/1.43 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_28_local_Oinf_Oidem,axiom,
% 2.48/1.43 ! [A2: a] :
% 2.48/1.43 ( ( inf @ A2 @ A2 )
% 2.48/1.43 = A2 ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_29_local_Oinf_Oleft__idem,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( inf @ A2 @ ( inf @ A2 @ B2 ) )
% 2.48/1.43 = ( inf @ A2 @ B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_30_local_Oinf_Oright__idem,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( inf @ ( inf @ A2 @ B2 ) @ B2 )
% 2.48/1.43 = ( inf @ A2 @ B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_31_local_Oinf__idem,axiom,
% 2.48/1.43 ! [X: a] :
% 2.48/1.43 ( ( inf @ X @ X )
% 2.48/1.43 = X ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_32_local_Oinf__left__idem,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( inf @ X @ ( inf @ X @ Y ) )
% 2.48/1.43 = ( inf @ X @ Y ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_33_local_Oinf__right__idem,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 2.48/1.43 = ( inf @ X @ Y ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_34_local_Osup_Oidem,axiom,
% 2.48/1.43 ! [A2: a] :
% 2.48/1.43 ( ( sup @ A2 @ A2 )
% 2.48/1.43 = A2 ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_35_local_Osup_Oleft__idem,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( sup @ A2 @ ( sup @ A2 @ B2 ) )
% 2.48/1.43 = ( sup @ A2 @ B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_36_local_Osup_Oright__idem,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( sup @ ( sup @ A2 @ B2 ) @ B2 )
% 2.48/1.43 = ( sup @ A2 @ B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_37_local_Osup__idem,axiom,
% 2.48/1.43 ! [X: a] :
% 2.48/1.43 ( ( sup @ X @ X )
% 2.48/1.43 = X ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_38_local_Osup__left__idem,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( sup @ X @ ( sup @ X @ Y ) )
% 2.48/1.43 = ( sup @ X @ Y ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_39_calculation,axiom,
% 2.48/1.43 ( ( sup @ ( inf @ ( sup @ a2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( sup @ b @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) )
% 2.48/1.43 = ( sup @ ( inf @ ( sup @ b @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_40_local_Oinf__sup__absorb,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( inf @ X @ ( sup @ X @ Y ) )
% 2.48/1.43 = X ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_41_local_Osup__inf__absorb,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( sup @ X @ ( inf @ X @ Y ) )
% 2.48/1.43 = X ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_42_local_Ob__aux__def,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( sup @ ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_43_local_Oc__aux__def,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( sup @ ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_44_local_Oa__aux__def,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( sup @ ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_45_mem__Collect__eq,axiom,
% 2.48/1.43 ! [A: $tType,A2: A,P: A > $o] :
% 2.48/1.43 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.48/1.43 = ( P @ A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_46_Collect__mem__eq,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A] :
% 2.48/1.43 ( ( collect @ A
% 2.48/1.43 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 2.48/1.43 = A3 ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_47_Collect__cong,axiom,
% 2.48/1.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.48/1.43 ( ! [X2: A] :
% 2.48/1.43 ( ( P @ X2 )
% 2.48/1.43 = ( Q @ X2 ) )
% 2.48/1.43 => ( ( collect @ A @ P )
% 2.48/1.43 = ( collect @ A @ Q ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_48_ext,axiom,
% 2.48/1.43 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.48/1.43 ( ! [X2: A] :
% 2.48/1.43 ( ( F @ X2 )
% 2.48/1.43 = ( G @ X2 ) )
% 2.48/1.43 => ( F = G ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_49_lattice_Od__aux_Ocong,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( modula1221160330_d_aux @ A )
% 2.48/1.43 = ( modula1221160330_d_aux @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_50_lattice_Oe__aux_Ocong,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( modula1593167561_e_aux @ A )
% 2.48/1.43 = ( modula1593167561_e_aux @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_51_d__less__e,axiom,
% 2.48/1.43 less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_52_local_Ocomp__fun__idem__sup,axiom,
% 2.48/1.43 finite_comp_fun_idem @ a @ a @ sup ).
% 2.48/1.43
% 2.48/1.43 thf(fact_53_local_Ocomp__fun__idem__inf,axiom,
% 2.48/1.43 finite_comp_fun_idem @ a @ a @ inf ).
% 2.48/1.43
% 2.48/1.43 thf(fact_54_local_Osup_Osemigroup__axioms,axiom,
% 2.48/1.43 semigroup @ a @ sup ).
% 2.48/1.43
% 2.48/1.43 thf(fact_55_local_Oinf_Osemigroup__axioms,axiom,
% 2.48/1.43 semigroup @ a @ inf ).
% 2.48/1.43
% 2.48/1.43 thf(fact_56_local_Osup_Osemilattice__axioms,axiom,
% 2.48/1.43 semilattice @ a @ sup ).
% 2.48/1.43
% 2.48/1.43 thf(fact_57_local_Oinf_Osemilattice__axioms,axiom,
% 2.48/1.43 semilattice @ a @ inf ).
% 2.48/1.43
% 2.48/1.43 thf(fact_58_local_Osup_Oabel__semigroup__axioms,axiom,
% 2.48/1.43 abel_semigroup @ a @ sup ).
% 2.48/1.43
% 2.48/1.43 thf(fact_59_local_Oinf_Oabel__semigroup__axioms,axiom,
% 2.48/1.43 abel_semigroup @ a @ inf ).
% 2.48/1.43
% 2.48/1.43 thf(fact_60_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 2.48/1.43 lattic35693393ce_set @ a @ sup ).
% 2.48/1.43
% 2.48/1.43 thf(fact_61_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 2.48/1.43 lattic35693393ce_set @ a @ inf ).
% 2.48/1.43
% 2.48/1.43 thf(fact_62_local_Ob__a,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( modula105138637_a_aux @ a @ inf @ sup @ B2 @ C @ A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_63_local_Oantisym,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ( less_eq @ Y @ X )
% 2.48/1.43 => ( X = Y ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_64_local_Oantisym__conv,axiom,
% 2.48/1.43 ! [Y: a,X: a] :
% 2.48/1.43 ( ( less_eq @ Y @ X )
% 2.48/1.43 => ( ( less_eq @ X @ Y )
% 2.48/1.43 = ( X = Y ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_65_local_Odual__order_Oantisym,axiom,
% 2.48/1.43 ! [B2: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 => ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( A2 = B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_66_local_Odual__order_Oeq__iff,axiom,
% 2.48/1.43 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 2.48/1.43 = ( ^ [A4: a,B3: a] :
% 2.48/1.43 ( ( less_eq @ B3 @ A4 )
% 2.48/1.43 & ( less_eq @ A4 @ B3 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_67_local_Odual__order_Otrans,axiom,
% 2.48/1.43 ! [B2: a,A2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 => ( ( less_eq @ C @ B2 )
% 2.48/1.43 => ( less_eq @ C @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_68_local_Oeq__iff,axiom,
% 2.48/1.43 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 2.48/1.43 = ( ^ [X3: a,Y4: a] :
% 2.48/1.43 ( ( less_eq @ X3 @ Y4 )
% 2.48/1.43 & ( less_eq @ Y4 @ X3 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_69_local_Oeq__refl,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( X = Y )
% 2.48/1.43 => ( less_eq @ X @ Y ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_70_local_Oord__eq__le__trans,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( A2 = B2 )
% 2.48/1.43 => ( ( less_eq @ B2 @ C )
% 2.48/1.43 => ( less_eq @ A2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_71_local_Oord__le__eq__trans,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( B2 = C )
% 2.48/1.43 => ( less_eq @ A2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_72_local_Oorder_Oantisym,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 => ( A2 = B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_73_local_Oorder_Oeq__iff,axiom,
% 2.48/1.43 ( ( ^ [Y3: a,Z3: a] : ( Y3 = Z3 ) )
% 2.48/1.43 = ( ^ [A4: a,B3: a] :
% 2.48/1.43 ( ( less_eq @ A4 @ B3 )
% 2.48/1.43 & ( less_eq @ B3 @ A4 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_74_local_Oorder_Otrans,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( less_eq @ B2 @ C )
% 2.48/1.43 => ( less_eq @ A2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_75_local_Oorder__trans,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ( less_eq @ Y @ Z )
% 2.48/1.43 => ( less_eq @ X @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_76_local_Ole__infI2,axiom,
% 2.48/1.43 ! [B2: a,X: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ X )
% 2.48/1.43 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_77_local_Ole__infI1,axiom,
% 2.48/1.43 ! [A2: a,X: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ X )
% 2.48/1.43 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_78_local_Ole__infI,axiom,
% 2.48/1.43 ! [X: a,A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ X @ A2 )
% 2.48/1.43 => ( ( less_eq @ X @ B2 )
% 2.48/1.43 => ( less_eq @ X @ ( inf @ A2 @ B2 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_79_local_Ole__infE,axiom,
% 2.48/1.43 ! [X: a,A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ X @ ( inf @ A2 @ B2 ) )
% 2.48/1.43 => ~ ( ( less_eq @ X @ A2 )
% 2.48/1.43 => ~ ( less_eq @ X @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_80_local_Ole__iff__inf,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( less_eq @ X @ Y )
% 2.48/1.43 = ( ( inf @ X @ Y )
% 2.48/1.43 = X ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_81_local_Oinf__unique,axiom,
% 2.48/1.43 ! [F: a > a > a,X: a,Y: a] :
% 2.48/1.43 ( ! [X2: a,Y2: a] : ( less_eq @ ( F @ X2 @ Y2 ) @ X2 )
% 2.48/1.43 => ( ! [X2: a,Y2: a] : ( less_eq @ ( F @ X2 @ Y2 ) @ Y2 )
% 2.48/1.43 => ( ! [X2: a,Y2: a,Z2: a] :
% 2.48/1.43 ( ( less_eq @ X2 @ Y2 )
% 2.48/1.43 => ( ( less_eq @ X2 @ Z2 )
% 2.48/1.43 => ( less_eq @ X2 @ ( F @ Y2 @ Z2 ) ) ) )
% 2.48/1.43 => ( ( inf @ X @ Y )
% 2.48/1.43 = ( F @ X @ Y ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_82_local_Oinf__mono,axiom,
% 2.48/1.43 ! [A2: a,C: a,B2: a,D: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ C )
% 2.48/1.43 => ( ( less_eq @ B2 @ D )
% 2.48/1.43 => ( less_eq @ ( inf @ A2 @ B2 ) @ ( inf @ C @ D ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_83_local_Oinf__le2,axiom,
% 2.48/1.43 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_84_local_Oinf__le1,axiom,
% 2.48/1.43 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_85_local_Oinf__greatest,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ( less_eq @ X @ Z )
% 2.48/1.43 => ( less_eq @ X @ ( inf @ Y @ Z ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_86_local_Oinf__absorb2,axiom,
% 2.48/1.43 ! [Y: a,X: a] :
% 2.48/1.43 ( ( less_eq @ Y @ X )
% 2.48/1.43 => ( ( inf @ X @ Y )
% 2.48/1.43 = Y ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_87_local_Oinf__absorb1,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ( inf @ X @ Y )
% 2.48/1.43 = X ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_88_local_Oinf_Oorder__iff,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 = ( A2
% 2.48/1.43 = ( inf @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_89_local_Oinf_OorderI,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( A2
% 2.48/1.43 = ( inf @ A2 @ B2 ) )
% 2.48/1.43 => ( less_eq @ A2 @ B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_90_local_Oinf_OorderE,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( A2
% 2.48/1.43 = ( inf @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_91_local_Oinf_OcoboundedI2,axiom,
% 2.48/1.43 ! [B2: a,C: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ C )
% 2.48/1.43 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_92_local_Oinf_OcoboundedI1,axiom,
% 2.48/1.43 ! [A2: a,C: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ C )
% 2.48/1.43 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_93_local_Oinf_Ocobounded2,axiom,
% 2.48/1.43 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ B2 ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_94_local_Oinf_Ocobounded1,axiom,
% 2.48/1.43 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ A2 ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_95_local_Oinf_OboundedI,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( less_eq @ A2 @ C )
% 2.48/1.43 => ( less_eq @ A2 @ ( inf @ B2 @ C ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_96_local_Oinf_OboundedE,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 2.48/1.43 => ~ ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ~ ( less_eq @ A2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_97_local_Oinf_Oabsorb__iff2,axiom,
% 2.48/1.43 ! [B2: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 = ( ( inf @ A2 @ B2 )
% 2.48/1.43 = B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_98_local_Oinf_Oabsorb__iff1,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 = ( ( inf @ A2 @ B2 )
% 2.48/1.43 = A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_99_local_Oinf_Oabsorb2,axiom,
% 2.48/1.43 ! [B2: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 => ( ( inf @ A2 @ B2 )
% 2.48/1.43 = B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_100_local_Oinf_Oabsorb1,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( inf @ A2 @ B2 )
% 2.48/1.43 = A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_101_local_Osup__unique,axiom,
% 2.48/1.43 ! [F: a > a > a,X: a,Y: a] :
% 2.48/1.43 ( ! [X2: a,Y2: a] : ( less_eq @ X2 @ ( F @ X2 @ Y2 ) )
% 2.48/1.43 => ( ! [X2: a,Y2: a] : ( less_eq @ Y2 @ ( F @ X2 @ Y2 ) )
% 2.48/1.43 => ( ! [X2: a,Y2: a,Z2: a] :
% 2.48/1.43 ( ( less_eq @ Y2 @ X2 )
% 2.48/1.43 => ( ( less_eq @ Z2 @ X2 )
% 2.48/1.43 => ( less_eq @ ( F @ Y2 @ Z2 ) @ X2 ) ) )
% 2.48/1.43 => ( ( sup @ X @ Y )
% 2.48/1.43 = ( F @ X @ Y ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_102_local_Osup__mono,axiom,
% 2.48/1.43 ! [A2: a,C: a,B2: a,D: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ C )
% 2.48/1.43 => ( ( less_eq @ B2 @ D )
% 2.48/1.43 => ( less_eq @ ( sup @ A2 @ B2 ) @ ( sup @ C @ D ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_103_local_Osup__least,axiom,
% 2.48/1.43 ! [Y: a,X: a,Z: a] :
% 2.48/1.43 ( ( less_eq @ Y @ X )
% 2.48/1.43 => ( ( less_eq @ Z @ X )
% 2.48/1.43 => ( less_eq @ ( sup @ Y @ Z ) @ X ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_104_local_Osup__ge2,axiom,
% 2.48/1.43 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_105_local_Osup__ge1,axiom,
% 2.48/1.43 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_106_local_Osup__absorb2,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ( sup @ X @ Y )
% 2.48/1.43 = Y ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_107_local_Osup__absorb1,axiom,
% 2.48/1.43 ! [Y: a,X: a] :
% 2.48/1.43 ( ( less_eq @ Y @ X )
% 2.48/1.43 => ( ( sup @ X @ Y )
% 2.48/1.43 = X ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_108_local_Osup_Oorder__iff,axiom,
% 2.48/1.43 ! [B2: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 = ( A2
% 2.48/1.43 = ( sup @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_109_local_Osup_OorderI,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( A2
% 2.48/1.43 = ( sup @ A2 @ B2 ) )
% 2.48/1.43 => ( less_eq @ B2 @ A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_110_local_Osup_OorderE,axiom,
% 2.48/1.43 ! [B2: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 => ( A2
% 2.48/1.43 = ( sup @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_111_local_Osup_Omono,axiom,
% 2.48/1.43 ! [C: a,A2: a,D: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ C @ A2 )
% 2.48/1.43 => ( ( less_eq @ D @ B2 )
% 2.48/1.43 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A2 @ B2 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_112_local_Osup_OcoboundedI2,axiom,
% 2.48/1.43 ! [C: a,B2: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ C @ B2 )
% 2.48/1.43 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_113_local_Osup_OcoboundedI1,axiom,
% 2.48/1.43 ! [C: a,A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ C @ A2 )
% 2.48/1.43 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_114_local_Osup_Ocobounded2,axiom,
% 2.48/1.43 ! [B2: a,A2: a] : ( less_eq @ B2 @ ( sup @ A2 @ B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_115_local_Osup_Ocobounded1,axiom,
% 2.48/1.43 ! [A2: a,B2: a] : ( less_eq @ A2 @ ( sup @ A2 @ B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_116_local_Osup_OboundedI,axiom,
% 2.48/1.43 ! [B2: a,A2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 => ( ( less_eq @ C @ A2 )
% 2.48/1.43 => ( less_eq @ ( sup @ B2 @ C ) @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_117_local_Osup_OboundedE,axiom,
% 2.48/1.43 ! [B2: a,C: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 2.48/1.43 => ~ ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 => ~ ( less_eq @ C @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_118_local_Osup_Oabsorb__iff2,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 = ( ( sup @ A2 @ B2 )
% 2.48/1.43 = B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_119_local_Osup_Oabsorb__iff1,axiom,
% 2.48/1.43 ! [B2: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 = ( ( sup @ A2 @ B2 )
% 2.48/1.43 = A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_120_local_Osup_Oabsorb2,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( sup @ A2 @ B2 )
% 2.48/1.43 = B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_121_local_Osup_Oabsorb1,axiom,
% 2.48/1.43 ! [B2: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 => ( ( sup @ A2 @ B2 )
% 2.48/1.43 = A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_122_local_Ole__supI2,axiom,
% 2.48/1.43 ! [X: a,B2: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ X @ B2 )
% 2.48/1.43 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_123_local_Ole__supI1,axiom,
% 2.48/1.43 ! [X: a,A2: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ X @ A2 )
% 2.48/1.43 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_124_local_Ole__supI,axiom,
% 2.48/1.43 ! [A2: a,X: a,B2: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ X )
% 2.48/1.43 => ( ( less_eq @ B2 @ X )
% 2.48/1.43 => ( less_eq @ ( sup @ A2 @ B2 ) @ X ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_125_local_Ole__supE,axiom,
% 2.48/1.43 ! [A2: a,B2: a,X: a] :
% 2.48/1.43 ( ( less_eq @ ( sup @ A2 @ B2 ) @ X )
% 2.48/1.43 => ~ ( ( less_eq @ A2 @ X )
% 2.48/1.43 => ~ ( less_eq @ B2 @ X ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_126_local_Ole__iff__sup,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( less_eq @ X @ Y )
% 2.48/1.43 = ( ( sup @ X @ Y )
% 2.48/1.43 = Y ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_127_local_Omodular,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ( sup @ X @ ( inf @ Y @ Z ) )
% 2.48/1.43 = ( inf @ Y @ ( sup @ X @ Z ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_128_local_Odistrib__sup__le,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_129_local_Odistrib__inf__le,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z ) ) @ ( inf @ X @ ( sup @ Y @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_130_local_Oincomp__def,axiom,
% 2.48/1.43 ! [X: a,Y: a] :
% 2.48/1.43 ( ( modula1937309406incomp @ a @ less_eq @ X @ Y )
% 2.48/1.43 = ( ~ ( less_eq @ X @ Y )
% 2.48/1.43 & ~ ( less_eq @ Y @ X ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_131_local_Oc__a,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( modula105138637_a_aux @ a @ inf @ sup @ C @ A2 @ B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_132_local_Oorder_Orefl,axiom,
% 2.48/1.43 ! [A2: a] : ( less_eq @ A2 @ A2 ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_133_local_Oorder__refl,axiom,
% 2.48/1.43 ! [X: a] : ( less_eq @ X @ X ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_134_local_OGreatestI2__order,axiom,
% 2.48/1.43 ! [P: a > $o,X: a,Q: a > $o] :
% 2.48/1.43 ( ( P @ X )
% 2.48/1.43 => ( ! [Y2: a] :
% 2.48/1.43 ( ( P @ Y2 )
% 2.48/1.43 => ( less_eq @ Y2 @ X ) )
% 2.48/1.43 => ( ! [X2: a] :
% 2.48/1.43 ( ( P @ X2 )
% 2.48/1.43 => ( ! [Y5: a] :
% 2.48/1.43 ( ( P @ Y5 )
% 2.48/1.43 => ( less_eq @ Y5 @ X2 ) )
% 2.48/1.43 => ( Q @ X2 ) ) )
% 2.48/1.43 => ( Q @ ( greatest @ a @ less_eq @ P ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_135_local_OGreatest__equality,axiom,
% 2.48/1.43 ! [P: a > $o,X: a] :
% 2.48/1.43 ( ( P @ X )
% 2.48/1.43 => ( ! [Y2: a] :
% 2.48/1.43 ( ( P @ Y2 )
% 2.48/1.43 => ( less_eq @ Y2 @ X ) )
% 2.48/1.43 => ( ( greatest @ a @ less_eq @ P )
% 2.48/1.43 = X ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_136_local_Omax__def,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 2.48/1.43 = B2 ) )
% 2.48/1.43 & ( ~ ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 2.48/1.43 = A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_137_local_Omin__def,axiom,
% 2.48/1.43 ! [A2: a,B2: a] :
% 2.48/1.43 ( ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 2.48/1.43 = A2 ) )
% 2.48/1.43 & ( ~ ( less_eq @ A2 @ B2 )
% 2.48/1.43 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 2.48/1.43 = B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_138_a__def__equiv,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 => ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( inf @ ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_139_c__def__equiv,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 => ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( inf @ ( sup @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_140_b__def__equiv,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 => ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.48/1.43 = ( inf @ ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_141_c__meet__a__eq__d,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 => ( ( inf @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_142_a__meet__b__eq__d,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 => ( ( inf @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_143_b__meet__c__eq__d,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 => ( ( inf @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.48/1.43 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_144_local_Ole__inf__iff,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ( less_eq @ X @ ( inf @ Y @ Z ) )
% 2.48/1.43 = ( ( less_eq @ X @ Y )
% 2.48/1.43 & ( less_eq @ X @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_145_local_Oinf_Obounded__iff,axiom,
% 2.48/1.43 ! [A2: a,B2: a,C: a] :
% 2.48/1.43 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 2.48/1.43 = ( ( less_eq @ A2 @ B2 )
% 2.48/1.43 & ( less_eq @ A2 @ C ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_146_local_Osup_Obounded__iff,axiom,
% 2.48/1.43 ! [B2: a,C: a,A2: a] :
% 2.48/1.43 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 2.48/1.43 = ( ( less_eq @ B2 @ A2 )
% 2.48/1.43 & ( less_eq @ C @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_147_local_Ole__sup__iff,axiom,
% 2.48/1.43 ! [X: a,Y: a,Z: a] :
% 2.48/1.43 ( ( less_eq @ ( sup @ X @ Y ) @ Z )
% 2.48/1.43 = ( ( less_eq @ X @ Z )
% 2.48/1.43 & ( less_eq @ Y @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_148_local_OLeast1I,axiom,
% 2.48/1.43 ! [P: a > $o] :
% 2.48/1.43 ( ? [X4: a] :
% 2.48/1.43 ( ( P @ X4 )
% 2.48/1.43 & ! [Y2: a] :
% 2.48/1.43 ( ( P @ Y2 )
% 2.48/1.43 => ( less_eq @ X4 @ Y2 ) )
% 2.48/1.43 & ! [Y2: a] :
% 2.48/1.43 ( ( ( P @ Y2 )
% 2.48/1.43 & ! [Ya: a] :
% 2.48/1.43 ( ( P @ Ya )
% 2.48/1.43 => ( less_eq @ Y2 @ Ya ) ) )
% 2.48/1.43 => ( Y2 = X4 ) ) )
% 2.48/1.43 => ( P @ ( least @ a @ less_eq @ P ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_149_local_OLeast1__le,axiom,
% 2.48/1.43 ! [P: a > $o,Z: a] :
% 2.48/1.43 ( ? [X4: a] :
% 2.48/1.43 ( ( P @ X4 )
% 2.48/1.43 & ! [Y2: a] :
% 2.48/1.43 ( ( P @ Y2 )
% 2.48/1.43 => ( less_eq @ X4 @ Y2 ) )
% 2.48/1.43 & ! [Y2: a] :
% 2.48/1.43 ( ( ( P @ Y2 )
% 2.48/1.43 & ! [Ya: a] :
% 2.48/1.43 ( ( P @ Ya )
% 2.48/1.43 => ( less_eq @ Y2 @ Ya ) ) )
% 2.48/1.43 => ( Y2 = X4 ) ) )
% 2.48/1.43 => ( ( P @ Z )
% 2.48/1.43 => ( less_eq @ ( least @ a @ less_eq @ P ) @ Z ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_150_local_OLeastI2__order,axiom,
% 2.48/1.43 ! [P: a > $o,X: a,Q: a > $o] :
% 2.48/1.43 ( ( P @ X )
% 2.48/1.43 => ( ! [Y2: a] :
% 2.48/1.43 ( ( P @ Y2 )
% 2.48/1.43 => ( less_eq @ X @ Y2 ) )
% 2.48/1.43 => ( ! [X2: a] :
% 2.48/1.43 ( ( P @ X2 )
% 2.48/1.43 => ( ! [Y5: a] :
% 2.48/1.43 ( ( P @ Y5 )
% 2.48/1.43 => ( less_eq @ X2 @ Y5 ) )
% 2.48/1.43 => ( Q @ X2 ) ) )
% 2.48/1.43 => ( Q @ ( least @ a @ less_eq @ P ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_151_local_OLeast__equality,axiom,
% 2.48/1.43 ! [P: a > $o,X: a] :
% 2.48/1.43 ( ( P @ X )
% 2.48/1.43 => ( ! [Y2: a] :
% 2.48/1.43 ( ( P @ Y2 )
% 2.48/1.43 => ( less_eq @ X @ Y2 ) )
% 2.48/1.43 => ( ( least @ a @ less_eq @ P )
% 2.48/1.43 = X ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_152_lattice_Oc__aux_Ocong,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( modula849153099_c_aux @ A )
% 2.48/1.43 = ( modula849153099_c_aux @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_153_lattice_Ob__aux_Ocong,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( modula477145868_b_aux @ A )
% 2.48/1.43 = ( modula477145868_b_aux @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_154_lattice_Oa__aux_Ocong,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( modula105138637_a_aux @ A )
% 2.48/1.43 = ( modula105138637_a_aux @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_155_abel__semigroup_Oaxioms_I1_J,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A] :
% 2.48/1.43 ( ( abel_semigroup @ A @ F )
% 2.48/1.43 => ( semigroup @ A @ F ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_156_semilattice__set__def,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( lattic35693393ce_set @ A )
% 2.48/1.43 = ( semilattice @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_157_semilattice__set_Ointro,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A] :
% 2.48/1.43 ( ( semilattice @ A @ F )
% 2.48/1.43 => ( lattic35693393ce_set @ A @ F ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_158_semilattice__set_Oaxioms,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A] :
% 2.48/1.43 ( ( lattic35693393ce_set @ A @ F )
% 2.48/1.43 => ( semilattice @ A @ F ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_159_semilattice_Oaxioms_I1_J,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A] :
% 2.48/1.43 ( ( semilattice @ A @ F )
% 2.48/1.43 => ( abel_semigroup @ A @ F ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_160_local_Obdd__above__def,axiom,
% 2.48/1.43 ! [A3: set @ a] :
% 2.48/1.43 ( ( condit2040224947_above @ a @ less_eq @ A3 )
% 2.48/1.43 = ( ? [M: a] :
% 2.48/1.43 ! [X3: a] :
% 2.48/1.43 ( ( member @ a @ X3 @ A3 )
% 2.48/1.43 => ( less_eq @ X3 @ M ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_161_local_Obdd__below__def,axiom,
% 2.48/1.43 ! [A3: set @ a] :
% 2.48/1.43 ( ( condit1201339847_below @ a @ less_eq @ A3 )
% 2.48/1.43 = ( ? [M2: a] :
% 2.48/1.43 ! [X3: a] :
% 2.48/1.43 ( ( member @ a @ X3 @ A3 )
% 2.48/1.43 => ( less_eq @ M2 @ X3 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_162_local_Obdd__belowI,axiom,
% 2.48/1.43 ! [A3: set @ a,M3: a] :
% 2.48/1.43 ( ! [X2: a] :
% 2.48/1.43 ( ( member @ a @ X2 @ A3 )
% 2.48/1.43 => ( less_eq @ M3 @ X2 ) )
% 2.48/1.43 => ( condit1201339847_below @ a @ less_eq @ A3 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_163_local_Obdd__aboveI,axiom,
% 2.48/1.43 ! [A3: set @ a,M4: a] :
% 2.48/1.43 ( ! [X2: a] :
% 2.48/1.43 ( ( member @ a @ X2 @ A3 )
% 2.48/1.43 => ( less_eq @ X2 @ M4 ) )
% 2.48/1.43 => ( condit2040224947_above @ a @ less_eq @ A3 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_164_lattice_Oincomp_Ocong,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( modula1937309406incomp @ A )
% 2.48/1.43 = ( modula1937309406incomp @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_165_abel__semigroup_Oleft__commute,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A,B2: A,A2: A,C: A] :
% 2.48/1.43 ( ( abel_semigroup @ A @ F )
% 2.48/1.43 => ( ( F @ B2 @ ( F @ A2 @ C ) )
% 2.48/1.43 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_166_semilattice_Oright__idem,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 2.48/1.43 ( ( semilattice @ A @ F )
% 2.48/1.43 => ( ( F @ ( F @ A2 @ B2 ) @ B2 )
% 2.48/1.43 = ( F @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_167_semilattice_Oleft__idem,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 2.48/1.43 ( ( semilattice @ A @ F )
% 2.48/1.43 => ( ( F @ A2 @ ( F @ A2 @ B2 ) )
% 2.48/1.43 = ( F @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_168_abel__semigroup_Ocommute,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 2.48/1.43 ( ( abel_semigroup @ A @ F )
% 2.48/1.43 => ( ( F @ A2 @ B2 )
% 2.48/1.43 = ( F @ B2 @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_169_semilattice_Oidem,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A,A2: A] :
% 2.48/1.43 ( ( semilattice @ A @ F )
% 2.48/1.43 => ( ( F @ A2 @ A2 )
% 2.48/1.43 = A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_170_semigroup_Ointro,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A] :
% 2.48/1.43 ( ! [A5: A,B4: A,C2: A] :
% 2.48/1.43 ( ( F @ ( F @ A5 @ B4 ) @ C2 )
% 2.48/1.43 = ( F @ A5 @ ( F @ B4 @ C2 ) ) )
% 2.48/1.43 => ( semigroup @ A @ F ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_171_semigroup_Oassoc,axiom,
% 2.48/1.43 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 2.48/1.43 ( ( semigroup @ A @ F )
% 2.48/1.43 => ( ( F @ ( F @ A2 @ B2 ) @ C )
% 2.48/1.43 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_172_semigroup__def,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( semigroup @ A )
% 2.48/1.43 = ( ^ [F2: A > A > A] :
% 2.48/1.43 ! [A4: A,B3: A,C3: A] :
% 2.48/1.43 ( ( F2 @ ( F2 @ A4 @ B3 ) @ C3 )
% 2.48/1.43 = ( F2 @ A4 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_173_local_Obdd__below__mono,axiom,
% 2.48/1.43 ! [B5: set @ a,A3: set @ a] :
% 2.48/1.43 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 2.48/1.43 => ( ( ord_less_eq @ ( set @ a ) @ A3 @ B5 )
% 2.48/1.43 => ( condit1201339847_below @ a @ less_eq @ A3 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_174_local_Obdd__above__mono,axiom,
% 2.48/1.43 ! [B5: set @ a,A3: set @ a] :
% 2.48/1.43 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 2.48/1.43 => ( ( ord_less_eq @ ( set @ a ) @ A3 @ B5 )
% 2.48/1.43 => ( condit2040224947_above @ a @ less_eq @ A3 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_175_local_Obdd__below__finite,axiom,
% 2.48/1.43 ! [A3: set @ a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( condit1201339847_below @ a @ less_eq @ A3 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_176_local_Ofinite__has__maximal2,axiom,
% 2.48/1.43 ! [A3: set @ a,A2: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( member @ a @ A2 @ A3 )
% 2.48/1.43 => ? [X2: a] :
% 2.48/1.43 ( ( member @ a @ X2 @ A3 )
% 2.48/1.43 & ( less_eq @ A2 @ X2 )
% 2.48/1.43 & ! [Xa: a] :
% 2.48/1.43 ( ( member @ a @ Xa @ A3 )
% 2.48/1.43 => ( ( less_eq @ X2 @ Xa )
% 2.48/1.43 => ( X2 = Xa ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_177_local_Ofinite__has__minimal2,axiom,
% 2.48/1.43 ! [A3: set @ a,A2: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( member @ a @ A2 @ A3 )
% 2.48/1.43 => ? [X2: a] :
% 2.48/1.43 ( ( member @ a @ X2 @ A3 )
% 2.48/1.43 & ( less_eq @ X2 @ A2 )
% 2.48/1.43 & ! [Xa: a] :
% 2.48/1.43 ( ( member @ a @ Xa @ A3 )
% 2.48/1.43 => ( ( less_eq @ Xa @ X2 )
% 2.48/1.43 => ( X2 = Xa ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_178_local_Obdd__above__finite,axiom,
% 2.48/1.43 ! [A3: set @ a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( condit2040224947_above @ a @ less_eq @ A3 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_179_local_OantimonoD,axiom,
% 2.48/1.43 ! [B: $tType] :
% 2.48/1.43 ( ( order @ B )
% 2.48/1.43 => ! [F: a > B,X: a,Y: a] :
% 2.48/1.43 ( ( antimono @ a @ B @ less_eq @ F )
% 2.48/1.43 => ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_180_local_OantimonoE,axiom,
% 2.48/1.43 ! [B: $tType] :
% 2.48/1.43 ( ( order @ B )
% 2.48/1.43 => ! [F: a > B,X: a,Y: a] :
% 2.48/1.43 ( ( antimono @ a @ B @ less_eq @ F )
% 2.48/1.43 => ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_181_local_OantimonoI,axiom,
% 2.48/1.43 ! [B: $tType] :
% 2.48/1.43 ( ( order @ B )
% 2.48/1.43 => ! [F: a > B] :
% 2.48/1.43 ( ! [X2: a,Y2: a] :
% 2.48/1.43 ( ( less_eq @ X2 @ Y2 )
% 2.48/1.43 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X2 ) ) )
% 2.48/1.43 => ( antimono @ a @ B @ less_eq @ F ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_182_local_Oantimono__def,axiom,
% 2.48/1.43 ! [B: $tType] :
% 2.48/1.43 ( ( order @ B )
% 2.48/1.43 => ! [F: a > B] :
% 2.48/1.43 ( ( antimono @ a @ B @ less_eq @ F )
% 2.48/1.43 = ( ! [X3: a,Y4: a] :
% 2.48/1.43 ( ( less_eq @ X3 @ Y4 )
% 2.48/1.43 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X3 ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_183_local_Omono__def,axiom,
% 2.48/1.43 ! [B: $tType] :
% 2.48/1.43 ( ( order @ B )
% 2.48/1.43 => ! [F: a > B] :
% 2.48/1.43 ( ( mono @ a @ B @ less_eq @ F )
% 2.48/1.43 = ( ! [X3: a,Y4: a] :
% 2.48/1.43 ( ( less_eq @ X3 @ Y4 )
% 2.48/1.43 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_184_local_OmonoI,axiom,
% 2.48/1.43 ! [B: $tType] :
% 2.48/1.43 ( ( order @ B )
% 2.48/1.43 => ! [F: a > B] :
% 2.48/1.43 ( ! [X2: a,Y2: a] :
% 2.48/1.43 ( ( less_eq @ X2 @ Y2 )
% 2.48/1.43 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.48/1.43 => ( mono @ a @ B @ less_eq @ F ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_185_local_OmonoE,axiom,
% 2.48/1.43 ! [B: $tType] :
% 2.48/1.43 ( ( order @ B )
% 2.48/1.43 => ! [F: a > B,X: a,Y: a] :
% 2.48/1.43 ( ( mono @ a @ B @ less_eq @ F )
% 2.48/1.43 => ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_186_local_OmonoD,axiom,
% 2.48/1.43 ! [B: $tType] :
% 2.48/1.43 ( ( order @ B )
% 2.48/1.43 => ! [F: a > B,X: a,Y: a] :
% 2.48/1.43 ( ( mono @ a @ B @ less_eq @ F )
% 2.48/1.43 => ( ( less_eq @ X @ Y )
% 2.48/1.43 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_187_local_OSup__fin_OcoboundedI,axiom,
% 2.48/1.43 ! [A3: set @ a,A2: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( member @ a @ A2 @ A3 )
% 2.48/1.43 => ( less_eq @ A2 @ ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_188_local_OInf__fin_OcoboundedI,axiom,
% 2.48/1.43 ! [A3: set @ a,A2: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( member @ a @ A2 @ A3 )
% 2.48/1.43 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) @ A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_189_local_OSup__fin_Oin__idem,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( member @ a @ X @ A3 )
% 2.48/1.43 => ( ( sup @ X @ ( lattic1039401930up_fin @ a @ sup @ A3 ) )
% 2.48/1.43 = ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_190_local_OInf__fin_Oin__idem,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( member @ a @ X @ A3 )
% 2.48/1.43 => ( ( inf @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) )
% 2.48/1.43 = ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_191_local_Osup__Inf__absorb,axiom,
% 2.48/1.43 ! [A3: set @ a,A2: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( member @ a @ A2 @ A3 )
% 2.48/1.43 => ( ( sup @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) @ A2 )
% 2.48/1.43 = A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_192_local_Oinf__Sup__absorb,axiom,
% 2.48/1.43 ! [A3: set @ a,A2: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( member @ a @ A2 @ A3 )
% 2.48/1.43 => ( ( inf @ A2 @ ( lattic1039401930up_fin @ a @ sup @ A3 ) )
% 2.48/1.43 = A2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_193_semilattice__inf_OInf__fin_Ocong,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( lattic1263571978nf_fin @ A )
% 2.48/1.43 = ( lattic1263571978nf_fin @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_194_semilattice__sup_OSup__fin_Ocong,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( lattic1039401930up_fin @ A )
% 2.48/1.43 = ( lattic1039401930up_fin @ A ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_195_local_OInf__fin__le__Sup__fin,axiom,
% 2.48/1.43 ! [A3: set @ a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) @ ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_196_local_OSup__fin_Osubset__imp,axiom,
% 2.48/1.43 ! [A3: set @ a,B5: set @ a] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ a ) @ A3 @ B5 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( finite_finite @ a @ B5 )
% 2.48/1.43 => ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A3 ) @ ( lattic1039401930up_fin @ a @ sup @ B5 ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_197_local_Ofinite__has__minimal,axiom,
% 2.48/1.43 ! [A3: set @ a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ? [X2: a] :
% 2.48/1.43 ( ( member @ a @ X2 @ A3 )
% 2.48/1.43 & ! [Xa: a] :
% 2.48/1.43 ( ( member @ a @ Xa @ A3 )
% 2.48/1.43 => ( ( less_eq @ Xa @ X2 )
% 2.48/1.43 => ( X2 = Xa ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_198_local_Ofinite__has__maximal,axiom,
% 2.48/1.43 ! [A3: set @ a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ? [X2: a] :
% 2.48/1.43 ( ( member @ a @ X2 @ A3 )
% 2.48/1.43 & ! [Xa: a] :
% 2.48/1.43 ( ( member @ a @ Xa @ A3 )
% 2.48/1.43 => ( ( less_eq @ X2 @ Xa )
% 2.48/1.43 => ( X2 = Xa ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_199_local_OInf__fin_Osubset,axiom,
% 2.48/1.43 ! [A3: set @ a,B5: set @ a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( B5
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( ord_less_eq @ ( set @ a ) @ B5 @ A3 )
% 2.48/1.43 => ( ( inf @ ( lattic1263571978nf_fin @ a @ inf @ B5 ) @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) )
% 2.48/1.43 = ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_200_local_OSup__fin_Osubset,axiom,
% 2.48/1.43 ! [A3: set @ a,B5: set @ a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( B5
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( ord_less_eq @ ( set @ a ) @ B5 @ A3 )
% 2.48/1.43 => ( ( sup @ ( lattic1039401930up_fin @ a @ sup @ B5 ) @ ( lattic1039401930up_fin @ a @ sup @ A3 ) )
% 2.48/1.43 = ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_201_local_OInf__fin_Obounded__iff,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) )
% 2.48/1.43 = ( ! [X3: a] :
% 2.48/1.43 ( ( member @ a @ X3 @ A3 )
% 2.48/1.43 => ( less_eq @ X @ X3 ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_202_local_OInf__fin_OboundedI,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ! [A5: a] :
% 2.48/1.43 ( ( member @ a @ A5 @ A3 )
% 2.48/1.43 => ( less_eq @ X @ A5 ) )
% 2.48/1.43 => ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_203_local_OInf__fin_OboundedE,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) )
% 2.48/1.43 => ! [A6: a] :
% 2.48/1.43 ( ( member @ a @ A6 @ A3 )
% 2.48/1.43 => ( less_eq @ X @ A6 ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_204_local_OSup__fin_Obounded__iff,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A3 ) @ X )
% 2.48/1.43 = ( ! [X3: a] :
% 2.48/1.43 ( ( member @ a @ X3 @ A3 )
% 2.48/1.43 => ( less_eq @ X3 @ X ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_205_local_OSup__fin_OboundedI,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ! [A5: a] :
% 2.48/1.43 ( ( member @ a @ A5 @ A3 )
% 2.48/1.43 => ( less_eq @ A5 @ X ) )
% 2.48/1.43 => ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A3 ) @ X ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_206_local_OSup__fin_OboundedE,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A3 ) @ X )
% 2.48/1.43 => ! [A6: a] :
% 2.48/1.43 ( ( member @ a @ A6 @ A3 )
% 2.48/1.43 => ( less_eq @ A6 @ X ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_207_local_OInf__fin_Osubset__imp,axiom,
% 2.48/1.43 ! [A3: set @ a,B5: set @ a] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ a ) @ A3 @ B5 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( finite_finite @ a @ B5 )
% 2.48/1.43 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ B5 ) @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_208_local_Obdd__above__empty,axiom,
% 2.48/1.43 condit2040224947_above @ a @ less_eq @ ( bot_bot @ ( set @ a ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_209_local_Obdd__below__empty,axiom,
% 2.48/1.43 condit1201339847_below @ a @ less_eq @ ( bot_bot @ ( set @ a ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_210_local_Onot__empty__eq__Iic__eq__empty,axiom,
% 2.48/1.43 ! [H: a] :
% 2.48/1.43 ( ( bot_bot @ ( set @ a ) )
% 2.48/1.43 != ( set_atMost @ a @ less_eq @ H ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_211_local_Onot__empty__eq__Ici__eq__empty,axiom,
% 2.48/1.43 ! [L: a] :
% 2.48/1.43 ( ( bot_bot @ ( set @ a ) )
% 2.48/1.43 != ( set_atLeast @ a @ less_eq @ L ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_212_local_OatLeast__iff,axiom,
% 2.48/1.43 ! [I: a,K: a] :
% 2.48/1.43 ( ( member @ a @ I @ ( set_atLeast @ a @ less_eq @ K ) )
% 2.48/1.43 = ( less_eq @ K @ I ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_213_local_OatMost__iff,axiom,
% 2.48/1.43 ! [I: a,K: a] :
% 2.48/1.43 ( ( member @ a @ I @ ( set_atMost @ a @ less_eq @ K ) )
% 2.48/1.43 = ( less_eq @ I @ K ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_214_local_Obdd__below__Ici,axiom,
% 2.48/1.43 ! [A2: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeast @ a @ less_eq @ A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_215_local_Obdd__above__Iic,axiom,
% 2.48/1.43 ! [B2: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atMost @ a @ less_eq @ B2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_216_empty__subsetI,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_217_subset__empty,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.48/1.43 = ( A3
% 2.48/1.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_218_empty__iff,axiom,
% 2.48/1.43 ! [A: $tType,C: A] :
% 2.48/1.43 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_219_all__not__in__conv,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A] :
% 2.48/1.43 ( ( ! [X3: A] :
% 2.48/1.43 ~ ( member @ A @ X3 @ A3 ) )
% 2.48/1.43 = ( A3
% 2.48/1.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_220_Collect__empty__eq,axiom,
% 2.48/1.43 ! [A: $tType,P: A > $o] :
% 2.48/1.43 ( ( ( collect @ A @ P )
% 2.48/1.43 = ( bot_bot @ ( set @ A ) ) )
% 2.48/1.43 = ( ! [X3: A] :
% 2.48/1.43 ~ ( P @ X3 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_221_empty__Collect__eq,axiom,
% 2.48/1.43 ! [A: $tType,P: A > $o] :
% 2.48/1.43 ( ( ( bot_bot @ ( set @ A ) )
% 2.48/1.43 = ( collect @ A @ P ) )
% 2.48/1.43 = ( ! [X3: A] :
% 2.48/1.43 ~ ( P @ X3 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_222_subsetI,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 2.48/1.43 ( ! [X2: A] :
% 2.48/1.43 ( ( member @ A @ X2 @ A3 )
% 2.48/1.43 => ( member @ A @ X2 @ B5 ) )
% 2.48/1.43 => ( ord_less_eq @ ( set @ A ) @ A3 @ B5 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_223_subset__antisym,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 2.48/1.43 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A3 )
% 2.48/1.43 => ( A3 = B5 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_224_emptyE,axiom,
% 2.48/1.43 ! [A: $tType,A2: A] :
% 2.48/1.43 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_225_equals0D,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A,A2: A] :
% 2.48/1.43 ( ( A3
% 2.48/1.43 = ( bot_bot @ ( set @ A ) ) )
% 2.48/1.43 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_226_equals0I,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A] :
% 2.48/1.43 ( ! [Y2: A] :
% 2.48/1.43 ~ ( member @ A @ Y2 @ A3 )
% 2.48/1.43 => ( A3
% 2.48/1.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_227_ex__in__conv,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A] :
% 2.48/1.43 ( ( ? [X3: A] : ( member @ A @ X3 @ A3 ) )
% 2.48/1.43 = ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_228_in__mono,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A,B5: set @ A,X: A] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 2.48/1.43 => ( ( member @ A @ X @ A3 )
% 2.48/1.43 => ( member @ A @ X @ B5 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_229_subsetD,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A,B5: set @ A,C: A] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 2.48/1.43 => ( ( member @ A @ C @ A3 )
% 2.48/1.43 => ( member @ A @ C @ B5 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_230_equalityE,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 2.48/1.43 ( ( A3 = B5 )
% 2.48/1.43 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 2.48/1.43 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A3 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_231_subset__eq,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) )
% 2.48/1.43 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.48/1.43 ! [X3: A] :
% 2.48/1.43 ( ( member @ A @ X3 @ A7 )
% 2.48/1.43 => ( member @ A @ X3 @ B6 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_232_equalityD1,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 2.48/1.43 ( ( A3 = B5 )
% 2.48/1.43 => ( ord_less_eq @ ( set @ A ) @ A3 @ B5 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_233_equalityD2,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A,B5: set @ A] :
% 2.48/1.43 ( ( A3 = B5 )
% 2.48/1.43 => ( ord_less_eq @ ( set @ A ) @ B5 @ A3 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_234_subset__iff,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) )
% 2.48/1.43 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.48/1.43 ! [T: A] :
% 2.48/1.43 ( ( member @ A @ T @ A7 )
% 2.48/1.43 => ( member @ A @ T @ B6 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_235_subset__refl,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_236_Collect__mono,axiom,
% 2.48/1.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.48/1.43 ( ! [X2: A] :
% 2.48/1.43 ( ( P @ X2 )
% 2.48/1.43 => ( Q @ X2 ) )
% 2.48/1.43 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_237_subset__trans,axiom,
% 2.48/1.43 ! [A: $tType,A3: set @ A,B5: set @ A,C4: set @ A] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B5 )
% 2.48/1.43 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 2.48/1.43 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_238_set__eq__subset,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( ^ [Y3: set @ A,Z3: set @ A] : ( Y3 = Z3 ) )
% 2.48/1.43 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B6 )
% 2.48/1.43 & ( ord_less_eq @ ( set @ A ) @ B6 @ A7 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_239_Collect__mono__iff,axiom,
% 2.48/1.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.48/1.43 = ( ! [X3: A] :
% 2.48/1.43 ( ( P @ X3 )
% 2.48/1.43 => ( Q @ X3 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_240_local_Omono__inf,axiom,
% 2.48/1.43 ! [B: $tType] :
% 2.48/1.43 ( ( semilattice_inf @ B )
% 2.48/1.43 => ! [F: a > B,A3: a,B5: a] :
% 2.48/1.43 ( ( mono @ a @ B @ less_eq @ F )
% 2.48/1.43 => ( ord_less_eq @ B @ ( F @ ( inf @ A3 @ B5 ) ) @ ( inf_inf @ B @ ( F @ A3 ) @ ( F @ B5 ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_241_local_OSup__fin_Oinsert__not__elem,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ~ ( member @ a @ X @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ X @ A3 ) )
% 2.48/1.43 = ( sup @ X @ ( lattic1039401930up_fin @ a @ sup @ A3 ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_242_local_Obdd__below__Int2,axiom,
% 2.48/1.43 ! [B5: set @ a,A3: set @ a] :
% 2.48/1.43 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 2.48/1.43 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A3 @ B5 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_243_local_Obdd__below__Int1,axiom,
% 2.48/1.43 ! [A3: set @ a,B5: set @ a] :
% 2.48/1.43 ( ( condit1201339847_below @ a @ less_eq @ A3 )
% 2.48/1.43 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A3 @ B5 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_244_local_Obdd__above__Int2,axiom,
% 2.48/1.43 ! [B5: set @ a,A3: set @ a] :
% 2.48/1.43 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 2.48/1.43 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A3 @ B5 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_245_local_Obdd__above__Int1,axiom,
% 2.48/1.43 ! [A3: set @ a,B5: set @ a] :
% 2.48/1.43 ( ( condit2040224947_above @ a @ less_eq @ A3 )
% 2.48/1.43 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A3 @ B5 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_246_Int__subset__iff,axiom,
% 2.48/1.43 ! [A: $tType,C4: set @ A,A3: set @ A,B5: set @ A] :
% 2.48/1.43 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A3 @ B5 ) )
% 2.48/1.43 = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A3 )
% 2.48/1.43 & ( ord_less_eq @ ( set @ A ) @ C4 @ B5 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_247_inf__apply,axiom,
% 2.48/1.43 ! [B: $tType,A: $tType] :
% 2.48/1.43 ( ( semilattice_inf @ B )
% 2.48/1.43 => ( ( inf_inf @ ( A > B ) )
% 2.48/1.43 = ( ^ [F2: A > B,G2: A > B,X3: A] : ( inf_inf @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_248_semilattice__inf__class_Oinf_Oidem,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( semilattice_inf @ A )
% 2.48/1.43 => ! [A2: A] :
% 2.48/1.43 ( ( inf_inf @ A @ A2 @ A2 )
% 2.48/1.43 = A2 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_249_semilattice__inf__class_Oinf__idem,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( semilattice_inf @ A )
% 2.48/1.43 => ! [X: A] :
% 2.48/1.43 ( ( inf_inf @ A @ X @ X )
% 2.48/1.43 = X ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_250_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( semilattice_inf @ A )
% 2.48/1.43 => ! [A2: A,B2: A] :
% 2.48/1.43 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 2.48/1.43 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_251_semilattice__inf__class_Oinf__left__idem,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( semilattice_inf @ A )
% 2.48/1.43 => ! [X: A,Y: A] :
% 2.48/1.43 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 2.48/1.43 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_252_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( semilattice_inf @ A )
% 2.48/1.43 => ! [A2: A,B2: A] :
% 2.48/1.43 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 2.48/1.43 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_253_semilattice__inf__class_Oinf__right__idem,axiom,
% 2.48/1.43 ! [A: $tType] :
% 2.48/1.43 ( ( semilattice_inf @ A )
% 2.48/1.43 => ! [X: A,Y: A] :
% 2.48/1.43 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 2.48/1.43 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_254_local_OInf__fin_Oclosed,axiom,
% 2.48/1.43 ! [A3: set @ a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ! [X2: a,Y2: a] : ( member @ a @ ( inf @ X2 @ Y2 ) @ ( insert @ a @ X2 @ ( insert @ a @ Y2 @ ( bot_bot @ ( set @ a ) ) ) ) )
% 2.48/1.43 => ( member @ a @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) @ A3 ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(fact_255_local_OInf__fin_Oinsert__not__elem,axiom,
% 2.48/1.43 ! [A3: set @ a,X: a] :
% 2.48/1.43 ( ( finite_finite @ a @ A3 )
% 2.48/1.43 => ( ~ ( member @ a @ X @ A3 )
% 2.48/1.43 => ( ( A3
% 2.48/1.43 != ( bot_bot @ ( set @ a ) ) )
% 2.48/1.43 => ( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ X @ A3 ) )
% 2.48/1.43 = ( inf @ X @ ( lattic1263571978nf_fin @ a @ inf @ A3 ) ) ) ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 2.48/1.43 ! [A8: $tType,A9: $tType] :
% 2.48/1.43 ( ( semilattice_inf @ A9 )
% 2.48/1.43 => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.48/1.43 ! [A8: $tType,A9: $tType] :
% 2.48/1.43 ( ( order @ A9 )
% 2.48/1.43 => ( order @ ( A8 > A9 ) ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_1,axiom,
% 2.48/1.43 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 2.48/1.43 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 2.48/1.43
% 2.48/1.43 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_3,axiom,
% 2.48/1.43 semilattice_inf @ $o ).
% 2.48/1.43
% 2.48/1.43 thf(tcon_HOL_Obool___Orderings_Oorder_4,axiom,
% 2.48/1.43 order @ $o ).
% 2.48/1.43
% 2.48/1.43 thf(conj_0,conjecture,
% 2.48/1.43 ( ( sup @ ( inf @ ( sup @ b @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( inf @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ a2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ) )
% 2.48/1.43 = ( inf @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( sup @ ( inf @ ( sup @ b @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) @ ( sup @ a2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ) ) ) ).
% 2.48/1.43 ------------------------
% 2.48/1.45 % (13300)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/183Mi)
% 2.48/1.45 % (13301)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_13195 for (2999ds/4Mi)
% 2.48/1.45 % (13302)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_13195 for (2999ds/27Mi)
% 2.48/1.45 % (13305)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_13195 for (2999ds/275Mi)
% 2.48/1.45 % (13303)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/2Mi)
% 2.48/1.45 % (13304)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_13195 for (2999ds/2Mi)
% 2.48/1.45 % (13306)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/18Mi)
% 2.48/1.46 % (13303)Instruction limit reached!
% 2.48/1.46 % (13303)------------------------------
% 2.48/1.46 % (13303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.46 % (13303)Termination reason: Unknown
% 2.48/1.46 % (13303)Termination phase: shuffling
% 2.48/1.46
% 2.48/1.46 % (13303)Memory used [KB]: 1279
% 2.48/1.46 % (13303)Time elapsed: 0.003 s
% 2.48/1.46 % (13303)Instructions burned: 3 (million)
% 2.48/1.46 % (13303)------------------------------
% 2.48/1.46 % (13303)------------------------------
% 2.48/1.46 % (13304)Instruction limit reached!
% 2.48/1.46 % (13304)------------------------------
% 2.48/1.46 % (13304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.46 % (13304)Termination reason: Unknown
% 2.48/1.46 % (13304)Termination phase: shuffling
% 2.48/1.46
% 2.48/1.46 % (13304)Memory used [KB]: 1279
% 2.48/1.46 % (13304)Time elapsed: 0.003 s
% 2.48/1.46 % (13304)Instructions burned: 3 (million)
% 2.48/1.46 % (13304)------------------------------
% 2.48/1.46 % (13304)------------------------------
% 2.48/1.46 % (13301)Instruction limit reached!
% 2.48/1.46 % (13301)------------------------------
% 2.48/1.46 % (13301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.46 % (13301)Termination reason: Unknown
% 2.48/1.46 % (13301)Termination phase: shuffling
% 2.48/1.46
% 2.48/1.46 % (13301)Memory used [KB]: 1279
% 2.48/1.46 % (13301)Time elapsed: 0.004 s
% 2.48/1.46 % (13301)Instructions burned: 6 (million)
% 2.48/1.46 % (13301)------------------------------
% 2.48/1.46 % (13301)------------------------------
% 2.48/1.46 % (13306)Instruction limit reached!
% 2.48/1.46 % (13306)------------------------------
% 2.48/1.46 % (13306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.46 % (13306)Termination reason: Unknown
% 2.48/1.46 % (13306)Termination phase: Property scanning
% 2.48/1.46
% 2.48/1.46 % (13306)Memory used [KB]: 1535
% 2.48/1.46 % (13306)Time elapsed: 0.011 s
% 2.48/1.46 % (13306)Instructions burned: 19 (million)
% 2.48/1.46 % (13306)------------------------------
% 2.48/1.46 % (13306)------------------------------
% 2.48/1.47 % (13302)Instruction limit reached!
% 2.48/1.47 % (13302)------------------------------
% 2.48/1.47 % (13302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.47 % (13302)Termination reason: Unknown
% 2.48/1.47 % (13302)Termination phase: Property scanning
% 2.48/1.47
% 2.48/1.47 % (13302)Memory used [KB]: 1535
% 2.48/1.47 % (13302)Time elapsed: 0.015 s
% 2.48/1.47 % (13302)Instructions burned: 28 (million)
% 2.48/1.47 % (13302)------------------------------
% 2.48/1.47 % (13302)------------------------------
% 2.48/1.47 % (13308)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_13195 for (2999ds/37Mi)
% 2.48/1.47 % (13307)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/3Mi)
% 2.48/1.47 % (13307)Instruction limit reached!
% 2.48/1.47 % (13307)------------------------------
% 2.48/1.47 % (13307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.47 % (13307)Termination reason: Unknown
% 2.48/1.47 % (13307)Termination phase: shuffling
% 2.48/1.47
% 2.48/1.47 % (13307)Memory used [KB]: 1279
% 2.48/1.47 % (13307)Time elapsed: 0.003 s
% 2.48/1.47 % (13307)Instructions burned: 4 (million)
% 2.48/1.47 % (13307)------------------------------
% 2.48/1.47 % (13307)------------------------------
% 2.48/1.47 % (13309)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_13195 for (2999ds/15Mi)
% 2.48/1.48 % (13309)Instruction limit reached!
% 2.48/1.48 % (13309)------------------------------
% 2.48/1.48 % (13309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.48 % (13309)Termination reason: Unknown
% 2.48/1.48 % (13309)Termination phase: shuffling
% 2.48/1.48
% 2.48/1.48 % (13309)Memory used [KB]: 1407
% 2.48/1.48 % (13309)Time elapsed: 0.009 s
% 2.48/1.48 % (13309)Instructions burned: 15 (million)
% 2.48/1.48 % (13309)------------------------------
% 2.48/1.48 % (13309)------------------------------
% 2.48/1.48 % (13310)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_13195 for (2999ds/3Mi)
% 2.48/1.48 % (13310)Instruction limit reached!
% 2.48/1.48 % (13310)------------------------------
% 2.48/1.48 % (13310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.48 % (13310)Termination reason: Unknown
% 2.48/1.48 % (13310)Termination phase: shuffling
% 2.48/1.48
% 2.48/1.48 % (13310)Memory used [KB]: 1279
% 2.48/1.48 % (13310)Time elapsed: 0.003 s
% 2.48/1.48 % (13310)Instructions burned: 4 (million)
% 2.48/1.48 % (13310)------------------------------
% 2.48/1.48 % (13310)------------------------------
% 2.48/1.48 % (13311)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_13195 for (2999ds/1041Mi)
% 2.48/1.49 % (13308)Instruction limit reached!
% 2.48/1.49 % (13308)------------------------------
% 2.48/1.49 % (13308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.49 % (13308)Termination reason: Unknown
% 2.48/1.49 % (13308)Termination phase: Property scanning
% 2.48/1.49
% 2.48/1.49 % (13308)Memory used [KB]: 1791
% 2.48/1.49 % (13308)Time elapsed: 0.019 s
% 2.48/1.49 % (13308)Instructions burned: 39 (million)
% 2.48/1.49 % (13308)------------------------------
% 2.48/1.49 % (13308)------------------------------
% 2.48/1.49 % (13312)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/7Mi)
% 2.48/1.49 % (13312)Instruction limit reached!
% 2.48/1.49 % (13312)------------------------------
% 2.48/1.49 % (13312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.49 % (13312)Termination reason: Unknown
% 2.48/1.49 % (13312)Termination phase: shuffling
% 2.48/1.49
% 2.48/1.49 % (13312)Memory used [KB]: 1279
% 2.48/1.49 % (13312)Time elapsed: 0.005 s
% 2.48/1.49 % (13312)Instructions burned: 7 (million)
% 2.48/1.49 % (13312)------------------------------
% 2.48/1.49 % (13312)------------------------------
% 2.52/1.50 % (13314)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_13195 for (2999ds/3Mi)
% 2.52/1.50 % (13313)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/16Mi)
% 2.52/1.50 % (13314)Instruction limit reached!
% 2.52/1.50 % (13314)------------------------------
% 2.52/1.50 % (13314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.50 % (13314)Termination reason: Unknown
% 2.52/1.50 % (13314)Termination phase: shuffling
% 2.52/1.50
% 2.52/1.50 % (13314)Memory used [KB]: 1279
% 2.52/1.50 % (13314)Time elapsed: 0.003 s
% 2.52/1.50 % (13314)Instructions burned: 4 (million)
% 2.52/1.50 % (13314)------------------------------
% 2.52/1.50 % (13314)------------------------------
% 2.52/1.51 % (13300)Instruction limit reached!
% 2.52/1.51 % (13300)------------------------------
% 2.52/1.51 % (13300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.51 % (13300)Termination reason: Unknown
% 2.52/1.51 % (13300)Termination phase: Saturation
% 2.52/1.51
% 2.52/1.51 % (13300)Memory used [KB]: 6652
% 2.52/1.51 % (13300)Time elapsed: 0.058 s
% 2.52/1.51 % (13300)Instructions burned: 184 (million)
% 2.52/1.51 % (13300)------------------------------
% 2.52/1.51 % (13300)------------------------------
% 2.52/1.51 % (13315)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_13195 for (2999ds/3Mi)
% 2.52/1.51 % (13315)Instruction limit reached!
% 2.52/1.51 % (13315)------------------------------
% 2.52/1.51 % (13315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.51 % (13315)Termination reason: Unknown
% 2.52/1.51 % (13315)Termination phase: shuffling
% 2.52/1.51
% 2.52/1.51 % (13315)Memory used [KB]: 1279
% 2.52/1.51 % (13315)Time elapsed: 0.003 s
% 2.52/1.51 % (13315)Instructions burned: 3 (million)
% 2.52/1.51 % (13315)------------------------------
% 2.52/1.51 % (13315)------------------------------
% 2.52/1.51 % (13313)Instruction limit reached!
% 2.52/1.51 % (13313)------------------------------
% 2.52/1.51 % (13313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.51 % (13316)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/7Mi)
% 2.52/1.51 % (13313)Termination reason: Unknown
% 2.52/1.51 % (13313)Termination phase: shuffling
% 2.52/1.51
% 2.52/1.51 % (13313)Memory used [KB]: 1407
% 2.52/1.51 % (13313)Time elapsed: 0.010 s
% 2.52/1.51 % (13313)Instructions burned: 17 (million)
% 2.52/1.51 % (13313)------------------------------
% 2.52/1.51 % (13313)------------------------------
% 2.52/1.51 % (13316)Instruction limit reached!
% 2.52/1.51 % (13316)------------------------------
% 2.52/1.51 % (13316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.51 % (13316)Termination reason: Unknown
% 2.52/1.51 % (13316)Termination phase: shuffling
% 2.52/1.51
% 2.52/1.51 % (13316)Memory used [KB]: 1407
% 2.52/1.51 % (13316)Time elapsed: 0.005 s
% 2.52/1.51 % (13316)Instructions burned: 8 (million)
% 2.52/1.51 % (13316)------------------------------
% 2.52/1.51 % (13316)------------------------------
% 2.52/1.51 % (13318)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/4Mi)
% 2.52/1.52 % (13318)Instruction limit reached!
% 2.52/1.52 % (13318)------------------------------
% 2.52/1.52 % (13318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.52 % (13318)Termination reason: Unknown
% 2.52/1.52 % (13318)Termination phase: shuffling
% 2.52/1.52
% 2.52/1.52 % (13318)Memory used [KB]: 1279
% 2.52/1.52 % (13318)Time elapsed: 0.003 s
% 2.52/1.52 % (13318)Instructions burned: 6 (million)
% 2.52/1.52 % (13318)------------------------------
% 2.52/1.52 % (13318)------------------------------
% 2.52/1.52 % (13317)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/3Mi)
% 2.52/1.52 % (13317)Instruction limit reached!
% 2.52/1.52 % (13317)------------------------------
% 2.52/1.52 % (13317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.52 % (13317)Termination reason: Unknown
% 2.52/1.52 % (13317)Termination phase: shuffling
% 2.52/1.52
% 2.52/1.52 % (13317)Memory used [KB]: 1279
% 2.52/1.52 % (13317)Time elapsed: 0.003 s
% 2.52/1.52 % (13317)Instructions burned: 3 (million)
% 2.52/1.52 % (13317)------------------------------
% 2.52/1.52 % (13317)------------------------------
% 2.52/1.52 % (13319)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/18Mi)
% 2.52/1.53 % (13320)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/710Mi)
% 2.52/1.53 % (13322)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_13195 for (2999ds/902Mi)
% 2.52/1.53 % (13321)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/6Mi)
% 2.52/1.53 % (13321)Instruction limit reached!
% 2.52/1.53 % (13321)------------------------------
% 2.52/1.53 % (13321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.53 % (13321)Termination reason: Unknown
% 2.52/1.53 % (13321)Termination phase: shuffling
% 2.52/1.53
% 2.52/1.53 % (13321)Memory used [KB]: 1279
% 2.52/1.53 % (13321)Time elapsed: 0.005 s
% 2.52/1.53 % (13321)Instructions burned: 6 (million)
% 2.52/1.53 % (13321)------------------------------
% 2.52/1.53 % (13321)------------------------------
% 2.52/1.53 % (13319)Instruction limit reached!
% 2.52/1.53 % (13319)------------------------------
% 2.52/1.53 % (13319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.53 % (13319)Termination reason: Unknown
% 2.52/1.53 % (13319)Termination phase: Property scanning
% 2.52/1.53
% 2.52/1.53 % (13319)Memory used [KB]: 1535
% 2.52/1.53 % (13319)Time elapsed: 0.011 s
% 2.52/1.53 % (13319)Instructions burned: 19 (million)
% 2.52/1.53 % (13319)------------------------------
% 2.52/1.53 % (13319)------------------------------
% 2.52/1.54 % (13323)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_13195 for (2999ds/21Mi)
% 2.52/1.55 % (13323)Instruction limit reached!
% 2.52/1.55 % (13323)------------------------------
% 2.52/1.55 % (13323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.55 % (13323)Termination reason: Unknown
% 2.52/1.55 % (13323)Termination phase: shuffling
% 2.52/1.55
% 2.52/1.55 % (13323)Memory used [KB]: 1535
% 2.52/1.55 % (13323)Time elapsed: 0.012 s
% 2.52/1.55 % (13323)Instructions burned: 22 (million)
% 2.52/1.55 % (13323)------------------------------
% 2.52/1.55 % (13323)------------------------------
% 2.52/1.55 % (13324)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13195 for (2999ds/5Mi)
% 2.52/1.55 % (13325)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_13195 for (2999ds/6Mi)
% 2.52/1.55 % (13324)Instruction limit reached!
% 2.52/1.55 % (13324)------------------------------
% 2.52/1.55 % (13324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.55 % (13324)Termination reason: Unknown
% 2.52/1.55 % (13324)Termination phase: shuffling
% 2.52/1.55
% 2.52/1.55 % (13324)Memory used [KB]: 1279
% 2.52/1.55 % (13324)Time elapsed: 0.004 s
% 2.52/1.55 % (13324)Instructions burned: 6 (million)
% 2.52/1.55 % (13324)------------------------------
% 2.52/1.55 % (13324)------------------------------
% 2.52/1.55 % (13325)Instruction limit reached!
% 2.52/1.55 % (13325)------------------------------
% 2.52/1.55 % (13325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.55 % (13325)Termination reason: Unknown
% 2.52/1.55 % (13325)Termination phase: shuffling
% 2.52/1.55
% 2.52/1.55 % (13325)Memory used [KB]: 1279
% 2.52/1.55 % (13325)Time elapsed: 0.004 s
% 2.52/1.55 % (13325)Instructions burned: 6 (million)
% 2.52/1.55 % (13325)------------------------------
% 2.52/1.55 % (13325)------------------------------
% 2.52/1.56 % (13326)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13195 for (2998ds/377Mi)
% 2.52/1.57 % (13328)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_13195 for (2998ds/19Mi)
% 2.52/1.57 % (13327)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_13195 for (2998ds/779Mi)
% 2.52/1.58 % (13328)Instruction limit reached!
% 2.52/1.58 % (13328)------------------------------
% 2.52/1.58 % (13328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.58 % (13328)Termination reason: Unknown
% 2.52/1.58 % (13328)Termination phase: shuffling
% 2.52/1.58
% 2.52/1.58 % (13328)Memory used [KB]: 1535
% 2.52/1.58 % (13328)Time elapsed: 0.010 s
% 2.52/1.58 % (13328)Instructions burned: 19 (million)
% 2.52/1.58 % (13328)------------------------------
% 2.52/1.58 % (13328)------------------------------
% 2.52/1.58 % (13305)Instruction limit reached!
% 2.52/1.58 % (13305)------------------------------
% 2.52/1.58 % (13305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.58 % (13305)Termination reason: Unknown
% 2.52/1.58 % (13305)Termination phase: Saturation
% 2.52/1.58
% 2.52/1.58 % (13305)Memory used [KB]: 6396
% 2.52/1.58 % (13305)Time elapsed: 0.125 s
% 2.52/1.58 % (13305)Instructions burned: 275 (million)
% 2.52/1.58 % (13305)------------------------------
% 2.52/1.58 % (13305)------------------------------
% 2.52/1.59 % (13330)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13195 for (2998ds/879Mi)
% 2.52/1.59 % (13331)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13195 for (2998ds/17Mi)
% 2.52/1.60 % (13331)Instruction limit reached!
% 2.52/1.60 % (13331)------------------------------
% 2.52/1.60 % (13331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.60 % (13331)Termination reason: Unknown
% 2.52/1.60 % (13331)Termination phase: shuffling
% 2.52/1.60
% 2.52/1.60 % (13331)Memory used [KB]: 1407
% 2.52/1.60 % (13331)Time elapsed: 0.010 s
% 2.52/1.60 % (13331)Instructions burned: 17 (million)
% 2.52/1.60 % (13331)------------------------------
% 2.52/1.60 % (13331)------------------------------
% 2.52/1.61 % (13332)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13195 for (2998ds/3Mi)
% 2.52/1.61 % (13332)Instruction limit reached!
% 2.52/1.61 % (13332)------------------------------
% 2.52/1.61 % (13332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.61 % (13332)Termination reason: Unknown
% 2.52/1.61 % (13332)Termination phase: shuffling
% 2.52/1.61
% 2.52/1.61 % (13332)Memory used [KB]: 1279
% 2.52/1.61 % (13332)Time elapsed: 0.002 s
% 2.52/1.61 % (13332)Instructions burned: 3 (million)
% 2.52/1.61 % (13332)------------------------------
% 2.52/1.61 % (13332)------------------------------
% 2.52/1.62 % (13333)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13195 for (2998ds/30Mi)
% 2.52/1.63 % (13333)Instruction limit reached!
% 2.52/1.63 % (13333)------------------------------
% 2.52/1.63 % (13333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.63 % (13333)Termination reason: Unknown
% 2.52/1.63 % (13333)Termination phase: Property scanning
% 2.52/1.63
% 2.52/1.63 % (13333)Memory used [KB]: 1535
% 2.52/1.63 % (13333)Time elapsed: 0.011 s
% 2.52/1.63 % (13333)Instructions burned: 33 (million)
% 2.52/1.63 % (13333)------------------------------
% 2.52/1.63 % (13333)------------------------------
% 2.52/1.64 % (13334)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13195 for (2998ds/127Mi)
% 2.52/1.69 % (13334)Instruction limit reached!
% 2.52/1.69 % (13334)------------------------------
% 2.52/1.69 % (13334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.69 % (13334)Termination reason: Unknown
% 2.52/1.69 % (13334)Termination phase: Saturation
% 2.52/1.69
% 2.52/1.69 % (13334)Memory used [KB]: 6524
% 2.52/1.69 % (13334)Time elapsed: 0.046 s
% 2.52/1.69 % (13334)Instructions burned: 128 (million)
% 2.52/1.69 % (13334)------------------------------
% 2.52/1.69 % (13334)------------------------------
% 2.52/1.70 % (13335)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13195 for (2997ds/100Mi)
% 2.52/1.74 % (13326)Instruction limit reached!
% 2.52/1.74 % (13326)------------------------------
% 2.52/1.74 % (13326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.74 % (13326)Termination reason: Unknown
% 2.52/1.74 % (13326)Termination phase: Saturation
% 2.52/1.74
% 2.52/1.74 % (13326)Memory used [KB]: 7164
% 2.52/1.74 % (13326)Time elapsed: 0.183 s
% 2.52/1.74 % (13326)Instructions burned: 379 (million)
% 2.52/1.74 % (13326)------------------------------
% 2.52/1.74 % (13326)------------------------------
% 2.52/1.75 % (13335)Instruction limit reached!
% 2.52/1.75 % (13335)------------------------------
% 2.52/1.75 % (13335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.75 % (13335)Termination reason: Unknown
% 2.52/1.75 % (13335)Termination phase: Saturation
% 2.52/1.75
% 2.52/1.75 % (13335)Memory used [KB]: 6396
% 2.52/1.75 % (13335)Time elapsed: 0.047 s
% 2.52/1.75 % (13335)Instructions burned: 100 (million)
% 2.52/1.75 % (13335)------------------------------
% 2.52/1.75 % (13335)------------------------------
% 2.52/1.76 % (13337)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_13195 for (2996ds/20Mi)
% 2.52/1.77 % (13336)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_13195 for (2997ds/3Mi)
% 2.52/1.77 % (13336)Instruction limit reached!
% 2.52/1.77 % (13336)------------------------------
% 2.52/1.77 % (13336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.77 % (13336)Termination reason: Unknown
% 2.52/1.77 % (13336)Termination phase: shuffling
% 2.52/1.77
% 2.52/1.77 % (13336)Memory used [KB]: 1279
% 2.52/1.77 % (13336)Time elapsed: 0.002 s
% 2.52/1.77 % (13336)Instructions burned: 4 (million)
% 2.52/1.77 % (13336)------------------------------
% 2.52/1.77 % (13336)------------------------------
% 2.52/1.77 % (13337)Instruction limit reached!
% 2.52/1.77 % (13337)------------------------------
% 2.52/1.77 % (13337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.77 % (13337)Termination reason: Unknown
% 2.52/1.77 % (13337)Termination phase: Property scanning
% 2.52/1.77
% 2.52/1.77 % (13337)Memory used [KB]: 1535
% 2.52/1.77 % (13337)Time elapsed: 0.012 s
% 2.52/1.77 % (13337)Instructions burned: 21 (million)
% 2.52/1.77 % (13337)------------------------------
% 2.52/1.77 % (13337)------------------------------
% 2.52/1.78 % (13338)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_13195 for (2996ds/86Mi)
% 2.52/1.80 % (13339)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_13195 for (2996ds/107Mi)
% 2.52/1.82 % (13338)Instruction limit reached!
% 2.52/1.82 % (13338)------------------------------
% 2.52/1.82 % (13338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.82 % (13338)Termination reason: Unknown
% 2.52/1.82 % (13338)Termination phase: Saturation
% 2.52/1.82
% 2.52/1.82 % (13338)Memory used [KB]: 6396
% 2.52/1.82 % (13338)Time elapsed: 0.041 s
% 2.52/1.82 % (13338)Instructions burned: 86 (million)
% 2.52/1.82 % (13338)------------------------------
% 2.52/1.82 % (13338)------------------------------
% 2.52/1.84 % (13340)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_13195 for (2996ds/39Mi)
% 2.52/1.84 % (13320)Instruction limit reached!
% 2.52/1.84 % (13320)------------------------------
% 2.52/1.84 % (13320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.84 % (13320)Termination reason: Unknown
% 2.52/1.84 % (13320)Termination phase: Saturation
% 2.52/1.84
% 2.52/1.84 % (13320)Memory used [KB]: 7036
% 2.52/1.84 % (13320)Time elapsed: 0.330 s
% 2.52/1.84 % (13320)Instructions burned: 713 (million)
% 2.52/1.84 % (13320)------------------------------
% 2.52/1.84 % (13320)------------------------------
% 2.52/1.86 % (13340)Instruction limit reached!
% 2.52/1.86 % (13340)------------------------------
% 2.52/1.86 % (13340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.86 % (13340)Termination reason: Unknown
% 2.52/1.86 % (13339)Instruction limit reached!
% 2.52/1.86 % (13339)------------------------------
% 2.52/1.86 % (13339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.86 % (13339)Termination reason: Unknown
% 2.52/1.86 % (13339)Termination phase: Saturation
% 2.52/1.86
% 2.52/1.86 % (13339)Memory used [KB]: 6268
% 2.52/1.86 % (13339)Time elapsed: 0.034 s
% 2.52/1.86 % (13339)Instructions burned: 107 (million)
% 2.52/1.86 % (13339)------------------------------
% 2.52/1.86 % (13339)------------------------------
% 2.52/1.86 % (13340)Termination phase: Property scanning
% 2.52/1.86
% 2.52/1.86 % (13340)Memory used [KB]: 1791
% 2.52/1.86 % (13340)Time elapsed: 0.019 s
% 2.52/1.86 % (13340)Instructions burned: 39 (million)
% 2.52/1.86 % (13340)------------------------------
% 2.52/1.86 % (13340)------------------------------
% 2.52/1.86 % (13341)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_13195 for (2995ds/448Mi)
% 2.52/1.87 % (13342)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_13195 for (2995ds/46Mi)
% 2.52/1.87 % (13322)Instruction limit reached!
% 2.52/1.87 % (13322)------------------------------
% 2.52/1.87 % (13322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.87 % (13322)Termination reason: Unknown
% 2.52/1.87 % (13322)Termination phase: Saturation
% 2.52/1.87
% 2.52/1.87 % (13322)Memory used [KB]: 7036
% 2.52/1.87 % (13322)Time elapsed: 0.342 s
% 2.52/1.87 % (13322)Instructions burned: 904 (million)
% 2.52/1.87 % (13322)------------------------------
% 2.52/1.87 % (13322)------------------------------
% 2.52/1.88 % (13343)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_13195 for (2995ds/98Mi)
% 2.52/1.88 % (13344)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_13195 for (2995ds/507Mi)
% 2.52/1.89 % (13342)Instruction limit reached!
% 2.52/1.89 % (13342)------------------------------
% 2.52/1.89 % (13342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.89 % (13342)Termination reason: Unknown
% 2.52/1.89 % (13342)Termination phase: Property scanning
% 2.52/1.89
% 2.52/1.89 % (13342)Memory used [KB]: 1535
% 2.52/1.89 % (13342)Time elapsed: 0.015 s
% 2.52/1.89 % (13342)Instructions burned: 46 (million)
% 2.52/1.89 % (13342)------------------------------
% 2.52/1.89 % (13342)------------------------------
% 2.52/1.91 % (13345)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_13195 for (2995ds/149Mi)
% 2.52/1.91 % (13343)Instruction limit reached!
% 2.52/1.91 % (13343)------------------------------
% 2.52/1.91 % (13343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.91 % (13343)Termination reason: Unknown
% 2.52/1.91 % (13343)Termination phase: Saturation
% 2.52/1.91
% 2.52/1.91 % (13343)Memory used [KB]: 1791
% 2.52/1.91 % (13343)Time elapsed: 0.027 s
% 2.52/1.91 % (13343)Instructions burned: 99 (million)
% 2.52/1.91 % (13343)------------------------------
% 2.52/1.91 % (13343)------------------------------
% 2.52/1.92 % (13346)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_13195 for (2995ds/39Mi)
% 2.52/1.93 % (13346)Instruction limit reached!
% 2.52/1.93 % (13346)------------------------------
% 2.52/1.93 % (13346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.93 % (13346)Termination reason: Unknown
% 2.52/1.93 % (13346)Termination phase: Property scanning
% 2.52/1.93
% 2.52/1.93 % (13346)Memory used [KB]: 1663
% 2.52/1.93 % (13346)Time elapsed: 0.013 s
% 2.52/1.93 % (13346)Instructions burned: 41 (million)
% 2.52/1.93 % (13346)------------------------------
% 2.52/1.93 % (13346)------------------------------
% 2.52/1.94 % (13327)Instruction limit reached!
% 2.52/1.94 % (13327)------------------------------
% 2.52/1.94 % (13327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.94 % (13327)Termination reason: Unknown
% 2.52/1.94 % (13327)Termination phase: Saturation
% 2.52/1.94
% 2.52/1.94 % (13327)Memory used [KB]: 7036
% 2.52/1.94 % (13327)Time elapsed: 0.370 s
% 2.52/1.94 % (13327)Instructions burned: 780 (million)
% 2.52/1.94 % (13327)------------------------------
% 2.52/1.94 % (13327)------------------------------
% 2.52/1.94 % (13344)First to succeed.
% 2.52/1.94 % (13347)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_13195 for (2994ds/6Mi)
% 2.52/1.95 % (13344)Refutation found. Thanks to Tanya!
% 2.52/1.95 % SZS status Theorem for DTF2THF_13195
% 2.52/1.95 % SZS output start Proof for DTF2THF_13195
% 2.52/1.95 thf(type_def_6, type, set: ($tType) > $tType).
% 2.52/1.95 thf(type_def_7, type, a: $tType).
% 2.52/1.95 thf(func_def_0, type, set: ($tType) > $tType).
% 2.52/1.95 thf(func_def_1, type, a: $tType).
% 2.52/1.95 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 2.52/1.95 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 2.52/1.95 thf(func_def_4, type, semilattice_inf: !>[X0: $tType]:($o)).
% 2.52/1.95 thf(func_def_5, type, condit2040224947_above: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 2.52/1.95 thf(func_def_6, type, condit1201339847_below: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 2.52/1.95 thf(func_def_7, type, finite_comp_fun_idem: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > $o)).
% 2.52/1.95 thf(func_def_8, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 2.52/1.95 thf(func_def_9, type, abel_semigroup: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 2.52/1.95 thf(func_def_10, type, semigroup: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 2.52/1.95 thf(func_def_11, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.52/1.95 thf(func_def_12, type, semilattice: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 2.52/1.95 thf(func_def_13, type, lattic1263571978nf_fin: !>[X0: $tType]:((X0 > X0 > X0) > set @ X0 > X0)).
% 2.52/1.95 thf(func_def_14, type, lattic35693393ce_set: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 2.52/1.95 thf(func_def_15, type, lattic1039401930up_fin: !>[X0: $tType]:((X0 > X0 > X0) > set @ X0 > X0)).
% 2.52/1.95 thf(func_def_16, type, modula105138637_a_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 2.52/1.95 thf(func_def_17, type, modula477145868_b_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 2.52/1.95 thf(func_def_18, type, modula849153099_c_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 2.52/1.95 thf(func_def_19, type, modula1221160330_d_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 2.52/1.95 thf(func_def_20, type, modula1593167561_e_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 2.52/1.95 thf(func_def_21, type, modula1937309406incomp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 2.52/1.95 thf(func_def_22, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.52/1.95 thf(func_def_23, type, least: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 2.52/1.95 thf(func_def_24, type, max: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 2.52/1.95 thf(func_def_25, type, min: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 2.52/1.95 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.52/1.95 thf(func_def_27, type, greatest: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 2.52/1.95 thf(func_def_28, type, antimono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 2.52/1.95 thf(func_def_29, type, mono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 2.52/1.95 thf(func_def_30, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.52/1.95 thf(func_def_31, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.52/1.95 thf(func_def_32, type, set_atLeast: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 2.52/1.95 thf(func_def_33, type, set_atMost: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 2.52/1.95 thf(func_def_34, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.52/1.95 thf(func_def_35, type, a2: a).
% 2.52/1.95 thf(func_def_36, type, b: a).
% 2.52/1.95 thf(func_def_37, type, c: a).
% 2.52/1.95 thf(func_def_38, type, inf: a > a > a).
% 2.52/1.95 thf(func_def_39, type, less_eq: a > a > $o).
% 2.52/1.95 thf(func_def_40, type, sup: a > a > a).
% 2.52/1.95 thf(func_def_55, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.52/1.95 thf(func_def_56, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.52/1.95 thf(func_def_58, type, sK2: a > (a > $o) > a).
% 2.52/1.95 thf(func_def_59, type, sK3: a > set @ a > a).
% 2.52/1.95 thf(func_def_60, type, sK4: set @ a > a).
% 2.52/1.95 thf(func_def_61, type, sK5: a > set @ a > a).
% 2.52/1.95 thf(func_def_62, type, sK6: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.52/1.95 thf(func_def_63, type, sK7: !>[X0: $tType]:((a > X0) > a)).
% 2.52/1.95 thf(func_def_64, type, sK8: !>[X0: $tType]:((a > X0) > a)).
% 2.52/1.95 thf(func_def_65, type, sK9: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.52/1.95 thf(func_def_66, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.52/1.95 thf(func_def_67, type, sK11: a > set @ a > a).
% 2.52/1.95 thf(func_def_68, type, sK12: a).
% 2.52/1.95 thf(func_def_69, type, sK13: a).
% 2.52/1.95 thf(func_def_70, type, sK14: a).
% 2.52/1.95 thf(func_def_71, type, sK15: a).
% 2.52/1.95 thf(func_def_72, type, sK16: a).
% 2.52/1.95 thf(func_def_73, type, sK17: a > set @ a > a).
% 2.52/1.95 thf(func_def_74, type, sK18: a > set @ a > a).
% 2.52/1.95 thf(func_def_75, type, sK19: (a > a > a) > a).
% 2.52/1.95 thf(func_def_76, type, sK20: (a > a > a) > a).
% 2.52/1.95 thf(func_def_77, type, sK21: (a > a > a) > a).
% 2.52/1.95 thf(func_def_78, type, sK22: (a > a > a) > a).
% 2.52/1.95 thf(func_def_79, type, sK23: (a > a > a) > a).
% 2.52/1.95 thf(func_def_80, type, sK24: (a > a > a) > a).
% 2.52/1.95 thf(func_def_81, type, sK25: (a > a > a) > a).
% 2.52/1.95 thf(func_def_82, type, sK26: a > set @ a > a).
% 2.52/1.95 thf(func_def_83, type, sK27: a).
% 2.52/1.95 thf(func_def_84, type, sK28: a).
% 2.52/1.95 thf(func_def_85, type, sK29: a).
% 2.52/1.95 thf(func_def_86, type, sK30: (a > $o) > (a > $o) > a).
% 2.52/1.95 thf(func_def_87, type, sK31: a > (a > $o) > a).
% 2.52/1.95 thf(func_def_88, type, sK32: !>[X0: $tType]:(set @ X0 > X0)).
% 2.52/1.95 thf(func_def_89, type, sK33: a > (a > $o) > a).
% 2.52/1.95 thf(func_def_90, type, sK34: (a > $o) > (a > $o) > a).
% 2.52/1.95 thf(func_def_91, type, sK35: (a > a > a) > a).
% 2.52/1.95 thf(func_def_92, type, sK36: (a > a > a) > a).
% 2.52/1.95 thf(func_def_93, type, sK37: (a > a > a) > a).
% 2.52/1.95 thf(func_def_94, type, sK38: (a > a > a) > a).
% 2.52/1.95 thf(func_def_95, type, sK39: (a > a > a) > a).
% 2.52/1.95 thf(func_def_96, type, sK40: (a > a > a) > a).
% 2.52/1.95 thf(func_def_97, type, sK41: (a > a > a) > a).
% 2.52/1.95 thf(func_def_98, type, sK42: set @ a > a).
% 2.52/1.95 thf(func_def_99, type, sK43: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.52/1.95 thf(func_def_100, type, sK44: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.52/1.95 thf(func_def_101, type, sK45: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.52/1.95 thf(func_def_102, type, sK46: a > (a > $o) > a).
% 2.52/1.95 thf(func_def_103, type, sK47: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 2.52/1.95 thf(func_def_104, type, sK48: a > (a > $o) > a).
% 2.52/1.95 thf(func_def_105, type, sK49: a > (a > $o) > a).
% 2.52/1.95 thf(func_def_106, type, sK50: !>[X0: $tType]:((a > X0) > a)).
% 2.52/1.95 thf(func_def_107, type, sK51: !>[X0: $tType]:((a > X0) > a)).
% 2.52/1.95 thf(func_def_108, type, sK52: a > (a > $o) > a).
% 2.52/1.95 thf(func_def_109, type, sK53: a > (a > $o) > a).
% 2.52/1.95 thf(func_def_111, type, ph55: !>[X0: $tType]:(X0)).
% 2.52/1.95 thf(f1458,plain,(
% 2.52/1.95 $false),
% 2.52/1.95 inference(subsumption_resolution,[status(thm)],[f1456,f1309])).
% 2.52/1.95 thf(f1309,plain,(
% 2.52/1.95 ( ! [X0 : a,X1 : a] : (($true = (less_eq @ (inf @ X0 @ X1) @ X1))) )),
% 2.52/1.95 inference(cnf_transformation,[status(thm)],[f542])).
% 2.52/1.95 thf(f542,plain,(
% 2.52/1.95 ! [X0 : a,X1 : a] : ($true = (less_eq @ (inf @ X0 @ X1) @ X1))),
% 2.52/1.95 inference(fool_elimination,[status(thm)],[f541])).
% 2.52/1.95 thf(f541,plain,(
% 2.52/1.95 ! [X0 : a,X1 : a] : (less_eq @ (inf @ X0 @ X1) @ X1)),
% 2.52/1.95 inference(rectify,[status(thm)],[f84])).
% 2.52/1.95 thf(f84,axiom,(
% 2.52/1.95 ! [X5 : a,X6 : a] : (less_eq @ (inf @ X5 @ X6) @ X6)),
% 2.52/1.95 file('/export/starexec/sandbox2/tmp/tmp.mcq7CuGXAr/DTF2THF_13195.p',fact_83_local_Oinf__le2)).
% 2.52/1.95 thf(f1456,plain,(
% 2.52/1.95 ($true != (less_eq @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 2.52/1.95 inference(trivial_inequality_removal,[status(thm)],[f1444])).
% 2.52/1.95 thf(f1444,plain,(
% 2.52/1.95 ((inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))) != (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c))))) | ($true != (less_eq @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 2.52/1.95 inference(superposition,[status(thm)],[f1351,f1168])).
% 2.52/1.95 thf(f1168,plain,(
% 2.52/1.95 ( ! [X2 : a,X0 : a,X1 : a] : (((sup @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (sup @ X0 @ X2))) | ($true != (less_eq @ X0 @ X1))) )),
% 2.52/1.95 inference(cnf_transformation,[status(thm)],[f858])).
% 2.52/1.95 thf(f858,plain,(
% 2.52/1.95 ! [X0 : a,X1 : a,X2 : a] : (((sup @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (sup @ X0 @ X2))) | ($true != (less_eq @ X0 @ X1)))),
% 2.52/1.95 inference(ennf_transformation,[status(thm)],[f267])).
% 2.52/1.95 thf(f267,plain,(
% 2.52/1.95 ! [X0 : a,X1 : a,X2 : a] : (($true = (less_eq @ X0 @ X1)) => ((sup @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (sup @ X0 @ X2))))),
% 2.52/1.95 inference(fool_elimination,[status(thm)],[f266])).
% 2.52/1.95 thf(f266,plain,(
% 2.52/1.95 ! [X0 : a,X1 : a,X2 : a] : ((less_eq @ X0 @ X1) => ((sup @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (sup @ X0 @ X2))))),
% 2.52/1.95 inference(rectify,[status(thm)],[f128])).
% 2.52/1.95 thf(f128,axiom,(
% 2.52/1.95 ! [X5 : a,X6 : a,X7 : a] : ((less_eq @ X5 @ X6) => ((sup @ X5 @ (inf @ X6 @ X7)) = (inf @ X6 @ (sup @ X5 @ X7))))),
% 2.52/1.95 file('/export/starexec/sandbox2/tmp/tmp.mcq7CuGXAr/DTF2THF_13195.p',fact_127_local_Omodular)).
% 2.52/1.95 thf(f1351,plain,(
% 2.52/1.95 ((sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))) != (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))))),
% 2.52/1.95 inference(cnf_transformation,[status(thm)],[f808])).
% 2.52/1.95 thf(f808,plain,(
% 2.52/1.95 ((sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))) != (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))))),
% 2.52/1.95 inference(flattening,[status(thm)],[f634])).
% 2.52/1.95 thf(f634,plain,(
% 2.52/1.95 ~((sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))) = (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))))),
% 2.52/1.95 inference(fool_elimination,[status(thm)],[f264])).
% 2.52/1.95 thf(f264,negated_conjecture,(
% 2.52/1.95 ~((sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))) = (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))))),
% 2.52/1.95 inference(negated_conjecture,[status(cth)],[f263])).
% 2.52/1.95 thf(f263,conjecture,(
% 2.52/1.95 ((sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))) = (inf @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c)))))),
% 2.52/1.95 file('/export/starexec/sandbox2/tmp/tmp.mcq7CuGXAr/DTF2THF_13195.p',conj_0)).
% 2.52/1.95 % SZS output end Proof for DTF2THF_13195
% 2.52/1.95 % (13344)------------------------------
% 2.52/1.95 % (13344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.95 % (13344)Termination reason: Refutation
% 2.52/1.95
% 2.52/1.95 % (13344)Memory used [KB]: 6780
% 2.52/1.95 % (13344)Time elapsed: 0.063 s
% 2.52/1.95 % (13344)Instructions burned: 124 (million)
% 2.52/1.95 % (13344)------------------------------
% 2.52/1.95 % (13344)------------------------------
% 2.52/1.95 % (13299)Success in time 0.515 s
%------------------------------------------------------------------------------