%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP122^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:44 AM UTC 2026
% Result : Theorem 8.04s 2.41s
% Output : Refutation 8.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP122^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 08:27:09 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : ITP122^2 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.44 % Domain : Interactive Theorem Proving
% 0.19/0.44 % Problem : Sledgehammer Modular_Distrib_Lattice problem prob_265__3262952_1
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English :
% 0.19/0.44
% 0.19/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Des21]
% 0.19/0.44 % Names : Modular_Distrib_Lattice/prob_265__3262952_1 [Des21]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0
% 0.19/0.44 % Syntax : Number of formulae : 313 ( 122 unt; 43 typ; 0 def)
% 0.19/0.44 % Number of atoms : 678 ( 208 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 7 ( 2 avg)
% 0.19/0.44 % Number of connectives : 2810 ( 35 ~; 0 |; 29 &;2465 @)
% 0.19/0.44 % ( 0 <=>; 281 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 16 ( 6 avg)
% 0.19/0.44 % Number of types : 2 ( 1 usr)
% 0.19/0.44 % Number of type conns : 198 ( 198 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 43 ( 42 usr; 3 con; 0-6 aty)
% 0.19/0.44 % Number of variables : 738 ( 25 ^; 667 !; 8 ?; 738 :)
% 0.19/0.44 % ( 38 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.44 % SPC : TH1_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 16:29:54.141
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % Could-be-implicit typings (2)
% 0.19/0.44 thf(ty_t_Set_Oset,type,
% 0.19/0.44 set: $tType > $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_tf_a,type,
% 0.19/0.44 a: $tType ).
% 0.19/0.44
% 0.19/0.44 % Explicit typings (41)
% 0.19/0.44 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.19/0.44 bounded_lattice:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_HOL_Otype,type,
% 0.19/0.44 type:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.44 order:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.19/0.44 semilattice_inf:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.19/0.44 bounded_lattice_bot:
% 0.19/0.44 !>[A: $tType] : $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above,type,
% 0.19/0.44 condit2040224947_above:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below,type,
% 0.19/0.44 condit1201339847_below:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Finite__Set_Ocomp__fun__idem,type,
% 0.19/0.44 finite_comp_fun_idem:
% 0.19/0.44 !>[A: $tType,B: $tType] : ( ( A > B > B ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Finite__Set_Ofinite,type,
% 0.19/0.44 finite_finite:
% 0.19/0.44 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Groups_Oabel__semigroup,type,
% 0.19/0.44 abel_semigroup:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Groups_Osemigroup,type,
% 0.19/0.44 semigroup:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.19/0.44 inf_inf:
% 0.19/0.44 !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Lattices_Osemilattice,type,
% 0.19/0.44 semilattice:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin,type,
% 0.19/0.44 lattic1263571978nf_fin:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > ( set @ A ) > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Lattices__Big_Osemilattice__set,type,
% 0.19/0.44 lattic35693393ce_set:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin,type,
% 0.19/0.44 lattic1039401930up_fin:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > ( set @ A ) > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oa__aux,type,
% 0.19/0.44 modula105138637_a_aux:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Ob__aux,type,
% 0.19/0.44 modula477145868_b_aux:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oc__aux,type,
% 0.19/0.44 modula849153099_c_aux:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Od__aux,type,
% 0.19/0.44 modula1221160330_d_aux:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oe__aux,type,
% 0.19/0.44 modula1593167561_e_aux:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oincomp,type,
% 0.19/0.44 modula1937309406incomp:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.19/0.44 bot_bot:
% 0.19/0.44 !>[A: $tType] : A ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Oord_OLeast,type,
% 0.19/0.44 least:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Oord_Omax,type,
% 0.19/0.44 max:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Oord_Omin,type,
% 0.19/0.44 min:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.19/0.44 ord_less_eq:
% 0.19/0.44 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Oorder_OGreatest,type,
% 0.19/0.44 greatest:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Oorder_Oantimono,type,
% 0.19/0.44 antimono:
% 0.19/0.44 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Oorder_Omono,type,
% 0.19/0.44 mono:
% 0.19/0.44 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Set_OCollect,type,
% 0.19/0.44 collect:
% 0.19/0.44 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Set_Oinsert,type,
% 0.19/0.44 insert:
% 0.19/0.44 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Set__Interval_Oord_OatLeast,type,
% 0.19/0.44 set_atLeast:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Set__Interval_Oord_OatMost,type,
% 0.19/0.44 set_atMost:
% 0.19/0.44 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_member,type,
% 0.19/0.44 member:
% 0.19/0.44 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_a,type,
% 0.19/0.44 a2: a ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_b,type,
% 0.19/0.44 b: a ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_c,type,
% 0.19/0.44 c: a ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_inf,type,
% 0.19/0.44 inf: a > a > a ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_less__eq,type,
% 0.19/0.44 less_eq: a > a > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_sup,type,
% 0.19/0.44 sup: a > a > a ).
% 0.19/0.44
% 0.19/0.44 % Relevant facts (256)
% 0.19/0.44 thf(fact_0_local_Oantisym,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ( less_eq @ Y @ X )
% 0.19/0.44 => ( X = Y ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.antisym
% 0.19/0.44 thf(fact_1_local_Oantisym__conv,axiom,
% 0.19/0.44 ! [Y: a,X: a] :
% 0.19/0.44 ( ( less_eq @ Y @ X )
% 0.19/0.44 => ( ( less_eq @ X @ Y )
% 0.19/0.44 = ( X = Y ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.antisym_conv
% 0.19/0.44 thf(fact_2_local_Odual__order_Oantisym,axiom,
% 0.19/0.44 ! [B2: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 => ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( A2 = B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.dual_order.antisym
% 0.19/0.44 thf(fact_3_local_Odual__order_Oeq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.19/0.44 = ( ^ [A3: a,B3: a] :
% 0.19/0.44 ( ( less_eq @ B3 @ A3 )
% 0.19/0.44 & ( less_eq @ A3 @ B3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.dual_order.eq_iff
% 0.19/0.44 thf(fact_4_local_Odual__order_Otrans,axiom,
% 0.19/0.44 ! [B2: a,A2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 => ( ( less_eq @ C @ B2 )
% 0.19/0.44 => ( less_eq @ C @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.dual_order.trans
% 0.19/0.44 thf(fact_5_local_Oeq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.19/0.44 = ( ^ [X2: a,Y3: a] :
% 0.19/0.44 ( ( less_eq @ X2 @ Y3 )
% 0.19/0.44 & ( less_eq @ Y3 @ X2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.eq_iff
% 0.19/0.44 thf(fact_6_local_Oeq__refl,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( X = Y )
% 0.19/0.44 => ( less_eq @ X @ Y ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.eq_refl
% 0.19/0.44 thf(fact_7_local_Oord__eq__le__trans,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( A2 = B2 )
% 0.19/0.44 => ( ( less_eq @ B2 @ C )
% 0.19/0.44 => ( less_eq @ A2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.ord_eq_le_trans
% 0.19/0.44 thf(fact_8_local_Oord__le__eq__trans,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( B2 = C )
% 0.19/0.44 => ( less_eq @ A2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.ord_le_eq_trans
% 0.19/0.44 thf(fact_9_local_Oorder_Oantisym,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 => ( A2 = B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.order.antisym
% 0.19/0.44 thf(fact_10_local_Oorder_Oeq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.19/0.44 = ( ^ [A3: a,B3: a] :
% 0.19/0.44 ( ( less_eq @ A3 @ B3 )
% 0.19/0.44 & ( less_eq @ B3 @ A3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.order.eq_iff
% 0.19/0.44 thf(fact_11_local_Oorder_Otrans,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( less_eq @ B2 @ C )
% 0.19/0.44 => ( less_eq @ A2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.order.trans
% 0.19/0.44 thf(fact_12_local_Oorder__trans,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ( less_eq @ Y @ Z2 )
% 0.19/0.44 => ( less_eq @ X @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.order_trans
% 0.19/0.44 thf(fact_13_local_Oinf_Oassoc,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( inf @ ( inf @ A2 @ B2 ) @ C )
% 0.19/0.44 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.assoc
% 0.19/0.44 thf(fact_14_local_Oinf_Ocommute,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( inf @ A2 @ B2 )
% 0.19/0.44 = ( inf @ B2 @ A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.commute
% 0.19/0.44 thf(fact_15_local_Oinf_Oleft__commute,axiom,
% 0.19/0.44 ! [B2: a,A2: a,C: a] :
% 0.19/0.44 ( ( inf @ B2 @ ( inf @ A2 @ C ) )
% 0.19/0.44 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.left_commute
% 0.19/0.44 thf(fact_16_local_Oinf__assoc,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ( inf @ ( inf @ X @ Y ) @ Z2 )
% 0.19/0.44 = ( inf @ X @ ( inf @ Y @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_assoc
% 0.19/0.44 thf(fact_17_local_Oinf__commute,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( inf @ X @ Y )
% 0.19/0.44 = ( inf @ Y @ X ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_commute
% 0.19/0.44 thf(fact_18_local_Oinf__left__commute,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ( inf @ X @ ( inf @ Y @ Z2 ) )
% 0.19/0.44 = ( inf @ Y @ ( inf @ X @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_left_commute
% 0.19/0.44 thf(fact_19_local_Osup_Oassoc,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( sup @ ( sup @ A2 @ B2 ) @ C )
% 0.19/0.44 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.assoc
% 0.19/0.44 thf(fact_20_local_Osup_Ocommute,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( sup @ A2 @ B2 )
% 0.19/0.44 = ( sup @ B2 @ A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.commute
% 0.19/0.44 thf(fact_21_local_Osup_Oleft__commute,axiom,
% 0.19/0.44 ! [B2: a,A2: a,C: a] :
% 0.19/0.44 ( ( sup @ B2 @ ( sup @ A2 @ C ) )
% 0.19/0.44 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.left_commute
% 0.19/0.44 thf(fact_22_local_Osup__assoc,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ( sup @ ( sup @ X @ Y ) @ Z2 )
% 0.19/0.44 = ( sup @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_assoc
% 0.19/0.44 thf(fact_23_local_Osup__commute,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( sup @ X @ Y )
% 0.19/0.44 = ( sup @ Y @ X ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_commute
% 0.19/0.44 thf(fact_24_local_Osup__left__commute,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ( sup @ X @ ( sup @ Y @ Z2 ) )
% 0.19/0.44 = ( sup @ Y @ ( sup @ X @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_left_commute
% 0.19/0.44 thf(fact_25_local_Oinf_Oabsorb1,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( inf @ A2 @ B2 )
% 0.19/0.44 = A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.absorb1
% 0.19/0.44 thf(fact_26_local_Oinf_Oabsorb2,axiom,
% 0.19/0.44 ! [B2: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 => ( ( inf @ A2 @ B2 )
% 0.19/0.44 = B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.absorb2
% 0.19/0.44 thf(fact_27_local_Oinf_Oabsorb__iff1,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 = ( ( inf @ A2 @ B2 )
% 0.19/0.44 = A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.absorb_iff1
% 0.19/0.44 thf(fact_28_local_Oinf_Oabsorb__iff2,axiom,
% 0.19/0.44 ! [B2: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 = ( ( inf @ A2 @ B2 )
% 0.19/0.44 = B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.absorb_iff2
% 0.19/0.44 thf(fact_29_local_Oinf_OboundedE,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 0.19/0.44 => ~ ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ~ ( less_eq @ A2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.boundedE
% 0.19/0.44 thf(fact_30_local_Oinf_OboundedI,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( less_eq @ A2 @ C )
% 0.19/0.44 => ( less_eq @ A2 @ ( inf @ B2 @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.boundedI
% 0.19/0.44 thf(fact_31_local_Oinf_Ocobounded1,axiom,
% 0.19/0.44 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ A2 ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.cobounded1
% 0.19/0.44 thf(fact_32_local_Oinf_Ocobounded2,axiom,
% 0.19/0.44 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ B2 ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.cobounded2
% 0.19/0.44 thf(fact_33_local_Oinf_OcoboundedI1,axiom,
% 0.19/0.44 ! [A2: a,C: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ C )
% 0.19/0.44 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.coboundedI1
% 0.19/0.44 thf(fact_34_local_Oinf_OcoboundedI2,axiom,
% 0.19/0.44 ! [B2: a,C: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ C )
% 0.19/0.44 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.coboundedI2
% 0.19/0.44 thf(fact_35_local_Oinf_OorderE,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( A2
% 0.19/0.44 = ( inf @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.orderE
% 0.19/0.44 thf(fact_36_local_Oinf_OorderI,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( A2
% 0.19/0.44 = ( inf @ A2 @ B2 ) )
% 0.19/0.44 => ( less_eq @ A2 @ B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.orderI
% 0.19/0.44 thf(fact_37_local_Oinf_Oorder__iff,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 = ( A2
% 0.19/0.44 = ( inf @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.order_iff
% 0.19/0.44 thf(fact_38_local_Oinf__absorb1,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ( inf @ X @ Y )
% 0.19/0.44 = X ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_absorb1
% 0.19/0.44 thf(fact_39_local_Oinf__absorb2,axiom,
% 0.19/0.44 ! [Y: a,X: a] :
% 0.19/0.44 ( ( less_eq @ Y @ X )
% 0.19/0.44 => ( ( inf @ X @ Y )
% 0.19/0.44 = Y ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_absorb2
% 0.19/0.44 thf(fact_40_local_Oinf__greatest,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ( less_eq @ X @ Z2 )
% 0.19/0.44 => ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_greatest
% 0.19/0.44 thf(fact_41_local_Oinf__le1,axiom,
% 0.19/0.44 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_le1
% 0.19/0.44 thf(fact_42_local_Oinf__le2,axiom,
% 0.19/0.44 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_le2
% 0.19/0.44 thf(fact_43_local_Oinf__mono,axiom,
% 0.19/0.44 ! [A2: a,C: a,B2: a,D: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ C )
% 0.19/0.44 => ( ( less_eq @ B2 @ D )
% 0.19/0.44 => ( less_eq @ ( inf @ A2 @ B2 ) @ ( inf @ C @ D ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_mono
% 0.19/0.44 thf(fact_44_local_Oinf__unique,axiom,
% 0.19/0.44 ! [F: a > a > a,X: a,Y: a] :
% 0.19/0.44 ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
% 0.19/0.44 => ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
% 0.19/0.44 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.19/0.44 ( ( less_eq @ X3 @ Y4 )
% 0.19/0.44 => ( ( less_eq @ X3 @ Z3 )
% 0.19/0.44 => ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 0.19/0.44 => ( ( inf @ X @ Y )
% 0.19/0.44 = ( F @ X @ Y ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_unique
% 0.19/0.44 thf(fact_45_mem__Collect__eq,axiom,
% 0.19/0.44 ! [A: $tType,A2: A,P: A > $o] :
% 0.19/0.44 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.19/0.44 = ( P @ A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % mem_Collect_eq
% 0.19/0.44 thf(fact_46_Collect__mem__eq,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A] :
% 0.19/0.44 ( ( collect @ A
% 0.19/0.44 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 0.19/0.44 = A4 ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mem_eq
% 0.19/0.44 thf(fact_47_Collect__cong,axiom,
% 0.19/0.44 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.44 ( ! [X3: A] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 = ( Q @ X3 ) )
% 0.19/0.44 => ( ( collect @ A @ P )
% 0.19/0.44 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_cong
% 0.19/0.44 thf(fact_48_ext,axiom,
% 0.19/0.44 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.19/0.44 ( ! [X3: A] :
% 0.19/0.44 ( ( F @ X3 )
% 0.19/0.44 = ( G @ X3 ) )
% 0.19/0.44 => ( F = G ) ) ).
% 0.19/0.44
% 0.19/0.44 % ext
% 0.19/0.44 thf(fact_49_local_Ole__iff__inf,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( less_eq @ X @ Y )
% 0.19/0.44 = ( ( inf @ X @ Y )
% 0.19/0.44 = X ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_iff_inf
% 0.19/0.44 thf(fact_50_local_Ole__infE,axiom,
% 0.19/0.44 ! [X: a,A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ X @ ( inf @ A2 @ B2 ) )
% 0.19/0.44 => ~ ( ( less_eq @ X @ A2 )
% 0.19/0.44 => ~ ( less_eq @ X @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_infE
% 0.19/0.44 thf(fact_51_local_Ole__infI,axiom,
% 0.19/0.44 ! [X: a,A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ X @ A2 )
% 0.19/0.44 => ( ( less_eq @ X @ B2 )
% 0.19/0.44 => ( less_eq @ X @ ( inf @ A2 @ B2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_infI
% 0.19/0.44 thf(fact_52_local_Ole__infI1,axiom,
% 0.19/0.44 ! [A2: a,X: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ X )
% 0.19/0.44 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_infI1
% 0.19/0.44 thf(fact_53_local_Ole__infI2,axiom,
% 0.19/0.44 ! [B2: a,X: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ X )
% 0.19/0.44 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_infI2
% 0.19/0.44 thf(fact_54_local_Ole__iff__sup,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( less_eq @ X @ Y )
% 0.19/0.44 = ( ( sup @ X @ Y )
% 0.19/0.44 = Y ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_iff_sup
% 0.19/0.44 thf(fact_55_local_Ole__supE,axiom,
% 0.19/0.44 ! [A2: a,B2: a,X: a] :
% 0.19/0.44 ( ( less_eq @ ( sup @ A2 @ B2 ) @ X )
% 0.19/0.44 => ~ ( ( less_eq @ A2 @ X )
% 0.19/0.44 => ~ ( less_eq @ B2 @ X ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_supE
% 0.19/0.44 thf(fact_56_local_Ole__supI,axiom,
% 0.19/0.44 ! [A2: a,X: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ X )
% 0.19/0.44 => ( ( less_eq @ B2 @ X )
% 0.19/0.44 => ( less_eq @ ( sup @ A2 @ B2 ) @ X ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_supI
% 0.19/0.44 thf(fact_57_local_Ole__supI1,axiom,
% 0.19/0.44 ! [X: a,A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ X @ A2 )
% 0.19/0.44 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_supI1
% 0.19/0.44 thf(fact_58_local_Ole__supI2,axiom,
% 0.19/0.44 ! [X: a,B2: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ X @ B2 )
% 0.19/0.44 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_supI2
% 0.19/0.44 thf(fact_59_local_Osup_Oabsorb1,axiom,
% 0.19/0.44 ! [B2: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 => ( ( sup @ A2 @ B2 )
% 0.19/0.44 = A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.absorb1
% 0.19/0.44 thf(fact_60_local_Osup_Oabsorb2,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( sup @ A2 @ B2 )
% 0.19/0.44 = B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.absorb2
% 0.19/0.44 thf(fact_61_local_Osup_Oabsorb__iff1,axiom,
% 0.19/0.44 ! [B2: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 = ( ( sup @ A2 @ B2 )
% 0.19/0.44 = A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.absorb_iff1
% 0.19/0.44 thf(fact_62_local_Osup_Oabsorb__iff2,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 = ( ( sup @ A2 @ B2 )
% 0.19/0.44 = B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.absorb_iff2
% 0.19/0.44 thf(fact_63_local_Osup_OboundedE,axiom,
% 0.19/0.44 ! [B2: a,C: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 0.19/0.44 => ~ ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 => ~ ( less_eq @ C @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.boundedE
% 0.19/0.44 thf(fact_64_local_Osup_OboundedI,axiom,
% 0.19/0.44 ! [B2: a,A2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 => ( ( less_eq @ C @ A2 )
% 0.19/0.44 => ( less_eq @ ( sup @ B2 @ C ) @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.boundedI
% 0.19/0.44 thf(fact_65_local_Osup_Ocobounded1,axiom,
% 0.19/0.44 ! [A2: a,B2: a] : ( less_eq @ A2 @ ( sup @ A2 @ B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.cobounded1
% 0.19/0.44 thf(fact_66_local_Osup_Ocobounded2,axiom,
% 0.19/0.44 ! [B2: a,A2: a] : ( less_eq @ B2 @ ( sup @ A2 @ B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.cobounded2
% 0.19/0.44 thf(fact_67_local_Osup_OcoboundedI1,axiom,
% 0.19/0.44 ! [C: a,A2: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ C @ A2 )
% 0.19/0.44 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.coboundedI1
% 0.19/0.44 thf(fact_68_local_Osup_OcoboundedI2,axiom,
% 0.19/0.44 ! [C: a,B2: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ C @ B2 )
% 0.19/0.44 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.coboundedI2
% 0.19/0.44 thf(fact_69_local_Osup_Omono,axiom,
% 0.19/0.44 ! [C: a,A2: a,D: a,B2: a] :
% 0.19/0.44 ( ( less_eq @ C @ A2 )
% 0.19/0.44 => ( ( less_eq @ D @ B2 )
% 0.19/0.44 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A2 @ B2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.mono
% 0.19/0.44 thf(fact_70_local_Osup_OorderE,axiom,
% 0.19/0.44 ! [B2: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 => ( A2
% 0.19/0.44 = ( sup @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.orderE
% 0.19/0.44 thf(fact_71_local_Osup_OorderI,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( A2
% 0.19/0.44 = ( sup @ A2 @ B2 ) )
% 0.19/0.44 => ( less_eq @ B2 @ A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.orderI
% 0.19/0.44 thf(fact_72_local_Osup_Oorder__iff,axiom,
% 0.19/0.44 ! [B2: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 = ( A2
% 0.19/0.44 = ( sup @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.order_iff
% 0.19/0.44 thf(fact_73_local_Osup__absorb1,axiom,
% 0.19/0.44 ! [Y: a,X: a] :
% 0.19/0.44 ( ( less_eq @ Y @ X )
% 0.19/0.44 => ( ( sup @ X @ Y )
% 0.19/0.44 = X ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_absorb1
% 0.19/0.44 thf(fact_74_local_Osup__absorb2,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ( sup @ X @ Y )
% 0.19/0.44 = Y ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_absorb2
% 0.19/0.44 thf(fact_75_local_Osup__ge1,axiom,
% 0.19/0.44 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_ge1
% 0.19/0.44 thf(fact_76_local_Osup__ge2,axiom,
% 0.19/0.44 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_ge2
% 0.19/0.44 thf(fact_77_local_Osup__least,axiom,
% 0.19/0.44 ! [Y: a,X: a,Z2: a] :
% 0.19/0.44 ( ( less_eq @ Y @ X )
% 0.19/0.44 => ( ( less_eq @ Z2 @ X )
% 0.19/0.44 => ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_least
% 0.19/0.44 thf(fact_78_local_Osup__mono,axiom,
% 0.19/0.44 ! [A2: a,C: a,B2: a,D: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ C )
% 0.19/0.44 => ( ( less_eq @ B2 @ D )
% 0.19/0.44 => ( less_eq @ ( sup @ A2 @ B2 ) @ ( sup @ C @ D ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_mono
% 0.19/0.44 thf(fact_79_local_Osup__unique,axiom,
% 0.19/0.44 ! [F: a > a > a,X: a,Y: a] :
% 0.19/0.44 ( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
% 0.19/0.44 => ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
% 0.19/0.44 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.19/0.44 ( ( less_eq @ Y4 @ X3 )
% 0.19/0.44 => ( ( less_eq @ Z3 @ X3 )
% 0.19/0.44 => ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
% 0.19/0.44 => ( ( sup @ X @ Y )
% 0.19/0.44 = ( F @ X @ Y ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_unique
% 0.19/0.44 thf(fact_80_local_Odistrib__imp1,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ! [X3: a,Y4: a,Z3: a] :
% 0.19/0.44 ( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
% 0.19/0.44 = ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
% 0.19/0.44 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.19/0.44 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.distrib_imp1
% 0.19/0.44 thf(fact_81_local_Odistrib__imp2,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ! [X3: a,Y4: a,Z3: a] :
% 0.19/0.44 ( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
% 0.19/0.44 = ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
% 0.19/0.44 => ( ( inf @ X @ ( sup @ Y @ Z2 ) )
% 0.19/0.44 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.distrib_imp2
% 0.19/0.44 thf(fact_82_local_Oa__join__d,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( sup @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.a_join_d
% 0.19/0.44 thf(fact_83_a__meet__d,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( inf @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ C @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % a_meet_d
% 0.19/0.44 thf(fact_84_local_Ob__join__d,axiom,
% 0.19/0.44 ! [B2: a,A2: a,C: a] :
% 0.19/0.44 ( ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( sup @ B2 @ ( inf @ C @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.b_join_d
% 0.19/0.44 thf(fact_85_b__meet__d,axiom,
% 0.19/0.44 ! [B2: a,A2: a,C: a] :
% 0.19/0.44 ( ( inf @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( sup @ ( inf @ B2 @ C ) @ ( inf @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % b_meet_d
% 0.19/0.44 thf(fact_86_c__meet__d,axiom,
% 0.19/0.44 ! [C: a,A2: a,B2: a] :
% 0.19/0.44 ( ( inf @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( sup @ ( inf @ C @ A2 ) @ ( inf @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % c_meet_d
% 0.19/0.44 thf(fact_87_local_Od__aux__def,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( sup @ ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ B2 @ C ) ) @ ( inf @ C @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.d_aux_def
% 0.19/0.44 thf(fact_88_local_Od__b__c__a,axiom,
% 0.19/0.44 ! [B2: a,C: a,A2: a] :
% 0.19/0.44 ( ( modula1221160330_d_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 0.19/0.44 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.d_b_c_a
% 0.19/0.44 thf(fact_89_local_Od__c__a__b,axiom,
% 0.19/0.44 ! [C: a,A2: a,B2: a] :
% 0.19/0.44 ( ( modula1221160330_d_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 0.19/0.44 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.d_c_a_b
% 0.19/0.44 thf(fact_90_local_Oa__meet__e,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( inf @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.a_meet_e
% 0.19/0.44 thf(fact_91_local_Ob__meet__e,axiom,
% 0.19/0.44 ! [B2: a,A2: a,C: a] :
% 0.19/0.44 ( ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( inf @ B2 @ ( sup @ C @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.b_meet_e
% 0.19/0.44 thf(fact_92_local_Oc__meet__e,axiom,
% 0.19/0.44 ! [C: a,A2: a,B2: a] :
% 0.19/0.44 ( ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( inf @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.c_meet_e
% 0.19/0.44 thf(fact_93_local_Oe__aux__def,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( inf @ ( inf @ ( sup @ A2 @ B2 ) @ ( sup @ B2 @ C ) ) @ ( sup @ C @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.e_aux_def
% 0.19/0.44 thf(fact_94_local_Oe__b__c__a,axiom,
% 0.19/0.44 ! [B2: a,C: a,A2: a] :
% 0.19/0.44 ( ( modula1593167561_e_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 0.19/0.44 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.e_b_c_a
% 0.19/0.44 thf(fact_95_local_Oe__c__a__b,axiom,
% 0.19/0.44 ! [C: a,A2: a,B2: a] :
% 0.19/0.44 ( ( modula1593167561_e_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 0.19/0.44 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.e_c_a_b
% 0.19/0.44 thf(fact_96_local_Odistrib__inf__le,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.distrib_inf_le
% 0.19/0.44 thf(fact_97_local_Odistrib__sup__le,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.distrib_sup_le
% 0.19/0.44 thf(fact_98_local_Omodular,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.19/0.44 = ( inf @ Y @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.modular
% 0.19/0.44 thf(fact_99_local_Oincomp__def,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( modula1937309406incomp @ a @ less_eq @ X @ Y )
% 0.19/0.44 = ( ~ ( less_eq @ X @ Y )
% 0.19/0.44 & ~ ( less_eq @ Y @ X ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.incomp_def
% 0.19/0.44 thf(fact_100_local_Oorder_Orefl,axiom,
% 0.19/0.44 ! [A2: a] : ( less_eq @ A2 @ A2 ) ).
% 0.19/0.44
% 0.19/0.44 % local.order.refl
% 0.19/0.44 thf(fact_101_local_Oorder__refl,axiom,
% 0.19/0.44 ! [X: a] : ( less_eq @ X @ X ) ).
% 0.19/0.44
% 0.19/0.44 % local.order_refl
% 0.19/0.44 thf(fact_102_local_Oinf_Oidem,axiom,
% 0.19/0.44 ! [A2: a] :
% 0.19/0.44 ( ( inf @ A2 @ A2 )
% 0.19/0.44 = A2 ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.idem
% 0.19/0.44 thf(fact_103_local_Oinf_Oleft__idem,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( inf @ A2 @ ( inf @ A2 @ B2 ) )
% 0.19/0.44 = ( inf @ A2 @ B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.left_idem
% 0.19/0.44 thf(fact_104_local_Oinf_Oright__idem,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( inf @ ( inf @ A2 @ B2 ) @ B2 )
% 0.19/0.44 = ( inf @ A2 @ B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.right_idem
% 0.19/0.44 thf(fact_105_local_Oinf__idem,axiom,
% 0.19/0.44 ! [X: a] :
% 0.19/0.44 ( ( inf @ X @ X )
% 0.19/0.44 = X ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_idem
% 0.19/0.44 thf(fact_106_local_Oinf__left__idem,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( inf @ X @ ( inf @ X @ Y ) )
% 0.19/0.44 = ( inf @ X @ Y ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_left_idem
% 0.19/0.44 thf(fact_107_local_Oinf__right__idem,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 0.19/0.44 = ( inf @ X @ Y ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_right_idem
% 0.19/0.44 thf(fact_108_local_Osup_Oidem,axiom,
% 0.19/0.44 ! [A2: a] :
% 0.19/0.44 ( ( sup @ A2 @ A2 )
% 0.19/0.44 = A2 ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.idem
% 0.19/0.44 thf(fact_109_local_Osup_Oleft__idem,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( sup @ A2 @ ( sup @ A2 @ B2 ) )
% 0.19/0.44 = ( sup @ A2 @ B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.left_idem
% 0.19/0.44 thf(fact_110_local_Osup_Oright__idem,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( sup @ ( sup @ A2 @ B2 ) @ B2 )
% 0.19/0.44 = ( sup @ A2 @ B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.right_idem
% 0.19/0.44 thf(fact_111_local_Osup__idem,axiom,
% 0.19/0.44 ! [X: a] :
% 0.19/0.44 ( ( sup @ X @ X )
% 0.19/0.44 = X ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_idem
% 0.19/0.44 thf(fact_112_local_Osup__left__idem,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( sup @ X @ ( sup @ X @ Y ) )
% 0.19/0.44 = ( sup @ X @ Y ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_left_idem
% 0.19/0.44 thf(fact_113_local_OGreatestI2__order,axiom,
% 0.19/0.44 ! [P: a > $o,X: a,Q: a > $o] :
% 0.19/0.44 ( ( P @ X )
% 0.19/0.44 => ( ! [Y4: a] :
% 0.19/0.44 ( ( P @ Y4 )
% 0.19/0.44 => ( less_eq @ Y4 @ X ) )
% 0.19/0.44 => ( ! [X3: a] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 => ( ! [Y5: a] :
% 0.19/0.44 ( ( P @ Y5 )
% 0.19/0.44 => ( less_eq @ Y5 @ X3 ) )
% 0.19/0.44 => ( Q @ X3 ) ) )
% 0.19/0.44 => ( Q @ ( greatest @ a @ less_eq @ P ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.GreatestI2_order
% 0.19/0.44 thf(fact_114_local_OGreatest__equality,axiom,
% 0.19/0.44 ! [P: a > $o,X: a] :
% 0.19/0.44 ( ( P @ X )
% 0.19/0.44 => ( ! [Y4: a] :
% 0.19/0.44 ( ( P @ Y4 )
% 0.19/0.44 => ( less_eq @ Y4 @ X ) )
% 0.19/0.44 => ( ( greatest @ a @ less_eq @ P )
% 0.19/0.44 = X ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Greatest_equality
% 0.19/0.44 thf(fact_115_local_Omax__def,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.19/0.44 = B2 ) )
% 0.19/0.44 & ( ~ ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.19/0.44 = A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.max_def
% 0.19/0.44 thf(fact_116_local_Omin__def,axiom,
% 0.19/0.44 ! [A2: a,B2: a] :
% 0.19/0.44 ( ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.19/0.44 = A2 ) )
% 0.19/0.44 & ( ~ ( less_eq @ A2 @ B2 )
% 0.19/0.44 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.19/0.44 = B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.min_def
% 0.19/0.44 thf(fact_117_local_Oa__aux__def,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( sup @ ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.a_aux_def
% 0.19/0.44 thf(fact_118_a__def__equiv,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 => ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( inf @ ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % a_def_equiv
% 0.19/0.44 thf(fact_119_local_Oinf_Obounded__iff,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 0.19/0.44 = ( ( less_eq @ A2 @ B2 )
% 0.19/0.44 & ( less_eq @ A2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf.bounded_iff
% 0.19/0.44 thf(fact_120_local_Ole__inf__iff,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
% 0.19/0.44 = ( ( less_eq @ X @ Y )
% 0.19/0.44 & ( less_eq @ X @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_inf_iff
% 0.19/0.44 thf(fact_121_local_Ole__sup__iff,axiom,
% 0.19/0.44 ! [X: a,Y: a,Z2: a] :
% 0.19/0.44 ( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
% 0.19/0.44 = ( ( less_eq @ X @ Z2 )
% 0.19/0.44 & ( less_eq @ Y @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.le_sup_iff
% 0.19/0.44 thf(fact_122_local_Osup_Obounded__iff,axiom,
% 0.19/0.44 ! [B2: a,C: a,A2: a] :
% 0.19/0.44 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 0.19/0.44 = ( ( less_eq @ B2 @ A2 )
% 0.19/0.44 & ( less_eq @ C @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup.bounded_iff
% 0.19/0.44 thf(fact_123_local_Oinf__sup__absorb,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( inf @ X @ ( sup @ X @ Y ) )
% 0.19/0.44 = X ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_sup_absorb
% 0.19/0.44 thf(fact_124_local_Osup__inf__absorb,axiom,
% 0.19/0.44 ! [X: a,Y: a] :
% 0.19/0.44 ( ( sup @ X @ ( inf @ X @ Y ) )
% 0.19/0.44 = X ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_inf_absorb
% 0.19/0.44 thf(fact_125_local_OLeast1I,axiom,
% 0.19/0.44 ! [P: a > $o] :
% 0.19/0.44 ( ? [X4: a] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 & ! [Y4: a] :
% 0.19/0.44 ( ( P @ Y4 )
% 0.19/0.44 => ( less_eq @ X4 @ Y4 ) )
% 0.19/0.44 & ! [Y4: a] :
% 0.19/0.44 ( ( ( P @ Y4 )
% 0.19/0.44 & ! [Ya: a] :
% 0.19/0.44 ( ( P @ Ya )
% 0.19/0.44 => ( less_eq @ Y4 @ Ya ) ) )
% 0.19/0.44 => ( Y4 = X4 ) ) )
% 0.19/0.44 => ( P @ ( least @ a @ less_eq @ P ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Least1I
% 0.19/0.44 thf(fact_126_local_OLeast1__le,axiom,
% 0.19/0.44 ! [P: a > $o,Z2: a] :
% 0.19/0.44 ( ? [X4: a] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 & ! [Y4: a] :
% 0.19/0.44 ( ( P @ Y4 )
% 0.19/0.44 => ( less_eq @ X4 @ Y4 ) )
% 0.19/0.44 & ! [Y4: a] :
% 0.19/0.44 ( ( ( P @ Y4 )
% 0.19/0.44 & ! [Ya: a] :
% 0.19/0.44 ( ( P @ Ya )
% 0.19/0.44 => ( less_eq @ Y4 @ Ya ) ) )
% 0.19/0.44 => ( Y4 = X4 ) ) )
% 0.19/0.44 => ( ( P @ Z2 )
% 0.19/0.44 => ( less_eq @ ( least @ a @ less_eq @ P ) @ Z2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Least1_le
% 0.19/0.44 thf(fact_127_local_OLeastI2__order,axiom,
% 0.19/0.44 ! [P: a > $o,X: a,Q: a > $o] :
% 0.19/0.44 ( ( P @ X )
% 0.19/0.44 => ( ! [Y4: a] :
% 0.19/0.44 ( ( P @ Y4 )
% 0.19/0.44 => ( less_eq @ X @ Y4 ) )
% 0.19/0.44 => ( ! [X3: a] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 => ( ! [Y5: a] :
% 0.19/0.44 ( ( P @ Y5 )
% 0.19/0.44 => ( less_eq @ X3 @ Y5 ) )
% 0.19/0.44 => ( Q @ X3 ) ) )
% 0.19/0.44 => ( Q @ ( least @ a @ less_eq @ P ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.LeastI2_order
% 0.19/0.44 thf(fact_128_local_OLeast__equality,axiom,
% 0.19/0.44 ! [P: a > $o,X: a] :
% 0.19/0.44 ( ( P @ X )
% 0.19/0.44 => ( ! [Y4: a] :
% 0.19/0.44 ( ( P @ Y4 )
% 0.19/0.44 => ( less_eq @ X @ Y4 ) )
% 0.19/0.44 => ( ( least @ a @ less_eq @ P )
% 0.19/0.44 = X ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Least_equality
% 0.19/0.44 thf(fact_129_local_Oc__a,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( modula105138637_a_aux @ a @ inf @ sup @ C @ A2 @ B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.c_a
% 0.19/0.44 thf(fact_130_local_Oc__aux__def,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( sup @ ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.c_aux_def
% 0.19/0.44 thf(fact_131_c__def__equiv,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 => ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( inf @ ( sup @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % c_def_equiv
% 0.19/0.44 thf(fact_132_c__meet__a__eq__d,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 => ( ( inf @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % c_meet_a_eq_d
% 0.19/0.44 thf(fact_133_local_Ob__a,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( modula105138637_a_aux @ a @ inf @ sup @ B2 @ C @ A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.b_a
% 0.19/0.44 thf(fact_134_local_Ob__aux__def,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( sup @ ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.b_aux_def
% 0.19/0.44 thf(fact_135_b__def__equiv,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 => ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.19/0.44 = ( inf @ ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % b_def_equiv
% 0.19/0.44 thf(fact_136_a__join__b__eq__e,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 => ( ( sup @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % a_join_b_eq_e
% 0.19/0.44 thf(fact_137_a__meet__b__eq__d,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 => ( ( inf @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % a_meet_b_eq_d
% 0.19/0.44 thf(fact_138_lattice_Oa__aux_Ocong,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( modula105138637_a_aux @ A )
% 0.19/0.44 = ( modula105138637_a_aux @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % lattice.a_aux.cong
% 0.19/0.44 thf(fact_139_lattice_Od__aux_Ocong,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( modula1221160330_d_aux @ A )
% 0.19/0.44 = ( modula1221160330_d_aux @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % lattice.d_aux.cong
% 0.19/0.44 thf(fact_140_lattice_Oe__aux_Ocong,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( modula1593167561_e_aux @ A )
% 0.19/0.44 = ( modula1593167561_e_aux @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % lattice.e_aux.cong
% 0.19/0.44 thf(fact_141_local_Ocomp__fun__idem__sup,axiom,
% 0.19/0.44 finite_comp_fun_idem @ a @ a @ sup ).
% 0.19/0.44
% 0.19/0.44 % local.comp_fun_idem_sup
% 0.19/0.44 thf(fact_142_local_Ocomp__fun__idem__inf,axiom,
% 0.19/0.44 finite_comp_fun_idem @ a @ a @ inf ).
% 0.19/0.44
% 0.19/0.44 % local.comp_fun_idem_inf
% 0.19/0.44 thf(fact_143_b__join__c__eq__e,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 => ( ( sup @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % b_join_c_eq_e
% 0.19/0.44 thf(fact_144_b__meet__c__eq__d,axiom,
% 0.19/0.44 ! [A2: a,B2: a,C: a] :
% 0.19/0.44 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 => ( ( inf @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.19/0.44 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % b_meet_c_eq_d
% 0.19/0.44 thf(fact_145_local_Osup_Osemigroup__axioms,axiom,
% 0.19/0.44 semigroup @ a @ sup ).
% 0.19/0.44
% 0.19/0.44 % local.sup.semigroup_axioms
% 0.19/0.44 thf(fact_146_local_Oinf_Osemigroup__axioms,axiom,
% 0.19/0.44 semigroup @ a @ inf ).
% 0.19/0.44
% 0.19/0.44 % local.inf.semigroup_axioms
% 0.19/0.44 thf(fact_147_local_Osup_Osemilattice__axioms,axiom,
% 0.19/0.44 semilattice @ a @ sup ).
% 0.19/0.44
% 0.19/0.44 % local.sup.semilattice_axioms
% 0.19/0.44 thf(fact_148_local_Oinf_Osemilattice__axioms,axiom,
% 0.19/0.44 semilattice @ a @ inf ).
% 0.19/0.44
% 0.19/0.44 % local.inf.semilattice_axioms
% 0.19/0.44 thf(fact_149_local_Osup_Oabel__semigroup__axioms,axiom,
% 0.19/0.44 abel_semigroup @ a @ sup ).
% 0.19/0.44
% 0.19/0.44 % local.sup.abel_semigroup_axioms
% 0.19/0.44 thf(fact_150_local_Oinf_Oabel__semigroup__axioms,axiom,
% 0.19/0.44 abel_semigroup @ a @ inf ).
% 0.19/0.44
% 0.19/0.44 % local.inf.abel_semigroup_axioms
% 0.19/0.44 thf(fact_151_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 0.19/0.44 lattic35693393ce_set @ a @ sup ).
% 0.19/0.44
% 0.19/0.44 % local.Sup_fin.semilattice_set_axioms
% 0.19/0.44 thf(fact_152_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 0.19/0.44 lattic35693393ce_set @ a @ inf ).
% 0.19/0.44
% 0.19/0.44 % local.Inf_fin.semilattice_set_axioms
% 0.19/0.44 thf(fact_153_lattice_Oincomp_Ocong,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( modula1937309406incomp @ A )
% 0.19/0.44 = ( modula1937309406incomp @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % lattice.incomp.cong
% 0.19/0.44 thf(fact_154_lattice_Oc__aux_Ocong,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( modula849153099_c_aux @ A )
% 0.19/0.44 = ( modula849153099_c_aux @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % lattice.c_aux.cong
% 0.19/0.44 thf(fact_155_lattice_Ob__aux_Ocong,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( modula477145868_b_aux @ A )
% 0.19/0.44 = ( modula477145868_b_aux @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % lattice.b_aux.cong
% 0.19/0.44 thf(fact_156_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A] :
% 0.19/0.44 ( ( abel_semigroup @ A @ F )
% 0.19/0.44 => ( semigroup @ A @ F ) ) ).
% 0.19/0.44
% 0.19/0.44 % abel_semigroup.axioms(1)
% 0.19/0.44 thf(fact_157_semilattice__set__def,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( lattic35693393ce_set @ A )
% 0.19/0.44 = ( semilattice @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % semilattice_set_def
% 0.19/0.44 thf(fact_158_semilattice__set_Ointro,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A] :
% 0.19/0.44 ( ( semilattice @ A @ F )
% 0.19/0.44 => ( lattic35693393ce_set @ A @ F ) ) ).
% 0.19/0.44
% 0.19/0.44 % semilattice_set.intro
% 0.19/0.44 thf(fact_159_abel__semigroup_Oleft__commute,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A,B2: A,A2: A,C: A] :
% 0.19/0.44 ( ( abel_semigroup @ A @ F )
% 0.19/0.44 => ( ( F @ B2 @ ( F @ A2 @ C ) )
% 0.19/0.44 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % abel_semigroup.left_commute
% 0.19/0.44 thf(fact_160_abel__semigroup_Ocommute,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.19/0.44 ( ( abel_semigroup @ A @ F )
% 0.19/0.44 => ( ( F @ A2 @ B2 )
% 0.19/0.44 = ( F @ B2 @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % abel_semigroup.commute
% 0.19/0.44 thf(fact_161_semigroup_Ointro,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A] :
% 0.19/0.44 ( ! [A5: A,B4: A,C2: A] :
% 0.19/0.44 ( ( F @ ( F @ A5 @ B4 ) @ C2 )
% 0.19/0.44 = ( F @ A5 @ ( F @ B4 @ C2 ) ) )
% 0.19/0.44 => ( semigroup @ A @ F ) ) ).
% 0.19/0.44
% 0.19/0.44 % semigroup.intro
% 0.19/0.44 thf(fact_162_semigroup_Oassoc,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 0.19/0.44 ( ( semigroup @ A @ F )
% 0.19/0.44 => ( ( F @ ( F @ A2 @ B2 ) @ C )
% 0.19/0.44 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % semigroup.assoc
% 0.19/0.44 thf(fact_163_semigroup__def,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( semigroup @ A )
% 0.19/0.44 = ( ^ [F2: A > A > A] :
% 0.19/0.44 ! [A3: A,B3: A,C3: A] :
% 0.19/0.44 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 0.19/0.44 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % semigroup_def
% 0.19/0.44 thf(fact_164_semilattice__set_Oaxioms,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A] :
% 0.19/0.44 ( ( lattic35693393ce_set @ A @ F )
% 0.19/0.44 => ( semilattice @ A @ F ) ) ).
% 0.19/0.44
% 0.19/0.44 % semilattice_set.axioms
% 0.19/0.44 thf(fact_165_semilattice_Oaxioms_I1_J,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A] :
% 0.19/0.44 ( ( semilattice @ A @ F )
% 0.19/0.44 => ( abel_semigroup @ A @ F ) ) ).
% 0.19/0.44
% 0.19/0.44 % semilattice.axioms(1)
% 0.19/0.44 thf(fact_166_local_Obdd__above__def,axiom,
% 0.19/0.44 ! [A4: set @ a] :
% 0.19/0.44 ( ( condit2040224947_above @ a @ less_eq @ A4 )
% 0.19/0.44 = ( ? [M: a] :
% 0.19/0.44 ! [X2: a] :
% 0.19/0.44 ( ( member @ a @ X2 @ A4 )
% 0.19/0.44 => ( less_eq @ X2 @ M ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_above_def
% 0.19/0.44 thf(fact_167_local_Obdd__below__def,axiom,
% 0.19/0.44 ! [A4: set @ a] :
% 0.19/0.44 ( ( condit1201339847_below @ a @ less_eq @ A4 )
% 0.19/0.44 = ( ? [M2: a] :
% 0.19/0.44 ! [X2: a] :
% 0.19/0.44 ( ( member @ a @ X2 @ A4 )
% 0.19/0.44 => ( less_eq @ M2 @ X2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_below_def
% 0.19/0.44 thf(fact_168_local_Obdd__belowI,axiom,
% 0.19/0.44 ! [A4: set @ a,M3: a] :
% 0.19/0.44 ( ! [X3: a] :
% 0.19/0.44 ( ( member @ a @ X3 @ A4 )
% 0.19/0.44 => ( less_eq @ M3 @ X3 ) )
% 0.19/0.44 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_belowI
% 0.19/0.44 thf(fact_169_local_Obdd__aboveI,axiom,
% 0.19/0.44 ! [A4: set @ a,M4: a] :
% 0.19/0.44 ( ! [X3: a] :
% 0.19/0.44 ( ( member @ a @ X3 @ A4 )
% 0.19/0.44 => ( less_eq @ X3 @ M4 ) )
% 0.19/0.44 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_aboveI
% 0.19/0.44 thf(fact_170_semilattice_Oidem,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A,A2: A] :
% 0.19/0.44 ( ( semilattice @ A @ F )
% 0.19/0.44 => ( ( F @ A2 @ A2 )
% 0.19/0.44 = A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % semilattice.idem
% 0.19/0.44 thf(fact_171_semilattice_Oleft__idem,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.19/0.44 ( ( semilattice @ A @ F )
% 0.19/0.44 => ( ( F @ A2 @ ( F @ A2 @ B2 ) )
% 0.19/0.44 = ( F @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % semilattice.left_idem
% 0.19/0.44 thf(fact_172_semilattice_Oright__idem,axiom,
% 0.19/0.44 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.19/0.44 ( ( semilattice @ A @ F )
% 0.19/0.44 => ( ( F @ ( F @ A2 @ B2 ) @ B2 )
% 0.19/0.44 = ( F @ A2 @ B2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % semilattice.right_idem
% 0.19/0.44 thf(fact_173_local_Obdd__above__mono,axiom,
% 0.19/0.44 ! [B5: set @ a,A4: set @ a] :
% 0.19/0.44 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 0.19/0.44 => ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 0.19/0.44 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_above_mono
% 0.19/0.44 thf(fact_174_local_Obdd__below__mono,axiom,
% 0.19/0.44 ! [B5: set @ a,A4: set @ a] :
% 0.19/0.44 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 0.19/0.44 => ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 0.19/0.44 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_below_mono
% 0.19/0.44 thf(fact_175_local_Obdd__above__finite,axiom,
% 0.19/0.44 ! [A4: set @ a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_above_finite
% 0.19/0.44 thf(fact_176_local_Ofinite__has__maximal2,axiom,
% 0.19/0.44 ! [A4: set @ a,A2: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( member @ a @ A2 @ A4 )
% 0.19/0.44 => ? [X3: a] :
% 0.19/0.44 ( ( member @ a @ X3 @ A4 )
% 0.19/0.44 & ( less_eq @ A2 @ X3 )
% 0.19/0.44 & ! [Xa: a] :
% 0.19/0.44 ( ( member @ a @ Xa @ A4 )
% 0.19/0.44 => ( ( less_eq @ X3 @ Xa )
% 0.19/0.44 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.finite_has_maximal2
% 0.19/0.44 thf(fact_177_local_Ofinite__has__minimal2,axiom,
% 0.19/0.44 ! [A4: set @ a,A2: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( member @ a @ A2 @ A4 )
% 0.19/0.44 => ? [X3: a] :
% 0.19/0.44 ( ( member @ a @ X3 @ A4 )
% 0.19/0.44 & ( less_eq @ X3 @ A2 )
% 0.19/0.44 & ! [Xa: a] :
% 0.19/0.44 ( ( member @ a @ Xa @ A4 )
% 0.19/0.44 => ( ( less_eq @ Xa @ X3 )
% 0.19/0.44 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.finite_has_minimal2
% 0.19/0.44 thf(fact_178_local_Obdd__below__finite,axiom,
% 0.19/0.44 ! [A4: set @ a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_below_finite
% 0.19/0.44 thf(fact_179_local_OantimonoD,axiom,
% 0.19/0.44 ! [B: $tType] :
% 0.19/0.44 ( ( order @ B )
% 0.19/0.44 => ! [F: a > B,X: a,Y: a] :
% 0.19/0.44 ( ( antimono @ a @ B @ less_eq @ F )
% 0.19/0.44 => ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.antimonoD
% 0.19/0.44 thf(fact_180_local_OantimonoE,axiom,
% 0.19/0.44 ! [B: $tType] :
% 0.19/0.44 ( ( order @ B )
% 0.19/0.44 => ! [F: a > B,X: a,Y: a] :
% 0.19/0.44 ( ( antimono @ a @ B @ less_eq @ F )
% 0.19/0.44 => ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.antimonoE
% 0.19/0.44 thf(fact_181_local_OantimonoI,axiom,
% 0.19/0.44 ! [B: $tType] :
% 0.19/0.44 ( ( order @ B )
% 0.19/0.44 => ! [F: a > B] :
% 0.19/0.44 ( ! [X3: a,Y4: a] :
% 0.19/0.44 ( ( less_eq @ X3 @ Y4 )
% 0.19/0.44 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.19/0.44 => ( antimono @ a @ B @ less_eq @ F ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.antimonoI
% 0.19/0.44 thf(fact_182_local_Oantimono__def,axiom,
% 0.19/0.44 ! [B: $tType] :
% 0.19/0.44 ( ( order @ B )
% 0.19/0.44 => ! [F: a > B] :
% 0.19/0.44 ( ( antimono @ a @ B @ less_eq @ F )
% 0.19/0.44 = ( ! [X2: a,Y3: a] :
% 0.19/0.44 ( ( less_eq @ X2 @ Y3 )
% 0.19/0.44 => ( ord_less_eq @ B @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.antimono_def
% 0.19/0.44 thf(fact_183_local_Omono__def,axiom,
% 0.19/0.44 ! [B: $tType] :
% 0.19/0.44 ( ( order @ B )
% 0.19/0.44 => ! [F: a > B] :
% 0.19/0.44 ( ( mono @ a @ B @ less_eq @ F )
% 0.19/0.44 = ( ! [X2: a,Y3: a] :
% 0.19/0.44 ( ( less_eq @ X2 @ Y3 )
% 0.19/0.44 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.mono_def
% 0.19/0.44 thf(fact_184_local_OmonoI,axiom,
% 0.19/0.44 ! [B: $tType] :
% 0.19/0.44 ( ( order @ B )
% 0.19/0.44 => ! [F: a > B] :
% 0.19/0.44 ( ! [X3: a,Y4: a] :
% 0.19/0.44 ( ( less_eq @ X3 @ Y4 )
% 0.19/0.44 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.19/0.44 => ( mono @ a @ B @ less_eq @ F ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.monoI
% 0.19/0.44 thf(fact_185_local_OmonoE,axiom,
% 0.19/0.44 ! [B: $tType] :
% 0.19/0.44 ( ( order @ B )
% 0.19/0.44 => ! [F: a > B,X: a,Y: a] :
% 0.19/0.44 ( ( mono @ a @ B @ less_eq @ F )
% 0.19/0.44 => ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.monoE
% 0.19/0.44 thf(fact_186_local_OmonoD,axiom,
% 0.19/0.44 ! [B: $tType] :
% 0.19/0.44 ( ( order @ B )
% 0.19/0.44 => ! [F: a > B,X: a,Y: a] :
% 0.19/0.44 ( ( mono @ a @ B @ less_eq @ F )
% 0.19/0.44 => ( ( less_eq @ X @ Y )
% 0.19/0.44 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.monoD
% 0.19/0.44 thf(fact_187_local_OSup__fin_OcoboundedI,axiom,
% 0.19/0.44 ! [A4: set @ a,A2: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( member @ a @ A2 @ A4 )
% 0.19/0.44 => ( less_eq @ A2 @ ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Sup_fin.coboundedI
% 0.19/0.44 thf(fact_188_local_OInf__fin_OcoboundedI,axiom,
% 0.19/0.44 ! [A4: set @ a,A2: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( member @ a @ A2 @ A4 )
% 0.19/0.44 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) @ A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Inf_fin.coboundedI
% 0.19/0.44 thf(fact_189_local_OSup__fin_Oin__idem,axiom,
% 0.19/0.44 ! [A4: set @ a,X: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( member @ a @ X @ A4 )
% 0.19/0.44 => ( ( sup @ X @ ( lattic1039401930up_fin @ a @ sup @ A4 ) )
% 0.19/0.44 = ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Sup_fin.in_idem
% 0.19/0.44 thf(fact_190_local_OInf__fin_Oin__idem,axiom,
% 0.19/0.44 ! [A4: set @ a,X: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( member @ a @ X @ A4 )
% 0.19/0.44 => ( ( inf @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) )
% 0.19/0.44 = ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Inf_fin.in_idem
% 0.19/0.44 thf(fact_191_local_Oinf__Sup__absorb,axiom,
% 0.19/0.44 ! [A4: set @ a,A2: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( member @ a @ A2 @ A4 )
% 0.19/0.44 => ( ( inf @ A2 @ ( lattic1039401930up_fin @ a @ sup @ A4 ) )
% 0.19/0.44 = A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.inf_Sup_absorb
% 0.19/0.44 thf(fact_192_local_Osup__Inf__absorb,axiom,
% 0.19/0.44 ! [A4: set @ a,A2: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( member @ a @ A2 @ A4 )
% 0.19/0.44 => ( ( sup @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) @ A2 )
% 0.19/0.44 = A2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.sup_Inf_absorb
% 0.19/0.44 thf(fact_193_semilattice__sup_OSup__fin_Ocong,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( lattic1039401930up_fin @ A )
% 0.19/0.44 = ( lattic1039401930up_fin @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % semilattice_sup.Sup_fin.cong
% 0.19/0.44 thf(fact_194_semilattice__inf_OInf__fin_Ocong,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( lattic1263571978nf_fin @ A )
% 0.19/0.44 = ( lattic1263571978nf_fin @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % semilattice_inf.Inf_fin.cong
% 0.19/0.44 thf(fact_195_local_OInf__fin__le__Sup__fin,axiom,
% 0.19/0.44 ! [A4: set @ a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) @ ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Inf_fin_le_Sup_fin
% 0.19/0.44 thf(fact_196_local_OSup__fin_Osubset__imp,axiom,
% 0.19/0.44 ! [A4: set @ a,B5: set @ a] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ( finite_finite @ a @ B5 )
% 0.19/0.44 => ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ ( lattic1039401930up_fin @ a @ sup @ B5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Sup_fin.subset_imp
% 0.19/0.44 thf(fact_197_local_Ofinite__has__minimal,axiom,
% 0.19/0.44 ! [A4: set @ a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ? [X3: a] :
% 0.19/0.44 ( ( member @ a @ X3 @ A4 )
% 0.19/0.44 & ! [Xa: a] :
% 0.19/0.44 ( ( member @ a @ Xa @ A4 )
% 0.19/0.44 => ( ( less_eq @ Xa @ X3 )
% 0.19/0.44 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.finite_has_minimal
% 0.19/0.44 thf(fact_198_local_Ofinite__has__maximal,axiom,
% 0.19/0.44 ! [A4: set @ a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ? [X3: a] :
% 0.19/0.44 ( ( member @ a @ X3 @ A4 )
% 0.19/0.44 & ! [Xa: a] :
% 0.19/0.44 ( ( member @ a @ Xa @ A4 )
% 0.19/0.44 => ( ( less_eq @ X3 @ Xa )
% 0.19/0.44 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.finite_has_maximal
% 0.19/0.44 thf(fact_199_local_OInf__fin_Osubset,axiom,
% 0.19/0.44 ! [A4: set @ a,B5: set @ a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( B5
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ( ord_less_eq @ ( set @ a ) @ B5 @ A4 )
% 0.19/0.44 => ( ( inf @ ( lattic1263571978nf_fin @ a @ inf @ B5 ) @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) )
% 0.19/0.44 = ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Inf_fin.subset
% 0.19/0.44 thf(fact_200_local_OSup__fin_Osubset,axiom,
% 0.19/0.44 ! [A4: set @ a,B5: set @ a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( B5
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ( ord_less_eq @ ( set @ a ) @ B5 @ A4 )
% 0.19/0.44 => ( ( sup @ ( lattic1039401930up_fin @ a @ sup @ B5 ) @ ( lattic1039401930up_fin @ a @ sup @ A4 ) )
% 0.19/0.44 = ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Sup_fin.subset
% 0.19/0.44 thf(fact_201_local_OInf__fin_Obounded__iff,axiom,
% 0.19/0.44 ! [A4: set @ a,X: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) )
% 0.19/0.44 = ( ! [X2: a] :
% 0.19/0.44 ( ( member @ a @ X2 @ A4 )
% 0.19/0.44 => ( less_eq @ X @ X2 ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Inf_fin.bounded_iff
% 0.19/0.44 thf(fact_202_local_OInf__fin_OboundedI,axiom,
% 0.19/0.44 ! [A4: set @ a,X: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ! [A5: a] :
% 0.19/0.44 ( ( member @ a @ A5 @ A4 )
% 0.19/0.44 => ( less_eq @ X @ A5 ) )
% 0.19/0.44 => ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Inf_fin.boundedI
% 0.19/0.44 thf(fact_203_local_OInf__fin_OboundedE,axiom,
% 0.19/0.44 ! [A4: set @ a,X: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) )
% 0.19/0.44 => ! [A6: a] :
% 0.19/0.44 ( ( member @ a @ A6 @ A4 )
% 0.19/0.44 => ( less_eq @ X @ A6 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Inf_fin.boundedE
% 0.19/0.44 thf(fact_204_local_OSup__fin_Obounded__iff,axiom,
% 0.19/0.44 ! [A4: set @ a,X: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ X )
% 0.19/0.44 = ( ! [X2: a] :
% 0.19/0.44 ( ( member @ a @ X2 @ A4 )
% 0.19/0.44 => ( less_eq @ X2 @ X ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Sup_fin.bounded_iff
% 0.19/0.44 thf(fact_205_local_OSup__fin_OboundedI,axiom,
% 0.19/0.44 ! [A4: set @ a,X: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ! [A5: a] :
% 0.19/0.44 ( ( member @ a @ A5 @ A4 )
% 0.19/0.44 => ( less_eq @ A5 @ X ) )
% 0.19/0.44 => ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ X ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Sup_fin.boundedI
% 0.19/0.44 thf(fact_206_local_OSup__fin_OboundedE,axiom,
% 0.19/0.44 ! [A4: set @ a,X: a] :
% 0.19/0.44 ( ( finite_finite @ a @ A4 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ X )
% 0.19/0.44 => ! [A6: a] :
% 0.19/0.44 ( ( member @ a @ A6 @ A4 )
% 0.19/0.44 => ( less_eq @ A6 @ X ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Sup_fin.boundedE
% 0.19/0.44 thf(fact_207_local_OInf__fin_Osubset__imp,axiom,
% 0.19/0.44 ! [A4: set @ a,B5: set @ a] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 0.19/0.44 => ( ( A4
% 0.19/0.44 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.44 => ( ( finite_finite @ a @ B5 )
% 0.19/0.44 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ B5 ) @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.Inf_fin.subset_imp
% 0.19/0.44 thf(fact_208_local_Obdd__below__empty,axiom,
% 0.19/0.44 condit1201339847_below @ a @ less_eq @ ( bot_bot @ ( set @ a ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_below_empty
% 0.19/0.44 thf(fact_209_local_Obdd__above__empty,axiom,
% 0.19/0.44 condit2040224947_above @ a @ less_eq @ ( bot_bot @ ( set @ a ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_above_empty
% 0.19/0.44 thf(fact_210_local_Onot__empty__eq__Iic__eq__empty,axiom,
% 0.19/0.44 ! [H: a] :
% 0.19/0.44 ( ( bot_bot @ ( set @ a ) )
% 0.19/0.44 != ( set_atMost @ a @ less_eq @ H ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.not_empty_eq_Iic_eq_empty
% 0.19/0.44 thf(fact_211_local_Onot__empty__eq__Ici__eq__empty,axiom,
% 0.19/0.44 ! [L: a] :
% 0.19/0.44 ( ( bot_bot @ ( set @ a ) )
% 0.19/0.44 != ( set_atLeast @ a @ less_eq @ L ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.not_empty_eq_Ici_eq_empty
% 0.19/0.44 thf(fact_212_local_OatLeast__iff,axiom,
% 0.19/0.44 ! [I: a,K: a] :
% 0.19/0.44 ( ( member @ a @ I @ ( set_atLeast @ a @ less_eq @ K ) )
% 0.19/0.44 = ( less_eq @ K @ I ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.atLeast_iff
% 0.19/0.44 thf(fact_213_local_OatMost__iff,axiom,
% 0.19/0.44 ! [I: a,K: a] :
% 0.19/0.44 ( ( member @ a @ I @ ( set_atMost @ a @ less_eq @ K ) )
% 0.19/0.44 = ( less_eq @ I @ K ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.atMost_iff
% 0.19/0.44 thf(fact_214_local_Obdd__below__Ici,axiom,
% 0.19/0.44 ! [A2: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeast @ a @ less_eq @ A2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_below_Ici
% 0.19/0.44 thf(fact_215_local_Obdd__above__Iic,axiom,
% 0.19/0.44 ! [B2: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atMost @ a @ less_eq @ B2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.bdd_above_Iic
% 0.19/0.44 thf(fact_216_subset__empty,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.44 = ( A4
% 0.19/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_empty
% 0.19/0.44 thf(fact_217_empty__subsetI,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 0.19/0.44
% 0.19/0.44 % empty_subsetI
% 0.19/0.44 thf(fact_218_subset__antisym,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.19/0.44 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.19/0.44 => ( A4 = B5 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_antisym
% 0.19/0.44 thf(fact_219_subsetI,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.19/0.44 ( ! [X3: A] :
% 0.19/0.44 ( ( member @ A @ X3 @ A4 )
% 0.19/0.44 => ( member @ A @ X3 @ B5 ) )
% 0.19/0.44 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.19/0.44
% 0.19/0.44 % subsetI
% 0.19/0.44 thf(fact_220_Collect__mono__iff,axiom,
% 0.19/0.44 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.19/0.44 = ( ! [X2: A] :
% 0.19/0.44 ( ( P @ X2 )
% 0.19/0.44 => ( Q @ X2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mono_iff
% 0.19/0.44 thf(fact_221_set__eq__subset,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( ^ [Y2: set @ A,Z: set @ A] : ( Y2 = Z ) )
% 0.19/0.44 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B6 )
% 0.19/0.44 & ( ord_less_eq @ ( set @ A ) @ B6 @ A7 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % set_eq_subset
% 0.19/0.44 thf(fact_222_subset__trans,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.19/0.44 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 0.19/0.44 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_trans
% 0.19/0.44 thf(fact_223_Collect__mono,axiom,
% 0.19/0.44 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.44 ( ! [X3: A] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 => ( Q @ X3 ) )
% 0.19/0.44 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mono
% 0.19/0.44 thf(fact_224_subset__refl,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.19/0.44
% 0.19/0.44 % subset_refl
% 0.19/0.44 thf(fact_225_subset__iff,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.44 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.19/0.44 ! [T: A] :
% 0.19/0.44 ( ( member @ A @ T @ A7 )
% 0.19/0.44 => ( member @ A @ T @ B6 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_iff
% 0.19/0.44 thf(fact_226_equalityD2,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.19/0.44 ( ( A4 = B5 )
% 0.19/0.44 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % equalityD2
% 0.19/0.44 thf(fact_227_equalityD1,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.19/0.44 ( ( A4 = B5 )
% 0.19/0.44 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.19/0.44
% 0.19/0.44 % equalityD1
% 0.19/0.44 thf(fact_228_subset__eq,axiom,
% 0.19/0.44 ! [A: $tType] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.44 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.19/0.44 ! [X2: A] :
% 0.19/0.44 ( ( member @ A @ X2 @ A7 )
% 0.19/0.44 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_eq
% 0.19/0.44 thf(fact_229_equalityE,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.19/0.44 ( ( A4 = B5 )
% 0.19/0.44 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.19/0.44 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % equalityE
% 0.19/0.44 thf(fact_230_subsetD,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A,B5: set @ A,C: A] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.19/0.44 => ( ( member @ A @ C @ A4 )
% 0.19/0.44 => ( member @ A @ C @ B5 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subsetD
% 0.19/0.44 thf(fact_231_in__mono,axiom,
% 0.19/0.44 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 0.19/0.44 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.19/0.44 => ( ( member @ A @ X @ A4 )
% 0.19/0.44 => ( member @ A @ X @ B5 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_mono
% 0.19/0.44 thf(fact_232_local_Omono__inf,axiom,
% 0.19/0.44 ! [B: $tType] :
% 0.19/0.44 ( ( semilattice_inf @ B )
% 0.19/0.44 => ! [F: a > B,A4: a,B5: a] :
% 0.19/0.44 ( ( mono @ a @ B @ less_eq @ F )
% 0.19/0.44 => ( ord_less_eq @ B @ ( F @ ( inf @ A4 @ B5 ) ) @ ( inf_inf @ B @ ( F @ A4 ) @ ( F @ B5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % local.mono_inf
% 0.19/0.44 thf(fact_233_local_OSup__fin_Oclosed,axiom,
% 0.19/0.45 ! [A4: set @ a] :
% 0.19/0.45 ( ( finite_finite @ a @ A4 )
% 0.19/0.45 => ( ( A4
% 0.19/0.45 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.45 => ( ! [X3: a,Y4: a] : ( member @ a @ ( sup @ X3 @ Y4 ) @ ( insert @ a @ X3 @ ( insert @ a @ Y4 @ ( bot_bot @ ( set @ a ) ) ) ) )
% 0.19/0.45 => ( member @ a @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ A4 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.Sup_fin.closed
% 0.19/0.45 thf(fact_234_local_Obdd__above__Int1,axiom,
% 0.19/0.45 ! [A4: set @ a,B5: set @ a] :
% 0.19/0.45 ( ( condit2040224947_above @ a @ less_eq @ A4 )
% 0.19/0.45 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.bdd_above_Int1
% 0.19/0.45 thf(fact_235_local_Obdd__above__Int2,axiom,
% 0.19/0.45 ! [B5: set @ a,A4: set @ a] :
% 0.19/0.45 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 0.19/0.45 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.bdd_above_Int2
% 0.19/0.45 thf(fact_236_local_Obdd__below__Int1,axiom,
% 0.19/0.45 ! [A4: set @ a,B5: set @ a] :
% 0.19/0.45 ( ( condit1201339847_below @ a @ less_eq @ A4 )
% 0.19/0.45 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.bdd_below_Int1
% 0.19/0.45 thf(fact_237_local_Obdd__below__Int2,axiom,
% 0.19/0.45 ! [B5: set @ a,A4: set @ a] :
% 0.19/0.45 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 0.19/0.45 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.bdd_below_Int2
% 0.19/0.45 thf(fact_238_Int__subset__iff,axiom,
% 0.19/0.45 ! [A: $tType,C4: set @ A,A4: set @ A,B5: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A4 @ B5 ) )
% 0.19/0.45 = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A4 )
% 0.19/0.45 & ( ord_less_eq @ ( set @ A ) @ C4 @ B5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Int_subset_iff
% 0.19/0.45 thf(fact_239_semilattice__inf__class_Oinf__right__idem,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ A )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 0.19/0.45 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % semilattice_inf_class.inf_right_idem
% 0.19/0.45 thf(fact_240_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ A )
% 0.19/0.45 => ! [A2: A,B2: A] :
% 0.19/0.45 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.19/0.45 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % semilattice_inf_class.inf.right_idem
% 0.19/0.45 thf(fact_241_semilattice__inf__class_Oinf__left__idem,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ A )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.19/0.45 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % semilattice_inf_class.inf_left_idem
% 0.19/0.45 thf(fact_242_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ A )
% 0.19/0.45 => ! [A2: A,B2: A] :
% 0.19/0.45 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.19/0.45 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % semilattice_inf_class.inf.left_idem
% 0.19/0.45 thf(fact_243_semilattice__inf__class_Oinf__idem,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ A )
% 0.19/0.45 => ! [X: A] :
% 0.19/0.45 ( ( inf_inf @ A @ X @ X )
% 0.19/0.45 = X ) ) ).
% 0.19/0.45
% 0.19/0.45 % semilattice_inf_class.inf_idem
% 0.19/0.45 thf(fact_244_semilattice__inf__class_Oinf_Oidem,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ A )
% 0.19/0.45 => ! [A2: A] :
% 0.19/0.45 ( ( inf_inf @ A @ A2 @ A2 )
% 0.19/0.45 = A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % semilattice_inf_class.inf.idem
% 0.19/0.45 thf(fact_245_inf__apply,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ B )
% 0.19/0.45 => ( ( inf_inf @ ( A > B ) )
% 0.19/0.45 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( inf_inf @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inf_apply
% 0.19/0.45 thf(fact_246_local_OInf__fin_Oinsert__not__elem,axiom,
% 0.19/0.45 ! [A4: set @ a,X: a] :
% 0.19/0.45 ( ( finite_finite @ a @ A4 )
% 0.19/0.45 => ( ~ ( member @ a @ X @ A4 )
% 0.19/0.45 => ( ( A4
% 0.19/0.45 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.45 => ( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ X @ A4 ) )
% 0.19/0.45 = ( inf @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.Inf_fin.insert_not_elem
% 0.19/0.45 thf(fact_247_local_OInf__fin_Oclosed,axiom,
% 0.19/0.45 ! [A4: set @ a] :
% 0.19/0.45 ( ( finite_finite @ a @ A4 )
% 0.19/0.45 => ( ( A4
% 0.19/0.45 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.45 => ( ! [X3: a,Y4: a] : ( member @ a @ ( inf @ X3 @ Y4 ) @ ( insert @ a @ X3 @ ( insert @ a @ Y4 @ ( bot_bot @ ( set @ a ) ) ) ) )
% 0.19/0.45 => ( member @ a @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) @ A4 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.Inf_fin.closed
% 0.19/0.45 thf(fact_248_local_OSup__fin_Oinsert__not__elem,axiom,
% 0.19/0.45 ! [A4: set @ a,X: a] :
% 0.19/0.45 ( ( finite_finite @ a @ A4 )
% 0.19/0.45 => ( ~ ( member @ a @ X @ A4 )
% 0.19/0.45 => ( ( A4
% 0.19/0.45 != ( bot_bot @ ( set @ a ) ) )
% 0.19/0.45 => ( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ X @ A4 ) )
% 0.19/0.45 = ( sup @ X @ ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.Sup_fin.insert_not_elem
% 0.19/0.45 thf(fact_249_semilattice__inf__class_Ole__inf__iff,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ A )
% 0.19/0.45 => ! [X: A,Y: A,Z2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z2 ) )
% 0.19/0.45 = ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 & ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % semilattice_inf_class.le_inf_iff
% 0.19/0.45 thf(fact_250_semilattice__inf__class_Oinf_Obounded__iff,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ A )
% 0.19/0.45 => ! [A2: A,B2: A,C: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 0.19/0.45 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.45 & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % semilattice_inf_class.inf.bounded_iff
% 0.19/0.45 thf(fact_251_inf__bot__right,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( bounded_lattice_bot @ A )
% 0.19/0.45 => ! [X: A] :
% 0.19/0.45 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 0.19/0.45 = ( bot_bot @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inf_bot_right
% 0.19/0.45 thf(fact_252_inf__bot__left,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( bounded_lattice_bot @ A )
% 0.19/0.45 => ! [X: A] :
% 0.19/0.45 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 0.19/0.45 = ( bot_bot @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inf_bot_left
% 0.19/0.45 thf(fact_253_insert__subset,axiom,
% 0.19/0.45 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B5 )
% 0.19/0.45 = ( ( member @ A @ X @ B5 )
% 0.19/0.45 & ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_subset
% 0.19/0.45 thf(fact_254_singleton__insert__inj__eq,axiom,
% 0.19/0.45 ! [A: $tType,B2: A,A2: A,A4: set @ A] :
% 0.19/0.45 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.45 = ( insert @ A @ A2 @ A4 ) )
% 0.19/0.45 = ( ( A2 = B2 )
% 0.19/0.45 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % singleton_insert_inj_eq
% 0.19/0.45 thf(fact_255_singleton__insert__inj__eq_H,axiom,
% 0.19/0.45 ! [A: $tType,A2: A,A4: set @ A,B2: A] :
% 0.19/0.45 ( ( ( insert @ A @ A2 @ A4 )
% 0.19/0.45 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.45 = ( ( A2 = B2 )
% 0.19/0.45 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % singleton_insert_inj_eq'
% 0.19/0.45
% 0.19/0.45 % Type constructors (12)
% 0.19/0.45 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.19/0.45 bounded_lattice @ $o ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.19/0.45 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.19/0.45 ! [A8: $tType,A9: $tType] :
% 0.19/0.45 ( ( bounded_lattice @ A9 )
% 0.19/0.45 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.19/0.45 ! [A8: $tType,A9: $tType] :
% 0.19/0.45 ( ( bounded_lattice @ A9 )
% 0.19/0.45 => ( bounded_lattice_bot @ ( A8 > A9 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.19/0.45 ! [A8: $tType,A9: $tType] :
% 0.19/0.45 ( ( semilattice_inf @ A9 )
% 0.19/0.45 => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.19/0.45 ! [A8: $tType,A9: $tType] :
% 0.19/0.45 ( ( order @ A9 )
% 0.19/0.45 => ( order @ ( A8 > A9 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 0.19/0.45 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 0.19/0.45 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.19/0.45 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_6,axiom,
% 0.19/0.45 bounded_lattice_bot @ $o ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_7,axiom,
% 0.19/0.45 semilattice_inf @ $o ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Oorder_8,axiom,
% 0.19/0.45 order @ $o ).
% 0.19/0.45
% 0.19/0.45 % Conjectures (2)
% 0.19/0.45 thf(conj_0,hypothesis,
% 0.19/0.45 less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ).
% 0.19/0.45
% 0.19/0.45 thf(conj_1,conjecture,
% 0.19/0.45 ( ( sup @ ( modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b ) @ ( modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c ) )
% 0.19/0.45 = ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 2.64/1.55 ---- Embedded in THF ---
% 2.64/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.64/1.55 %%% Generated on Tue Feb 24 08:27:10 EST 2026
% 2.64/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.64/1.55 %%% Logic specification used:
% 2.64/1.55 %%% thf(spec, logic, $$dhol).
% 2.64/1.55
% 2.64/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2DTF5305.p
% 2.64/1.55 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.64/1.55 thf(ty_tf_a, type, a: $tType).
% 2.64/1.55 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.64/1.55 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.64/1.55 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.64/1.55 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 2.64/1.55 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: ($o))).
% 2.64/1.55 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above, type, condit2040224947_above: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.64/1.55 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below, type, condit1201339847_below: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.64/1.55 thf(sy_c_Finite__Set_Ocomp__fun__idem, type, finite_comp_fun_idem: (!> [A:$tType,B:$tType]: (((A > (B > B)) > $o)))).
% 2.64/1.55 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.64/1.55 thf(sy_c_Groups_Oabel__semigroup, type, abel_semigroup: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.64/1.55 thf(sy_c_Groups_Osemigroup, type, semigroup: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.64/1.55 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.64/1.55 thf(sy_c_Lattices_Osemilattice, type, semilattice: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.64/1.55 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin, type, lattic1263571978nf_fin: (!> [A:$tType]: (((A > (A > A)) > ((set @ A) > A))))).
% 2.64/1.55 thf(sy_c_Lattices__Big_Osemilattice__set, type, lattic35693393ce_set: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.64/1.55 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin, type, lattic1039401930up_fin: (!> [A:$tType]: (((A > (A > A)) > ((set @ A) > A))))).
% 2.64/1.55 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oa__aux, type, modula105138637_a_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.64/1.55 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Ob__aux, type, modula477145868_b_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.64/1.55 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oc__aux, type, modula849153099_c_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.64/1.55 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Od__aux, type, modula1221160330_d_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.64/1.55 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oe__aux, type, modula1593167561_e_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.64/1.55 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oincomp, type, modula1937309406incomp: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > $o)))))).
% 2.64/1.55 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.64/1.55 thf(sy_c_Orderings_Oord_OLeast, type, least: (!> [A:$tType]: (((A > (A > $o)) > ((A > $o) > A))))).
% 2.64/1.55 thf(sy_c_Orderings_Oord_Omax, type, max: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > A)))))).
% 2.64/1.55 thf(sy_c_Orderings_Oord_Omin, type, min: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > A)))))).
% 2.64/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.64/1.55 thf(sy_c_Orderings_Oorder_OGreatest, type, greatest: (!> [A:$tType]: (((A > (A > $o)) > ((A > $o) > A))))).
% 2.64/1.55 thf(sy_c_Orderings_Oorder_Oantimono, type, antimono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.64/1.55 thf(sy_c_Orderings_Oorder_Omono, type, mono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.64/1.55 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.64/1.55 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.64/1.55 thf(sy_c_Set__Interval_Oord_OatLeast, type, set_atLeast: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.64/1.55 thf(sy_c_Set__Interval_Oord_OatMost, type, set_atMost: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.64/1.55 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.64/1.55 thf(sy_v_a, type, a2: a).
% 2.64/1.55 thf(sy_v_b, type, b: a).
% 2.64/1.55 thf(sy_v_c, type, c: a).
% 2.64/1.55 thf(sy_v_inf, type, inf: (a > (a > a))).
% 2.64/1.55 thf(sy_v_less__eq, type, less_eq: (a > (a > $o))).
% 2.64/1.55 thf(sy_v_sup, type, sup: (a > (a > a))).
% 2.64/1.55 thf(fact_0_local_Oantisym, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) => (((less_eq @ Y) @ X) => (X = Y)))))).
% 2.64/1.55 thf(fact_1_local_Oantisym__conv, axiom, (! [Y:a,X:a]: ((((less_eq @ Y) @ X) => (((less_eq @ X) @ Y) = (X = Y)))))).
% 2.64/1.55 thf(fact_2_local_Odual__order_Oantisym, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (((less_eq @ A2) @ B2) => (A2 = B2)))))).
% 2.64/1.55 thf(fact_3_local_Odual__order_Oeq__iff, axiom, ((^ [Y2:a,Z:a]: ((Y2 = Z))) = (^ [A3:a,B3:a]: ((((less_eq @ B3) @ A3) & ((less_eq @ A3) @ B3)))))).
% 2.64/1.55 thf(fact_4_local_Odual__order_Otrans, axiom, (! [B2:a,A2:a,C:a]: ((((less_eq @ B2) @ A2) => (((less_eq @ C) @ B2) => ((less_eq @ C) @ A2)))))).
% 2.64/1.55 thf(fact_5_local_Oeq__iff, axiom, ((^ [Y2:a,Z:a]: ((Y2 = Z))) = (^ [X2:a,Y3:a]: ((((less_eq @ X2) @ Y3) & ((less_eq @ Y3) @ X2)))))).
% 2.64/1.55 thf(fact_6_local_Oeq__refl, axiom, (! [X:a,Y:a]: (((X = Y) => ((less_eq @ X) @ Y))))).
% 2.64/1.55 thf(fact_7_local_Oord__eq__le__trans, axiom, (! [A2:a,B2:a,C:a]: (((A2 = B2) => (((less_eq @ B2) @ C) => ((less_eq @ A2) @ C)))))).
% 2.64/1.55 thf(fact_8_local_Oord__le__eq__trans, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ B2) => ((B2 = C) => ((less_eq @ A2) @ C)))))).
% 2.64/1.55 thf(fact_9_local_Oorder_Oantisym, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (((less_eq @ B2) @ A2) => (A2 = B2)))))).
% 2.64/1.55 thf(fact_10_local_Oorder_Oeq__iff, axiom, ((^ [Y2:a,Z:a]: ((Y2 = Z))) = (^ [A3:a,B3:a]: ((((less_eq @ A3) @ B3) & ((less_eq @ B3) @ A3)))))).
% 2.64/1.55 thf(fact_11_local_Oorder_Otrans, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ B2) => (((less_eq @ B2) @ C) => ((less_eq @ A2) @ C)))))).
% 2.64/1.55 thf(fact_12_local_Oorder__trans, axiom, (! [X:a,Y:a,Z2:a]: ((((less_eq @ X) @ Y) => (((less_eq @ Y) @ Z2) => ((less_eq @ X) @ Z2)))))).
% 2.64/1.55 thf(fact_13_local_Oinf_Oassoc, axiom, (! [A2:a,B2:a,C:a]: ((((inf @ ((inf @ A2) @ B2)) @ C) = ((inf @ A2) @ ((inf @ B2) @ C)))))).
% 2.64/1.55 thf(fact_14_local_Oinf_Ocommute, axiom, (! [A2:a,B2:a]: ((((inf @ A2) @ B2) = ((inf @ B2) @ A2))))).
% 2.64/1.55 thf(fact_15_local_Oinf_Oleft__commute, axiom, (! [B2:a,A2:a,C:a]: ((((inf @ B2) @ ((inf @ A2) @ C)) = ((inf @ A2) @ ((inf @ B2) @ C)))))).
% 2.64/1.55 thf(fact_16_local_Oinf__assoc, axiom, (! [X:a,Y:a,Z2:a]: ((((inf @ ((inf @ X) @ Y)) @ Z2) = ((inf @ X) @ ((inf @ Y) @ Z2)))))).
% 2.64/1.55 thf(fact_17_local_Oinf__commute, axiom, (! [X:a,Y:a]: ((((inf @ X) @ Y) = ((inf @ Y) @ X))))).
% 2.64/1.55 thf(fact_18_local_Oinf__left__commute, axiom, (! [X:a,Y:a,Z2:a]: ((((inf @ X) @ ((inf @ Y) @ Z2)) = ((inf @ Y) @ ((inf @ X) @ Z2)))))).
% 2.64/1.55 thf(fact_19_local_Osup_Oassoc, axiom, (! [A2:a,B2:a,C:a]: ((((sup @ ((sup @ A2) @ B2)) @ C) = ((sup @ A2) @ ((sup @ B2) @ C)))))).
% 2.64/1.55 thf(fact_20_local_Osup_Ocommute, axiom, (! [A2:a,B2:a]: ((((sup @ A2) @ B2) = ((sup @ B2) @ A2))))).
% 2.64/1.55 thf(fact_21_local_Osup_Oleft__commute, axiom, (! [B2:a,A2:a,C:a]: ((((sup @ B2) @ ((sup @ A2) @ C)) = ((sup @ A2) @ ((sup @ B2) @ C)))))).
% 2.64/1.55 thf(fact_22_local_Osup__assoc, axiom, (! [X:a,Y:a,Z2:a]: ((((sup @ ((sup @ X) @ Y)) @ Z2) = ((sup @ X) @ ((sup @ Y) @ Z2)))))).
% 2.64/1.55 thf(fact_23_local_Osup__commute, axiom, (! [X:a,Y:a]: ((((sup @ X) @ Y) = ((sup @ Y) @ X))))).
% 2.64/1.55 thf(fact_24_local_Osup__left__commute, axiom, (! [X:a,Y:a,Z2:a]: ((((sup @ X) @ ((sup @ Y) @ Z2)) = ((sup @ Y) @ ((sup @ X) @ Z2)))))).
% 2.64/1.55 thf(fact_25_local_Oinf_Oabsorb1, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (((inf @ A2) @ B2) = A2))))).
% 2.64/1.55 thf(fact_26_local_Oinf_Oabsorb2, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (((inf @ A2) @ B2) = B2))))).
% 2.64/1.55 thf(fact_27_local_Oinf_Oabsorb__iff1, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) = (((inf @ A2) @ B2) = A2))))).
% 2.64/1.55 thf(fact_28_local_Oinf_Oabsorb__iff2, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) = (((inf @ A2) @ B2) = B2))))).
% 2.64/1.55 thf(fact_29_local_Oinf_OboundedE, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ ((inf @ B2) @ C)) => (~ ((((less_eq @ A2) @ B2) => (~ (((less_eq @ A2) @ C)))))))))).
% 2.64/1.55 thf(fact_30_local_Oinf_OboundedI, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ B2) => (((less_eq @ A2) @ C) => ((less_eq @ A2) @ ((inf @ B2) @ C))))))).
% 2.64/1.55 thf(fact_31_local_Oinf_Ocobounded1, axiom, (! [A2:a,B2:a]: (((less_eq @ ((inf @ A2) @ B2)) @ A2)))).
% 2.64/1.55 thf(fact_32_local_Oinf_Ocobounded2, axiom, (! [A2:a,B2:a]: (((less_eq @ ((inf @ A2) @ B2)) @ B2)))).
% 2.64/1.55 thf(fact_33_local_Oinf_OcoboundedI1, axiom, (! [A2:a,C:a,B2:a]: ((((less_eq @ A2) @ C) => ((less_eq @ ((inf @ A2) @ B2)) @ C))))).
% 2.64/1.55 thf(fact_34_local_Oinf_OcoboundedI2, axiom, (! [B2:a,C:a,A2:a]: ((((less_eq @ B2) @ C) => ((less_eq @ ((inf @ A2) @ B2)) @ C))))).
% 2.64/1.55 thf(fact_35_local_Oinf_OorderE, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (A2 = ((inf @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_36_local_Oinf_OorderI, axiom, (! [A2:a,B2:a]: (((A2 = ((inf @ A2) @ B2)) => ((less_eq @ A2) @ B2))))).
% 2.64/1.55 thf(fact_37_local_Oinf_Oorder__iff, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) = (A2 = ((inf @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_38_local_Oinf__absorb1, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) => (((inf @ X) @ Y) = X))))).
% 2.64/1.55 thf(fact_39_local_Oinf__absorb2, axiom, (! [Y:a,X:a]: ((((less_eq @ Y) @ X) => (((inf @ X) @ Y) = Y))))).
% 2.64/1.55 thf(fact_40_local_Oinf__greatest, axiom, (! [X:a,Y:a,Z2:a]: ((((less_eq @ X) @ Y) => (((less_eq @ X) @ Z2) => ((less_eq @ X) @ ((inf @ Y) @ Z2))))))).
% 2.64/1.55 thf(fact_41_local_Oinf__le1, axiom, (! [X:a,Y:a]: (((less_eq @ ((inf @ X) @ Y)) @ X)))).
% 2.64/1.55 thf(fact_42_local_Oinf__le2, axiom, (! [X:a,Y:a]: (((less_eq @ ((inf @ X) @ Y)) @ Y)))).
% 2.64/1.55 thf(fact_43_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))))))).
% 2.64/1.55 thf(fact_44_local_Oinf__unique, axiom, (! [F:(a > (a > a)),X:a,Y:a]: (((! [X3:a,Y4:a]: (((less_eq @ ((F @ X3) @ Y4)) @ X3))) => ((! [X3:a,Y4:a]: (((less_eq @ ((F @ X3) @ Y4)) @ Y4))) => ((! [X3:a,Y4:a,Z3:a]: ((((less_eq @ X3) @ Y4) => (((less_eq @ X3) @ Z3) => ((less_eq @ X3) @ ((F @ Y4) @ Z3)))))) => (((inf @ X) @ Y) = ((F @ X) @ Y)))))))).
% 2.64/1.55 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.64/1.55 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A4)))) = A4)))).
% 2.64/1.55 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.64/1.55 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.64/1.55 thf(fact_49_local_Ole__iff__inf, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) = (((inf @ X) @ Y) = X))))).
% 2.64/1.55 thf(fact_50_local_Ole__infE, axiom, (! [X:a,A2:a,B2:a]: ((((less_eq @ X) @ ((inf @ A2) @ B2)) => (~ ((((less_eq @ X) @ A2) => (~ (((less_eq @ X) @ B2)))))))))).
% 2.64/1.55 thf(fact_51_local_Ole__infI, axiom, (! [X:a,A2:a,B2:a]: ((((less_eq @ X) @ A2) => (((less_eq @ X) @ B2) => ((less_eq @ X) @ ((inf @ A2) @ B2))))))).
% 2.64/1.55 thf(fact_52_local_Ole__infI1, axiom, (! [A2:a,X:a,B2:a]: ((((less_eq @ A2) @ X) => ((less_eq @ ((inf @ A2) @ B2)) @ X))))).
% 2.64/1.55 thf(fact_53_local_Ole__infI2, axiom, (! [B2:a,X:a,A2:a]: ((((less_eq @ B2) @ X) => ((less_eq @ ((inf @ A2) @ B2)) @ X))))).
% 2.64/1.55 thf(fact_54_local_Ole__iff__sup, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) = (((sup @ X) @ Y) = Y))))).
% 2.64/1.55 thf(fact_55_local_Ole__supE, axiom, (! [A2:a,B2:a,X:a]: ((((less_eq @ ((sup @ A2) @ B2)) @ X) => (~ ((((less_eq @ A2) @ X) => (~ (((less_eq @ B2) @ X)))))))))).
% 2.64/1.55 thf(fact_56_local_Ole__supI, axiom, (! [A2:a,X:a,B2:a]: ((((less_eq @ A2) @ X) => (((less_eq @ B2) @ X) => ((less_eq @ ((sup @ A2) @ B2)) @ X)))))).
% 2.64/1.55 thf(fact_57_local_Ole__supI1, axiom, (! [X:a,A2:a,B2:a]: ((((less_eq @ X) @ A2) => ((less_eq @ X) @ ((sup @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_58_local_Ole__supI2, axiom, (! [X:a,B2:a,A2:a]: ((((less_eq @ X) @ B2) => ((less_eq @ X) @ ((sup @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_59_local_Osup_Oabsorb1, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (((sup @ A2) @ B2) = A2))))).
% 2.64/1.55 thf(fact_60_local_Osup_Oabsorb2, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (((sup @ A2) @ B2) = B2))))).
% 2.64/1.55 thf(fact_61_local_Osup_Oabsorb__iff1, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) = (((sup @ A2) @ B2) = A2))))).
% 2.64/1.55 thf(fact_62_local_Osup_Oabsorb__iff2, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) = (((sup @ A2) @ B2) = B2))))).
% 2.64/1.55 thf(fact_63_local_Osup_OboundedE, axiom, (! [B2:a,C:a,A2:a]: ((((less_eq @ ((sup @ B2) @ C)) @ A2) => (~ ((((less_eq @ B2) @ A2) => (~ (((less_eq @ C) @ A2)))))))))).
% 2.64/1.55 thf(fact_64_local_Osup_OboundedI, axiom, (! [B2:a,A2:a,C:a]: ((((less_eq @ B2) @ A2) => (((less_eq @ C) @ A2) => ((less_eq @ ((sup @ B2) @ C)) @ A2)))))).
% 2.64/1.55 thf(fact_65_local_Osup_Ocobounded1, axiom, (! [A2:a,B2:a]: (((less_eq @ A2) @ ((sup @ A2) @ B2))))).
% 2.64/1.55 thf(fact_66_local_Osup_Ocobounded2, axiom, (! [B2:a,A2:a]: (((less_eq @ B2) @ ((sup @ A2) @ B2))))).
% 2.64/1.55 thf(fact_67_local_Osup_OcoboundedI1, axiom, (! [C:a,A2:a,B2:a]: ((((less_eq @ C) @ A2) => ((less_eq @ C) @ ((sup @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_68_local_Osup_OcoboundedI2, axiom, (! [C:a,B2:a,A2:a]: ((((less_eq @ C) @ B2) => ((less_eq @ C) @ ((sup @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_69_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))))))).
% 2.64/1.55 thf(fact_70_local_Osup_OorderE, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (A2 = ((sup @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_71_local_Osup_OorderI, axiom, (! [A2:a,B2:a]: (((A2 = ((sup @ A2) @ B2)) => ((less_eq @ B2) @ A2))))).
% 2.64/1.55 thf(fact_72_local_Osup_Oorder__iff, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) = (A2 = ((sup @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_73_local_Osup__absorb1, axiom, (! [Y:a,X:a]: ((((less_eq @ Y) @ X) => (((sup @ X) @ Y) = X))))).
% 2.64/1.55 thf(fact_74_local_Osup__absorb2, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) => (((sup @ X) @ Y) = Y))))).
% 2.64/1.55 thf(fact_75_local_Osup__ge1, axiom, (! [X:a,Y:a]: (((less_eq @ X) @ ((sup @ X) @ Y))))).
% 2.64/1.55 thf(fact_76_local_Osup__ge2, axiom, (! [Y:a,X:a]: (((less_eq @ Y) @ ((sup @ X) @ Y))))).
% 2.64/1.55 thf(fact_77_local_Osup__least, axiom, (! [Y:a,X:a,Z2:a]: ((((less_eq @ Y) @ X) => (((less_eq @ Z2) @ X) => ((less_eq @ ((sup @ Y) @ Z2)) @ X)))))).
% 2.64/1.55 thf(fact_78_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))))))).
% 2.64/1.55 thf(fact_79_local_Osup__unique, axiom, (! [F:(a > (a > a)),X:a,Y:a]: (((! [X3:a,Y4:a]: (((less_eq @ X3) @ ((F @ X3) @ Y4)))) => ((! [X3:a,Y4:a]: (((less_eq @ Y4) @ ((F @ X3) @ Y4)))) => ((! [X3:a,Y4:a,Z3:a]: ((((less_eq @ Y4) @ X3) => (((less_eq @ Z3) @ X3) => ((less_eq @ ((F @ Y4) @ Z3)) @ X3))))) => (((sup @ X) @ Y) = ((F @ X) @ Y)))))))).
% 2.64/1.55 thf(fact_80_local_Odistrib__imp1, axiom, (! [X:a,Y:a,Z2:a]: (((! [X3:a,Y4:a,Z3:a]: ((((inf @ X3) @ ((sup @ Y4) @ Z3)) = ((sup @ ((inf @ X3) @ Y4)) @ ((inf @ X3) @ Z3))))) => (((sup @ X) @ ((inf @ Y) @ Z2)) = ((inf @ ((sup @ X) @ Y)) @ ((sup @ X) @ Z2))))))).
% 2.64/1.55 thf(fact_81_local_Odistrib__imp2, axiom, (! [X:a,Y:a,Z2:a]: (((! [X3:a,Y4:a,Z3:a]: ((((sup @ X3) @ ((inf @ Y4) @ Z3)) = ((inf @ ((sup @ X3) @ Y4)) @ ((sup @ X3) @ Z3))))) => (((inf @ X) @ ((sup @ Y) @ Z2)) = ((sup @ ((inf @ X) @ Y)) @ ((inf @ X) @ Z2))))))).
% 2.64/1.55 thf(fact_82_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)))))).
% 2.64/1.55 thf(fact_83_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)))))).
% 2.64/1.55 thf(fact_84_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)))))).
% 2.64/1.55 thf(fact_85_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)))))).
% 2.64/1.55 thf(fact_86_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)))))).
% 2.64/1.55 thf(fact_87_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)))))).
% 2.64/1.55 thf(fact_88_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))))).
% 2.64/1.55 thf(fact_89_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))))).
% 2.64/1.55 thf(fact_90_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)))))).
% 2.64/1.55 thf(fact_91_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)))))).
% 2.64/1.55 thf(fact_92_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)))))).
% 2.64/1.55 thf(fact_93_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)))))).
% 2.64/1.55 thf(fact_94_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))))).
% 2.64/1.55 thf(fact_95_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))))).
% 2.64/1.55 thf(fact_96_local_Odistrib__inf__le, axiom, (! [X:a,Y:a,Z2:a]: (((less_eq @ ((sup @ ((inf @ X) @ Y)) @ ((inf @ X) @ Z2))) @ ((inf @ X) @ ((sup @ Y) @ Z2)))))).
% 2.64/1.55 thf(fact_97_local_Odistrib__sup__le, axiom, (! [X:a,Y:a,Z2:a]: (((less_eq @ ((sup @ X) @ ((inf @ Y) @ Z2))) @ ((inf @ ((sup @ X) @ Y)) @ ((sup @ X) @ Z2)))))).
% 2.64/1.55 thf(fact_98_local_Omodular, axiom, (! [X:a,Y:a,Z2:a]: ((((less_eq @ X) @ Y) => (((sup @ X) @ ((inf @ Y) @ Z2)) = ((inf @ Y) @ ((sup @ X) @ Z2))))))).
% 2.64/1.55 thf(fact_99_local_Oincomp__def, axiom, (! [X:a,Y:a]: ((((((modula1937309406incomp @ a) @ less_eq) @ X) @ Y) = ((~ (((less_eq @ X) @ Y))) & (~ (((less_eq @ Y) @ X)))))))).
% 2.64/1.55 thf(fact_100_local_Oorder_Orefl, axiom, (! [A2:a]: (((less_eq @ A2) @ A2)))).
% 2.64/1.55 thf(fact_101_local_Oorder__refl, axiom, (! [X:a]: (((less_eq @ X) @ X)))).
% 2.64/1.55 thf(fact_102_local_Oinf_Oidem, axiom, (! [A2:a]: ((((inf @ A2) @ A2) = A2)))).
% 2.64/1.55 thf(fact_103_local_Oinf_Oleft__idem, axiom, (! [A2:a,B2:a]: ((((inf @ A2) @ ((inf @ A2) @ B2)) = ((inf @ A2) @ B2))))).
% 2.64/1.55 thf(fact_104_local_Oinf_Oright__idem, axiom, (! [A2:a,B2:a]: ((((inf @ ((inf @ A2) @ B2)) @ B2) = ((inf @ A2) @ B2))))).
% 2.64/1.55 thf(fact_105_local_Oinf__idem, axiom, (! [X:a]: ((((inf @ X) @ X) = X)))).
% 2.64/1.55 thf(fact_106_local_Oinf__left__idem, axiom, (! [X:a,Y:a]: ((((inf @ X) @ ((inf @ X) @ Y)) = ((inf @ X) @ Y))))).
% 2.64/1.55 thf(fact_107_local_Oinf__right__idem, axiom, (! [X:a,Y:a]: ((((inf @ ((inf @ X) @ Y)) @ Y) = ((inf @ X) @ Y))))).
% 2.64/1.55 thf(fact_108_local_Osup_Oidem, axiom, (! [A2:a]: ((((sup @ A2) @ A2) = A2)))).
% 2.64/1.55 thf(fact_109_local_Osup_Oleft__idem, axiom, (! [A2:a,B2:a]: ((((sup @ A2) @ ((sup @ A2) @ B2)) = ((sup @ A2) @ B2))))).
% 2.64/1.55 thf(fact_110_local_Osup_Oright__idem, axiom, (! [A2:a,B2:a]: ((((sup @ ((sup @ A2) @ B2)) @ B2) = ((sup @ A2) @ B2))))).
% 2.64/1.55 thf(fact_111_local_Osup__idem, axiom, (! [X:a]: ((((sup @ X) @ X) = X)))).
% 2.64/1.55 thf(fact_112_local_Osup__left__idem, axiom, (! [X:a,Y:a]: ((((sup @ X) @ ((sup @ X) @ Y)) = ((sup @ X) @ Y))))).
% 2.64/1.55 thf(fact_113_local_OGreatestI2__order, axiom, (! [P:(a > $o),X:a,Q:(a > $o)]: (((P @ X) => ((! [Y4:a]: (((P @ Y4) => ((less_eq @ Y4) @ X)))) => ((! [X3:a]: (((P @ X3) => ((! [Y5:a]: (((P @ Y5) => ((less_eq @ Y5) @ X3)))) => (Q @ X3))))) => (Q @ (((greatest @ a) @ less_eq) @ P)))))))).
% 2.64/1.55 thf(fact_114_local_OGreatest__equality, axiom, (! [P:(a > $o),X:a]: (((P @ X) => ((! [Y4:a]: (((P @ Y4) => ((less_eq @ Y4) @ X)))) => ((((greatest @ a) @ less_eq) @ P) = X)))))).
% 2.64/1.55 thf(fact_115_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)))))).
% 2.64/1.55 thf(fact_116_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)))))).
% 2.64/1.55 thf(fact_117_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)))))).
% 2.64/1.55 thf(fact_118_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))))))).
% 2.64/1.55 thf(fact_119_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)))))).
% 2.64/1.55 thf(fact_120_local_Ole__inf__iff, axiom, (! [X:a,Y:a,Z2:a]: ((((less_eq @ X) @ ((inf @ Y) @ Z2)) = (((less_eq @ X) @ Y) & ((less_eq @ X) @ Z2)))))).
% 2.64/1.55 thf(fact_121_local_Ole__sup__iff, axiom, (! [X:a,Y:a,Z2:a]: ((((less_eq @ ((sup @ X) @ Y)) @ Z2) = (((less_eq @ X) @ Z2) & ((less_eq @ Y) @ Z2)))))).
% 2.64/1.55 thf(fact_122_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)))))).
% 2.64/1.55 thf(fact_123_local_Oinf__sup__absorb, axiom, (! [X:a,Y:a]: ((((inf @ X) @ ((sup @ X) @ Y)) = X)))).
% 2.64/1.55 thf(fact_124_local_Osup__inf__absorb, axiom, (! [X:a,Y:a]: ((((sup @ X) @ ((inf @ X) @ Y)) = X)))).
% 2.64/1.55 thf(fact_125_local_OLeast1I, axiom, (! [P:(a > $o)]: (((? [X4:a]: (((P @ X4) & ((! [Y4:a]: (((P @ Y4) => ((less_eq @ X4) @ Y4)))) & (! [Y4:a]: ((((P @ Y4) & (! [Ya:a]: (((P @ Ya) => ((less_eq @ Y4) @ Ya))))) => (Y4 = X4)))))))) => (P @ (((least @ a) @ less_eq) @ P)))))).
% 2.64/1.55 thf(fact_126_local_OLeast1__le, axiom, (! [P:(a > $o),Z2:a]: (((? [X4:a]: (((P @ X4) & ((! [Y4:a]: (((P @ Y4) => ((less_eq @ X4) @ Y4)))) & (! [Y4:a]: ((((P @ Y4) & (! [Ya:a]: (((P @ Ya) => ((less_eq @ Y4) @ Ya))))) => (Y4 = X4)))))))) => ((P @ Z2) => ((less_eq @ (((least @ a) @ less_eq) @ P)) @ Z2)))))).
% 2.64/1.55 thf(fact_127_local_OLeastI2__order, axiom, (! [P:(a > $o),X:a,Q:(a > $o)]: (((P @ X) => ((! [Y4:a]: (((P @ Y4) => ((less_eq @ X) @ Y4)))) => ((! [X3:a]: (((P @ X3) => ((! [Y5:a]: (((P @ Y5) => ((less_eq @ X3) @ Y5)))) => (Q @ X3))))) => (Q @ (((least @ a) @ less_eq) @ P)))))))).
% 2.64/1.55 thf(fact_128_local_OLeast__equality, axiom, (! [P:(a > $o),X:a]: (((P @ X) => ((! [Y4:a]: (((P @ Y4) => ((less_eq @ X) @ Y4)))) => ((((least @ a) @ less_eq) @ P) = X)))))).
% 2.64/1.55 thf(fact_129_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))))).
% 2.64/1.55 thf(fact_130_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)))))).
% 2.64/1.55 thf(fact_131_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))))))).
% 2.64/1.55 thf(fact_132_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)))))).
% 2.64/1.55 thf(fact_133_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))))).
% 2.64/1.55 thf(fact_134_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)))))).
% 2.64/1.55 thf(fact_135_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))))))).
% 2.64/1.55 thf(fact_136_a__join__b__eq__e, 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)) => (((sup @ ((((((modula105138637_a_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula477145868_b_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.64/1.55 thf(fact_137_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)))))).
% 2.64/1.55 thf(fact_138_lattice_Oa__aux_Ocong, axiom, (! [A:$tType]: (((modula105138637_a_aux @ A) = (modula105138637_a_aux @ A))))).
% 2.64/1.55 thf(fact_139_lattice_Od__aux_Ocong, axiom, (! [A:$tType]: (((modula1221160330_d_aux @ A) = (modula1221160330_d_aux @ A))))).
% 2.64/1.55 thf(fact_140_lattice_Oe__aux_Ocong, axiom, (! [A:$tType]: (((modula1593167561_e_aux @ A) = (modula1593167561_e_aux @ A))))).
% 2.64/1.55 thf(fact_141_local_Ocomp__fun__idem__sup, axiom, (((finite_comp_fun_idem @ a) @ a) @ sup)).
% 2.64/1.55 thf(fact_142_local_Ocomp__fun__idem__inf, axiom, (((finite_comp_fun_idem @ a) @ a) @ inf)).
% 2.64/1.55 thf(fact_143_b__join__c__eq__e, 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)) => (((sup @ ((((((modula477145868_b_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula849153099_c_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.64/1.55 thf(fact_144_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)))))).
% 2.64/1.55 thf(fact_145_local_Osup_Osemigroup__axioms, axiom, ((semigroup @ a) @ sup)).
% 2.64/1.55 thf(fact_146_local_Oinf_Osemigroup__axioms, axiom, ((semigroup @ a) @ inf)).
% 2.64/1.55 thf(fact_147_local_Osup_Osemilattice__axioms, axiom, ((semilattice @ a) @ sup)).
% 2.64/1.55 thf(fact_148_local_Oinf_Osemilattice__axioms, axiom, ((semilattice @ a) @ inf)).
% 2.64/1.55 thf(fact_149_local_Osup_Oabel__semigroup__axioms, axiom, ((abel_semigroup @ a) @ sup)).
% 2.64/1.55 thf(fact_150_local_Oinf_Oabel__semigroup__axioms, axiom, ((abel_semigroup @ a) @ inf)).
% 2.64/1.55 thf(fact_151_local_OSup__fin_Osemilattice__set__axioms, axiom, ((lattic35693393ce_set @ a) @ sup)).
% 2.64/1.55 thf(fact_152_local_OInf__fin_Osemilattice__set__axioms, axiom, ((lattic35693393ce_set @ a) @ inf)).
% 2.64/1.55 thf(fact_153_lattice_Oincomp_Ocong, axiom, (! [A:$tType]: (((modula1937309406incomp @ A) = (modula1937309406incomp @ A))))).
% 2.64/1.55 thf(fact_154_lattice_Oc__aux_Ocong, axiom, (! [A:$tType]: (((modula849153099_c_aux @ A) = (modula849153099_c_aux @ A))))).
% 2.64/1.55 thf(fact_155_lattice_Ob__aux_Ocong, axiom, (! [A:$tType]: (((modula477145868_b_aux @ A) = (modula477145868_b_aux @ A))))).
% 2.64/1.55 thf(fact_156_abel__semigroup_Oaxioms_I1_J, axiom, (! [A:$tType,F:(A > (A > A))]: ((((abel_semigroup @ A) @ F) => ((semigroup @ A) @ F))))).
% 2.64/1.55 thf(fact_157_semilattice__set__def, axiom, (! [A:$tType]: (((lattic35693393ce_set @ A) = (semilattice @ A))))).
% 2.64/1.55 thf(fact_158_semilattice__set_Ointro, axiom, (! [A:$tType,F:(A > (A > A))]: ((((semilattice @ A) @ F) => ((lattic35693393ce_set @ A) @ F))))).
% 2.64/1.55 thf(fact_159_abel__semigroup_Oleft__commute, axiom, (! [A:$tType,F:(A > (A > A)),B2:A,A2:A,C:A]: ((((abel_semigroup @ A) @ F) => (((F @ B2) @ ((F @ A2) @ C)) = ((F @ A2) @ ((F @ B2) @ C))))))).
% 2.64/1.55 thf(fact_160_abel__semigroup_Ocommute, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A]: ((((abel_semigroup @ A) @ F) => (((F @ A2) @ B2) = ((F @ B2) @ A2)))))).
% 2.64/1.55 thf(fact_161_semigroup_Ointro, axiom, (! [A:$tType,F:(A > (A > A))]: (((! [A5:A,B4:A,C2:A]: ((((F @ ((F @ A5) @ B4)) @ C2) = ((F @ A5) @ ((F @ B4) @ C2))))) => ((semigroup @ A) @ F))))).
% 2.64/1.55 thf(fact_162_semigroup_Oassoc, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A,C:A]: ((((semigroup @ A) @ F) => (((F @ ((F @ A2) @ B2)) @ C) = ((F @ A2) @ ((F @ B2) @ C))))))).
% 2.64/1.55 thf(fact_163_semigroup__def, axiom, (! [A:$tType]: (((semigroup @ A) = (^ [F2:(A > (A > A))]: ((! [A3:A,B3:A,C3:A]: ((((F2 @ ((F2 @ A3) @ B3)) @ C3) = ((F2 @ A3) @ ((F2 @ B3) @ C3))))))))))).
% 2.64/1.55 thf(fact_164_semilattice__set_Oaxioms, axiom, (! [A:$tType,F:(A > (A > A))]: ((((lattic35693393ce_set @ A) @ F) => ((semilattice @ A) @ F))))).
% 2.64/1.55 thf(fact_165_semilattice_Oaxioms_I1_J, axiom, (! [A:$tType,F:(A > (A > A))]: ((((semilattice @ A) @ F) => ((abel_semigroup @ A) @ F))))).
% 2.64/1.55 thf(fact_166_local_Obdd__above__def, axiom, (! [A4:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ A4) = (? [M:a]: ((! [X2:a]: (((((member @ a) @ X2) @ A4) => ((less_eq @ X2) @ M)))))))))).
% 2.64/1.55 thf(fact_167_local_Obdd__below__def, axiom, (! [A4:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ A4) = (? [M2:a]: ((! [X2:a]: (((((member @ a) @ X2) @ A4) => ((less_eq @ M2) @ X2)))))))))).
% 2.64/1.55 thf(fact_168_local_Obdd__belowI, axiom, (! [A4:(set @ a),M3:a]: (((! [X3:a]: (((((member @ a) @ X3) @ A4) => ((less_eq @ M3) @ X3)))) => (((condit1201339847_below @ a) @ less_eq) @ A4))))).
% 2.64/1.55 thf(fact_169_local_Obdd__aboveI, axiom, (! [A4:(set @ a),M4:a]: (((! [X3:a]: (((((member @ a) @ X3) @ A4) => ((less_eq @ X3) @ M4)))) => (((condit2040224947_above @ a) @ less_eq) @ A4))))).
% 2.64/1.55 thf(fact_170_semilattice_Oidem, axiom, (! [A:$tType,F:(A > (A > A)),A2:A]: ((((semilattice @ A) @ F) => (((F @ A2) @ A2) = A2))))).
% 2.64/1.55 thf(fact_171_semilattice_Oleft__idem, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A]: ((((semilattice @ A) @ F) => (((F @ A2) @ ((F @ A2) @ B2)) = ((F @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_172_semilattice_Oright__idem, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A]: ((((semilattice @ A) @ F) => (((F @ ((F @ A2) @ B2)) @ B2) = ((F @ A2) @ B2)))))).
% 2.64/1.55 thf(fact_173_local_Obdd__above__mono, axiom, (! [B5:(set @ a),A4:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ B5) => ((((ord_less_eq @ (set @ a)) @ A4) @ B5) => (((condit2040224947_above @ a) @ less_eq) @ A4)))))).
% 2.64/1.55 thf(fact_174_local_Obdd__below__mono, axiom, (! [B5:(set @ a),A4:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ B5) => ((((ord_less_eq @ (set @ a)) @ A4) @ B5) => (((condit1201339847_below @ a) @ less_eq) @ A4)))))).
% 2.64/1.55 thf(fact_175_local_Obdd__above__finite, axiom, (! [A4:(set @ a)]: ((((finite_finite @ a) @ A4) => (((condit2040224947_above @ a) @ less_eq) @ A4))))).
% 2.64/1.55 thf(fact_176_local_Ofinite__has__maximal2, axiom, (! [A4:(set @ a),A2:a]: ((((finite_finite @ a) @ A4) => ((((member @ a) @ A2) @ A4) => (? [X3:a]: (((((member @ a) @ X3) @ A4) & (((less_eq @ A2) @ X3) & (! [Xa:a]: (((((member @ a) @ Xa) @ A4) => (((less_eq @ X3) @ Xa) => (X3 = Xa)))))))))))))).
% 2.64/1.55 thf(fact_177_local_Ofinite__has__minimal2, axiom, (! [A4:(set @ a),A2:a]: ((((finite_finite @ a) @ A4) => ((((member @ a) @ A2) @ A4) => (? [X3:a]: (((((member @ a) @ X3) @ A4) & (((less_eq @ X3) @ A2) & (! [Xa:a]: (((((member @ a) @ Xa) @ A4) => (((less_eq @ Xa) @ X3) => (X3 = Xa)))))))))))))).
% 2.64/1.55 thf(fact_178_local_Obdd__below__finite, axiom, (! [A4:(set @ a)]: ((((finite_finite @ a) @ A4) => (((condit1201339847_below @ a) @ less_eq) @ A4))))).
% 2.64/1.55 thf(fact_179_local_OantimonoD, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B),X:a,Y:a]: ((((((antimono @ a) @ B) @ less_eq) @ F) => (((less_eq @ X) @ Y) => (((ord_less_eq @ B) @ (F @ Y)) @ (F @ X)))))))))).
% 2.64/1.55 thf(fact_180_local_OantimonoE, axiom, (! [B:$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)))))))))).
% 2.64/1.55 thf(fact_181_local_OantimonoI, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: (((! [X3:a,Y4:a]: ((((less_eq @ X3) @ Y4) => (((ord_less_eq @ B) @ (F @ Y4)) @ (F @ X3))))) => ((((antimono @ a) @ B) @ less_eq) @ F)))))))).
% 2.64/1.55 thf(fact_182_local_Oantimono__def, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: ((((((antimono @ a) @ B) @ less_eq) @ F) = (! [X2:a,Y3:a]: ((((less_eq @ X2) @ Y3) => (((ord_less_eq @ B) @ (F @ Y3)) @ (F @ X2)))))))))))).
% 2.64/1.55 thf(fact_183_local_Omono__def, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: ((((((mono @ a) @ B) @ less_eq) @ F) = (! [X2:a,Y3:a]: ((((less_eq @ X2) @ Y3) => (((ord_less_eq @ B) @ (F @ X2)) @ (F @ Y3)))))))))))).
% 2.64/1.55 thf(fact_184_local_OmonoI, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: (((! [X3:a,Y4:a]: ((((less_eq @ X3) @ Y4) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y4))))) => ((((mono @ a) @ B) @ less_eq) @ F)))))))).
% 2.64/1.55 thf(fact_185_local_OmonoE, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B),X:a,Y:a]: ((((((mono @ a) @ B) @ less_eq) @ F) => (((less_eq @ X) @ Y) => (((ord_less_eq @ B) @ (F @ X)) @ (F @ Y)))))))))).
% 2.64/1.55 thf(fact_186_local_OmonoD, axiom, (! [B:$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)))))))))).
% 2.64/1.55 thf(fact_187_local_OSup__fin_OcoboundedI, axiom, (! [A4:(set @ a),A2:a]: ((((finite_finite @ a) @ A4) => ((((member @ a) @ A2) @ A4) => ((less_eq @ A2) @ (((lattic1039401930up_fin @ a) @ sup) @ A4))))))).
% 2.64/1.55 thf(fact_188_local_OInf__fin_OcoboundedI, axiom, (! [A4:(set @ a),A2:a]: ((((finite_finite @ a) @ A4) => ((((member @ a) @ A2) @ A4) => ((less_eq @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)) @ A2)))))).
% 2.64/1.55 thf(fact_189_local_OSup__fin_Oin__idem, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((((member @ a) @ X) @ A4) => (((sup @ X) @ (((lattic1039401930up_fin @ a) @ sup) @ A4)) = (((lattic1039401930up_fin @ a) @ sup) @ A4))))))).
% 2.64/1.55 thf(fact_190_local_OInf__fin_Oin__idem, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((((member @ a) @ X) @ A4) => (((inf @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)) = (((lattic1263571978nf_fin @ a) @ inf) @ A4))))))).
% 2.64/1.55 thf(fact_191_local_Oinf__Sup__absorb, axiom, (! [A4:(set @ a),A2:a]: ((((finite_finite @ a) @ A4) => ((((member @ a) @ A2) @ A4) => (((inf @ A2) @ (((lattic1039401930up_fin @ a) @ sup) @ A4)) = A2)))))).
% 2.64/1.55 thf(fact_192_local_Osup__Inf__absorb, axiom, (! [A4:(set @ a),A2:a]: ((((finite_finite @ a) @ A4) => ((((member @ a) @ A2) @ A4) => (((sup @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)) @ A2) = A2)))))).
% 2.64/1.55 thf(fact_193_semilattice__sup_OSup__fin_Ocong, axiom, (! [A:$tType]: (((lattic1039401930up_fin @ A) = (lattic1039401930up_fin @ A))))).
% 2.64/1.55 thf(fact_194_semilattice__inf_OInf__fin_Ocong, axiom, (! [A:$tType]: (((lattic1263571978nf_fin @ A) = (lattic1263571978nf_fin @ A))))).
% 2.64/1.55 thf(fact_195_local_OInf__fin__le__Sup__fin, axiom, (! [A4:(set @ a)]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => ((less_eq @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)) @ (((lattic1039401930up_fin @ a) @ sup) @ A4))))))).
% 2.64/1.55 thf(fact_196_local_OSup__fin_Osubset__imp, axiom, (! [A4:(set @ a),B5:(set @ a)]: (((((ord_less_eq @ (set @ a)) @ A4) @ B5) => ((A4 != (bot_bot @ (set @ a))) => (((finite_finite @ a) @ B5) => ((less_eq @ (((lattic1039401930up_fin @ a) @ sup) @ A4)) @ (((lattic1039401930up_fin @ a) @ sup) @ B5)))))))).
% 2.64/1.55 thf(fact_197_local_Ofinite__has__minimal, axiom, (! [A4:(set @ a)]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => (? [X3:a]: (((((member @ a) @ X3) @ A4) & (! [Xa:a]: (((((member @ a) @ Xa) @ A4) => (((less_eq @ Xa) @ X3) => (X3 = Xa))))))))))))).
% 2.64/1.55 thf(fact_198_local_Ofinite__has__maximal, axiom, (! [A4:(set @ a)]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => (? [X3:a]: (((((member @ a) @ X3) @ A4) & (! [Xa:a]: (((((member @ a) @ Xa) @ A4) => (((less_eq @ X3) @ Xa) => (X3 = Xa))))))))))))).
% 2.64/1.55 thf(fact_199_local_OInf__fin_Osubset, axiom, (! [A4:(set @ a),B5:(set @ a)]: ((((finite_finite @ a) @ A4) => ((B5 != (bot_bot @ (set @ a))) => ((((ord_less_eq @ (set @ a)) @ B5) @ A4) => (((inf @ (((lattic1263571978nf_fin @ a) @ inf) @ B5)) @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)) = (((lattic1263571978nf_fin @ a) @ inf) @ A4)))))))).
% 2.64/1.55 thf(fact_200_local_OSup__fin_Osubset, axiom, (! [A4:(set @ a),B5:(set @ a)]: ((((finite_finite @ a) @ A4) => ((B5 != (bot_bot @ (set @ a))) => ((((ord_less_eq @ (set @ a)) @ B5) @ A4) => (((sup @ (((lattic1039401930up_fin @ a) @ sup) @ B5)) @ (((lattic1039401930up_fin @ a) @ sup) @ A4)) = (((lattic1039401930up_fin @ a) @ sup) @ A4)))))))).
% 2.64/1.55 thf(fact_201_local_OInf__fin_Obounded__iff, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => (((less_eq @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)) = (! [X2:a]: (((((member @ a) @ X2) @ A4) => ((less_eq @ X) @ X2)))))))))).
% 2.64/1.55 thf(fact_202_local_OInf__fin_OboundedI, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => ((! [A5:a]: (((((member @ a) @ A5) @ A4) => ((less_eq @ X) @ A5)))) => ((less_eq @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)))))))).
% 2.64/1.55 thf(fact_203_local_OInf__fin_OboundedE, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => (((less_eq @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)) => (! [A6:a]: (((((member @ a) @ A6) @ A4) => ((less_eq @ X) @ A6)))))))))).
% 2.64/1.55 thf(fact_204_local_OSup__fin_Obounded__iff, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => (((less_eq @ (((lattic1039401930up_fin @ a) @ sup) @ A4)) @ X) = (! [X2:a]: (((((member @ a) @ X2) @ A4) => ((less_eq @ X2) @ X)))))))))).
% 2.64/1.55 thf(fact_205_local_OSup__fin_OboundedI, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => ((! [A5:a]: (((((member @ a) @ A5) @ A4) => ((less_eq @ A5) @ X)))) => ((less_eq @ (((lattic1039401930up_fin @ a) @ sup) @ A4)) @ X))))))).
% 2.64/1.55 thf(fact_206_local_OSup__fin_OboundedE, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => (((less_eq @ (((lattic1039401930up_fin @ a) @ sup) @ A4)) @ X) => (! [A6:a]: (((((member @ a) @ A6) @ A4) => ((less_eq @ A6) @ X)))))))))).
% 2.64/1.55 thf(fact_207_local_OInf__fin_Osubset__imp, axiom, (! [A4:(set @ a),B5:(set @ a)]: (((((ord_less_eq @ (set @ a)) @ A4) @ B5) => ((A4 != (bot_bot @ (set @ a))) => (((finite_finite @ a) @ B5) => ((less_eq @ (((lattic1263571978nf_fin @ a) @ inf) @ B5)) @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)))))))).
% 2.64/1.55 thf(fact_208_local_Obdd__below__empty, axiom, (((condit1201339847_below @ a) @ less_eq) @ (bot_bot @ (set @ a)))).
% 2.64/1.55 thf(fact_209_local_Obdd__above__empty, axiom, (((condit2040224947_above @ a) @ less_eq) @ (bot_bot @ (set @ a)))).
% 2.64/1.55 thf(fact_210_local_Onot__empty__eq__Iic__eq__empty, axiom, (! [H:a]: (((bot_bot @ (set @ a)) != (((set_atMost @ a) @ less_eq) @ H))))).
% 2.64/1.55 thf(fact_211_local_Onot__empty__eq__Ici__eq__empty, axiom, (! [L:a]: (((bot_bot @ (set @ a)) != (((set_atLeast @ a) @ less_eq) @ L))))).
% 2.64/1.55 thf(fact_212_local_OatLeast__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_atLeast @ a) @ less_eq) @ K)) = ((less_eq @ K) @ I))))).
% 2.64/1.55 thf(fact_213_local_OatMost__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_atMost @ a) @ less_eq) @ K)) = ((less_eq @ I) @ K))))).
% 2.64/1.55 thf(fact_214_local_Obdd__below__Ici, axiom, (! [A2:a]: ((((condit1201339847_below @ a) @ less_eq) @ (((set_atLeast @ a) @ less_eq) @ A2))))).
% 2.64/1.55 thf(fact_215_local_Obdd__above__Iic, axiom, (! [B2:a]: ((((condit2040224947_above @ a) @ less_eq) @ (((set_atMost @ a) @ less_eq) @ B2))))).
% 2.64/1.55 thf(fact_216_subset__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.64/1.55 thf(fact_217_empty__subsetI, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4)))).
% 2.64/1.55 thf(fact_218_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A4) => (A4 = B5)))))).
% 2.64/1.55 thf(fact_219_subsetI, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A4) => (((member @ A) @ X3) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.64/1.55 thf(fact_220_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P @ X2) => (Q @ X2)))))))).
% 2.64/1.55 thf(fact_221_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y2:(set @ A),Z:(set @ A)]: ((Y2 = Z))) = (^ [A7:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A7)))))))).
% 2.64/1.55 thf(fact_222_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C4) => (((ord_less_eq @ (set @ A)) @ A4) @ C4)))))).
% 2.64/1.55 thf(fact_223_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.64/1.55 thf(fact_224_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 2.64/1.55 thf(fact_225_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B6:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A7) => (((member @ A) @ T) @ B6)))))))))).
% 2.64/1.55 thf(fact_226_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A4))))).
% 2.64/1.55 thf(fact_227_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.64/1.55 thf(fact_228_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B6:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A7) => (((member @ A) @ X2) @ B6)))))))))).
% 2.64/1.55 thf(fact_229_equalityE, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))))).
% 2.64/1.55 thf(fact_230_subsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C) @ A4) => (((member @ A) @ C) @ B5)))))).
% 2.64/1.55 thf(fact_231_in__mono, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B5)))))).
% 2.64/1.55 thf(fact_232_local_Omono__inf, axiom, (! [B:$tType]: (((semilattice_inf @ B) => (! [F:(a > B),A4:a,B5:a]: ((((((mono @ a) @ B) @ less_eq) @ F) => (((ord_less_eq @ B) @ (F @ ((inf @ A4) @ B5))) @ (((inf_inf @ B) @ (F @ A4)) @ (F @ B5)))))))))).
% 2.64/1.55 thf(fact_233_local_OSup__fin_Oclosed, axiom, (! [A4:(set @ a)]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => ((! [X3:a,Y4:a]: ((((member @ a) @ ((sup @ X3) @ Y4)) @ (((insert @ a) @ X3) @ (((insert @ a) @ Y4) @ (bot_bot @ (set @ a))))))) => (((member @ a) @ (((lattic1039401930up_fin @ a) @ sup) @ A4)) @ A4))))))).
% 2.64/1.55 thf(fact_234_local_Obdd__above__Int1, axiom, (! [A4:(set @ a),B5:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ A4) => (((condit2040224947_above @ a) @ less_eq) @ (((inf_inf @ (set @ a)) @ A4) @ B5)))))).
% 2.64/1.55 thf(fact_235_local_Obdd__above__Int2, axiom, (! [B5:(set @ a),A4:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ B5) => (((condit2040224947_above @ a) @ less_eq) @ (((inf_inf @ (set @ a)) @ A4) @ B5)))))).
% 2.64/1.55 thf(fact_236_local_Obdd__below__Int1, axiom, (! [A4:(set @ a),B5:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ A4) => (((condit1201339847_below @ a) @ less_eq) @ (((inf_inf @ (set @ a)) @ A4) @ B5)))))).
% 2.64/1.55 thf(fact_237_local_Obdd__below__Int2, axiom, (! [B5:(set @ a),A4:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ B5) => (((condit1201339847_below @ a) @ less_eq) @ (((inf_inf @ (set @ a)) @ A4) @ B5)))))).
% 2.64/1.55 thf(fact_238_Int__subset__iff, axiom, (! [A:$tType,C4:(set @ A),A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((inf_inf @ (set @ A)) @ A4) @ B5)) = ((((ord_less_eq @ (set @ A)) @ C4) @ A4) & (((ord_less_eq @ (set @ A)) @ C4) @ B5)))))).
% 2.64/1.55 thf(fact_239_semilattice__inf__class_Oinf__right__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Y) = (((inf_inf @ A) @ X) @ Y)))))))).
% 2.64/1.55 thf(fact_240_semilattice__inf__class_Oinf_Oright__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.64/1.55 thf(fact_241_semilattice__inf__class_Oinf__left__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = (((inf_inf @ A) @ X) @ Y)))))))).
% 2.64/1.55 thf(fact_242_semilattice__inf__class_Oinf_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B2)) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.64/1.55 thf(fact_243_semilattice__inf__class_Oinf__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A]: (((((inf_inf @ A) @ X) @ X) = X))))))).
% 2.64/1.55 thf(fact_244_semilattice__inf__class_Oinf_Oidem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 2.64/1.55 thf(fact_245_inf__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((inf_inf @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 2.64/1.55 thf(fact_246_local_OInf__fin_Oinsert__not__elem, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((~ ((((member @ a) @ X) @ A4))) => ((A4 != (bot_bot @ (set @ a))) => ((((lattic1263571978nf_fin @ a) @ inf) @ (((insert @ a) @ X) @ A4)) = ((inf @ X) @ (((lattic1263571978nf_fin @ a) @ inf) @ A4))))))))).
% 2.64/1.55 thf(fact_247_local_OInf__fin_Oclosed, axiom, (! [A4:(set @ a)]: ((((finite_finite @ a) @ A4) => ((A4 != (bot_bot @ (set @ a))) => ((! [X3:a,Y4:a]: ((((member @ a) @ ((inf @ X3) @ Y4)) @ (((insert @ a) @ X3) @ (((insert @ a) @ Y4) @ (bot_bot @ (set @ a))))))) => (((member @ a) @ (((lattic1263571978nf_fin @ a) @ inf) @ A4)) @ A4))))))).
% 2.64/1.55 thf(fact_248_local_OSup__fin_Oinsert__not__elem, axiom, (! [A4:(set @ a),X:a]: ((((finite_finite @ a) @ A4) => ((~ ((((member @ a) @ X) @ A4))) => ((A4 != (bot_bot @ (set @ a))) => ((((lattic1039401930up_fin @ a) @ sup) @ (((insert @ a) @ X) @ A4)) = ((sup @ X) @ (((lattic1039401930up_fin @ a) @ sup) @ A4))))))))).
% 2.64/1.55 thf(fact_249_semilattice__inf__class_Ole__inf__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z2)) = ((((ord_less_eq @ A) @ X) @ Y) & (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 2.64/1.55 thf(fact_250_semilattice__inf__class_Oinf_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C)) = ((((ord_less_eq @ A) @ A2) @ B2) & (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.64/1.55 thf(fact_251_inf__bot__right, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X:A]: (((((inf_inf @ A) @ X) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 2.64/1.55 thf(fact_252_inf__bot__left, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X) = (bot_bot @ A)))))))).
% 2.64/1.55 thf(fact_253_insert__subset, axiom, (! [A:$tType,X:A,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X) @ A4)) @ B5) = ((((member @ A) @ X) @ B5) & (((ord_less_eq @ (set @ A)) @ A4) @ B5)))))).
% 2.64/1.55 thf(fact_254_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A2:A,A4:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A2) @ A4)) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.64/1.55 thf(fact_255_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A2:A,A4:(set @ A),B2:A]: ((((((insert @ A) @ A2) @ A4) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.64/1.55 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 2.64/1.55 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: ((bounded_lattice @ (set @ A8))))).
% 2.64/1.55 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice @ (A8 > A9)))))).
% 2.64/1.55 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice_bot @ (A8 > A9)))))).
% 2.64/1.55 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A8:$tType,A9:$tType]: (((semilattice_inf @ A9) => (semilattice_inf @ (A8 > A9)))))).
% 2.64/1.55 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 2.64/1.55 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3, axiom, (! [A8:$tType]: ((bounded_lattice_bot @ (set @ A8))))).
% 2.64/1.55 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4, axiom, (! [A8:$tType]: ((semilattice_inf @ (set @ A8))))).
% 2.64/1.55 thf(tcon_Set_Oset___Orderings_Oorder_5, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 2.64/1.55 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_6, axiom, (bounded_lattice_bot @ $o)).
% 2.64/1.55 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_7, axiom, (semilattice_inf @ $o)).
% 2.64/1.55 thf(tcon_HOL_Obool___Orderings_Oorder_8, axiom, (order @ $o)).
% 2.64/1.55 thf(conj_0, hypothesis, ((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))).
% 2.64/1.55 thf(conj_1, conjecture, (((sup @ ((((((modula105138637_a_aux @ a) @ inf) @ sup) @ c) @ a2) @ b)) @ ((((((modula105138637_a_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)) = ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))).
% 2.64/1.55 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2DTF5305.p
% 2.64/1.55 ------------------------
% 2.64/1.57 ---- Cleaned THF ---
% 2.64/1.57 thf(ty_t_Set_Oset,type,
% 2.64/1.57 set: $tType > $tType ).
% 2.64/1.57
% 2.64/1.57 thf(ty_tf_a,type,
% 2.64/1.57 a: $tType ).
% 2.64/1.57
% 2.64/1.57 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.64/1.57 bounded_lattice:
% 2.64/1.57 !>[A: $tType] : $o ).
% 2.64/1.57
% 2.64/1.57 thf(sy_cl_HOL_Otype,type,
% 2.64/1.57 type:
% 2.64/1.57 !>[A: $tType] : $o ).
% 2.64/1.57
% 2.64/1.57 thf(sy_cl_Orderings_Oorder,type,
% 2.64/1.57 order:
% 2.64/1.57 !>[A: $tType] : $o ).
% 2.64/1.57
% 2.64/1.57 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 2.64/1.57 semilattice_inf:
% 2.64/1.57 !>[A: $tType] : $o ).
% 2.64/1.57
% 2.64/1.57 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 2.64/1.57 bounded_lattice_bot:
% 2.64/1.57 !>[A: $tType] : $o ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above,type,
% 2.64/1.57 condit2040224947_above:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below,type,
% 2.64/1.57 condit1201339847_below:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Finite__Set_Ocomp__fun__idem,type,
% 2.64/1.57 finite_comp_fun_idem:
% 2.64/1.57 !>[A: $tType,B: $tType] : ( ( A > B > B ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Finite__Set_Ofinite,type,
% 2.64/1.57 finite_finite:
% 2.64/1.57 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Groups_Oabel__semigroup,type,
% 2.64/1.57 abel_semigroup:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Groups_Osemigroup,type,
% 2.64/1.57 semigroup:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 2.64/1.57 inf_inf:
% 2.64/1.57 !>[A: $tType] : ( A > A > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Lattices_Osemilattice,type,
% 2.64/1.57 semilattice:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin,type,
% 2.64/1.57 lattic1263571978nf_fin:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > ( set @ A ) > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Lattices__Big_Osemilattice__set,type,
% 2.64/1.57 lattic35693393ce_set:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Lattices__Big_Osemilattice__sup_OSup__fin,type,
% 2.64/1.57 lattic1039401930up_fin:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > ( set @ A ) > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oa__aux,type,
% 2.64/1.57 modula105138637_a_aux:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Ob__aux,type,
% 2.64/1.57 modula477145868_b_aux:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oc__aux,type,
% 2.64/1.57 modula849153099_c_aux:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Od__aux,type,
% 2.64/1.57 modula1221160330_d_aux:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oe__aux,type,
% 2.64/1.57 modula1593167561_e_aux:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oincomp,type,
% 2.64/1.57 modula1937309406incomp:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.64/1.57 bot_bot:
% 2.64/1.57 !>[A: $tType] : A ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Orderings_Oord_OLeast,type,
% 2.64/1.57 least:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Orderings_Oord_Omax,type,
% 2.64/1.57 max:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Orderings_Oord_Omin,type,
% 2.64/1.57 min:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.64/1.57 ord_less_eq:
% 2.64/1.57 !>[A: $tType] : ( A > A > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Orderings_Oorder_OGreatest,type,
% 2.64/1.57 greatest:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Orderings_Oorder_Oantimono,type,
% 2.64/1.57 antimono:
% 2.64/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Orderings_Oorder_Omono,type,
% 2.64/1.57 mono:
% 2.64/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Set_OCollect,type,
% 2.64/1.57 collect:
% 2.64/1.57 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Set_Oinsert,type,
% 2.64/1.57 insert:
% 2.64/1.57 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Set__Interval_Oord_OatLeast,type,
% 2.64/1.57 set_atLeast:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_Set__Interval_Oord_OatMost,type,
% 2.64/1.57 set_atMost:
% 2.64/1.57 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_c_member,type,
% 2.64/1.57 member:
% 2.64/1.57 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.64/1.57
% 2.64/1.57 thf(sy_v_a,type,
% 2.64/1.57 a2: a ).
% 2.64/1.57
% 2.64/1.57 thf(sy_v_b,type,
% 2.64/1.57 b: a ).
% 2.64/1.57
% 2.64/1.57 thf(sy_v_c,type,
% 2.64/1.57 c: a ).
% 2.64/1.57
% 2.64/1.57 thf(sy_v_inf,type,
% 2.64/1.57 inf: a > a > a ).
% 2.64/1.57
% 2.64/1.57 thf(sy_v_less__eq,type,
% 2.64/1.57 less_eq: a > a > $o ).
% 2.64/1.57
% 2.64/1.57 thf(sy_v_sup,type,
% 2.64/1.57 sup: a > a > a ).
% 2.64/1.57
% 2.64/1.57 thf(fact_0_local_Oantisym,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ( less_eq @ Y @ X )
% 2.64/1.57 => ( X = Y ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_1_local_Oantisym__conv,axiom,
% 2.64/1.57 ! [Y: a,X: a] :
% 2.64/1.57 ( ( less_eq @ Y @ X )
% 2.64/1.57 => ( ( less_eq @ X @ Y )
% 2.64/1.57 = ( X = Y ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_2_local_Odual__order_Oantisym,axiom,
% 2.64/1.57 ! [B2: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 => ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( A2 = B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_3_local_Odual__order_Oeq__iff,axiom,
% 2.64/1.57 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.64/1.57 = ( ^ [A3: a,B3: a] :
% 2.64/1.57 ( ( less_eq @ B3 @ A3 )
% 2.64/1.57 & ( less_eq @ A3 @ B3 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_4_local_Odual__order_Otrans,axiom,
% 2.64/1.57 ! [B2: a,A2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 => ( ( less_eq @ C @ B2 )
% 2.64/1.57 => ( less_eq @ C @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_5_local_Oeq__iff,axiom,
% 2.64/1.57 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.64/1.57 = ( ^ [X2: a,Y3: a] :
% 2.64/1.57 ( ( less_eq @ X2 @ Y3 )
% 2.64/1.57 & ( less_eq @ Y3 @ X2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_6_local_Oeq__refl,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( X = Y )
% 2.64/1.57 => ( less_eq @ X @ Y ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_7_local_Oord__eq__le__trans,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( A2 = B2 )
% 2.64/1.57 => ( ( less_eq @ B2 @ C )
% 2.64/1.57 => ( less_eq @ A2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_8_local_Oord__le__eq__trans,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( B2 = C )
% 2.64/1.57 => ( less_eq @ A2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_9_local_Oorder_Oantisym,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 => ( A2 = B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_10_local_Oorder_Oeq__iff,axiom,
% 2.64/1.57 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.64/1.57 = ( ^ [A3: a,B3: a] :
% 2.64/1.57 ( ( less_eq @ A3 @ B3 )
% 2.64/1.57 & ( less_eq @ B3 @ A3 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_11_local_Oorder_Otrans,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( less_eq @ B2 @ C )
% 2.64/1.57 => ( less_eq @ A2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_12_local_Oorder__trans,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ( less_eq @ Y @ Z2 )
% 2.64/1.57 => ( less_eq @ X @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_13_local_Oinf_Oassoc,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( inf @ ( inf @ A2 @ B2 ) @ C )
% 2.64/1.57 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_14_local_Oinf_Ocommute,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( inf @ A2 @ B2 )
% 2.64/1.57 = ( inf @ B2 @ A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_15_local_Oinf_Oleft__commute,axiom,
% 2.64/1.57 ! [B2: a,A2: a,C: a] :
% 2.64/1.57 ( ( inf @ B2 @ ( inf @ A2 @ C ) )
% 2.64/1.57 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_16_local_Oinf__assoc,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ( inf @ ( inf @ X @ Y ) @ Z2 )
% 2.64/1.57 = ( inf @ X @ ( inf @ Y @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_17_local_Oinf__commute,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( inf @ X @ Y )
% 2.64/1.57 = ( inf @ Y @ X ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_18_local_Oinf__left__commute,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ( inf @ X @ ( inf @ Y @ Z2 ) )
% 2.64/1.57 = ( inf @ Y @ ( inf @ X @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_19_local_Osup_Oassoc,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( sup @ ( sup @ A2 @ B2 ) @ C )
% 2.64/1.57 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_20_local_Osup_Ocommute,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( sup @ A2 @ B2 )
% 2.64/1.57 = ( sup @ B2 @ A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_21_local_Osup_Oleft__commute,axiom,
% 2.64/1.57 ! [B2: a,A2: a,C: a] :
% 2.64/1.57 ( ( sup @ B2 @ ( sup @ A2 @ C ) )
% 2.64/1.57 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_22_local_Osup__assoc,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ( sup @ ( sup @ X @ Y ) @ Z2 )
% 2.64/1.57 = ( sup @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_23_local_Osup__commute,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( sup @ X @ Y )
% 2.64/1.57 = ( sup @ Y @ X ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_24_local_Osup__left__commute,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ( sup @ X @ ( sup @ Y @ Z2 ) )
% 2.64/1.57 = ( sup @ Y @ ( sup @ X @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_25_local_Oinf_Oabsorb1,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( inf @ A2 @ B2 )
% 2.64/1.57 = A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_26_local_Oinf_Oabsorb2,axiom,
% 2.64/1.57 ! [B2: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 => ( ( inf @ A2 @ B2 )
% 2.64/1.57 = B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_27_local_Oinf_Oabsorb__iff1,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 = ( ( inf @ A2 @ B2 )
% 2.64/1.57 = A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_28_local_Oinf_Oabsorb__iff2,axiom,
% 2.64/1.57 ! [B2: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 = ( ( inf @ A2 @ B2 )
% 2.64/1.57 = B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_29_local_Oinf_OboundedE,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 2.64/1.57 => ~ ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ~ ( less_eq @ A2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_30_local_Oinf_OboundedI,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( less_eq @ A2 @ C )
% 2.64/1.57 => ( less_eq @ A2 @ ( inf @ B2 @ C ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_31_local_Oinf_Ocobounded1,axiom,
% 2.64/1.57 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ A2 ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_32_local_Oinf_Ocobounded2,axiom,
% 2.64/1.57 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ B2 ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_33_local_Oinf_OcoboundedI1,axiom,
% 2.64/1.57 ! [A2: a,C: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ C )
% 2.64/1.57 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_34_local_Oinf_OcoboundedI2,axiom,
% 2.64/1.57 ! [B2: a,C: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ C )
% 2.64/1.57 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_35_local_Oinf_OorderE,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( A2
% 2.64/1.57 = ( inf @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_36_local_Oinf_OorderI,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( A2
% 2.64/1.57 = ( inf @ A2 @ B2 ) )
% 2.64/1.57 => ( less_eq @ A2 @ B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_37_local_Oinf_Oorder__iff,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 = ( A2
% 2.64/1.57 = ( inf @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_38_local_Oinf__absorb1,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ( inf @ X @ Y )
% 2.64/1.57 = X ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_39_local_Oinf__absorb2,axiom,
% 2.64/1.57 ! [Y: a,X: a] :
% 2.64/1.57 ( ( less_eq @ Y @ X )
% 2.64/1.57 => ( ( inf @ X @ Y )
% 2.64/1.57 = Y ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_40_local_Oinf__greatest,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ( less_eq @ X @ Z2 )
% 2.64/1.57 => ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_41_local_Oinf__le1,axiom,
% 2.64/1.57 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_42_local_Oinf__le2,axiom,
% 2.64/1.57 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_43_local_Oinf__mono,axiom,
% 2.64/1.57 ! [A2: a,C: a,B2: a,D: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ C )
% 2.64/1.57 => ( ( less_eq @ B2 @ D )
% 2.64/1.57 => ( less_eq @ ( inf @ A2 @ B2 ) @ ( inf @ C @ D ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_44_local_Oinf__unique,axiom,
% 2.64/1.57 ! [F: a > a > a,X: a,Y: a] :
% 2.64/1.57 ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
% 2.64/1.57 => ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
% 2.64/1.57 => ( ! [X3: a,Y4: a,Z3: a] :
% 2.64/1.57 ( ( less_eq @ X3 @ Y4 )
% 2.64/1.57 => ( ( less_eq @ X3 @ Z3 )
% 2.64/1.57 => ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 2.64/1.57 => ( ( inf @ X @ Y )
% 2.64/1.57 = ( F @ X @ Y ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_45_mem__Collect__eq,axiom,
% 2.64/1.57 ! [A: $tType,A2: A,P: A > $o] :
% 2.64/1.57 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.64/1.57 = ( P @ A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_46_Collect__mem__eq,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A] :
% 2.64/1.57 ( ( collect @ A
% 2.64/1.57 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 2.64/1.57 = A4 ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_47_Collect__cong,axiom,
% 2.64/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.64/1.57 ( ! [X3: A] :
% 2.64/1.57 ( ( P @ X3 )
% 2.64/1.57 = ( Q @ X3 ) )
% 2.64/1.57 => ( ( collect @ A @ P )
% 2.64/1.57 = ( collect @ A @ Q ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_48_ext,axiom,
% 2.64/1.57 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.64/1.57 ( ! [X3: A] :
% 2.64/1.57 ( ( F @ X3 )
% 2.64/1.57 = ( G @ X3 ) )
% 2.64/1.57 => ( F = G ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_49_local_Ole__iff__inf,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( less_eq @ X @ Y )
% 2.64/1.57 = ( ( inf @ X @ Y )
% 2.64/1.57 = X ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_50_local_Ole__infE,axiom,
% 2.64/1.57 ! [X: a,A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ X @ ( inf @ A2 @ B2 ) )
% 2.64/1.57 => ~ ( ( less_eq @ X @ A2 )
% 2.64/1.57 => ~ ( less_eq @ X @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_51_local_Ole__infI,axiom,
% 2.64/1.57 ! [X: a,A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ X @ A2 )
% 2.64/1.57 => ( ( less_eq @ X @ B2 )
% 2.64/1.57 => ( less_eq @ X @ ( inf @ A2 @ B2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_52_local_Ole__infI1,axiom,
% 2.64/1.57 ! [A2: a,X: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ X )
% 2.64/1.57 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_53_local_Ole__infI2,axiom,
% 2.64/1.57 ! [B2: a,X: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ X )
% 2.64/1.57 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_54_local_Ole__iff__sup,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( less_eq @ X @ Y )
% 2.64/1.57 = ( ( sup @ X @ Y )
% 2.64/1.57 = Y ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_55_local_Ole__supE,axiom,
% 2.64/1.57 ! [A2: a,B2: a,X: a] :
% 2.64/1.57 ( ( less_eq @ ( sup @ A2 @ B2 ) @ X )
% 2.64/1.57 => ~ ( ( less_eq @ A2 @ X )
% 2.64/1.57 => ~ ( less_eq @ B2 @ X ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_56_local_Ole__supI,axiom,
% 2.64/1.57 ! [A2: a,X: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ X )
% 2.64/1.57 => ( ( less_eq @ B2 @ X )
% 2.64/1.57 => ( less_eq @ ( sup @ A2 @ B2 ) @ X ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_57_local_Ole__supI1,axiom,
% 2.64/1.57 ! [X: a,A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ X @ A2 )
% 2.64/1.57 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_58_local_Ole__supI2,axiom,
% 2.64/1.57 ! [X: a,B2: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ X @ B2 )
% 2.64/1.57 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_59_local_Osup_Oabsorb1,axiom,
% 2.64/1.57 ! [B2: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 => ( ( sup @ A2 @ B2 )
% 2.64/1.57 = A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_60_local_Osup_Oabsorb2,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( sup @ A2 @ B2 )
% 2.64/1.57 = B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_61_local_Osup_Oabsorb__iff1,axiom,
% 2.64/1.57 ! [B2: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 = ( ( sup @ A2 @ B2 )
% 2.64/1.57 = A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_62_local_Osup_Oabsorb__iff2,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 = ( ( sup @ A2 @ B2 )
% 2.64/1.57 = B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_63_local_Osup_OboundedE,axiom,
% 2.64/1.57 ! [B2: a,C: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 2.64/1.57 => ~ ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 => ~ ( less_eq @ C @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_64_local_Osup_OboundedI,axiom,
% 2.64/1.57 ! [B2: a,A2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 => ( ( less_eq @ C @ A2 )
% 2.64/1.57 => ( less_eq @ ( sup @ B2 @ C ) @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_65_local_Osup_Ocobounded1,axiom,
% 2.64/1.57 ! [A2: a,B2: a] : ( less_eq @ A2 @ ( sup @ A2 @ B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_66_local_Osup_Ocobounded2,axiom,
% 2.64/1.57 ! [B2: a,A2: a] : ( less_eq @ B2 @ ( sup @ A2 @ B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_67_local_Osup_OcoboundedI1,axiom,
% 2.64/1.57 ! [C: a,A2: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ C @ A2 )
% 2.64/1.57 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_68_local_Osup_OcoboundedI2,axiom,
% 2.64/1.57 ! [C: a,B2: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ C @ B2 )
% 2.64/1.57 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_69_local_Osup_Omono,axiom,
% 2.64/1.57 ! [C: a,A2: a,D: a,B2: a] :
% 2.64/1.57 ( ( less_eq @ C @ A2 )
% 2.64/1.57 => ( ( less_eq @ D @ B2 )
% 2.64/1.57 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A2 @ B2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_70_local_Osup_OorderE,axiom,
% 2.64/1.57 ! [B2: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 => ( A2
% 2.64/1.57 = ( sup @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_71_local_Osup_OorderI,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( A2
% 2.64/1.57 = ( sup @ A2 @ B2 ) )
% 2.64/1.57 => ( less_eq @ B2 @ A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_72_local_Osup_Oorder__iff,axiom,
% 2.64/1.57 ! [B2: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 = ( A2
% 2.64/1.57 = ( sup @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_73_local_Osup__absorb1,axiom,
% 2.64/1.57 ! [Y: a,X: a] :
% 2.64/1.57 ( ( less_eq @ Y @ X )
% 2.64/1.57 => ( ( sup @ X @ Y )
% 2.64/1.57 = X ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_74_local_Osup__absorb2,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ( sup @ X @ Y )
% 2.64/1.57 = Y ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_75_local_Osup__ge1,axiom,
% 2.64/1.57 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_76_local_Osup__ge2,axiom,
% 2.64/1.57 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_77_local_Osup__least,axiom,
% 2.64/1.57 ! [Y: a,X: a,Z2: a] :
% 2.64/1.57 ( ( less_eq @ Y @ X )
% 2.64/1.57 => ( ( less_eq @ Z2 @ X )
% 2.64/1.57 => ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_78_local_Osup__mono,axiom,
% 2.64/1.57 ! [A2: a,C: a,B2: a,D: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ C )
% 2.64/1.57 => ( ( less_eq @ B2 @ D )
% 2.64/1.57 => ( less_eq @ ( sup @ A2 @ B2 ) @ ( sup @ C @ D ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_79_local_Osup__unique,axiom,
% 2.64/1.57 ! [F: a > a > a,X: a,Y: a] :
% 2.64/1.57 ( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
% 2.64/1.57 => ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
% 2.64/1.57 => ( ! [X3: a,Y4: a,Z3: a] :
% 2.64/1.57 ( ( less_eq @ Y4 @ X3 )
% 2.64/1.57 => ( ( less_eq @ Z3 @ X3 )
% 2.64/1.57 => ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
% 2.64/1.57 => ( ( sup @ X @ Y )
% 2.64/1.57 = ( F @ X @ Y ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_80_local_Odistrib__imp1,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ! [X3: a,Y4: a,Z3: a] :
% 2.64/1.57 ( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
% 2.64/1.57 = ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
% 2.64/1.57 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 2.64/1.57 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_81_local_Odistrib__imp2,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ! [X3: a,Y4: a,Z3: a] :
% 2.64/1.57 ( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
% 2.64/1.57 = ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
% 2.64/1.57 => ( ( inf @ X @ ( sup @ Y @ Z2 ) )
% 2.64/1.57 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_82_local_Oa__join__d,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( sup @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_83_a__meet__d,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( inf @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ C @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_84_local_Ob__join__d,axiom,
% 2.64/1.57 ! [B2: a,A2: a,C: a] :
% 2.64/1.57 ( ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( sup @ B2 @ ( inf @ C @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_85_b__meet__d,axiom,
% 2.64/1.57 ! [B2: a,A2: a,C: a] :
% 2.64/1.57 ( ( inf @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( sup @ ( inf @ B2 @ C ) @ ( inf @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_86_c__meet__d,axiom,
% 2.64/1.57 ! [C: a,A2: a,B2: a] :
% 2.64/1.57 ( ( inf @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( sup @ ( inf @ C @ A2 ) @ ( inf @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_87_local_Od__aux__def,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( sup @ ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ B2 @ C ) ) @ ( inf @ C @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_88_local_Od__b__c__a,axiom,
% 2.64/1.57 ! [B2: a,C: a,A2: a] :
% 2.64/1.57 ( ( modula1221160330_d_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 2.64/1.57 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_89_local_Od__c__a__b,axiom,
% 2.64/1.57 ! [C: a,A2: a,B2: a] :
% 2.64/1.57 ( ( modula1221160330_d_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 2.64/1.57 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_90_local_Oa__meet__e,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( inf @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_91_local_Ob__meet__e,axiom,
% 2.64/1.57 ! [B2: a,A2: a,C: a] :
% 2.64/1.57 ( ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( inf @ B2 @ ( sup @ C @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_92_local_Oc__meet__e,axiom,
% 2.64/1.57 ! [C: a,A2: a,B2: a] :
% 2.64/1.57 ( ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( inf @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_93_local_Oe__aux__def,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( inf @ ( inf @ ( sup @ A2 @ B2 ) @ ( sup @ B2 @ C ) ) @ ( sup @ C @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_94_local_Oe__b__c__a,axiom,
% 2.64/1.57 ! [B2: a,C: a,A2: a] :
% 2.64/1.57 ( ( modula1593167561_e_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 2.64/1.57 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_95_local_Oe__c__a__b,axiom,
% 2.64/1.57 ! [C: a,A2: a,B2: a] :
% 2.64/1.57 ( ( modula1593167561_e_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 2.64/1.57 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_96_local_Odistrib__inf__le,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_97_local_Odistrib__sup__le,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_98_local_Omodular,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 2.64/1.57 = ( inf @ Y @ ( sup @ X @ Z2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_99_local_Oincomp__def,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( modula1937309406incomp @ a @ less_eq @ X @ Y )
% 2.64/1.57 = ( ~ ( less_eq @ X @ Y )
% 2.64/1.57 & ~ ( less_eq @ Y @ X ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_100_local_Oorder_Orefl,axiom,
% 2.64/1.57 ! [A2: a] : ( less_eq @ A2 @ A2 ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_101_local_Oorder__refl,axiom,
% 2.64/1.57 ! [X: a] : ( less_eq @ X @ X ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_102_local_Oinf_Oidem,axiom,
% 2.64/1.57 ! [A2: a] :
% 2.64/1.57 ( ( inf @ A2 @ A2 )
% 2.64/1.57 = A2 ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_103_local_Oinf_Oleft__idem,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( inf @ A2 @ ( inf @ A2 @ B2 ) )
% 2.64/1.57 = ( inf @ A2 @ B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_104_local_Oinf_Oright__idem,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( inf @ ( inf @ A2 @ B2 ) @ B2 )
% 2.64/1.57 = ( inf @ A2 @ B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_105_local_Oinf__idem,axiom,
% 2.64/1.57 ! [X: a] :
% 2.64/1.57 ( ( inf @ X @ X )
% 2.64/1.57 = X ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_106_local_Oinf__left__idem,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( inf @ X @ ( inf @ X @ Y ) )
% 2.64/1.57 = ( inf @ X @ Y ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_107_local_Oinf__right__idem,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 2.64/1.57 = ( inf @ X @ Y ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_108_local_Osup_Oidem,axiom,
% 2.64/1.57 ! [A2: a] :
% 2.64/1.57 ( ( sup @ A2 @ A2 )
% 2.64/1.57 = A2 ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_109_local_Osup_Oleft__idem,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( sup @ A2 @ ( sup @ A2 @ B2 ) )
% 2.64/1.57 = ( sup @ A2 @ B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_110_local_Osup_Oright__idem,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( sup @ ( sup @ A2 @ B2 ) @ B2 )
% 2.64/1.57 = ( sup @ A2 @ B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_111_local_Osup__idem,axiom,
% 2.64/1.57 ! [X: a] :
% 2.64/1.57 ( ( sup @ X @ X )
% 2.64/1.57 = X ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_112_local_Osup__left__idem,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( sup @ X @ ( sup @ X @ Y ) )
% 2.64/1.57 = ( sup @ X @ Y ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_113_local_OGreatestI2__order,axiom,
% 2.64/1.57 ! [P: a > $o,X: a,Q: a > $o] :
% 2.64/1.57 ( ( P @ X )
% 2.64/1.57 => ( ! [Y4: a] :
% 2.64/1.57 ( ( P @ Y4 )
% 2.64/1.57 => ( less_eq @ Y4 @ X ) )
% 2.64/1.57 => ( ! [X3: a] :
% 2.64/1.57 ( ( P @ X3 )
% 2.64/1.57 => ( ! [Y5: a] :
% 2.64/1.57 ( ( P @ Y5 )
% 2.64/1.57 => ( less_eq @ Y5 @ X3 ) )
% 2.64/1.57 => ( Q @ X3 ) ) )
% 2.64/1.57 => ( Q @ ( greatest @ a @ less_eq @ P ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_114_local_OGreatest__equality,axiom,
% 2.64/1.57 ! [P: a > $o,X: a] :
% 2.64/1.57 ( ( P @ X )
% 2.64/1.57 => ( ! [Y4: a] :
% 2.64/1.57 ( ( P @ Y4 )
% 2.64/1.57 => ( less_eq @ Y4 @ X ) )
% 2.64/1.57 => ( ( greatest @ a @ less_eq @ P )
% 2.64/1.57 = X ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_115_local_Omax__def,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 2.64/1.57 = B2 ) )
% 2.64/1.57 & ( ~ ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 2.64/1.57 = A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_116_local_Omin__def,axiom,
% 2.64/1.57 ! [A2: a,B2: a] :
% 2.64/1.57 ( ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 2.64/1.57 = A2 ) )
% 2.64/1.57 & ( ~ ( less_eq @ A2 @ B2 )
% 2.64/1.57 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 2.64/1.57 = B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_117_local_Oa__aux__def,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( sup @ ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_118_a__def__equiv,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 => ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( inf @ ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_119_local_Oinf_Obounded__iff,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 2.64/1.57 = ( ( less_eq @ A2 @ B2 )
% 2.64/1.57 & ( less_eq @ A2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_120_local_Ole__inf__iff,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
% 2.64/1.57 = ( ( less_eq @ X @ Y )
% 2.64/1.57 & ( less_eq @ X @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_121_local_Ole__sup__iff,axiom,
% 2.64/1.57 ! [X: a,Y: a,Z2: a] :
% 2.64/1.57 ( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
% 2.64/1.57 = ( ( less_eq @ X @ Z2 )
% 2.64/1.57 & ( less_eq @ Y @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_122_local_Osup_Obounded__iff,axiom,
% 2.64/1.57 ! [B2: a,C: a,A2: a] :
% 2.64/1.57 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 2.64/1.57 = ( ( less_eq @ B2 @ A2 )
% 2.64/1.57 & ( less_eq @ C @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_123_local_Oinf__sup__absorb,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( inf @ X @ ( sup @ X @ Y ) )
% 2.64/1.57 = X ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_124_local_Osup__inf__absorb,axiom,
% 2.64/1.57 ! [X: a,Y: a] :
% 2.64/1.57 ( ( sup @ X @ ( inf @ X @ Y ) )
% 2.64/1.57 = X ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_125_local_OLeast1I,axiom,
% 2.64/1.57 ! [P: a > $o] :
% 2.64/1.57 ( ? [X4: a] :
% 2.64/1.57 ( ( P @ X4 )
% 2.64/1.57 & ! [Y4: a] :
% 2.64/1.57 ( ( P @ Y4 )
% 2.64/1.57 => ( less_eq @ X4 @ Y4 ) )
% 2.64/1.57 & ! [Y4: a] :
% 2.64/1.57 ( ( ( P @ Y4 )
% 2.64/1.57 & ! [Ya: a] :
% 2.64/1.57 ( ( P @ Ya )
% 2.64/1.57 => ( less_eq @ Y4 @ Ya ) ) )
% 2.64/1.57 => ( Y4 = X4 ) ) )
% 2.64/1.57 => ( P @ ( least @ a @ less_eq @ P ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_126_local_OLeast1__le,axiom,
% 2.64/1.57 ! [P: a > $o,Z2: a] :
% 2.64/1.57 ( ? [X4: a] :
% 2.64/1.57 ( ( P @ X4 )
% 2.64/1.57 & ! [Y4: a] :
% 2.64/1.57 ( ( P @ Y4 )
% 2.64/1.57 => ( less_eq @ X4 @ Y4 ) )
% 2.64/1.57 & ! [Y4: a] :
% 2.64/1.57 ( ( ( P @ Y4 )
% 2.64/1.57 & ! [Ya: a] :
% 2.64/1.57 ( ( P @ Ya )
% 2.64/1.57 => ( less_eq @ Y4 @ Ya ) ) )
% 2.64/1.57 => ( Y4 = X4 ) ) )
% 2.64/1.57 => ( ( P @ Z2 )
% 2.64/1.57 => ( less_eq @ ( least @ a @ less_eq @ P ) @ Z2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_127_local_OLeastI2__order,axiom,
% 2.64/1.57 ! [P: a > $o,X: a,Q: a > $o] :
% 2.64/1.57 ( ( P @ X )
% 2.64/1.57 => ( ! [Y4: a] :
% 2.64/1.57 ( ( P @ Y4 )
% 2.64/1.57 => ( less_eq @ X @ Y4 ) )
% 2.64/1.57 => ( ! [X3: a] :
% 2.64/1.57 ( ( P @ X3 )
% 2.64/1.57 => ( ! [Y5: a] :
% 2.64/1.57 ( ( P @ Y5 )
% 2.64/1.57 => ( less_eq @ X3 @ Y5 ) )
% 2.64/1.57 => ( Q @ X3 ) ) )
% 2.64/1.57 => ( Q @ ( least @ a @ less_eq @ P ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_128_local_OLeast__equality,axiom,
% 2.64/1.57 ! [P: a > $o,X: a] :
% 2.64/1.57 ( ( P @ X )
% 2.64/1.57 => ( ! [Y4: a] :
% 2.64/1.57 ( ( P @ Y4 )
% 2.64/1.57 => ( less_eq @ X @ Y4 ) )
% 2.64/1.57 => ( ( least @ a @ less_eq @ P )
% 2.64/1.57 = X ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_129_local_Oc__a,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( modula105138637_a_aux @ a @ inf @ sup @ C @ A2 @ B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_130_local_Oc__aux__def,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( sup @ ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_131_c__def__equiv,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 => ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( inf @ ( sup @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_132_c__meet__a__eq__d,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 => ( ( inf @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_133_local_Ob__a,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( modula105138637_a_aux @ a @ inf @ sup @ B2 @ C @ A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_134_local_Ob__aux__def,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( sup @ ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_135_b__def__equiv,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 => ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.64/1.57 = ( inf @ ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_136_a__join__b__eq__e,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 => ( ( sup @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_137_a__meet__b__eq__d,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 => ( ( inf @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_138_lattice_Oa__aux_Ocong,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( modula105138637_a_aux @ A )
% 2.64/1.57 = ( modula105138637_a_aux @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_139_lattice_Od__aux_Ocong,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( modula1221160330_d_aux @ A )
% 2.64/1.57 = ( modula1221160330_d_aux @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_140_lattice_Oe__aux_Ocong,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( modula1593167561_e_aux @ A )
% 2.64/1.57 = ( modula1593167561_e_aux @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_141_local_Ocomp__fun__idem__sup,axiom,
% 2.64/1.57 finite_comp_fun_idem @ a @ a @ sup ).
% 2.64/1.57
% 2.64/1.57 thf(fact_142_local_Ocomp__fun__idem__inf,axiom,
% 2.64/1.57 finite_comp_fun_idem @ a @ a @ inf ).
% 2.64/1.57
% 2.64/1.57 thf(fact_143_b__join__c__eq__e,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 => ( ( sup @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_144_b__meet__c__eq__d,axiom,
% 2.64/1.57 ! [A2: a,B2: a,C: a] :
% 2.64/1.57 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 => ( ( inf @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.64/1.57 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_145_local_Osup_Osemigroup__axioms,axiom,
% 2.64/1.57 semigroup @ a @ sup ).
% 2.64/1.57
% 2.64/1.57 thf(fact_146_local_Oinf_Osemigroup__axioms,axiom,
% 2.64/1.57 semigroup @ a @ inf ).
% 2.64/1.57
% 2.64/1.57 thf(fact_147_local_Osup_Osemilattice__axioms,axiom,
% 2.64/1.57 semilattice @ a @ sup ).
% 2.64/1.57
% 2.64/1.57 thf(fact_148_local_Oinf_Osemilattice__axioms,axiom,
% 2.64/1.57 semilattice @ a @ inf ).
% 2.64/1.57
% 2.64/1.57 thf(fact_149_local_Osup_Oabel__semigroup__axioms,axiom,
% 2.64/1.57 abel_semigroup @ a @ sup ).
% 2.64/1.57
% 2.64/1.57 thf(fact_150_local_Oinf_Oabel__semigroup__axioms,axiom,
% 2.64/1.57 abel_semigroup @ a @ inf ).
% 2.64/1.57
% 2.64/1.57 thf(fact_151_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 2.64/1.57 lattic35693393ce_set @ a @ sup ).
% 2.64/1.57
% 2.64/1.57 thf(fact_152_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 2.64/1.57 lattic35693393ce_set @ a @ inf ).
% 2.64/1.57
% 2.64/1.57 thf(fact_153_lattice_Oincomp_Ocong,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( modula1937309406incomp @ A )
% 2.64/1.57 = ( modula1937309406incomp @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_154_lattice_Oc__aux_Ocong,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( modula849153099_c_aux @ A )
% 2.64/1.57 = ( modula849153099_c_aux @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_155_lattice_Ob__aux_Ocong,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( modula477145868_b_aux @ A )
% 2.64/1.57 = ( modula477145868_b_aux @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_156_abel__semigroup_Oaxioms_I1_J,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A] :
% 2.64/1.57 ( ( abel_semigroup @ A @ F )
% 2.64/1.57 => ( semigroup @ A @ F ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_157_semilattice__set__def,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( lattic35693393ce_set @ A )
% 2.64/1.57 = ( semilattice @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_158_semilattice__set_Ointro,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A] :
% 2.64/1.57 ( ( semilattice @ A @ F )
% 2.64/1.57 => ( lattic35693393ce_set @ A @ F ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_159_abel__semigroup_Oleft__commute,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A,B2: A,A2: A,C: A] :
% 2.64/1.57 ( ( abel_semigroup @ A @ F )
% 2.64/1.57 => ( ( F @ B2 @ ( F @ A2 @ C ) )
% 2.64/1.57 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_160_abel__semigroup_Ocommute,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 2.64/1.57 ( ( abel_semigroup @ A @ F )
% 2.64/1.57 => ( ( F @ A2 @ B2 )
% 2.64/1.57 = ( F @ B2 @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_161_semigroup_Ointro,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A] :
% 2.64/1.57 ( ! [A5: A,B4: A,C2: A] :
% 2.64/1.57 ( ( F @ ( F @ A5 @ B4 ) @ C2 )
% 2.64/1.57 = ( F @ A5 @ ( F @ B4 @ C2 ) ) )
% 2.64/1.57 => ( semigroup @ A @ F ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_162_semigroup_Oassoc,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 2.64/1.57 ( ( semigroup @ A @ F )
% 2.64/1.57 => ( ( F @ ( F @ A2 @ B2 ) @ C )
% 2.64/1.57 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_163_semigroup__def,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( semigroup @ A )
% 2.64/1.57 = ( ^ [F2: A > A > A] :
% 2.64/1.57 ! [A3: A,B3: A,C3: A] :
% 2.64/1.57 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 2.64/1.57 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_164_semilattice__set_Oaxioms,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A] :
% 2.64/1.57 ( ( lattic35693393ce_set @ A @ F )
% 2.64/1.57 => ( semilattice @ A @ F ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_165_semilattice_Oaxioms_I1_J,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A] :
% 2.64/1.57 ( ( semilattice @ A @ F )
% 2.64/1.57 => ( abel_semigroup @ A @ F ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_166_local_Obdd__above__def,axiom,
% 2.64/1.57 ! [A4: set @ a] :
% 2.64/1.57 ( ( condit2040224947_above @ a @ less_eq @ A4 )
% 2.64/1.57 = ( ? [M: a] :
% 2.64/1.57 ! [X2: a] :
% 2.64/1.57 ( ( member @ a @ X2 @ A4 )
% 2.64/1.57 => ( less_eq @ X2 @ M ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_167_local_Obdd__below__def,axiom,
% 2.64/1.57 ! [A4: set @ a] :
% 2.64/1.57 ( ( condit1201339847_below @ a @ less_eq @ A4 )
% 2.64/1.57 = ( ? [M2: a] :
% 2.64/1.57 ! [X2: a] :
% 2.64/1.57 ( ( member @ a @ X2 @ A4 )
% 2.64/1.57 => ( less_eq @ M2 @ X2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_168_local_Obdd__belowI,axiom,
% 2.64/1.57 ! [A4: set @ a,M3: a] :
% 2.64/1.57 ( ! [X3: a] :
% 2.64/1.57 ( ( member @ a @ X3 @ A4 )
% 2.64/1.57 => ( less_eq @ M3 @ X3 ) )
% 2.64/1.57 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_169_local_Obdd__aboveI,axiom,
% 2.64/1.57 ! [A4: set @ a,M4: a] :
% 2.64/1.57 ( ! [X3: a] :
% 2.64/1.57 ( ( member @ a @ X3 @ A4 )
% 2.64/1.57 => ( less_eq @ X3 @ M4 ) )
% 2.64/1.57 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_170_semilattice_Oidem,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A,A2: A] :
% 2.64/1.57 ( ( semilattice @ A @ F )
% 2.64/1.57 => ( ( F @ A2 @ A2 )
% 2.64/1.57 = A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_171_semilattice_Oleft__idem,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 2.64/1.57 ( ( semilattice @ A @ F )
% 2.64/1.57 => ( ( F @ A2 @ ( F @ A2 @ B2 ) )
% 2.64/1.57 = ( F @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_172_semilattice_Oright__idem,axiom,
% 2.64/1.57 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 2.64/1.57 ( ( semilattice @ A @ F )
% 2.64/1.57 => ( ( F @ ( F @ A2 @ B2 ) @ B2 )
% 2.64/1.57 = ( F @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_173_local_Obdd__above__mono,axiom,
% 2.64/1.57 ! [B5: set @ a,A4: set @ a] :
% 2.64/1.57 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 2.64/1.57 => ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 2.64/1.57 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_174_local_Obdd__below__mono,axiom,
% 2.64/1.57 ! [B5: set @ a,A4: set @ a] :
% 2.64/1.57 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 2.64/1.57 => ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 2.64/1.57 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_175_local_Obdd__above__finite,axiom,
% 2.64/1.57 ! [A4: set @ a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_176_local_Ofinite__has__maximal2,axiom,
% 2.64/1.57 ! [A4: set @ a,A2: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( member @ a @ A2 @ A4 )
% 2.64/1.57 => ? [X3: a] :
% 2.64/1.57 ( ( member @ a @ X3 @ A4 )
% 2.64/1.57 & ( less_eq @ A2 @ X3 )
% 2.64/1.57 & ! [Xa: a] :
% 2.64/1.57 ( ( member @ a @ Xa @ A4 )
% 2.64/1.57 => ( ( less_eq @ X3 @ Xa )
% 2.64/1.57 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_177_local_Ofinite__has__minimal2,axiom,
% 2.64/1.57 ! [A4: set @ a,A2: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( member @ a @ A2 @ A4 )
% 2.64/1.57 => ? [X3: a] :
% 2.64/1.57 ( ( member @ a @ X3 @ A4 )
% 2.64/1.57 & ( less_eq @ X3 @ A2 )
% 2.64/1.57 & ! [Xa: a] :
% 2.64/1.57 ( ( member @ a @ Xa @ A4 )
% 2.64/1.57 => ( ( less_eq @ Xa @ X3 )
% 2.64/1.57 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_178_local_Obdd__below__finite,axiom,
% 2.64/1.57 ! [A4: set @ a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_179_local_OantimonoD,axiom,
% 2.64/1.57 ! [B: $tType] :
% 2.64/1.57 ( ( order @ B )
% 2.64/1.57 => ! [F: a > B,X: a,Y: a] :
% 2.64/1.57 ( ( antimono @ a @ B @ less_eq @ F )
% 2.64/1.57 => ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_180_local_OantimonoE,axiom,
% 2.64/1.57 ! [B: $tType] :
% 2.64/1.57 ( ( order @ B )
% 2.64/1.57 => ! [F: a > B,X: a,Y: a] :
% 2.64/1.57 ( ( antimono @ a @ B @ less_eq @ F )
% 2.64/1.57 => ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_181_local_OantimonoI,axiom,
% 2.64/1.57 ! [B: $tType] :
% 2.64/1.57 ( ( order @ B )
% 2.64/1.57 => ! [F: a > B] :
% 2.64/1.57 ( ! [X3: a,Y4: a] :
% 2.64/1.57 ( ( less_eq @ X3 @ Y4 )
% 2.64/1.57 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 2.64/1.57 => ( antimono @ a @ B @ less_eq @ F ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_182_local_Oantimono__def,axiom,
% 2.64/1.57 ! [B: $tType] :
% 2.64/1.57 ( ( order @ B )
% 2.64/1.57 => ! [F: a > B] :
% 2.64/1.57 ( ( antimono @ a @ B @ less_eq @ F )
% 2.64/1.57 = ( ! [X2: a,Y3: a] :
% 2.64/1.57 ( ( less_eq @ X2 @ Y3 )
% 2.64/1.57 => ( ord_less_eq @ B @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_183_local_Omono__def,axiom,
% 2.64/1.57 ! [B: $tType] :
% 2.64/1.57 ( ( order @ B )
% 2.64/1.57 => ! [F: a > B] :
% 2.64/1.57 ( ( mono @ a @ B @ less_eq @ F )
% 2.64/1.57 = ( ! [X2: a,Y3: a] :
% 2.64/1.57 ( ( less_eq @ X2 @ Y3 )
% 2.64/1.57 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_184_local_OmonoI,axiom,
% 2.64/1.57 ! [B: $tType] :
% 2.64/1.57 ( ( order @ B )
% 2.64/1.57 => ! [F: a > B] :
% 2.64/1.57 ( ! [X3: a,Y4: a] :
% 2.64/1.57 ( ( less_eq @ X3 @ Y4 )
% 2.64/1.57 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.64/1.57 => ( mono @ a @ B @ less_eq @ F ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_185_local_OmonoE,axiom,
% 2.64/1.57 ! [B: $tType] :
% 2.64/1.57 ( ( order @ B )
% 2.64/1.57 => ! [F: a > B,X: a,Y: a] :
% 2.64/1.57 ( ( mono @ a @ B @ less_eq @ F )
% 2.64/1.57 => ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_186_local_OmonoD,axiom,
% 2.64/1.57 ! [B: $tType] :
% 2.64/1.57 ( ( order @ B )
% 2.64/1.57 => ! [F: a > B,X: a,Y: a] :
% 2.64/1.57 ( ( mono @ a @ B @ less_eq @ F )
% 2.64/1.57 => ( ( less_eq @ X @ Y )
% 2.64/1.57 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_187_local_OSup__fin_OcoboundedI,axiom,
% 2.64/1.57 ! [A4: set @ a,A2: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( member @ a @ A2 @ A4 )
% 2.64/1.57 => ( less_eq @ A2 @ ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_188_local_OInf__fin_OcoboundedI,axiom,
% 2.64/1.57 ! [A4: set @ a,A2: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( member @ a @ A2 @ A4 )
% 2.64/1.57 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) @ A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_189_local_OSup__fin_Oin__idem,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( member @ a @ X @ A4 )
% 2.64/1.57 => ( ( sup @ X @ ( lattic1039401930up_fin @ a @ sup @ A4 ) )
% 2.64/1.57 = ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_190_local_OInf__fin_Oin__idem,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( member @ a @ X @ A4 )
% 2.64/1.57 => ( ( inf @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) )
% 2.64/1.57 = ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_191_local_Oinf__Sup__absorb,axiom,
% 2.64/1.57 ! [A4: set @ a,A2: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( member @ a @ A2 @ A4 )
% 2.64/1.57 => ( ( inf @ A2 @ ( lattic1039401930up_fin @ a @ sup @ A4 ) )
% 2.64/1.57 = A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_192_local_Osup__Inf__absorb,axiom,
% 2.64/1.57 ! [A4: set @ a,A2: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( member @ a @ A2 @ A4 )
% 2.64/1.57 => ( ( sup @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) @ A2 )
% 2.64/1.57 = A2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_193_semilattice__sup_OSup__fin_Ocong,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( lattic1039401930up_fin @ A )
% 2.64/1.57 = ( lattic1039401930up_fin @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_194_semilattice__inf_OInf__fin_Ocong,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( lattic1263571978nf_fin @ A )
% 2.64/1.57 = ( lattic1263571978nf_fin @ A ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_195_local_OInf__fin__le__Sup__fin,axiom,
% 2.64/1.57 ! [A4: set @ a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) @ ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_196_local_OSup__fin_Osubset__imp,axiom,
% 2.64/1.57 ! [A4: set @ a,B5: set @ a] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( finite_finite @ a @ B5 )
% 2.64/1.57 => ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ ( lattic1039401930up_fin @ a @ sup @ B5 ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_197_local_Ofinite__has__minimal,axiom,
% 2.64/1.57 ! [A4: set @ a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ? [X3: a] :
% 2.64/1.57 ( ( member @ a @ X3 @ A4 )
% 2.64/1.57 & ! [Xa: a] :
% 2.64/1.57 ( ( member @ a @ Xa @ A4 )
% 2.64/1.57 => ( ( less_eq @ Xa @ X3 )
% 2.64/1.57 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_198_local_Ofinite__has__maximal,axiom,
% 2.64/1.57 ! [A4: set @ a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ? [X3: a] :
% 2.64/1.57 ( ( member @ a @ X3 @ A4 )
% 2.64/1.57 & ! [Xa: a] :
% 2.64/1.57 ( ( member @ a @ Xa @ A4 )
% 2.64/1.57 => ( ( less_eq @ X3 @ Xa )
% 2.64/1.57 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_199_local_OInf__fin_Osubset,axiom,
% 2.64/1.57 ! [A4: set @ a,B5: set @ a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( B5
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( ord_less_eq @ ( set @ a ) @ B5 @ A4 )
% 2.64/1.57 => ( ( inf @ ( lattic1263571978nf_fin @ a @ inf @ B5 ) @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) )
% 2.64/1.57 = ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_200_local_OSup__fin_Osubset,axiom,
% 2.64/1.57 ! [A4: set @ a,B5: set @ a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( B5
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( ord_less_eq @ ( set @ a ) @ B5 @ A4 )
% 2.64/1.57 => ( ( sup @ ( lattic1039401930up_fin @ a @ sup @ B5 ) @ ( lattic1039401930up_fin @ a @ sup @ A4 ) )
% 2.64/1.57 = ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_201_local_OInf__fin_Obounded__iff,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) )
% 2.64/1.57 = ( ! [X2: a] :
% 2.64/1.57 ( ( member @ a @ X2 @ A4 )
% 2.64/1.57 => ( less_eq @ X @ X2 ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_202_local_OInf__fin_OboundedI,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ! [A5: a] :
% 2.64/1.57 ( ( member @ a @ A5 @ A4 )
% 2.64/1.57 => ( less_eq @ X @ A5 ) )
% 2.64/1.57 => ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_203_local_OInf__fin_OboundedE,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( less_eq @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) )
% 2.64/1.57 => ! [A6: a] :
% 2.64/1.57 ( ( member @ a @ A6 @ A4 )
% 2.64/1.57 => ( less_eq @ X @ A6 ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_204_local_OSup__fin_Obounded__iff,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ X )
% 2.64/1.57 = ( ! [X2: a] :
% 2.64/1.57 ( ( member @ a @ X2 @ A4 )
% 2.64/1.57 => ( less_eq @ X2 @ X ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_205_local_OSup__fin_OboundedI,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ! [A5: a] :
% 2.64/1.57 ( ( member @ a @ A5 @ A4 )
% 2.64/1.57 => ( less_eq @ A5 @ X ) )
% 2.64/1.57 => ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ X ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_206_local_OSup__fin_OboundedE,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ X )
% 2.64/1.57 => ! [A6: a] :
% 2.64/1.57 ( ( member @ a @ A6 @ A4 )
% 2.64/1.57 => ( less_eq @ A6 @ X ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_207_local_OInf__fin_Osubset__imp,axiom,
% 2.64/1.57 ! [A4: set @ a,B5: set @ a] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( finite_finite @ a @ B5 )
% 2.64/1.57 => ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ B5 ) @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_208_local_Obdd__below__empty,axiom,
% 2.64/1.57 condit1201339847_below @ a @ less_eq @ ( bot_bot @ ( set @ a ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_209_local_Obdd__above__empty,axiom,
% 2.64/1.57 condit2040224947_above @ a @ less_eq @ ( bot_bot @ ( set @ a ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_210_local_Onot__empty__eq__Iic__eq__empty,axiom,
% 2.64/1.57 ! [H: a] :
% 2.64/1.57 ( ( bot_bot @ ( set @ a ) )
% 2.64/1.57 != ( set_atMost @ a @ less_eq @ H ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_211_local_Onot__empty__eq__Ici__eq__empty,axiom,
% 2.64/1.57 ! [L: a] :
% 2.64/1.57 ( ( bot_bot @ ( set @ a ) )
% 2.64/1.57 != ( set_atLeast @ a @ less_eq @ L ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_212_local_OatLeast__iff,axiom,
% 2.64/1.57 ! [I: a,K: a] :
% 2.64/1.57 ( ( member @ a @ I @ ( set_atLeast @ a @ less_eq @ K ) )
% 2.64/1.57 = ( less_eq @ K @ I ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_213_local_OatMost__iff,axiom,
% 2.64/1.57 ! [I: a,K: a] :
% 2.64/1.57 ( ( member @ a @ I @ ( set_atMost @ a @ less_eq @ K ) )
% 2.64/1.57 = ( less_eq @ I @ K ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_214_local_Obdd__below__Ici,axiom,
% 2.64/1.57 ! [A2: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeast @ a @ less_eq @ A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_215_local_Obdd__above__Iic,axiom,
% 2.64/1.57 ! [B2: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atMost @ a @ less_eq @ B2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_216_subset__empty,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.64/1.57 = ( A4
% 2.64/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_217_empty__subsetI,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_218_subset__antisym,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.64/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 2.64/1.57 => ( A4 = B5 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_219_subsetI,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.64/1.57 ( ! [X3: A] :
% 2.64/1.57 ( ( member @ A @ X3 @ A4 )
% 2.64/1.57 => ( member @ A @ X3 @ B5 ) )
% 2.64/1.57 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_220_Collect__mono__iff,axiom,
% 2.64/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.64/1.57 = ( ! [X2: A] :
% 2.64/1.57 ( ( P @ X2 )
% 2.64/1.57 => ( Q @ X2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_221_set__eq__subset,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( ^ [Y2: set @ A,Z: set @ A] : ( Y2 = Z ) )
% 2.64/1.57 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B6 )
% 2.64/1.57 & ( ord_less_eq @ ( set @ A ) @ B6 @ A7 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_222_subset__trans,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.64/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 2.64/1.57 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_223_Collect__mono,axiom,
% 2.64/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.64/1.57 ( ! [X3: A] :
% 2.64/1.57 ( ( P @ X3 )
% 2.64/1.57 => ( Q @ X3 ) )
% 2.64/1.57 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_224_subset__refl,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_225_subset__iff,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) )
% 2.64/1.57 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.64/1.57 ! [T: A] :
% 2.64/1.57 ( ( member @ A @ T @ A7 )
% 2.64/1.57 => ( member @ A @ T @ B6 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_226_equalityD2,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.64/1.57 ( ( A4 = B5 )
% 2.64/1.57 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_227_equalityD1,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.64/1.57 ( ( A4 = B5 )
% 2.64/1.57 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_228_subset__eq,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) )
% 2.64/1.57 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.64/1.57 ! [X2: A] :
% 2.64/1.57 ( ( member @ A @ X2 @ A7 )
% 2.64/1.57 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_229_equalityE,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.64/1.57 ( ( A4 = B5 )
% 2.64/1.57 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.64/1.57 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_230_subsetD,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,C: A] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.64/1.57 => ( ( member @ A @ C @ A4 )
% 2.64/1.57 => ( member @ A @ C @ B5 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_231_in__mono,axiom,
% 2.64/1.57 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.64/1.57 => ( ( member @ A @ X @ A4 )
% 2.64/1.57 => ( member @ A @ X @ B5 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_232_local_Omono__inf,axiom,
% 2.64/1.57 ! [B: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ B )
% 2.64/1.57 => ! [F: a > B,A4: a,B5: a] :
% 2.64/1.57 ( ( mono @ a @ B @ less_eq @ F )
% 2.64/1.57 => ( ord_less_eq @ B @ ( F @ ( inf @ A4 @ B5 ) ) @ ( inf_inf @ B @ ( F @ A4 ) @ ( F @ B5 ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_233_local_OSup__fin_Oclosed,axiom,
% 2.64/1.57 ! [A4: set @ a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ! [X3: a,Y4: a] : ( member @ a @ ( sup @ X3 @ Y4 ) @ ( insert @ a @ X3 @ ( insert @ a @ Y4 @ ( bot_bot @ ( set @ a ) ) ) ) )
% 2.64/1.57 => ( member @ a @ ( lattic1039401930up_fin @ a @ sup @ A4 ) @ A4 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_234_local_Obdd__above__Int1,axiom,
% 2.64/1.57 ! [A4: set @ a,B5: set @ a] :
% 2.64/1.57 ( ( condit2040224947_above @ a @ less_eq @ A4 )
% 2.64/1.57 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_235_local_Obdd__above__Int2,axiom,
% 2.64/1.57 ! [B5: set @ a,A4: set @ a] :
% 2.64/1.57 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 2.64/1.57 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_236_local_Obdd__below__Int1,axiom,
% 2.64/1.57 ! [A4: set @ a,B5: set @ a] :
% 2.64/1.57 ( ( condit1201339847_below @ a @ less_eq @ A4 )
% 2.64/1.57 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_237_local_Obdd__below__Int2,axiom,
% 2.64/1.57 ! [B5: set @ a,A4: set @ a] :
% 2.64/1.57 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 2.64/1.57 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_238_Int__subset__iff,axiom,
% 2.64/1.57 ! [A: $tType,C4: set @ A,A4: set @ A,B5: set @ A] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A4 @ B5 ) )
% 2.64/1.57 = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A4 )
% 2.64/1.57 & ( ord_less_eq @ ( set @ A ) @ C4 @ B5 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_239_semilattice__inf__class_Oinf__right__idem,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ A )
% 2.64/1.57 => ! [X: A,Y: A] :
% 2.64/1.57 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 2.64/1.57 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_240_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ A )
% 2.64/1.57 => ! [A2: A,B2: A] :
% 2.64/1.57 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 2.64/1.57 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_241_semilattice__inf__class_Oinf__left__idem,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ A )
% 2.64/1.57 => ! [X: A,Y: A] :
% 2.64/1.57 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 2.64/1.57 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_242_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ A )
% 2.64/1.57 => ! [A2: A,B2: A] :
% 2.64/1.57 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 2.64/1.57 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_243_semilattice__inf__class_Oinf__idem,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ A )
% 2.64/1.57 => ! [X: A] :
% 2.64/1.57 ( ( inf_inf @ A @ X @ X )
% 2.64/1.57 = X ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_244_semilattice__inf__class_Oinf_Oidem,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ A )
% 2.64/1.57 => ! [A2: A] :
% 2.64/1.57 ( ( inf_inf @ A @ A2 @ A2 )
% 2.64/1.57 = A2 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_245_inf__apply,axiom,
% 2.64/1.57 ! [B: $tType,A: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ B )
% 2.64/1.57 => ( ( inf_inf @ ( A > B ) )
% 2.64/1.57 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( inf_inf @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_246_local_OInf__fin_Oinsert__not__elem,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ~ ( member @ a @ X @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ X @ A4 ) )
% 2.64/1.57 = ( inf @ X @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_247_local_OInf__fin_Oclosed,axiom,
% 2.64/1.57 ! [A4: set @ a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ! [X3: a,Y4: a] : ( member @ a @ ( inf @ X3 @ Y4 ) @ ( insert @ a @ X3 @ ( insert @ a @ Y4 @ ( bot_bot @ ( set @ a ) ) ) ) )
% 2.64/1.57 => ( member @ a @ ( lattic1263571978nf_fin @ a @ inf @ A4 ) @ A4 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_248_local_OSup__fin_Oinsert__not__elem,axiom,
% 2.64/1.57 ! [A4: set @ a,X: a] :
% 2.64/1.57 ( ( finite_finite @ a @ A4 )
% 2.64/1.57 => ( ~ ( member @ a @ X @ A4 )
% 2.64/1.57 => ( ( A4
% 2.64/1.57 != ( bot_bot @ ( set @ a ) ) )
% 2.64/1.57 => ( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ X @ A4 ) )
% 2.64/1.57 = ( sup @ X @ ( lattic1039401930up_fin @ a @ sup @ A4 ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_249_semilattice__inf__class_Ole__inf__iff,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ A )
% 2.64/1.57 => ! [X: A,Y: A,Z2: A] :
% 2.64/1.57 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z2 ) )
% 2.64/1.57 = ( ( ord_less_eq @ A @ X @ Y )
% 2.64/1.57 & ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_250_semilattice__inf__class_Oinf_Obounded__iff,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ A )
% 2.64/1.57 => ! [A2: A,B2: A,C: A] :
% 2.64/1.57 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 2.64/1.57 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.64/1.57 & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_251_inf__bot__right,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( bounded_lattice_bot @ A )
% 2.64/1.57 => ! [X: A] :
% 2.64/1.57 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 2.64/1.57 = ( bot_bot @ A ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_252_inf__bot__left,axiom,
% 2.64/1.57 ! [A: $tType] :
% 2.64/1.57 ( ( bounded_lattice_bot @ A )
% 2.64/1.57 => ! [X: A] :
% 2.64/1.57 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 2.64/1.57 = ( bot_bot @ A ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_253_insert__subset,axiom,
% 2.64/1.57 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 2.64/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A4 ) @ B5 )
% 2.64/1.57 = ( ( member @ A @ X @ B5 )
% 2.64/1.57 & ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_254_singleton__insert__inj__eq,axiom,
% 2.64/1.57 ! [A: $tType,B2: A,A2: A,A4: set @ A] :
% 2.64/1.57 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 2.64/1.57 = ( insert @ A @ A2 @ A4 ) )
% 2.64/1.57 = ( ( A2 = B2 )
% 2.64/1.57 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(fact_255_singleton__insert__inj__eq_H,axiom,
% 2.64/1.57 ! [A: $tType,A2: A,A4: set @ A,B2: A] :
% 2.64/1.57 ( ( ( insert @ A @ A2 @ A4 )
% 2.64/1.57 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.64/1.57 = ( ( A2 = B2 )
% 2.64/1.57 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.64/1.57 bounded_lattice @ $o ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.64/1.57 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.64/1.57 ! [A8: $tType,A9: $tType] :
% 2.64/1.57 ( ( bounded_lattice @ A9 )
% 2.64/1.57 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 2.64/1.57 ! [A8: $tType,A9: $tType] :
% 2.64/1.57 ( ( bounded_lattice @ A9 )
% 2.64/1.57 => ( bounded_lattice_bot @ ( A8 > A9 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 2.64/1.57 ! [A8: $tType,A9: $tType] :
% 2.64/1.57 ( ( semilattice_inf @ A9 )
% 2.64/1.57 => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.64/1.57 ! [A8: $tType,A9: $tType] :
% 2.64/1.57 ( ( order @ A9 )
% 2.64/1.57 => ( order @ ( A8 > A9 ) ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_3,axiom,
% 2.64/1.57 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_4,axiom,
% 2.64/1.57 ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 2.64/1.57 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_6,axiom,
% 2.64/1.57 bounded_lattice_bot @ $o ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_7,axiom,
% 2.64/1.57 semilattice_inf @ $o ).
% 2.64/1.57
% 2.64/1.57 thf(tcon_HOL_Obool___Orderings_Oorder_8,axiom,
% 2.64/1.57 order @ $o ).
% 2.64/1.57
% 2.64/1.57 thf(conj_0,hypothesis,
% 2.64/1.57 less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ).
% 2.64/1.57
% 2.64/1.57 thf(conj_1,conjecture,
% 2.64/1.57 ( ( sup @ ( modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b ) @ ( modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c ) )
% 2.64/1.57 = ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ).
% 2.64/1.57 ------------------------
% 2.64/1.59 % (5512)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/183Mi)
% 2.75/1.60 % (5516)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_5305 for (2999ds/2Mi)
% 2.75/1.60 % (5516)Instruction limit reached!
% 2.75/1.60 % (5516)------------------------------
% 2.75/1.60 % (5516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.60 % (5516)Termination reason: Unknown
% 2.75/1.60 % (5516)Termination phase: shuffling
% 2.75/1.60
% 2.75/1.60 % (5516)Memory used [KB]: 1279
% 2.75/1.60 % (5516)Time elapsed: 0.003 s
% 2.75/1.60 % (5516)Instructions burned: 2 (million)
% 2.75/1.60 % (5516)------------------------------
% 2.75/1.60 % (5516)------------------------------
% 2.75/1.60 % (5514)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_5305 for (2999ds/27Mi)
% 2.75/1.60 % (5518)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/18Mi)
% 2.75/1.60 % (5517)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_5305 for (2999ds/275Mi)
% 2.75/1.60 % (5513)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_5305 for (2999ds/4Mi)
% 2.75/1.60 % (5515)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/2Mi)
% 2.75/1.60 % (5515)Instruction limit reached!
% 2.75/1.60 % (5515)------------------------------
% 2.75/1.60 % (5515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.60 % (5515)Termination reason: Unknown
% 2.75/1.60 % (5515)Termination phase: shuffling
% 2.75/1.60
% 2.75/1.60 % (5515)Memory used [KB]: 1279
% 2.75/1.60 % (5515)Time elapsed: 0.003 s
% 2.75/1.60 % (5515)Instructions burned: 2 (million)
% 2.75/1.60 % (5515)------------------------------
% 2.75/1.60 % (5515)------------------------------
% 2.75/1.60 % (5513)Instruction limit reached!
% 2.75/1.60 % (5513)------------------------------
% 2.75/1.60 % (5513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.60 % (5513)Termination reason: Unknown
% 2.75/1.60 % (5513)Termination phase: shuffling
% 2.75/1.60
% 2.75/1.60 % (5513)Memory used [KB]: 1279
% 2.75/1.60 % (5513)Time elapsed: 0.004 s
% 2.75/1.60 % (5513)Instructions burned: 5 (million)
% 2.75/1.60 % (5513)------------------------------
% 2.75/1.60 % (5513)------------------------------
% 2.75/1.61 % (5518)Instruction limit reached!
% 2.75/1.61 % (5518)------------------------------
% 2.75/1.61 % (5518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.61 % (5518)Termination reason: Unknown
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% 2.75/1.61
% 2.75/1.61 % (5518)Memory used [KB]: 1535
% 2.75/1.61 % (5518)Time elapsed: 0.011 s
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% 2.75/1.61 % (5518)------------------------------
% 2.75/1.61 % (5514)Instruction limit reached!
% 2.75/1.61 % (5514)------------------------------
% 2.75/1.61 % (5514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.61 % (5514)Termination reason: Unknown
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% 2.75/1.61 % (5514)Time elapsed: 0.015 s
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% 2.75/1.61 % (5514)------------------------------
% 2.75/1.62 % (5528)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_5305 for (2999ds/3Mi)
% 2.75/1.62 % (5524)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_5305 for (2999ds/37Mi)
% 2.75/1.62 % (5528)Instruction limit reached!
% 2.75/1.62 % (5528)------------------------------
% 2.75/1.62 % (5528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.62 % (5528)Termination reason: Unknown
% 2.75/1.62 % (5528)Termination phase: shuffling
% 2.75/1.62
% 2.75/1.62 % (5528)Memory used [KB]: 1279
% 2.75/1.62 % (5528)Time elapsed: 0.002 s
% 2.75/1.62 % (5528)Instructions burned: 3 (million)
% 2.75/1.62 % (5528)------------------------------
% 2.75/1.62 % (5528)------------------------------
% 2.75/1.62 % (5523)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/3Mi)
% 2.75/1.62 % (5525)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_5305 for (2999ds/15Mi)
% 2.75/1.62 % (5523)Instruction limit reached!
% 2.75/1.62 % (5523)------------------------------
% 2.75/1.62 % (5523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.62 % (5523)Termination reason: Unknown
% 2.75/1.62 % (5523)Termination phase: shuffling
% 2.75/1.62
% 2.75/1.62 % (5523)Memory used [KB]: 1279
% 2.75/1.62 % (5523)Time elapsed: 0.003 s
% 2.75/1.62 % (5523)Instructions burned: 3 (million)
% 2.75/1.62 % (5523)------------------------------
% 2.75/1.62 % (5523)------------------------------
% 2.75/1.63 % (5525)Instruction limit reached!
% 2.75/1.63 % (5525)------------------------------
% 2.75/1.63 % (5525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.63 % (5525)Termination reason: Unknown
% 2.75/1.63 % (5525)Termination phase: shuffling
% 2.75/1.63
% 2.75/1.63 % (5525)Memory used [KB]: 1535
% 2.75/1.63 % (5525)Time elapsed: 0.010 s
% 2.75/1.63 % (5525)Instructions burned: 16 (million)
% 2.75/1.63 % (5525)------------------------------
% 2.75/1.63 % (5525)------------------------------
% 2.75/1.63 % (5529)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_5305 for (2999ds/1041Mi)
% 2.75/1.63 % (5533)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/7Mi)
% 2.75/1.63 % (5533)Instruction limit reached!
% 2.75/1.63 % (5533)------------------------------
% 2.75/1.63 % (5533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.63 % (5533)Termination reason: Unknown
% 2.75/1.63 % (5533)Termination phase: shuffling
% 2.75/1.63
% 2.75/1.63 % (5533)Memory used [KB]: 1407
% 2.75/1.63 % (5533)Time elapsed: 0.004 s
% 2.75/1.63 % (5533)Instructions burned: 9 (million)
% 2.75/1.63 % (5533)------------------------------
% 2.75/1.63 % (5533)------------------------------
% 2.75/1.64 % (5524)Instruction limit reached!
% 2.75/1.64 % (5524)------------------------------
% 2.75/1.64 % (5524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.64 % (5524)Termination reason: Unknown
% 2.75/1.64 % (5524)Termination phase: Property scanning
% 2.75/1.64
% 2.75/1.64 % (5524)Memory used [KB]: 1791
% 2.75/1.64 % (5524)Time elapsed: 0.020 s
% 2.75/1.64 % (5524)Instructions burned: 37 (million)
% 2.75/1.64 % (5524)------------------------------
% 2.75/1.64 % (5524)------------------------------
% 2.75/1.64 % (5534)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/16Mi)
% 2.75/1.65 % (5538)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_5305 for (2999ds/3Mi)
% 2.75/1.65 % (5534)Instruction limit reached!
% 2.75/1.65 % (5534)------------------------------
% 2.75/1.65 % (5534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.65 % (5534)Termination reason: Unknown
% 2.75/1.65 % (5534)Termination phase: shuffling
% 2.75/1.65
% 2.75/1.65 % (5534)Memory used [KB]: 1535
% 2.75/1.65 % (5534)Time elapsed: 0.007 s
% 2.75/1.65 % (5534)Instructions burned: 17 (million)
% 2.75/1.65 % (5534)------------------------------
% 2.75/1.65 % (5534)------------------------------
% 2.75/1.65 % (5538)Instruction limit reached!
% 2.75/1.65 % (5538)------------------------------
% 2.75/1.65 % (5538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.65 % (5538)Termination reason: Unknown
% 2.75/1.65 % (5538)Termination phase: shuffling
% 2.75/1.65
% 2.75/1.65 % (5538)Memory used [KB]: 1279
% 2.75/1.65 % (5538)Time elapsed: 0.003 s
% 2.75/1.65 % (5538)Instructions burned: 3 (million)
% 2.75/1.65 % (5538)------------------------------
% 2.75/1.65 % (5538)------------------------------
% 2.75/1.65 % (5536)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_5305 for (2999ds/3Mi)
% 2.75/1.65 % (5536)Instruction limit reached!
% 2.75/1.65 % (5536)------------------------------
% 2.75/1.65 % (5536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.65 % (5536)Termination reason: Unknown
% 2.75/1.65 % (5536)Termination phase: shuffling
% 2.75/1.65
% 2.75/1.65 % (5536)Memory used [KB]: 1279
% 2.75/1.65 % (5536)Time elapsed: 0.003 s
% 2.75/1.65 % (5536)Instructions burned: 3 (million)
% 2.75/1.65 % (5536)------------------------------
% 2.75/1.65 % (5536)------------------------------
% 2.75/1.66 % (5541)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/7Mi)
% 2.75/1.66 % (5542)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/3Mi)
% 2.75/1.66 % (5541)Instruction limit reached!
% 2.75/1.66 % (5541)------------------------------
% 2.75/1.66 % (5541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.66 % (5541)Termination reason: Unknown
% 2.75/1.66 % (5541)Termination phase: shuffling
% 2.75/1.66
% 2.75/1.66 % (5541)Memory used [KB]: 1407
% 2.75/1.66 % (5541)Time elapsed: 0.006 s
% 2.75/1.66 % (5541)Instructions burned: 7 (million)
% 2.75/1.66 % (5541)------------------------------
% 2.75/1.66 % (5541)------------------------------
% 2.75/1.66 % (5542)Instruction limit reached!
% 2.75/1.66 % (5542)------------------------------
% 2.75/1.66 % (5542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.66 % (5542)Termination reason: Unknown
% 2.75/1.66 % (5542)Termination phase: shuffling
% 2.75/1.66
% 2.75/1.66 % (5542)Memory used [KB]: 1279
% 2.75/1.66 % (5542)Time elapsed: 0.004 s
% 2.75/1.66 % (5542)Instructions burned: 4 (million)
% 2.75/1.66 % (5542)------------------------------
% 2.75/1.66 % (5542)------------------------------
% 2.75/1.66 % (5543)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/4Mi)
% 2.75/1.67 % (5544)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/18Mi)
% 2.75/1.67 % (5512)Instruction limit reached!
% 2.75/1.67 % (5512)------------------------------
% 2.75/1.67 % (5512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.67 % (5512)Termination reason: Unknown
% 2.75/1.67 % (5512)Termination phase: Saturation
% 2.75/1.67
% 2.75/1.67 % (5512)Memory used [KB]: 6780
% 2.75/1.67 % (5512)Time elapsed: 0.073 s
% 2.75/1.67 % (5512)Instructions burned: 183 (million)
% 2.75/1.67 % (5512)------------------------------
% 2.75/1.67 % (5512)------------------------------
% 2.75/1.67 % (5543)Instruction limit reached!
% 2.75/1.67 % (5543)------------------------------
% 2.75/1.67 % (5543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.67 % (5543)Termination reason: Unknown
% 2.75/1.67 % (5543)Termination phase: shuffling
% 2.75/1.67
% 2.75/1.67 % (5543)Memory used [KB]: 1279
% 2.75/1.67 % (5543)Time elapsed: 0.004 s
% 2.75/1.67 % (5543)Instructions burned: 4 (million)
% 2.75/1.67 % (5543)------------------------------
% 2.75/1.67 % (5543)------------------------------
% 2.75/1.67 % (5547)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/710Mi)
% 2.75/1.67 % (5544)Instruction limit reached!
% 2.75/1.67 % (5544)------------------------------
% 2.75/1.67 % (5544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.67 % (5544)Termination reason: Unknown
% 2.75/1.67 % (5544)Termination phase: shuffling
% 2.75/1.67
% 2.75/1.67 % (5544)Memory used [KB]: 1535
% 2.75/1.67 % (5544)Time elapsed: 0.011 s
% 2.75/1.67 % (5544)Instructions burned: 19 (million)
% 2.75/1.67 % (5544)------------------------------
% 2.75/1.67 % (5544)------------------------------
% 2.75/1.68 % (5548)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/6Mi)
% 2.75/1.68 % (5548)Instruction limit reached!
% 2.75/1.68 % (5548)------------------------------
% 2.75/1.68 % (5548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.68 % (5548)Termination reason: Unknown
% 2.75/1.68 % (5548)Termination phase: shuffling
% 2.75/1.68
% 2.75/1.68 % (5548)Memory used [KB]: 1407
% 2.75/1.68 % (5548)Time elapsed: 0.005 s
% 2.75/1.68 % (5548)Instructions burned: 6 (million)
% 2.75/1.68 % (5548)------------------------------
% 2.75/1.68 % (5548)------------------------------
% 2.75/1.68 % (5551)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_5305 for (2999ds/902Mi)
% 2.75/1.69 % (5554)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5305 for (2999ds/5Mi)
% 2.75/1.69 % (5552)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_5305 for (2999ds/21Mi)
% 2.75/1.69 % (5554)Instruction limit reached!
% 2.75/1.69 % (5554)------------------------------
% 2.75/1.69 % (5554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.69 % (5554)Termination reason: Unknown
% 2.75/1.69 % (5554)Termination phase: shuffling
% 2.75/1.69
% 2.75/1.69 % (5554)Memory used [KB]: 1407
% 2.75/1.69 % (5554)Time elapsed: 0.004 s
% 2.75/1.69 % (5554)Instructions burned: 5 (million)
% 2.75/1.69 % (5554)------------------------------
% 2.75/1.69 % (5554)------------------------------
% 2.75/1.70 % (5552)Instruction limit reached!
% 2.75/1.70 % (5552)------------------------------
% 2.75/1.70 % (5552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.70 % (5552)Termination reason: Unknown
% 2.75/1.70 % (5552)Termination phase: shuffling
% 2.75/1.70
% 2.75/1.70 % (5552)Memory used [KB]: 1535
% 2.75/1.70 % (5552)Time elapsed: 0.014 s
% 2.75/1.70 % (5552)Instructions burned: 22 (million)
% 2.75/1.70 % (5552)------------------------------
% 2.75/1.70 % (5552)------------------------------
% 2.75/1.70 % (5556)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_5305 for (2999ds/6Mi)
% 2.75/1.71 % (5556)Instruction limit reached!
% 2.75/1.71 % (5556)------------------------------
% 2.75/1.71 % (5556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.71 % (5556)Termination reason: Unknown
% 2.75/1.71 % (5556)Termination phase: shuffling
% 2.75/1.71
% 2.75/1.71 % (5556)Memory used [KB]: 1407
% 2.75/1.71 % (5556)Time elapsed: 0.005 s
% 2.75/1.71 % (5556)Instructions burned: 6 (million)
% 2.75/1.71 % (5556)------------------------------
% 2.75/1.71 % (5556)------------------------------
% 2.75/1.71 % (5517)Instruction limit reached!
% 2.75/1.71 % (5517)------------------------------
% 2.75/1.71 % (5517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.71 % (5517)Termination reason: Unknown
% 2.75/1.71 % (5517)Termination phase: Saturation
% 2.75/1.71
% 2.75/1.71 % (5517)Memory used [KB]: 6524
% 2.75/1.71 % (5517)Time elapsed: 0.114 s
% 2.75/1.71 % (5517)Instructions burned: 277 (million)
% 2.75/1.71 % (5517)------------------------------
% 2.75/1.71 % (5517)------------------------------
% 2.75/1.72 % (5559)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_5305 for (2998ds/779Mi)
% 2.75/1.72 % (5557)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5305 for (2998ds/377Mi)
% 2.75/1.72 % (5560)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_5305 for (2998ds/19Mi)
% 2.75/1.72 % (5561)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5305 for (2998ds/879Mi)
% 2.75/1.73 % (5560)Instruction limit reached!
% 2.75/1.73 % (5560)------------------------------
% 2.75/1.73 % (5560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.73 % (5560)Termination reason: Unknown
% 2.75/1.73 % (5560)Termination phase: shuffling
% 2.75/1.73
% 2.75/1.73 % (5560)Memory used [KB]: 1663
% 2.75/1.73 % (5560)Time elapsed: 0.008 s
% 2.75/1.73 % (5560)Instructions burned: 21 (million)
% 2.75/1.73 % (5560)------------------------------
% 2.75/1.73 % (5560)------------------------------
% 2.75/1.74 % (5563)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5305 for (2998ds/17Mi)
% 2.75/1.74 % (5563)Instruction limit reached!
% 2.75/1.74 % (5563)------------------------------
% 2.75/1.74 % (5563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.74 % (5563)Termination reason: Unknown
% 2.75/1.74 % (5563)Termination phase: shuffling
% 2.75/1.74
% 2.75/1.74 % (5563)Memory used [KB]: 1535
% 2.75/1.74 % (5563)Time elapsed: 0.008 s
% 2.75/1.74 % (5563)Instructions burned: 19 (million)
% 2.75/1.74 % (5563)------------------------------
% 2.75/1.74 % (5563)------------------------------
% 2.75/1.75 % (5564)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5305 for (2998ds/3Mi)
% 2.75/1.75 % (5564)Instruction limit reached!
% 2.75/1.75 % (5564)------------------------------
% 2.75/1.75 % (5564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.75 % (5564)Termination reason: Unknown
% 2.75/1.75 % (5564)Termination phase: shuffling
% 2.75/1.75
% 2.75/1.75 % (5564)Memory used [KB]: 1279
% 2.75/1.75 % (5564)Time elapsed: 0.002 s
% 2.75/1.75 % (5564)Instructions burned: 3 (million)
% 2.75/1.75 % (5564)------------------------------
% 2.75/1.75 % (5564)------------------------------
% 2.75/1.76 % (5565)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5305 for (2998ds/30Mi)
% 2.75/1.77 % (5565)Instruction limit reached!
% 2.75/1.77 % (5565)------------------------------
% 2.75/1.77 % (5565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.77 % (5565)Termination reason: Unknown
% 2.75/1.77 % (5565)Termination phase: Property scanning
% 2.75/1.77
% 2.75/1.77 % (5565)Memory used [KB]: 1535
% 2.75/1.77 % (5565)Time elapsed: 0.010 s
% 2.75/1.77 % (5565)Instructions burned: 30 (million)
% 2.75/1.77 % (5565)------------------------------
% 2.75/1.77 % (5565)------------------------------
% 2.75/1.78 % (5566)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5305 for (2998ds/127Mi)
% 2.75/1.82 % (5566)Instruction limit reached!
% 2.75/1.82 % (5566)------------------------------
% 2.75/1.82 % (5566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.82 % (5566)Termination reason: Unknown
% 2.75/1.82 % (5566)Termination phase: Saturation
% 2.75/1.82
% 2.75/1.82 % (5566)Memory used [KB]: 6652
% 2.75/1.82 % (5566)Time elapsed: 0.039 s
% 2.75/1.82 % (5566)Instructions burned: 130 (million)
% 2.75/1.82 % (5566)------------------------------
% 2.75/1.82 % (5566)------------------------------
% 2.75/1.83 % (5567)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_5305 for (2997ds/100Mi)
% 2.75/1.85 % (5557)Instruction limit reached!
% 2.75/1.85 % (5557)------------------------------
% 2.75/1.85 % (5557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.85 % (5557)Termination reason: Unknown
% 2.75/1.85 % (5557)Termination phase: Saturation
% 2.75/1.85
% 2.75/1.85 % (5557)Memory used [KB]: 7291
% 2.75/1.85 % (5557)Time elapsed: 0.161 s
% 2.75/1.85 % (5557)Instructions burned: 379 (million)
% 2.75/1.85 % (5557)------------------------------
% 2.75/1.85 % (5557)------------------------------
% 2.75/1.86 % (5567)Instruction limit reached!
% 2.75/1.86 % (5567)------------------------------
% 2.75/1.86 % (5567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.86 % (5567)Termination reason: Unknown
% 2.75/1.86 % (5567)Termination phase: Saturation
% 2.75/1.86
% 2.75/1.86 % (5567)Memory used [KB]: 6524
% 2.75/1.86 % (5567)Time elapsed: 0.028 s
% 2.75/1.86 % (5567)Instructions burned: 101 (million)
% 2.75/1.86 % (5567)------------------------------
% 2.75/1.86 % (5567)------------------------------
% 2.75/1.86 % (5582)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_5305 for (2997ds/3Mi)
% 2.75/1.86 % (5582)Instruction limit reached!
% 2.75/1.86 % (5582)------------------------------
% 2.75/1.86 % (5582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.86 % (5582)Termination reason: Unknown
% 2.75/1.86 % (5582)Termination phase: shuffling
% 2.75/1.86
% 2.75/1.86 % (5582)Memory used [KB]: 1279
% 2.75/1.86 % (5582)Time elapsed: 0.002 s
% 2.75/1.86 % (5582)Instructions burned: 3 (million)
% 2.75/1.86 % (5582)------------------------------
% 2.75/1.86 % (5582)------------------------------
% 2.75/1.87 % (5584)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_5305 for (2997ds/20Mi)
% 2.75/1.87 % (5584)Instruction limit reached!
% 2.75/1.87 % (5584)------------------------------
% 2.75/1.87 % (5584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.87 % (5584)Termination reason: Unknown
% 2.75/1.87 % (5584)Termination phase: Property scanning
% 2.75/1.87
% 2.75/1.87 % (5584)Memory used [KB]: 1535
% 2.75/1.87 % (5584)Time elapsed: 0.008 s
% 2.75/1.87 % (5584)Instructions burned: 21 (million)
% 2.75/1.87 % (5584)------------------------------
% 2.75/1.87 % (5584)------------------------------
% 2.75/1.87 % (5589)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_5305 for (2997ds/86Mi)
% 2.75/1.88 % (5594)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_5305 for (2997ds/107Mi)
% 2.75/1.89 % (5547)Instruction limit reached!
% 2.75/1.89 % (5547)------------------------------
% 2.75/1.89 % (5547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.89 % (5547)Termination reason: Unknown
% 2.75/1.89 % (5547)Termination phase: Saturation
% 2.75/1.89
% 2.75/1.89 % (5547)Memory used [KB]: 7419
% 2.75/1.89 % (5547)Time elapsed: 0.220 s
% 2.75/1.89 % (5547)Instructions burned: 711 (million)
% 2.75/1.89 % (5547)------------------------------
% 2.75/1.89 % (5547)------------------------------
% 2.75/1.90 % (5589)Instruction limit reached!
% 2.75/1.90 % (5589)------------------------------
% 2.75/1.90 % (5589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.90 % (5589)Termination reason: Unknown
% 2.75/1.90 % (5589)Termination phase: Saturation
% 2.75/1.90
% 2.75/1.90 % (5589)Memory used [KB]: 6524
% 2.75/1.90 % (5589)Time elapsed: 0.027 s
% 2.75/1.90 % (5589)Instructions burned: 89 (million)
% 2.75/1.90 % (5589)------------------------------
% 2.75/1.90 % (5589)------------------------------
% 2.75/1.90 % (5606)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_5305 for (2996ds/39Mi)
% 2.75/1.91 % (5612)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_5305 for (2996ds/448Mi)
% 2.75/1.91 % (5606)Instruction limit reached!
% 2.75/1.91 % (5606)------------------------------
% 2.75/1.91 % (5606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.91 % (5606)Termination reason: Unknown
% 2.75/1.91 % (5606)Termination phase: Property scanning
% 2.75/1.91
% 2.75/1.91 % (5606)Memory used [KB]: 1791
% 2.75/1.91 % (5606)Time elapsed: 0.012 s
% 2.75/1.91 % (5606)Instructions burned: 42 (million)
% 2.75/1.91 % (5606)------------------------------
% 2.75/1.91 % (5606)------------------------------
% 2.75/1.92 % (5594)Instruction limit reached!
% 2.75/1.92 % (5594)------------------------------
% 2.75/1.92 % (5594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.92 % (5594)Termination reason: Unknown
% 2.75/1.92 % (5594)Termination phase: Saturation
% 2.75/1.92
% 2.75/1.92 % (5594)Memory used [KB]: 6524
% 2.75/1.92 % (5594)Time elapsed: 0.034 s
% 2.75/1.92 % (5594)Instructions burned: 108 (million)
% 2.75/1.92 % (5594)------------------------------
% 2.75/1.92 % (5594)------------------------------
% 2.75/1.92 % (5614)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_5305 for (2996ds/46Mi)
% 2.75/1.92 % (5618)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_5305 for (2996ds/98Mi)
% 2.75/1.93 % (5614)Instruction limit reached!
% 2.75/1.93 % (5614)------------------------------
% 2.75/1.93 % (5614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.93 % (5614)Termination reason: Unknown
% 2.75/1.93 % (5614)Termination phase: Property scanning
% 2.75/1.93
% 2.75/1.93 % (5614)Memory used [KB]: 1663
% 2.75/1.93 % (5614)Time elapsed: 0.015 s
% 2.75/1.93 % (5614)Instructions burned: 49 (million)
% 2.75/1.93 % (5614)------------------------------
% 2.75/1.93 % (5614)------------------------------
% 2.75/1.94 % (5628)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_5305 for (2996ds/507Mi)
% 2.75/1.95 % (5618)Instruction limit reached!
% 2.75/1.95 % (5618)------------------------------
% 2.75/1.95 % (5618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.95 % (5618)Termination reason: Unknown
% 2.75/1.95 % (5618)Termination phase: Saturation
% 2.75/1.95
% 2.75/1.95 % (5618)Memory used [KB]: 2046
% 2.75/1.95 % (5618)Time elapsed: 0.027 s
% 2.75/1.95 % (5618)Instructions burned: 100 (million)
% 2.75/1.95 % (5618)------------------------------
% 2.75/1.95 % (5618)------------------------------
% 2.75/1.95 % (5559)Instruction limit reached!
% 2.75/1.95 % (5559)------------------------------
% 2.75/1.95 % (5559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.95 % (5559)Termination reason: Unknown
% 2.75/1.95 % (5559)Termination phase: Saturation
% 2.75/1.95
% 2.75/1.95 % (5559)Memory used [KB]: 7291
% 2.75/1.95 % (5559)Time elapsed: 0.237 s
% 2.75/1.95 % (5559)Instructions burned: 782 (million)
% 2.75/1.95 % (5559)------------------------------
% 2.75/1.95 % (5559)------------------------------
% 2.75/1.96 % (5551)Instruction limit reached!
% 2.75/1.96 % (5551)------------------------------
% 2.75/1.96 % (5551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.96 % (5551)Termination reason: Unknown
% 2.75/1.96 % (5551)Termination phase: Saturation
% 2.75/1.96
% 2.75/1.96 % (5551)Memory used [KB]: 7675
% 2.75/1.96 % (5551)Time elapsed: 0.277 s
% 2.75/1.96 % (5551)Instructions burned: 904 (million)
% 2.75/1.96 % (5551)------------------------------
% 2.75/1.96 % (5551)------------------------------
% 2.75/1.96 % (5634)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_5305 for (2996ds/149Mi)
% 2.75/1.96 % (5635)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_5305 for (2996ds/39Mi)
% 2.75/1.97 % (5637)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_5305 for (2996ds/6Mi)
% 2.75/1.97 % (5637)Instruction limit reached!
% 2.75/1.97 % (5637)------------------------------
% 2.75/1.97 % (5637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.97 % (5637)Termination reason: Unknown
% 2.75/1.97 % (5637)Termination phase: shuffling
% 2.75/1.97
% 2.75/1.97 % (5637)Memory used [KB]: 1407
% 2.75/1.97 % (5637)Time elapsed: 0.003 s
% 2.75/1.97 % (5637)Instructions burned: 7 (million)
% 2.75/1.97 % (5637)------------------------------
% 2.75/1.97 % (5637)------------------------------
% 2.75/1.98 % (5635)Instruction limit reached!
% 2.75/1.98 % (5635)------------------------------
% 2.75/1.98 % (5635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.98 % (5635)Termination reason: Unknown
% 2.75/1.98 % (5635)Termination phase: Preprocessing 3
% 2.75/1.98
% 2.75/1.98 % (5635)Memory used [KB]: 1663
% 2.75/1.98 % (5635)Time elapsed: 0.013 s
% 2.75/1.98 % (5635)Instructions burned: 39 (million)
% 2.75/1.98 % (5635)------------------------------
% 2.75/1.98 % (5635)------------------------------
% 2.75/1.98 % (5529)Instruction limit reached!
% 2.75/1.98 % (5529)------------------------------
% 2.75/1.98 % (5529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.98 % (5529)Termination reason: Unknown
% 2.75/1.98 % (5529)Termination phase: Saturation
% 2.75/1.98
% 2.75/1.98 % (5529)Memory used [KB]: 9338
% 2.75/1.98 % (5529)Time elapsed: 0.350 s
% 2.75/1.98 % (5529)Instructions burned: 1044 (million)
% 2.75/1.98 % (5529)------------------------------
% 2.75/1.98 % (5529)------------------------------
% 2.75/1.98 % (5646)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_5305 for (2996ds/1087Mi)
% 2.75/1.99 % (5647)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_5305 for (2996ds/47Mi)
% 2.75/1.99 % (5648)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/44Mi)
% 2.75/1.99 % (5561)Instruction limit reached!
% 2.75/1.99 % (5561)------------------------------
% 2.75/1.99 % (5561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.99 % (5561)Termination reason: Unknown
% 2.75/1.99 % (5561)Termination phase: Saturation
% 2.75/1.99
% 2.75/1.99 % (5561)Memory used [KB]: 7675
% 2.75/1.99 % (5561)Time elapsed: 0.269 s
% 2.75/1.99 % (5561)Instructions burned: 881 (million)
% 2.75/1.99 % (5561)------------------------------
% 2.75/1.99 % (5561)------------------------------
% 2.75/2.00 % (5647)Instruction limit reached!
% 2.75/2.00 % (5647)------------------------------
% 2.75/2.00 % (5647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/2.00 % (5647)Termination reason: Unknown
% 2.75/2.00 % (5647)Termination phase: Property scanning
% 2.75/2.00
% 2.75/2.00 % (5647)Memory used [KB]: 1791
% 2.75/2.00 % (5647)Time elapsed: 0.016 s
% 2.75/2.00 % (5647)Instructions burned: 50 (million)
% 2.75/2.00 % (5647)------------------------------
% 2.75/2.00 % (5647)------------------------------
% 2.75/2.00 % (5648)Instruction limit reached!
% 2.75/2.00 % (5648)------------------------------
% 2.75/2.00 % (5648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/2.00 % (5657)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/432Mi)
% 2.75/2.00 % (5648)Termination reason: Unknown
% 2.75/2.00 % (5648)Termination phase: Property scanning
% 2.75/2.00
% 2.75/2.00 % (5648)Memory used [KB]: 1791
% 2.75/2.00 % (5648)Time elapsed: 0.014 s
% 2.75/2.00 % (5648)Instructions burned: 48 (million)
% 2.75/2.00 % (5648)------------------------------
% 2.75/2.00 % (5648)------------------------------
% 2.75/2.01 % (5634)Instruction limit reached!
% 2.75/2.01 % (5634)------------------------------
% 2.75/2.01 % (5634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/2.01 % (5634)Termination reason: Unknown
% 2.75/2.01 % (5634)Termination phase: Saturation
% 2.75/2.01
% 2.75/2.01 % (5634)Memory used [KB]: 6780
% 2.75/2.01 % (5634)Time elapsed: 0.048 s
% 2.75/2.01 % (5634)Instructions burned: 150 (million)
% 2.75/2.01 % (5634)------------------------------
% 2.75/2.01 % (5634)------------------------------
% 2.75/2.01 % (5662)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/62Mi)
% 2.75/2.01 % (5663)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/31Mi)
% 5.64/2.02 % (5668)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/96Mi)
% 5.64/2.02 % (5663)Instruction limit reached!
% 5.64/2.02 % (5663)------------------------------
% 5.64/2.02 % (5663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.02 % (5663)Termination reason: Unknown
% 5.64/2.02 % (5663)Termination phase: Preprocessing 2
% 5.64/2.02
% 5.64/2.02 % (5663)Memory used [KB]: 1535
% 5.64/2.02 % (5663)Time elapsed: 0.011 s
% 5.64/2.02 % (5663)Instructions burned: 34 (million)
% 5.64/2.02 % (5663)------------------------------
% 5.64/2.02 % (5663)------------------------------
% 5.64/2.03 % (5662)Instruction limit reached!
% 5.64/2.03 % (5662)------------------------------
% 5.64/2.03 % (5662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.03 % (5662)Termination reason: Unknown
% 5.64/2.03 % (5662)Termination phase: Property scanning
% 5.64/2.03
% 5.64/2.03 % (5662)Memory used [KB]: 1918
% 5.64/2.03 % (5662)Time elapsed: 0.017 s
% 5.64/2.03 % (5662)Instructions burned: 62 (million)
% 5.64/2.03 % (5662)------------------------------
% 5.64/2.03 % (5662)------------------------------
% 5.64/2.03 % (5673)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/453Mi)
% 5.64/2.04 % (5674)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/71Mi)
% 5.64/2.04 % (5612)Instruction limit reached!
% 5.64/2.04 % (5612)------------------------------
% 5.64/2.04 % (5612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.04 % (5612)Termination reason: Unknown
% 5.64/2.04 % (5612)Termination phase: Saturation
% 5.64/2.04
% 5.64/2.04 % (5612)Memory used [KB]: 7164
% 5.64/2.04 % (5612)Time elapsed: 0.134 s
% 5.64/2.04 % (5612)Instructions burned: 449 (million)
% 5.64/2.04 % (5612)------------------------------
% 5.64/2.04 % (5612)------------------------------
% 5.64/2.05 % (5668)Instruction limit reached!
% 5.64/2.05 % (5668)------------------------------
% 5.64/2.05 % (5668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.05 % (5668)Termination reason: Unknown
% 5.64/2.05 % (5668)Termination phase: Saturation
% 5.64/2.05
% 5.64/2.05 % (5668)Memory used [KB]: 6524
% 5.64/2.05 % (5668)Time elapsed: 0.030 s
% 5.64/2.05 % (5668)Instructions burned: 98 (million)
% 5.64/2.05 % (5668)------------------------------
% 5.64/2.05 % (5668)------------------------------
% 5.64/2.05 % (5690)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/83Mi)
% 5.64/2.05 % (5692)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/11Mi)
% 5.64/2.06 % (5674)Instruction limit reached!
% 5.64/2.06 % (5674)------------------------------
% 5.64/2.06 % (5674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.06 % (5674)Termination reason: Unknown
% 5.64/2.06 % (5674)Termination phase: Property scanning
% 5.64/2.06
% 5.64/2.06 % (5674)Memory used [KB]: 1791
% 5.64/2.06 % (5674)Time elapsed: 0.022 s
% 5.64/2.06 % (5674)Instructions burned: 72 (million)
% 5.64/2.06 % (5674)------------------------------
% 5.64/2.06 % (5674)------------------------------
% 5.64/2.06 % (5692)Instruction limit reached!
% 5.64/2.06 % (5692)------------------------------
% 5.64/2.06 % (5692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.06 % (5692)Termination reason: Unknown
% 5.64/2.06 % (5692)Termination phase: shuffling
% 5.64/2.06
% 5.64/2.06 % (5692)Memory used [KB]: 1535
% 5.64/2.06 % (5692)Time elapsed: 0.004 s
% 5.64/2.06 % (5692)Instructions burned: 11 (million)
% 5.64/2.06 % (5692)------------------------------
% 5.64/2.06 % (5692)------------------------------
% 5.64/2.07 % (5701)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/41Mi)
% 5.64/2.07 % (5702)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/6Mi)
% 5.64/2.07 % (5702)Instruction limit reached!
% 5.64/2.07 % (5702)------------------------------
% 5.64/2.07 % (5702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.07 % (5702)Termination reason: Unknown
% 5.64/2.07 % (5702)Termination phase: shuffling
% 5.64/2.07
% 5.64/2.07 % (5702)Memory used [KB]: 1407
% 5.64/2.07 % (5702)Time elapsed: 0.004 s
% 5.64/2.07 % (5702)Instructions burned: 8 (million)
% 5.64/2.07 % (5702)------------------------------
% 5.64/2.07 % (5702)------------------------------
% 5.64/2.08 % (5690)Instruction limit reached!
% 5.64/2.08 % (5690)------------------------------
% 5.64/2.08 % (5690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.08 % (5690)Termination reason: Unknown
% 5.64/2.08 % (5690)Termination phase: Saturation
% 5.64/2.08
% 5.64/2.08 % (5690)Memory used [KB]: 6268
% 5.64/2.08 % (5690)Time elapsed: 0.026 s
% 5.64/2.08 % (5690)Instructions burned: 83 (million)
% 5.64/2.08 % (5690)------------------------------
% 5.64/2.08 % (5690)------------------------------
% 5.64/2.08 % (5701)Instruction limit reached!
% 5.64/2.08 % (5701)------------------------------
% 5.64/2.08 % (5701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.08 % (5701)Termination reason: Unknown
% 5.64/2.08 % (5701)Termination phase: Property scanning
% 5.64/2.08
% 5.64/2.08 % (5701)Memory used [KB]: 1791
% 5.64/2.08 % (5701)Time elapsed: 0.012 s
% 5.64/2.08 % (5701)Instructions burned: 41 (million)
% 5.64/2.08 % (5701)------------------------------
% 5.64/2.08 % (5701)------------------------------
% 5.64/2.08 % (5703)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/150Mi)
% 5.64/2.09 % (5711)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/109Mi)
% 5.64/2.09 % (5710)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_5305 for (2995ds/343Mi)
% 5.64/2.09 % (5628)Instruction limit reached!
% 5.64/2.09 % (5628)------------------------------
% 5.64/2.09 % (5628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.09 % (5628)Termination reason: Unknown
% 5.64/2.09 % (5628)Termination phase: Saturation
% 5.64/2.09
% 5.64/2.09 % (5628)Memory used [KB]: 7419
% 5.64/2.09 % (5628)Time elapsed: 0.152 s
% 5.64/2.09 % (5628)Instructions burned: 507 (million)
% 5.64/2.09 % (5628)------------------------------
% 5.64/2.09 % (5628)------------------------------
% 5.64/2.10 % (5721)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_5305 for (2994ds/253Mi)
% 6.18/2.12 % (5711)Instruction limit reached!
% 6.18/2.12 % (5711)------------------------------
% 6.18/2.12 % (5711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.12 % (5711)Termination reason: Unknown
% 6.18/2.12 % (5711)Termination phase: Saturation
% 6.18/2.12
% 6.18/2.12 % (5711)Memory used [KB]: 6652
% 6.18/2.12 % (5711)Time elapsed: 0.033 s
% 6.18/2.12 % (5711)Instructions burned: 109 (million)
% 6.18/2.12 % (5711)------------------------------
% 6.18/2.12 % (5711)------------------------------
% 6.18/2.13 % (5703)Instruction limit reached!
% 6.18/2.13 % (5703)------------------------------
% 6.18/2.13 % (5703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.13 % (5703)Termination reason: Unknown
% 6.18/2.13 % (5703)Termination phase: Saturation
% 6.18/2.13
% 6.18/2.13 % (5703)Memory used [KB]: 6780
% 6.18/2.13 % (5703)Time elapsed: 0.048 s
% 6.18/2.13 % (5703)Instructions burned: 150 (million)
% 6.18/2.13 % (5703)------------------------------
% 6.18/2.13 % (5703)------------------------------
% 6.18/2.13 % (5734)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_5305 for (2994ds/140Mi)
% 6.18/2.13 % (5657)Instruction limit reached!
% 6.18/2.13 % (5657)------------------------------
% 6.18/2.13 % (5657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.13 % (5657)Termination reason: Unknown
% 6.18/2.13 % (5657)Termination phase: Saturation
% 6.18/2.13
% 6.18/2.13 % (5657)Memory used [KB]: 3582
% 6.18/2.13 % (5657)Time elapsed: 0.133 s
% 6.18/2.13 % (5657)Instructions burned: 433 (million)
% 6.18/2.13 % (5657)------------------------------
% 6.18/2.13 % (5657)------------------------------
% 6.18/2.14 % (5739)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_5305 for (2994ds/614Mi)
% 6.18/2.14 % (5740)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_5305 for (2994ds/202Mi)
% 6.18/2.17 % (5673)Instruction limit reached!
% 6.18/2.17 % (5673)------------------------------
% 6.18/2.17 % (5673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.17 % (5673)Termination reason: Unknown
% 6.18/2.17 % (5673)Termination phase: Saturation
% 6.18/2.17
% 6.18/2.17 % (5673)Memory used [KB]: 7164
% 6.18/2.17 % (5673)Time elapsed: 0.137 s
% 6.18/2.17 % (5673)Instructions burned: 454 (million)
% 6.18/2.17 % (5673)------------------------------
% 6.18/2.17 % (5673)------------------------------
% 6.18/2.17 % (5734)Instruction limit reached!
% 6.18/2.17 % (5734)------------------------------
% 6.18/2.17 % (5734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.17 % (5734)Termination reason: Unknown
% 6.18/2.17 % (5734)Termination phase: Saturation
% 6.18/2.17
% 6.18/2.17 % (5734)Memory used [KB]: 6524
% 6.18/2.17 % (5734)Time elapsed: 0.044 s
% 6.18/2.17 % (5734)Instructions burned: 141 (million)
% 6.18/2.17 % (5734)------------------------------
% 6.18/2.17 % (5734)------------------------------
% 6.18/2.18 % (5754)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_5305 for (2994ds/339Mi)
% 6.18/2.18 % (5721)Instruction limit reached!
% 6.18/2.18 % (5721)------------------------------
% 6.18/2.18 % (5721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.18 % (5721)Termination reason: Unknown
% 6.18/2.18 % (5721)Termination phase: Saturation
% 6.18/2.18
% 6.18/2.18 % (5721)Memory used [KB]: 6652
% 6.18/2.18 % (5721)Time elapsed: 0.073 s
% 6.18/2.18 % (5721)Instructions burned: 254 (million)
% 6.18/2.18 % (5721)------------------------------
% 6.18/2.18 % (5721)------------------------------
% 6.18/2.18 % (5756)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_5305 for (2994ds/283Mi)
% 6.18/2.19 % (5761)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_5305 for (2994ds/134Mi)
% 6.66/2.20 % (5740)Instruction limit reached!
% 6.66/2.20 % (5740)------------------------------
% 6.66/2.20 % (5740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.20 % (5740)Termination reason: Unknown
% 6.66/2.20 % (5740)Termination phase: Saturation
% 6.66/2.20
% 6.66/2.20 % (5740)Memory used [KB]: 6652
% 6.66/2.20 % (5740)Time elapsed: 0.059 s
% 6.66/2.20 % (5740)Instructions burned: 204 (million)
% 6.66/2.20 % (5740)------------------------------
% 6.66/2.20 % (5740)------------------------------
% 6.66/2.21 % (5771)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_5305 for (2993ds/298Mi)
% 6.66/2.21 % (5710)Instruction limit reached!
% 6.66/2.21 % (5710)------------------------------
% 6.66/2.21 % (5710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.21 % (5710)Termination reason: Unknown
% 6.66/2.21 % (5710)Termination phase: Saturation
% 6.66/2.21
% 6.66/2.21 % (5710)Memory used [KB]: 6908
% 6.66/2.21 % (5710)Time elapsed: 0.119 s
% 6.66/2.21 % (5710)Instructions burned: 346 (million)
% 6.66/2.21 % (5710)------------------------------
% 6.66/2.21 % (5710)------------------------------
% 6.66/2.22 % (5775)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_5305 for (2993ds/192Mi)
% 6.66/2.23 % (5761)Instruction limit reached!
% 6.66/2.23 % (5761)------------------------------
% 6.66/2.23 % (5761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.23 % (5761)Termination reason: Unknown
% 6.66/2.23 % (5761)Termination phase: Saturation
% 6.66/2.23
% 6.66/2.23 % (5761)Memory used [KB]: 6652
% 6.66/2.23 % (5761)Time elapsed: 0.042 s
% 6.66/2.23 % (5761)Instructions burned: 136 (million)
% 6.66/2.23 % (5761)------------------------------
% 6.66/2.23 % (5761)------------------------------
% 6.66/2.24 % (5780)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_5305 for (2993ds/258Mi)
% 6.66/2.27 % (5756)Instruction limit reached!
% 6.66/2.27 % (5756)------------------------------
% 6.66/2.27 % (5756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.27 % (5756)Termination reason: Unknown
% 6.66/2.27 % (5756)Termination phase: Saturation
% 6.66/2.27
% 6.66/2.27 % (5756)Memory used [KB]: 7164
% 6.66/2.27 % (5756)Time elapsed: 0.087 s
% 6.66/2.27 % (5756)Instructions burned: 284 (million)
% 6.66/2.27 % (5756)------------------------------
% 6.66/2.27 % (5756)------------------------------
% 6.66/2.28 % (5797)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_5305 for (2993ds/90Mi)
% 6.66/2.28 % (5775)Instruction limit reached!
% 6.66/2.28 % (5775)------------------------------
% 6.66/2.28 % (5775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.28 % (5775)Termination reason: Unknown
% 6.66/2.28 % (5775)Termination phase: Saturation
% 6.66/2.28
% 6.66/2.28 % (5775)Memory used [KB]: 7419
% 6.66/2.28 % (5775)Time elapsed: 0.058 s
% 6.66/2.28 % (5775)Instructions burned: 194 (million)
% 6.66/2.28 % (5775)------------------------------
% 6.66/2.28 % (5775)------------------------------
% 6.66/2.28 % (5754)Instruction limit reached!
% 6.66/2.28 % (5754)------------------------------
% 6.66/2.28 % (5754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.28 % (5754)Termination reason: Unknown
% 6.66/2.28 % (5754)Termination phase: Saturation
% 6.66/2.28
% 6.66/2.28 % (5754)Memory used [KB]: 6652
% 6.66/2.28 % (5754)Time elapsed: 0.105 s
% 6.66/2.28 % (5754)Instructions burned: 342 (million)
% 6.66/2.28 % (5754)------------------------------
% 6.66/2.28 % (5754)------------------------------
% 6.66/2.29 % (5804)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_5305 for (2993ds/231Mi)
% 6.66/2.29 % (5806)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_5305 for (2993ds/458Mi)
% 6.66/2.30 % (5771)Instruction limit reached!
% 6.66/2.30 % (5771)------------------------------
% 6.66/2.30 % (5771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.30 % (5771)Termination reason: Unknown
% 6.66/2.30 % (5771)Termination phase: Saturation
% 6.66/2.30
% 6.66/2.30 % (5771)Memory used [KB]: 7803
% 6.66/2.30 % (5771)Time elapsed: 0.087 s
% 6.66/2.30 % (5771)Instructions burned: 298 (million)
% 6.66/2.30 % (5771)------------------------------
% 6.66/2.30 % (5771)------------------------------
% 7.30/2.30 % (5797)Instruction limit reached!
% 7.30/2.30 % (5797)------------------------------
% 7.30/2.30 % (5797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.30 % (5797)Termination reason: Unknown
% 7.30/2.30 % (5797)Termination phase: Saturation
% 7.30/2.30
% 7.30/2.30 % (5797)Memory used [KB]: 6524
% 7.30/2.30 % (5797)Time elapsed: 0.028 s
% 7.30/2.30 % (5797)Instructions burned: 92 (million)
% 7.30/2.30 % (5797)------------------------------
% 7.30/2.30 % (5797)------------------------------
% 7.30/2.31 % (5818)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_5305 for (2992ds/31Mi)
% 7.30/2.31 % (5646)Instruction limit reached!
% 7.30/2.31 % (5646)------------------------------
% 7.30/2.31 % (5646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.31 % (5646)Termination reason: Unknown
% 7.30/2.31 % (5646)Termination phase: Saturation
% 7.30/2.31
% 7.30/2.31 % (5646)Memory used [KB]: 7675
% 7.30/2.31 % (5646)Time elapsed: 0.328 s
% 7.30/2.31 % (5646)Instructions burned: 1087 (million)
% 7.30/2.31 % (5646)------------------------------
% 7.30/2.31 % (5646)------------------------------
% 7.30/2.31 % (5780)Instruction limit reached!
% 7.30/2.31 % (5780)------------------------------
% 7.30/2.31 % (5780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.31 % (5780)Termination reason: Unknown
% 7.30/2.31 % (5780)Termination phase: Saturation
% 7.30/2.31
% 7.30/2.31 % (5780)Memory used [KB]: 6524
% 7.30/2.31 % (5780)Time elapsed: 0.075 s
% 7.30/2.31 % (5780)Instructions burned: 259 (million)
% 7.30/2.31 % (5780)------------------------------
% 7.30/2.31 % (5780)------------------------------
% 7.30/2.31 % (5823)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_5305 for (2992ds/297Mi)
% 7.30/2.32 % (5818)Instruction limit reached!
% 7.30/2.32 % (5818)------------------------------
% 7.30/2.32 % (5818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.32 % (5818)Termination reason: Unknown
% 7.30/2.32 % (5818)Termination phase: shuffling
% 7.30/2.32
% 7.30/2.32 % (5818)Memory used [KB]: 1535
% 7.30/2.32 % (5818)Time elapsed: 0.011 s
% 7.30/2.32 % (5818)Instructions burned: 33 (million)
% 7.30/2.32 % (5818)------------------------------
% 7.30/2.32 % (5818)------------------------------
% 7.30/2.32 % (5828)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_5305 for (2992ds/987Mi)
% 7.30/2.32 % (5831)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_5305 for (2992ds/182Mi)
% 7.30/2.32 % (5836)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_5305 for (2992ds/182Mi)
% 7.30/2.33 % (5739)Instruction limit reached!
% 7.30/2.33 % (5739)------------------------------
% 7.30/2.33 % (5739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.33 % (5739)Termination reason: Unknown
% 7.30/2.33 % (5739)Termination phase: Saturation
% 7.30/2.33
% 7.30/2.33 % (5739)Memory used [KB]: 8059
% 7.30/2.33 % (5739)Time elapsed: 0.196 s
% 7.30/2.33 % (5739)Instructions burned: 616 (million)
% 7.30/2.33 % (5739)------------------------------
% 7.30/2.33 % (5739)------------------------------
% 7.30/2.34 % (5841)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_5305 for (2992ds/154Mi)
% 7.30/2.35 % (5804)Instruction limit reached!
% 7.30/2.35 % (5804)------------------------------
% 7.30/2.35 % (5804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.35 % (5804)Termination reason: Unknown
% 7.30/2.35 % (5804)Termination phase: Saturation
% 7.30/2.35
% 7.30/2.35 % (5804)Memory used [KB]: 7036
% 7.30/2.35 % (5804)Time elapsed: 0.089 s
% 7.30/2.35 % (5804)Instructions burned: 232 (million)
% 7.30/2.35 % (5804)------------------------------
% 7.30/2.35 % (5804)------------------------------
% 7.30/2.36 % (5846)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_5305 for (2992ds/79Mi)
% 7.30/2.38 % (5831)Instruction limit reached!
% 7.30/2.38 % (5831)------------------------------
% 7.30/2.38 % (5831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.38 % (5831)Termination reason: Unknown
% 7.30/2.38 % (5831)Termination phase: Saturation
% 7.30/2.38
% 7.30/2.38 % (5831)Memory used [KB]: 6780
% 7.30/2.38 % (5831)Time elapsed: 0.058 s
% 7.30/2.38 % (5831)Instructions burned: 184 (million)
% 7.30/2.38 % (5831)------------------------------
% 7.30/2.38 % (5831)------------------------------
% 7.30/2.38 % (5841)Refutation not found, incomplete strategy
% 7.30/2.38 % (5841)------------------------------
% 7.30/2.38 % (5841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.38 % (5841)Termination reason: Refutation not found, incomplete strategy
% 7.30/2.38
% 7.30/2.38
% 7.30/2.38 % (5841)Memory used [KB]: 6908
% 7.30/2.38 % (5841)Time elapsed: 0.038 s
% 7.30/2.38 % (5841)Instructions burned: 129 (million)
% 7.30/2.38 % (5841)------------------------------
% 7.30/2.38 % (5841)------------------------------
% 7.30/2.38 % (5836)Instruction limit reached!
% 7.30/2.38 % (5836)------------------------------
% 7.30/2.38 % (5836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.38 % (5836)Termination reason: Unknown
% 7.30/2.38 % (5836)Termination phase: Saturation
% 7.30/2.38
% 7.30/2.38 % (5836)Memory used [KB]: 6780
% 7.30/2.38 % (5836)Time elapsed: 0.058 s
% 7.30/2.38 % (5836)Instructions burned: 183 (million)
% 7.30/2.38 % (5836)------------------------------
% 7.30/2.38 % (5836)------------------------------
% 7.30/2.39 % (5847)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_5305 for (2992ds/216Mi)
% 7.30/2.39 % (5846)Instruction limit reached!
% 7.30/2.39 % (5846)------------------------------
% 7.30/2.39 % (5846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.30/2.39 % (5846)Termination reason: Unknown
% 7.30/2.39 % (5846)Termination phase: Saturation
% 7.30/2.39
% 7.30/2.39 % (5846)Memory used [KB]: 6396
% 7.30/2.39 % (5846)Time elapsed: 0.024 s
% 7.30/2.39 % (5846)Instructions burned: 80 (million)
% 7.30/2.39 % (5846)------------------------------
% 7.30/2.39 % (5846)------------------------------
% 7.30/2.39 % (5848)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_5305 for (2992ds/114Mi)
% 7.30/2.39 % (5849)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_5305 for (2991ds/922Mi)
% 7.30/2.40 % (5850)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_5305 for (2991ds/182Mi)
% 8.04/2.40 % (5823)Instruction limit reached!
% 8.04/2.40 % (5823)------------------------------
% 8.04/2.40 % (5823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.40 % (5823)Termination reason: Unknown
% 8.04/2.40 % (5823)Termination phase: Saturation
% 8.04/2.40
% 8.04/2.40 % (5823)Memory used [KB]: 6908
% 8.04/2.40 % (5823)Time elapsed: 0.109 s
% 8.04/2.40 % (5823)Instructions burned: 297 (million)
% 8.04/2.40 % (5823)------------------------------
% 8.04/2.40 % (5823)------------------------------
% 8.04/2.41 % (5851)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_5305 for (2991ds/164Mi)
% 8.04/2.41 % (5806)First to succeed.
% 8.04/2.41 % (5806)Refutation found. Thanks to Tanya!
% 8.04/2.41 % SZS status Theorem for DTF2THF_5305
% 8.04/2.41 % SZS output start Proof for DTF2THF_5305
% 8.04/2.41 thf(type_def_6, type, set: ($tType) > $tType).
% 8.04/2.41 thf(type_def_7, type, a: $tType).
% 8.04/2.41 thf(func_def_0, type, set: ($tType) > $tType).
% 8.04/2.41 thf(func_def_1, type, a: $tType).
% 8.04/2.41 thf(func_def_2, type, bounded_lattice: !>[X0: $tType]:($o)).
% 8.04/2.41 thf(func_def_3, type, type: !>[X0: $tType]:($o)).
% 8.04/2.41 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 8.04/2.41 thf(func_def_5, type, semilattice_inf: !>[X0: $tType]:($o)).
% 8.04/2.41 thf(func_def_6, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 8.04/2.41 thf(func_def_7, type, condit2040224947_above: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 8.04/2.41 thf(func_def_8, type, condit1201339847_below: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 8.04/2.41 thf(func_def_9, type, finite_comp_fun_idem: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > $o)).
% 8.04/2.41 thf(func_def_10, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 8.04/2.41 thf(func_def_11, type, abel_semigroup: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 8.04/2.41 thf(func_def_12, type, semigroup: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 8.04/2.41 thf(func_def_13, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 8.04/2.41 thf(func_def_14, type, semilattice: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 8.04/2.41 thf(func_def_15, type, lattic1263571978nf_fin: !>[X0: $tType]:((X0 > X0 > X0) > set @ X0 > X0)).
% 8.04/2.41 thf(func_def_16, type, lattic35693393ce_set: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 8.04/2.41 thf(func_def_17, type, lattic1039401930up_fin: !>[X0: $tType]:((X0 > X0 > X0) > set @ X0 > X0)).
% 8.04/2.41 thf(func_def_18, type, modula105138637_a_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.04/2.41 thf(func_def_19, type, modula477145868_b_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.04/2.41 thf(func_def_20, type, modula849153099_c_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.04/2.41 thf(func_def_21, type, modula1221160330_d_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.04/2.41 thf(func_def_22, type, modula1593167561_e_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.04/2.41 thf(func_def_23, type, modula1937309406incomp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 8.04/2.41 thf(func_def_24, type, bot_bot: !>[X0: $tType]:(X0)).
% 8.04/2.41 thf(func_def_25, type, least: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 8.04/2.41 thf(func_def_26, type, max: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 8.04/2.41 thf(func_def_27, type, min: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 8.04/2.41 thf(func_def_28, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 8.04/2.41 thf(func_def_29, type, greatest: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 8.04/2.41 thf(func_def_30, type, antimono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 8.04/2.41 thf(func_def_31, type, mono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 8.04/2.41 thf(func_def_32, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 8.04/2.41 thf(func_def_33, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 8.04/2.41 thf(func_def_34, type, set_atLeast: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 8.04/2.41 thf(func_def_35, type, set_atMost: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 8.04/2.41 thf(func_def_36, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 8.04/2.41 thf(func_def_37, type, a2: a).
% 8.04/2.41 thf(func_def_38, type, b: a).
% 8.04/2.41 thf(func_def_39, type, c: a).
% 8.04/2.41 thf(func_def_40, type, inf: a > a > a).
% 8.04/2.41 thf(func_def_41, type, less_eq: a > a > $o).
% 8.04/2.41 thf(func_def_42, type, sup: a > a > a).
% 8.04/2.41 thf(func_def_57, type, sK0: (a > a > a) > a).
% 8.04/2.41 thf(func_def_58, type, sK1: (a > a > a) > a).
% 8.04/2.41 thf(func_def_59, type, sK2: (a > a > a) > a).
% 8.04/2.41 thf(func_def_60, type, sK3: (a > a > a) > a).
% 8.04/2.41 thf(func_def_61, type, sK4: (a > a > a) > a).
% 8.04/2.41 thf(func_def_62, type, sK5: (a > a > a) > a).
% 8.04/2.41 thf(func_def_63, type, sK6: (a > a > a) > a).
% 8.04/2.41 thf(func_def_64, type, sK7: (a > a > a) > a).
% 8.04/2.41 thf(func_def_65, type, sK8: (a > a > a) > a).
% 8.04/2.41 thf(func_def_66, type, sK9: (a > a > a) > a).
% 8.04/2.41 thf(func_def_67, type, sK10: (a > a > a) > a).
% 8.04/2.41 thf(func_def_68, type, sK11: (a > a > a) > a).
% 8.04/2.41 thf(func_def_69, type, sK12: (a > a > a) > a).
% 8.04/2.41 thf(func_def_70, type, sK13: (a > a > a) > a).
% 8.04/2.41 thf(func_def_71, type, sK14: a).
% 8.04/2.41 thf(func_def_72, type, sK15: a).
% 8.04/2.41 thf(func_def_73, type, sK16: a).
% 8.04/2.41 thf(func_def_74, type, sK17: a).
% 8.04/2.41 thf(func_def_75, type, sK18: a).
% 8.04/2.41 thf(func_def_76, type, sK19: a).
% 8.04/2.41 thf(func_def_77, type, sK20: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 8.04/2.41 thf(func_def_79, type, ph22: !>[X0: $tType]:(X0)).
% 8.04/2.41 thf(f1293,plain,(
% 8.04/2.41 $false),
% 8.04/2.41 inference(subsumption_resolution,[status(thm)],[f1292,f969])).
% 8.04/2.41 thf(f969,plain,(
% 8.04/2.41 ($true = (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f968,f888])).
% 8.04/2.41 thf(f888,plain,(
% 8.04/2.41 ( ! [X0 : a,X1 : a] : (((inf @ X0 @ X1) = (inf @ X1 @ X0))) )),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f701])).
% 8.04/2.41 thf(f701,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a] : ((inf @ X0 @ X1) = (inf @ X1 @ X0))),
% 8.04/2.41 inference(rectify,[status(thm)],[f15])).
% 8.04/2.41 thf(f15,axiom,(
% 8.04/2.41 ! [X5 : a,X4 : a] : ((inf @ X5 @ X4) = (inf @ X4 @ X5))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',fact_14_local_Oinf_Ocommute)).
% 8.04/2.41 thf(f968,plain,(
% 8.04/2.41 ($true = (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f967,f929])).
% 8.04/2.41 thf(f929,plain,(
% 8.04/2.41 ( ! [X0 : a,X1 : a] : (((sup @ X0 @ X1) = (sup @ X1 @ X0))) )),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f725])).
% 8.04/2.41 thf(f725,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a] : ((sup @ X0 @ X1) = (sup @ X1 @ X0))),
% 8.04/2.41 inference(rectify,[status(thm)],[f24])).
% 8.04/2.41 thf(f24,axiom,(
% 8.04/2.41 ! [X2 : a,X3 : a] : ((sup @ X2 @ X3) = (sup @ X3 @ X2))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',fact_23_local_Osup__commute)).
% 8.04/2.41 thf(f967,plain,(
% 8.04/2.41 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))) = $true)),
% 8.04/2.41 inference(backward_demodulation,[status(thm)],[f966,f888])).
% 8.04/2.41 thf(f966,plain,(
% 8.04/2.41 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))) = $true)),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f965,f929])).
% 8.04/2.41 thf(f965,plain,(
% 8.04/2.41 ($true = (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f964,f857])).
% 8.04/2.41 thf(f857,plain,(
% 8.04/2.41 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ (inf @ X0 @ X1) @ X2) = (inf @ X0 @ (inf @ X1 @ X2)))) )),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f705])).
% 8.04/2.41 thf(f705,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a,X2 : a] : ((inf @ (inf @ X0 @ X1) @ X2) = (inf @ X0 @ (inf @ X1 @ X2)))),
% 8.04/2.41 inference(rectify,[status(thm)],[f14])).
% 8.04/2.41 thf(f14,axiom,(
% 8.04/2.41 ! [X5 : a,X4 : a,X10 : a] : ((inf @ (inf @ X5 @ X4) @ X10) = (inf @ X5 @ (inf @ X4 @ X10)))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',fact_13_local_Oinf_Oassoc)).
% 8.04/2.41 thf(f964,plain,(
% 8.04/2.41 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2))) = $true)),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f963,f933])).
% 8.04/2.41 thf(f933,plain,(
% 8.04/2.41 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ (inf @ (sup @ X0 @ X1) @ (sup @ X1 @ X2)) @ (sup @ X2 @ X0)) = (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2))) )),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f691])).
% 8.04/2.41 thf(f691,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a,X2 : a] : ((inf @ (inf @ (sup @ X0 @ X1) @ (sup @ X1 @ X2)) @ (sup @ X2 @ X0)) = (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2))),
% 8.04/2.41 inference(rectify,[status(thm)],[f94])).
% 8.04/2.41 thf(f94,axiom,(
% 8.04/2.41 ! [X5 : a,X4 : a,X10 : a] : ((modula1593167561_e_aux @ a @ inf @ sup @ X5 @ X4 @ X10) = (inf @ (inf @ (sup @ X5 @ X4) @ (sup @ X4 @ X10)) @ (sup @ X10 @ X5)))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',fact_93_local_Oe__aux__def)).
% 8.04/2.41 thf(f963,plain,(
% 8.04/2.41 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f962,f929])).
% 8.04/2.41 thf(f962,plain,(
% 8.04/2.41 ($true = (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ c @ a2) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f961,f894])).
% 8.04/2.41 thf(f894,plain,(
% 8.04/2.41 ( ! [X2 : a,X0 : a,X1 : a] : (((sup @ X1 @ (sup @ X0 @ X2)) = (sup @ X0 @ (sup @ X1 @ X2)))) )),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f724])).
% 8.04/2.41 thf(f724,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a,X2 : a] : ((sup @ X1 @ (sup @ X0 @ X2)) = (sup @ X0 @ (sup @ X1 @ X2)))),
% 8.04/2.41 inference(rectify,[status(thm)],[f22])).
% 8.04/2.41 thf(f22,axiom,(
% 8.04/2.41 ! [X4 : a,X5 : a,X10 : a] : ((sup @ X5 @ (sup @ X4 @ X10)) = (sup @ X4 @ (sup @ X5 @ X10)))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',fact_21_local_Osup_Oleft__commute)).
% 8.04/2.41 thf(f961,plain,(
% 8.04/2.41 ($true = (less_eq @ (sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f960,f929])).
% 8.04/2.41 thf(f960,plain,(
% 8.04/2.41 ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f910,f862])).
% 8.04/2.41 thf(f862,plain,(
% 8.04/2.41 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (sup @ (sup @ (inf @ X0 @ X1) @ (inf @ X1 @ X2)) @ (inf @ X2 @ X0)))) )),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f731])).
% 8.04/2.41 thf(f731,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a,X2 : a] : ((modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (sup @ (sup @ (inf @ X0 @ X1) @ (inf @ X1 @ X2)) @ (inf @ X2 @ X0)))),
% 8.04/2.41 inference(rectify,[status(thm)],[f88])).
% 8.04/2.41 thf(f88,axiom,(
% 8.04/2.41 ! [X5 : a,X4 : a,X10 : a] : ((modula1221160330_d_aux @ a @ inf @ sup @ X5 @ X4 @ X10) = (sup @ (sup @ (inf @ X5 @ X4) @ (inf @ X4 @ X10)) @ (inf @ X10 @ X5)))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',fact_87_local_Od__aux__def)).
% 8.04/2.41 thf(f910,plain,(
% 8.04/2.41 ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f602])).
% 8.04/2.41 thf(f602,plain,(
% 8.04/2.41 ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.04/2.41 inference(fool_elimination,[status(thm)],[f601])).
% 8.04/2.41 thf(f601,plain,(
% 8.04/2.41 (less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c))),
% 8.04/2.41 inference(rectify,[status(thm)],[f269])).
% 8.04/2.41 thf(f269,axiom,(
% 8.04/2.41 (less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',conj_0)).
% 8.04/2.41 thf(f1292,plain,(
% 8.04/2.41 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1291,f888])).
% 8.04/2.41 thf(f1291,plain,(
% 8.04/2.41 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1290,f929])).
% 8.04/2.41 thf(f1290,plain,(
% 8.04/2.41 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1289,f920])).
% 8.04/2.41 thf(f920,plain,(
% 8.04/2.41 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (inf @ X0 @ X2)))) )),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f700])).
% 8.04/2.41 thf(f700,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a,X2 : a] : ((inf @ X0 @ (inf @ X1 @ X2)) = (inf @ X1 @ (inf @ X0 @ X2)))),
% 8.04/2.41 inference(rectify,[status(thm)],[f19])).
% 8.04/2.41 thf(f19,axiom,(
% 8.04/2.41 ! [X2 : a,X3 : a,X13 : a] : ((inf @ X2 @ (inf @ X3 @ X13)) = (inf @ X3 @ (inf @ X2 @ X13)))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',fact_18_local_Oinf__left__commute)).
% 8.04/2.41 thf(f1289,plain,(
% 8.04/2.41 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ b @ c) @ (inf @ (sup @ a2 @ b) @ (sup @ c @ a2)))) != $true)),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1288,f888])).
% 8.04/2.41 thf(f1288,plain,(
% 8.04/2.41 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ b @ c) @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b)))))),
% 8.04/2.41 inference(trivial_inequality_removal,[status(thm)],[f1287])).
% 8.04/2.41 thf(f1287,plain,(
% 8.04/2.41 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ b @ c) @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b))))) | ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1286,f888])).
% 8.04/2.41 thf(f1286,plain,(
% 8.04/2.41 ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) | ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ b @ c) @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1285,f929])).
% 8.04/2.41 thf(f1285,plain,(
% 8.04/2.41 ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) | ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ b @ c) @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1284,f920])).
% 8.04/2.41 thf(f1284,plain,(
% 8.04/2.41 ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (inf @ (sup @ b @ c) @ (inf @ (sup @ a2 @ b) @ (sup @ c @ a2)))) | ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ b @ c) @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1283,f888])).
% 8.04/2.41 thf(f1283,plain,(
% 8.04/2.41 ((inf @ (sup @ b @ c) @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) | ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ b @ c) @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b)))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1282,f888])).
% 8.04/2.41 thf(f1282,plain,(
% 8.04/2.41 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b)) @ (sup @ b @ c)))) | ((inf @ (sup @ b @ c) @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b))) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1281,f888])).
% 8.04/2.41 thf(f1281,plain,(
% 8.04/2.41 ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))) != (inf @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b)) @ (sup @ b @ c))) | ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b)) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1280,f933])).
% 8.04/2.41 thf(f1280,plain,(
% 8.04/2.41 ((modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) | ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (inf @ (sup @ c @ a2) @ (sup @ a2 @ b)) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1279,f933])).
% 8.04/2.41 thf(f1279,plain,(
% 8.04/2.41 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b))) | ((modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1278,f929])).
% 8.04/2.41 thf(f1278,plain,(
% 8.04/2.41 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b))) | ((modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1277,f888])).
% 8.04/2.41 thf(f1277,plain,(
% 8.04/2.41 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b))) | ((modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1276,f894])).
% 8.04/2.41 thf(f1276,plain,(
% 8.04/2.41 ((less_eq @ (sup @ (inf @ b @ c) @ (sup @ (inf @ a2 @ b) @ (inf @ c @ a2))) @ (modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b)) != $true) | ((modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1275,f929])).
% 8.04/2.41 thf(f1275,plain,(
% 8.04/2.41 ((less_eq @ (sup @ (inf @ b @ c) @ (sup @ (inf @ c @ a2) @ (inf @ a2 @ b))) @ (modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b)) != $true) | ((modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1274,f929])).
% 8.04/2.41 thf(f1274,plain,(
% 8.04/2.41 ((less_eq @ (sup @ (sup @ (inf @ c @ a2) @ (inf @ a2 @ b)) @ (inf @ b @ c)) @ (modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b)) != $true) | ((modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f1266,f862])).
% 8.04/2.41 thf(f1266,plain,(
% 8.04/2.41 ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b)) != $true) | ((modula1593167561_e_aux @ a @ inf @ sup @ c @ a2 @ b) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(superposition,[status(thm)],[f975,f1020])).
% 8.04/2.41 thf(f1020,plain,(
% 8.04/2.41 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (sup @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula105138637_a_aux @ a @ inf @ sup @ X1 @ X2 @ X0))) | ($true != (less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)))) )),
% 8.04/2.41 inference(superposition,[status(thm)],[f872,f833])).
% 8.04/2.41 thf(f833,plain,(
% 8.04/2.41 ( ! [X2 : a,X0 : a,X1 : a] : (((modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (modula105138637_a_aux @ a @ inf @ sup @ X1 @ X2 @ X0))) )),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f690])).
% 8.04/2.41 thf(f690,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a,X2 : a] : ((modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (modula105138637_a_aux @ a @ inf @ sup @ X1 @ X2 @ X0))),
% 8.04/2.41 inference(rectify,[status(thm)],[f134])).
% 8.04/2.41 thf(f134,axiom,(
% 8.04/2.41 ! [X5 : a,X4 : a,X10 : a] : ((modula477145868_b_aux @ a @ inf @ sup @ X5 @ X4 @ X10) = (modula105138637_a_aux @ a @ inf @ sup @ X4 @ X10 @ X5))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',fact_133_local_Ob__a)).
% 8.04/2.41 thf(f872,plain,(
% 8.04/2.41 ( ! [X2 : a,X0 : a,X1 : a] : (((sup @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) = (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) | ($true != (less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)))) )),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f783])).
% 8.04/2.41 thf(f783,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a,X2 : a] : (($true != (less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2))) | ((sup @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) = (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)))),
% 8.04/2.41 inference(ennf_transformation,[status(thm)],[f510])).
% 8.04/2.41 thf(f510,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a,X2 : a] : (($true = (less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2))) => ((sup @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) = (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)))),
% 8.04/2.41 inference(fool_elimination,[status(thm)],[f509])).
% 8.04/2.41 thf(f509,plain,(
% 8.04/2.41 ! [X0 : a,X1 : a,X2 : a] : ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) => ((sup @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) = (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)))),
% 8.04/2.41 inference(rectify,[status(thm)],[f137])).
% 8.04/2.41 thf(f137,axiom,(
% 8.04/2.41 ! [X5 : a,X4 : a,X10 : a] : ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ X5 @ X4 @ X10) @ (modula1593167561_e_aux @ a @ inf @ sup @ X5 @ X4 @ X10)) => ((modula1593167561_e_aux @ a @ inf @ sup @ X5 @ X4 @ X10) = (sup @ (modula105138637_a_aux @ a @ inf @ sup @ X5 @ X4 @ X10) @ (modula477145868_b_aux @ a @ inf @ sup @ X5 @ X4 @ X10))))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',fact_136_a__join__b__eq__e)).
% 8.04/2.41 thf(f975,plain,(
% 8.04/2.41 ((sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f974,f888])).
% 8.04/2.41 thf(f974,plain,(
% 8.04/2.41 ((sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f973,f929])).
% 8.04/2.41 thf(f973,plain,(
% 8.04/2.41 ((sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f972,f888])).
% 8.04/2.41 thf(f972,plain,(
% 8.04/2.41 ((sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)) != (inf @ (sup @ a2 @ b) @ (inf @ (sup @ c @ a2) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f971,f920])).
% 8.04/2.41 thf(f971,plain,(
% 8.04/2.41 ((sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)) != (inf @ (sup @ c @ a2) @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c))))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f970,f888])).
% 8.04/2.41 thf(f970,plain,(
% 8.04/2.41 ((sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)) != (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2)))),
% 8.04/2.41 inference(forward_demodulation,[status(thm)],[f918,f933])).
% 8.04/2.41 thf(f918,plain,(
% 8.04/2.41 ((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) != (sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.04/2.41 inference(cnf_transformation,[status(thm)],[f687])).
% 8.04/2.41 thf(f687,plain,(
% 8.04/2.41 ((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) != (sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.04/2.41 inference(flattening,[status(thm)],[f271])).
% 8.04/2.41 thf(f271,negated_conjecture,(
% 8.04/2.41 ~((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) = (sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.04/2.41 inference(negated_conjecture,[status(cth)],[f270])).
% 8.04/2.41 thf(f270,conjecture,(
% 8.04/2.41 ((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c) = (sup @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b) @ (modula105138637_a_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.04/2.41 file('/export/starexec/sandbox/tmp/tmp.upp1pXjEwW/DTF2THF_5305.p',conj_1)).
% 8.04/2.41 % SZS output end Proof for DTF2THF_5305
% 8.04/2.41 % (5806)------------------------------
% 8.04/2.41 % (5806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.41 % (5806)Termination reason: Refutation
% 8.04/2.41
% 8.04/2.41 % (5806)Memory used [KB]: 6652
% 8.04/2.41 % (5806)Time elapsed: 0.122 s
% 8.04/2.41 % (5806)Instructions burned: 401 (million)
% 8.04/2.41 % (5806)------------------------------
% 8.04/2.41 % (5806)------------------------------
% 8.04/2.41 % (5508)Success in time 0.832 s
%------------------------------------------------------------------------------