%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP120^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:43 AM UTC 2026
% Result : Theorem 8.27s 2.56s
% Output : Refutation 8.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP120^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:27:10 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ITP120^2 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46 % Domain : Interactive Theorem Proving
% 0.31/0.46 % Problem : Sledgehammer Modular_Distrib_Lattice problem prob_203__3262370_1
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Des21]
% 0.31/0.46 % Names : Modular_Distrib_Lattice/prob_203__3262370_1 [Des21]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0
% 0.31/0.46 % Syntax : Number of formulae : 322 ( 125 unt; 42 typ; 0 def)
% 0.31/0.46 % Number of atoms : 709 ( 195 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.31/0.46 % Number of connectives : 2527 ( 22 ~; 2 |; 34 &;2169 @)
% 0.31/0.46 % ( 0 <=>; 300 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 17 ( 6 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 213 ( 213 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 44 ( 41 usr; 5 con; 0-6 aty)
% 0.31/0.46 % Number of variables : 824 ( 48 ^; 733 !; 6 ?; 824 :)
% 0.31/0.46 % ( 37 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.46 % SPC : TH1_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:29:28.434
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % Could-be-implicit typings (2)
% 0.31/0.46 thf(ty_t_Set_Oset,type,
% 0.31/0.46 set: $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_tf_a,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 % Explicit typings (40)
% 0.31/0.46 thf(sy_cl_HOL_Otype,type,
% 0.31/0.46 type:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.31/0.46 ord:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.31/0.46 order:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Lattices_Olattice,type,
% 0.31/0.46 lattice:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/0.46 linorder:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.31/0.46 preorder:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.31/0.46 semilattice_inf:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.31/0.46 semilattice_sup:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above,type,
% 0.31/0.46 condit2040224947_above:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below,type,
% 0.31/0.46 condit1201339847_below:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ocomp__fun__idem,type,
% 0.31/0.46 finite_comp_fun_idem:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( A > B > B ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite,type,
% 0.31/0.46 finite_finite:
% 0.31/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Groups_Oabel__semigroup,type,
% 0.31/0.46 abel_semigroup:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Groups_Osemigroup,type,
% 0.31/0.46 semigroup:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_If,type,
% 0.31/0.46 if:
% 0.31/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.31/0.46 inf_inf:
% 0.31/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osemilattice,type,
% 0.31/0.46 semilattice:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.31/0.46 sup_sup:
% 0.31/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices__Big_Osemilattice__set,type,
% 0.31/0.46 lattic35693393ce_set:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oa__aux,type,
% 0.31/0.46 modula105138637_a_aux:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Ob__aux,type,
% 0.31/0.46 modula477145868_b_aux:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oc__aux,type,
% 0.31/0.46 modula849153099_c_aux:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Od__aux,type,
% 0.31/0.46 modula1221160330_d_aux:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oe__aux,type,
% 0.31/0.46 modula1593167561_e_aux:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oincomp,type,
% 0.31/0.46 modula1937309406incomp:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord_OLeast,type,
% 0.31/0.46 least:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord_Omax,type,
% 0.31/0.46 max:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord_Omin,type,
% 0.31/0.46 min:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/0.46 ord_less_eq:
% 0.31/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oorder_OGreatest,type,
% 0.31/0.46 greatest:
% 0.31/0.46 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oorder_Oantimono,type,
% 0.31/0.46 antimono:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oorder_Omono,type,
% 0.31/0.46 mono:
% 0.31/0.46 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect,type,
% 0.31/0.46 collect:
% 0.31/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member,type,
% 0.31/0.46 member:
% 0.31/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_a,type,
% 0.31/0.46 a2: a ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_b,type,
% 0.31/0.46 b: a ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_c,type,
% 0.31/0.46 c: a ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_inf,type,
% 0.31/0.46 inf: a > a > a ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_less__eq,type,
% 0.31/0.46 less_eq: a > a > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_sup,type,
% 0.31/0.46 sup: a > a > a ).
% 0.31/0.46
% 0.31/0.46 % Relevant facts (256)
% 0.31/0.46 thf(fact_0_local_Oantisym,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ( less_eq @ Y @ X )
% 0.31/0.46 => ( X = Y ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.antisym
% 0.31/0.46 thf(fact_1_local_Oantisym__conv,axiom,
% 0.31/0.46 ! [Y: a,X: a] :
% 0.31/0.46 ( ( less_eq @ Y @ X )
% 0.31/0.46 => ( ( less_eq @ X @ Y )
% 0.31/0.46 = ( X = Y ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.antisym_conv
% 0.31/0.46 thf(fact_2_local_Odual__order_Oantisym,axiom,
% 0.31/0.46 ! [B2: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 => ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( A2 = B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.dual_order.antisym
% 0.31/0.46 thf(fact_3_local_Odual__order_Oeq__iff,axiom,
% 0.31/0.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.31/0.46 = ( ^ [A3: a,B3: a] :
% 0.31/0.46 ( ( less_eq @ B3 @ A3 )
% 0.31/0.46 & ( less_eq @ A3 @ B3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.dual_order.eq_iff
% 0.31/0.46 thf(fact_4_local_Odual__order_Otrans,axiom,
% 0.31/0.46 ! [B2: a,A2: a,C: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 => ( ( less_eq @ C @ B2 )
% 0.31/0.46 => ( less_eq @ C @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.dual_order.trans
% 0.31/0.46 thf(fact_5_local_Oeq__iff,axiom,
% 0.31/0.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.31/0.46 = ( ^ [X2: a,Y3: a] :
% 0.31/0.46 ( ( less_eq @ X2 @ Y3 )
% 0.31/0.46 & ( less_eq @ Y3 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.eq_iff
% 0.31/0.46 thf(fact_6_local_Oeq__refl,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( X = Y )
% 0.31/0.46 => ( less_eq @ X @ Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.eq_refl
% 0.31/0.46 thf(fact_7_local_Oord__eq__le__trans,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( A2 = B2 )
% 0.31/0.46 => ( ( less_eq @ B2 @ C )
% 0.31/0.46 => ( less_eq @ A2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.ord_eq_le_trans
% 0.31/0.46 thf(fact_8_local_Oord__le__eq__trans,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( B2 = C )
% 0.31/0.46 => ( less_eq @ A2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.ord_le_eq_trans
% 0.31/0.46 thf(fact_9_local_Oorder_Oantisym,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 => ( A2 = B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.order.antisym
% 0.31/0.46 thf(fact_10_local_Oorder_Oeq__iff,axiom,
% 0.31/0.46 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 0.31/0.46 = ( ^ [A3: a,B3: a] :
% 0.31/0.46 ( ( less_eq @ A3 @ B3 )
% 0.31/0.46 & ( less_eq @ B3 @ A3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.order.eq_iff
% 0.31/0.46 thf(fact_11_local_Oorder_Otrans,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( less_eq @ B2 @ C )
% 0.31/0.46 => ( less_eq @ A2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.order.trans
% 0.31/0.46 thf(fact_12_local_Oorder__trans,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ( less_eq @ Y @ Z2 )
% 0.31/0.46 => ( less_eq @ X @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.order_trans
% 0.31/0.46 thf(fact_13_local_Oinf_Oassoc,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( inf @ ( inf @ A2 @ B2 ) @ C )
% 0.31/0.46 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.assoc
% 0.31/0.46 thf(fact_14_local_Oinf_Ocommute,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( inf @ A2 @ B2 )
% 0.31/0.46 = ( inf @ B2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.commute
% 0.31/0.46 thf(fact_15_local_Oinf_Oleft__commute,axiom,
% 0.31/0.46 ! [B2: a,A2: a,C: a] :
% 0.31/0.46 ( ( inf @ B2 @ ( inf @ A2 @ C ) )
% 0.31/0.46 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.left_commute
% 0.31/0.46 thf(fact_16_local_Oinf__assoc,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ( inf @ ( inf @ X @ Y ) @ Z2 )
% 0.31/0.46 = ( inf @ X @ ( inf @ Y @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_assoc
% 0.31/0.46 thf(fact_17_local_Oinf__commute,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( inf @ X @ Y )
% 0.31/0.46 = ( inf @ Y @ X ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_commute
% 0.31/0.46 thf(fact_18_local_Oinf__left__commute,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ( inf @ X @ ( inf @ Y @ Z2 ) )
% 0.31/0.46 = ( inf @ Y @ ( inf @ X @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_left_commute
% 0.31/0.46 thf(fact_19_local_Osup_Oassoc,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( sup @ ( sup @ A2 @ B2 ) @ C )
% 0.31/0.46 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.assoc
% 0.31/0.46 thf(fact_20_local_Osup_Ocommute,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( sup @ A2 @ B2 )
% 0.31/0.46 = ( sup @ B2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.commute
% 0.31/0.46 thf(fact_21_local_Osup_Oleft__commute,axiom,
% 0.31/0.46 ! [B2: a,A2: a,C: a] :
% 0.31/0.46 ( ( sup @ B2 @ ( sup @ A2 @ C ) )
% 0.31/0.46 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.left_commute
% 0.31/0.46 thf(fact_22_local_Osup__assoc,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ( sup @ ( sup @ X @ Y ) @ Z2 )
% 0.31/0.46 = ( sup @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_assoc
% 0.31/0.46 thf(fact_23_local_Osup__commute,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( sup @ X @ Y )
% 0.31/0.46 = ( sup @ Y @ X ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_commute
% 0.31/0.46 thf(fact_24_local_Osup__left__commute,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ( sup @ X @ ( sup @ Y @ Z2 ) )
% 0.31/0.46 = ( sup @ Y @ ( sup @ X @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_left_commute
% 0.31/0.46 thf(fact_25_local_Oinf_Oabsorb1,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( inf @ A2 @ B2 )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.absorb1
% 0.31/0.46 thf(fact_26_local_Oinf_Oabsorb2,axiom,
% 0.31/0.46 ! [B2: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 => ( ( inf @ A2 @ B2 )
% 0.31/0.46 = B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.absorb2
% 0.31/0.46 thf(fact_27_local_Oinf_Oabsorb__iff1,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 = ( ( inf @ A2 @ B2 )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.absorb_iff1
% 0.31/0.46 thf(fact_28_local_Oinf_Oabsorb__iff2,axiom,
% 0.31/0.46 ! [B2: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 = ( ( inf @ A2 @ B2 )
% 0.31/0.46 = B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.absorb_iff2
% 0.31/0.46 thf(fact_29_local_Oinf_OboundedE,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 0.31/0.46 => ~ ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ~ ( less_eq @ A2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.boundedE
% 0.31/0.46 thf(fact_30_local_Oinf_OboundedI,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( less_eq @ A2 @ C )
% 0.31/0.46 => ( less_eq @ A2 @ ( inf @ B2 @ C ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.boundedI
% 0.31/0.46 thf(fact_31_local_Oinf_Ocobounded1,axiom,
% 0.31/0.46 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ A2 ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.cobounded1
% 0.31/0.46 thf(fact_32_local_Oinf_Ocobounded2,axiom,
% 0.31/0.46 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ B2 ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.cobounded2
% 0.31/0.46 thf(fact_33_local_Oinf_OcoboundedI1,axiom,
% 0.31/0.46 ! [A2: a,C: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ C )
% 0.31/0.46 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.coboundedI1
% 0.31/0.46 thf(fact_34_local_Oinf_OcoboundedI2,axiom,
% 0.31/0.46 ! [B2: a,C: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ C )
% 0.31/0.46 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.coboundedI2
% 0.31/0.46 thf(fact_35_local_Oinf_OorderE,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( A2
% 0.31/0.46 = ( inf @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.orderE
% 0.31/0.46 thf(fact_36_local_Oinf_OorderI,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( inf @ A2 @ B2 ) )
% 0.31/0.46 => ( less_eq @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.orderI
% 0.31/0.46 thf(fact_37_local_Oinf_Oorder__iff,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 = ( A2
% 0.31/0.46 = ( inf @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.order_iff
% 0.31/0.46 thf(fact_38_local_Oinf__absorb1,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ( inf @ X @ Y )
% 0.31/0.46 = X ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_absorb1
% 0.31/0.46 thf(fact_39_local_Oinf__absorb2,axiom,
% 0.31/0.46 ! [Y: a,X: a] :
% 0.31/0.46 ( ( less_eq @ Y @ X )
% 0.31/0.46 => ( ( inf @ X @ Y )
% 0.31/0.46 = Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_absorb2
% 0.31/0.46 thf(fact_40_local_Oinf__greatest,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ( less_eq @ X @ Z2 )
% 0.31/0.46 => ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_greatest
% 0.31/0.46 thf(fact_41_local_Oinf__le1,axiom,
% 0.31/0.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_le1
% 0.31/0.46 thf(fact_42_local_Oinf__le2,axiom,
% 0.31/0.46 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_le2
% 0.31/0.46 thf(fact_43_local_Oinf__mono,axiom,
% 0.31/0.46 ! [A2: a,C: a,B2: a,D: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ C )
% 0.31/0.46 => ( ( less_eq @ B2 @ D )
% 0.31/0.46 => ( less_eq @ ( inf @ A2 @ B2 ) @ ( inf @ C @ D ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_mono
% 0.31/0.46 thf(fact_44_local_Oinf__unique,axiom,
% 0.31/0.46 ! [F: a > a > a,X: a,Y: a] :
% 0.31/0.46 ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
% 0.31/0.46 => ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
% 0.31/0.46 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.31/0.46 ( ( less_eq @ X3 @ Y4 )
% 0.31/0.46 => ( ( less_eq @ X3 @ Z3 )
% 0.31/0.46 => ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 0.31/0.46 => ( ( inf @ X @ Y )
% 0.31/0.46 = ( F @ X @ Y ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_unique
% 0.31/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.31/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.31/0.46 = ( P @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: $tType,A4: set @ A] :
% 0.31/0.46 ( ( collect @ A
% 0.31/0.46 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 0.31/0.46 = A4 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_47_Collect__cong,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.46 ( ! [X3: A] :
% 0.31/0.46 ( ( P @ X3 )
% 0.31/0.46 = ( Q @ X3 ) )
% 0.31/0.46 => ( ( collect @ A @ P )
% 0.31/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_cong
% 0.31/0.46 thf(fact_48_ext,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.31/0.46 ( ! [X3: A] :
% 0.31/0.46 ( ( F @ X3 )
% 0.31/0.46 = ( G @ X3 ) )
% 0.31/0.46 => ( F = G ) ) ).
% 0.31/0.46
% 0.31/0.46 % ext
% 0.31/0.46 thf(fact_49_local_Ole__iff__inf,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( less_eq @ X @ Y )
% 0.31/0.46 = ( ( inf @ X @ Y )
% 0.31/0.46 = X ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_iff_inf
% 0.31/0.46 thf(fact_50_local_Ole__infE,axiom,
% 0.31/0.46 ! [X: a,A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ X @ ( inf @ A2 @ B2 ) )
% 0.31/0.46 => ~ ( ( less_eq @ X @ A2 )
% 0.31/0.46 => ~ ( less_eq @ X @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_infE
% 0.31/0.46 thf(fact_51_local_Ole__infI,axiom,
% 0.31/0.46 ! [X: a,A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ X @ A2 )
% 0.31/0.46 => ( ( less_eq @ X @ B2 )
% 0.31/0.46 => ( less_eq @ X @ ( inf @ A2 @ B2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_infI
% 0.31/0.46 thf(fact_52_local_Ole__infI1,axiom,
% 0.31/0.46 ! [A2: a,X: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ X )
% 0.31/0.46 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_infI1
% 0.31/0.46 thf(fact_53_local_Ole__infI2,axiom,
% 0.31/0.46 ! [B2: a,X: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ X )
% 0.31/0.46 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_infI2
% 0.31/0.46 thf(fact_54_local_Ole__iff__sup,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( less_eq @ X @ Y )
% 0.31/0.46 = ( ( sup @ X @ Y )
% 0.31/0.46 = Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_iff_sup
% 0.31/0.46 thf(fact_55_local_Ole__supE,axiom,
% 0.31/0.46 ! [A2: a,B2: a,X: a] :
% 0.31/0.46 ( ( less_eq @ ( sup @ A2 @ B2 ) @ X )
% 0.31/0.46 => ~ ( ( less_eq @ A2 @ X )
% 0.31/0.46 => ~ ( less_eq @ B2 @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_supE
% 0.31/0.46 thf(fact_56_local_Ole__supI,axiom,
% 0.31/0.46 ! [A2: a,X: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ X )
% 0.31/0.46 => ( ( less_eq @ B2 @ X )
% 0.31/0.46 => ( less_eq @ ( sup @ A2 @ B2 ) @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_supI
% 0.31/0.46 thf(fact_57_local_Ole__supI1,axiom,
% 0.31/0.46 ! [X: a,A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ X @ A2 )
% 0.31/0.46 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_supI1
% 0.31/0.46 thf(fact_58_local_Ole__supI2,axiom,
% 0.31/0.46 ! [X: a,B2: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ X @ B2 )
% 0.31/0.46 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_supI2
% 0.31/0.46 thf(fact_59_local_Osup_Oabsorb1,axiom,
% 0.31/0.46 ! [B2: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 => ( ( sup @ A2 @ B2 )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.absorb1
% 0.31/0.46 thf(fact_60_local_Osup_Oabsorb2,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( sup @ A2 @ B2 )
% 0.31/0.46 = B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.absorb2
% 0.31/0.46 thf(fact_61_local_Osup_Oabsorb__iff1,axiom,
% 0.31/0.46 ! [B2: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 = ( ( sup @ A2 @ B2 )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.absorb_iff1
% 0.31/0.46 thf(fact_62_local_Osup_Oabsorb__iff2,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 = ( ( sup @ A2 @ B2 )
% 0.31/0.46 = B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.absorb_iff2
% 0.31/0.46 thf(fact_63_local_Osup_OboundedE,axiom,
% 0.31/0.46 ! [B2: a,C: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 0.31/0.46 => ~ ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 => ~ ( less_eq @ C @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.boundedE
% 0.31/0.46 thf(fact_64_local_Osup_OboundedI,axiom,
% 0.31/0.46 ! [B2: a,A2: a,C: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 => ( ( less_eq @ C @ A2 )
% 0.31/0.46 => ( less_eq @ ( sup @ B2 @ C ) @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.boundedI
% 0.31/0.46 thf(fact_65_local_Osup_Ocobounded1,axiom,
% 0.31/0.46 ! [A2: a,B2: a] : ( less_eq @ A2 @ ( sup @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.cobounded1
% 0.31/0.46 thf(fact_66_local_Osup_Ocobounded2,axiom,
% 0.31/0.46 ! [B2: a,A2: a] : ( less_eq @ B2 @ ( sup @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.cobounded2
% 0.31/0.46 thf(fact_67_local_Osup_OcoboundedI1,axiom,
% 0.31/0.46 ! [C: a,A2: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ C @ A2 )
% 0.31/0.46 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.coboundedI1
% 0.31/0.46 thf(fact_68_local_Osup_OcoboundedI2,axiom,
% 0.31/0.46 ! [C: a,B2: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ C @ B2 )
% 0.31/0.46 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.coboundedI2
% 0.31/0.46 thf(fact_69_local_Osup_Omono,axiom,
% 0.31/0.46 ! [C: a,A2: a,D: a,B2: a] :
% 0.31/0.46 ( ( less_eq @ C @ A2 )
% 0.31/0.46 => ( ( less_eq @ D @ B2 )
% 0.31/0.46 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A2 @ B2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.mono
% 0.31/0.46 thf(fact_70_local_Osup_OorderE,axiom,
% 0.31/0.46 ! [B2: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 => ( A2
% 0.31/0.46 = ( sup @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.orderE
% 0.31/0.46 thf(fact_71_local_Osup_OorderI,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( sup @ A2 @ B2 ) )
% 0.31/0.46 => ( less_eq @ B2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.orderI
% 0.31/0.46 thf(fact_72_local_Osup_Oorder__iff,axiom,
% 0.31/0.46 ! [B2: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 = ( A2
% 0.31/0.46 = ( sup @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.order_iff
% 0.31/0.46 thf(fact_73_local_Osup__absorb1,axiom,
% 0.31/0.46 ! [Y: a,X: a] :
% 0.31/0.46 ( ( less_eq @ Y @ X )
% 0.31/0.46 => ( ( sup @ X @ Y )
% 0.31/0.46 = X ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_absorb1
% 0.31/0.46 thf(fact_74_local_Osup__absorb2,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ( sup @ X @ Y )
% 0.31/0.46 = Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_absorb2
% 0.31/0.46 thf(fact_75_local_Osup__ge1,axiom,
% 0.31/0.46 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_ge1
% 0.31/0.46 thf(fact_76_local_Osup__ge2,axiom,
% 0.31/0.46 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_ge2
% 0.31/0.46 thf(fact_77_local_Osup__least,axiom,
% 0.31/0.46 ! [Y: a,X: a,Z2: a] :
% 0.31/0.46 ( ( less_eq @ Y @ X )
% 0.31/0.46 => ( ( less_eq @ Z2 @ X )
% 0.31/0.46 => ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_least
% 0.31/0.46 thf(fact_78_local_Osup__mono,axiom,
% 0.31/0.46 ! [A2: a,C: a,B2: a,D: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ C )
% 0.31/0.46 => ( ( less_eq @ B2 @ D )
% 0.31/0.46 => ( less_eq @ ( sup @ A2 @ B2 ) @ ( sup @ C @ D ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_mono
% 0.31/0.46 thf(fact_79_local_Osup__unique,axiom,
% 0.31/0.46 ! [F: a > a > a,X: a,Y: a] :
% 0.31/0.46 ( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
% 0.31/0.46 => ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
% 0.31/0.46 => ( ! [X3: a,Y4: a,Z3: a] :
% 0.31/0.46 ( ( less_eq @ Y4 @ X3 )
% 0.31/0.46 => ( ( less_eq @ Z3 @ X3 )
% 0.31/0.46 => ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
% 0.31/0.46 => ( ( sup @ X @ Y )
% 0.31/0.46 = ( F @ X @ Y ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_unique
% 0.31/0.46 thf(fact_80_local_Odistrib__imp1,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ! [X3: a,Y4: a,Z3: a] :
% 0.31/0.46 ( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
% 0.31/0.46 = ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
% 0.31/0.46 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.31/0.46 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.distrib_imp1
% 0.31/0.46 thf(fact_81_local_Odistrib__imp2,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ! [X3: a,Y4: a,Z3: a] :
% 0.31/0.46 ( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
% 0.31/0.46 = ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
% 0.31/0.46 => ( ( inf @ X @ ( sup @ Y @ Z2 ) )
% 0.31/0.46 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.distrib_imp2
% 0.31/0.46 thf(fact_82_local_Oa__join__d,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 = ( sup @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.a_join_d
% 0.31/0.46 thf(fact_83_a__meet__d,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( inf @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 = ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ C @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % a_meet_d
% 0.31/0.46 thf(fact_84_local_Ob__join__d,axiom,
% 0.31/0.46 ! [B2: a,A2: a,C: a] :
% 0.31/0.46 ( ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 = ( sup @ B2 @ ( inf @ C @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.b_join_d
% 0.31/0.46 thf(fact_85_b__meet__d,axiom,
% 0.31/0.46 ! [B2: a,A2: a,C: a] :
% 0.31/0.46 ( ( inf @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 = ( sup @ ( inf @ B2 @ C ) @ ( inf @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % b_meet_d
% 0.31/0.46 thf(fact_86_c__meet__d,axiom,
% 0.31/0.46 ! [C: a,A2: a,B2: a] :
% 0.31/0.46 ( ( inf @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 = ( sup @ ( inf @ C @ A2 ) @ ( inf @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % c_meet_d
% 0.31/0.46 thf(fact_87_local_Od__aux__def,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.31/0.46 = ( sup @ ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ B2 @ C ) ) @ ( inf @ C @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.d_aux_def
% 0.31/0.46 thf(fact_88_local_Od__b__c__a,axiom,
% 0.31/0.46 ! [B2: a,C: a,A2: a] :
% 0.31/0.46 ( ( modula1221160330_d_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 0.31/0.46 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.d_b_c_a
% 0.31/0.46 thf(fact_89_local_Od__c__a__b,axiom,
% 0.31/0.46 ! [C: a,A2: a,B2: a] :
% 0.31/0.46 ( ( modula1221160330_d_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 0.31/0.46 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.d_c_a_b
% 0.31/0.46 thf(fact_90_local_Oa__meet__e,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 = ( inf @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.a_meet_e
% 0.31/0.46 thf(fact_91_local_Ob__meet__e,axiom,
% 0.31/0.46 ! [B2: a,A2: a,C: a] :
% 0.31/0.46 ( ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 = ( inf @ B2 @ ( sup @ C @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.b_meet_e
% 0.31/0.46 thf(fact_92_local_Oc__meet__e,axiom,
% 0.31/0.46 ! [C: a,A2: a,B2: a] :
% 0.31/0.46 ( ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 = ( inf @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.c_meet_e
% 0.31/0.46 thf(fact_93_local_Oe__aux__def,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.31/0.46 = ( inf @ ( inf @ ( sup @ A2 @ B2 ) @ ( sup @ B2 @ C ) ) @ ( sup @ C @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.e_aux_def
% 0.31/0.46 thf(fact_94_local_Oe__b__c__a,axiom,
% 0.31/0.46 ! [B2: a,C: a,A2: a] :
% 0.31/0.46 ( ( modula1593167561_e_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 0.31/0.46 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.e_b_c_a
% 0.31/0.46 thf(fact_95_local_Oe__c__a__b,axiom,
% 0.31/0.46 ! [C: a,A2: a,B2: a] :
% 0.31/0.46 ( ( modula1593167561_e_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 0.31/0.46 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.e_c_a_b
% 0.31/0.46 thf(fact_96_local_Odistrib__inf__le,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.distrib_inf_le
% 0.31/0.46 thf(fact_97_local_Odistrib__sup__le,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.distrib_sup_le
% 0.31/0.46 thf(fact_98_local_Omodular,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 0.31/0.46 = ( inf @ Y @ ( sup @ X @ Z2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.modular
% 0.31/0.46 thf(fact_99_local_Oincomp__def,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( modula1937309406incomp @ a @ less_eq @ X @ Y )
% 0.31/0.46 = ( ~ ( less_eq @ X @ Y )
% 0.31/0.46 & ~ ( less_eq @ Y @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.incomp_def
% 0.31/0.46 thf(fact_100_local_Oorder_Orefl,axiom,
% 0.31/0.46 ! [A2: a] : ( less_eq @ A2 @ A2 ) ).
% 0.31/0.46
% 0.31/0.46 % local.order.refl
% 0.31/0.46 thf(fact_101_local_Oorder__refl,axiom,
% 0.31/0.46 ! [X: a] : ( less_eq @ X @ X ) ).
% 0.31/0.46
% 0.31/0.46 % local.order_refl
% 0.31/0.46 thf(fact_102_local_Oinf_Oidem,axiom,
% 0.31/0.46 ! [A2: a] :
% 0.31/0.46 ( ( inf @ A2 @ A2 )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.idem
% 0.31/0.46 thf(fact_103_local_Oinf_Oleft__idem,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( inf @ A2 @ ( inf @ A2 @ B2 ) )
% 0.31/0.46 = ( inf @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.left_idem
% 0.31/0.46 thf(fact_104_local_Oinf_Oright__idem,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( inf @ ( inf @ A2 @ B2 ) @ B2 )
% 0.31/0.46 = ( inf @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.right_idem
% 0.31/0.46 thf(fact_105_local_Oinf__idem,axiom,
% 0.31/0.46 ! [X: a] :
% 0.31/0.46 ( ( inf @ X @ X )
% 0.31/0.46 = X ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_idem
% 0.31/0.46 thf(fact_106_local_Oinf__left__idem,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( inf @ X @ ( inf @ X @ Y ) )
% 0.31/0.46 = ( inf @ X @ Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_left_idem
% 0.31/0.46 thf(fact_107_local_Oinf__right__idem,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 0.31/0.46 = ( inf @ X @ Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_right_idem
% 0.31/0.46 thf(fact_108_local_Osup_Oidem,axiom,
% 0.31/0.46 ! [A2: a] :
% 0.31/0.46 ( ( sup @ A2 @ A2 )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.idem
% 0.31/0.46 thf(fact_109_local_Osup_Oleft__idem,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( sup @ A2 @ ( sup @ A2 @ B2 ) )
% 0.31/0.46 = ( sup @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.left_idem
% 0.31/0.46 thf(fact_110_local_Osup_Oright__idem,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( sup @ ( sup @ A2 @ B2 ) @ B2 )
% 0.31/0.46 = ( sup @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.right_idem
% 0.31/0.46 thf(fact_111_local_Osup__idem,axiom,
% 0.31/0.46 ! [X: a] :
% 0.31/0.46 ( ( sup @ X @ X )
% 0.31/0.46 = X ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_idem
% 0.31/0.46 thf(fact_112_local_Osup__left__idem,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( sup @ X @ ( sup @ X @ Y ) )
% 0.31/0.46 = ( sup @ X @ Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_left_idem
% 0.31/0.46 thf(fact_113_local_Oc__a,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.31/0.46 = ( modula105138637_a_aux @ a @ inf @ sup @ C @ A2 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.c_a
% 0.31/0.46 thf(fact_114_local_OGreatestI2__order,axiom,
% 0.31/0.46 ! [P: a > $o,X: a,Q: a > $o] :
% 0.31/0.46 ( ( P @ X )
% 0.31/0.46 => ( ! [Y4: a] :
% 0.31/0.46 ( ( P @ Y4 )
% 0.31/0.46 => ( less_eq @ Y4 @ X ) )
% 0.31/0.46 => ( ! [X3: a] :
% 0.31/0.46 ( ( P @ X3 )
% 0.31/0.46 => ( ! [Y5: a] :
% 0.31/0.46 ( ( P @ Y5 )
% 0.31/0.46 => ( less_eq @ Y5 @ X3 ) )
% 0.31/0.46 => ( Q @ X3 ) ) )
% 0.31/0.46 => ( Q @ ( greatest @ a @ less_eq @ P ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.GreatestI2_order
% 0.31/0.46 thf(fact_115_local_OGreatest__equality,axiom,
% 0.31/0.46 ! [P: a > $o,X: a] :
% 0.31/0.46 ( ( P @ X )
% 0.31/0.46 => ( ! [Y4: a] :
% 0.31/0.46 ( ( P @ Y4 )
% 0.31/0.46 => ( less_eq @ Y4 @ X ) )
% 0.31/0.46 => ( ( greatest @ a @ less_eq @ P )
% 0.31/0.46 = X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.Greatest_equality
% 0.31/0.46 thf(fact_116_local_Omax__def,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.31/0.46 = B2 ) )
% 0.31/0.46 & ( ~ ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.31/0.46 = A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.max_def
% 0.31/0.46 thf(fact_117_local_Omin__def,axiom,
% 0.31/0.46 ! [A2: a,B2: a] :
% 0.31/0.46 ( ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.31/0.46 = A2 ) )
% 0.31/0.46 & ( ~ ( less_eq @ A2 @ B2 )
% 0.31/0.46 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.31/0.46 = B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.min_def
% 0.31/0.46 thf(fact_118_local_Oa__aux__def,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.31/0.46 = ( sup @ ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.a_aux_def
% 0.31/0.46 thf(fact_119_local_Oc__aux__def,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.31/0.46 = ( sup @ ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.c_aux_def
% 0.31/0.46 thf(fact_120_local_Oinf_Obounded__iff,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 0.31/0.46 = ( ( less_eq @ A2 @ B2 )
% 0.31/0.46 & ( less_eq @ A2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf.bounded_iff
% 0.31/0.46 thf(fact_121_local_Ole__inf__iff,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
% 0.31/0.46 = ( ( less_eq @ X @ Y )
% 0.31/0.46 & ( less_eq @ X @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_inf_iff
% 0.31/0.46 thf(fact_122_local_Ole__sup__iff,axiom,
% 0.31/0.46 ! [X: a,Y: a,Z2: a] :
% 0.31/0.46 ( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
% 0.31/0.46 = ( ( less_eq @ X @ Z2 )
% 0.31/0.46 & ( less_eq @ Y @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.le_sup_iff
% 0.31/0.46 thf(fact_123_local_Osup_Obounded__iff,axiom,
% 0.31/0.46 ! [B2: a,C: a,A2: a] :
% 0.31/0.46 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 0.31/0.46 = ( ( less_eq @ B2 @ A2 )
% 0.31/0.46 & ( less_eq @ C @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup.bounded_iff
% 0.31/0.46 thf(fact_124_local_Oinf__sup__absorb,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( inf @ X @ ( sup @ X @ Y ) )
% 0.31/0.46 = X ) ).
% 0.31/0.46
% 0.31/0.46 % local.inf_sup_absorb
% 0.31/0.46 thf(fact_125_local_Osup__inf__absorb,axiom,
% 0.31/0.46 ! [X: a,Y: a] :
% 0.31/0.46 ( ( sup @ X @ ( inf @ X @ Y ) )
% 0.31/0.46 = X ) ).
% 0.31/0.46
% 0.31/0.46 % local.sup_inf_absorb
% 0.31/0.46 thf(fact_126_local_Ob__a,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.31/0.46 = ( modula105138637_a_aux @ a @ inf @ sup @ B2 @ C @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.b_a
% 0.31/0.46 thf(fact_127_local_OLeast1I,axiom,
% 0.31/0.46 ! [P: a > $o] :
% 0.31/0.46 ( ? [X4: a] :
% 0.31/0.46 ( ( P @ X4 )
% 0.31/0.46 & ! [Y4: a] :
% 0.31/0.46 ( ( P @ Y4 )
% 0.31/0.46 => ( less_eq @ X4 @ Y4 ) )
% 0.31/0.46 & ! [Y4: a] :
% 0.31/0.46 ( ( ( P @ Y4 )
% 0.31/0.46 & ! [Ya: a] :
% 0.31/0.46 ( ( P @ Ya )
% 0.31/0.46 => ( less_eq @ Y4 @ Ya ) ) )
% 0.31/0.46 => ( Y4 = X4 ) ) )
% 0.31/0.46 => ( P @ ( least @ a @ less_eq @ P ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.Least1I
% 0.31/0.46 thf(fact_128_local_OLeast1__le,axiom,
% 0.31/0.46 ! [P: a > $o,Z2: a] :
% 0.31/0.46 ( ? [X4: a] :
% 0.31/0.46 ( ( P @ X4 )
% 0.31/0.46 & ! [Y4: a] :
% 0.31/0.46 ( ( P @ Y4 )
% 0.31/0.46 => ( less_eq @ X4 @ Y4 ) )
% 0.31/0.46 & ! [Y4: a] :
% 0.31/0.46 ( ( ( P @ Y4 )
% 0.31/0.46 & ! [Ya: a] :
% 0.31/0.46 ( ( P @ Ya )
% 0.31/0.46 => ( less_eq @ Y4 @ Ya ) ) )
% 0.31/0.46 => ( Y4 = X4 ) ) )
% 0.31/0.46 => ( ( P @ Z2 )
% 0.31/0.46 => ( less_eq @ ( least @ a @ less_eq @ P ) @ Z2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.Least1_le
% 0.31/0.46 thf(fact_129_local_OLeastI2__order,axiom,
% 0.31/0.46 ! [P: a > $o,X: a,Q: a > $o] :
% 0.31/0.46 ( ( P @ X )
% 0.31/0.46 => ( ! [Y4: a] :
% 0.31/0.46 ( ( P @ Y4 )
% 0.31/0.46 => ( less_eq @ X @ Y4 ) )
% 0.31/0.46 => ( ! [X3: a] :
% 0.31/0.46 ( ( P @ X3 )
% 0.31/0.46 => ( ! [Y5: a] :
% 0.31/0.46 ( ( P @ Y5 )
% 0.31/0.46 => ( less_eq @ X3 @ Y5 ) )
% 0.31/0.46 => ( Q @ X3 ) ) )
% 0.31/0.46 => ( Q @ ( least @ a @ less_eq @ P ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.LeastI2_order
% 0.31/0.46 thf(fact_130_local_OLeast__equality,axiom,
% 0.31/0.46 ! [P: a > $o,X: a] :
% 0.31/0.46 ( ( P @ X )
% 0.31/0.46 => ( ! [Y4: a] :
% 0.31/0.46 ( ( P @ Y4 )
% 0.31/0.46 => ( less_eq @ X @ Y4 ) )
% 0.31/0.46 => ( ( least @ a @ less_eq @ P )
% 0.31/0.46 = X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.Least_equality
% 0.31/0.46 thf(fact_131_local_Ob__aux__def,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 0.31/0.46 = ( sup @ ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.b_aux_def
% 0.31/0.46 thf(fact_132_a__meet__b__eq__d,axiom,
% 0.31/0.46 ! [A2: a,B2: a,C: a] :
% 0.31/0.46 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 => ( ( inf @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 0.31/0.46 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % a_meet_b_eq_d
% 0.31/0.46 thf(fact_133_lattice_Oa__aux_Ocong,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( modula105138637_a_aux @ A )
% 0.31/0.46 = ( modula105138637_a_aux @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lattice.a_aux.cong
% 0.31/0.46 thf(fact_134_lattice_Oc__aux_Ocong,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( modula849153099_c_aux @ A )
% 0.31/0.46 = ( modula849153099_c_aux @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lattice.c_aux.cong
% 0.31/0.46 thf(fact_135_lattice_Od__aux_Ocong,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( modula1221160330_d_aux @ A )
% 0.31/0.46 = ( modula1221160330_d_aux @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lattice.d_aux.cong
% 0.31/0.46 thf(fact_136_lattice_Oe__aux_Ocong,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( modula1593167561_e_aux @ A )
% 0.31/0.46 = ( modula1593167561_e_aux @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lattice.e_aux.cong
% 0.31/0.46 thf(fact_137_local_Ocomp__fun__idem__sup,axiom,
% 0.31/0.46 finite_comp_fun_idem @ a @ a @ sup ).
% 0.31/0.46
% 0.31/0.46 % local.comp_fun_idem_sup
% 0.31/0.46 thf(fact_138_local_Ocomp__fun__idem__inf,axiom,
% 0.31/0.46 finite_comp_fun_idem @ a @ a @ inf ).
% 0.31/0.46
% 0.31/0.46 % local.comp_fun_idem_inf
% 0.31/0.46 thf(fact_139_local_Osup_Osemigroup__axioms,axiom,
% 0.31/0.46 semigroup @ a @ sup ).
% 0.31/0.46
% 0.31/0.46 % local.sup.semigroup_axioms
% 0.31/0.46 thf(fact_140_local_Oinf_Osemigroup__axioms,axiom,
% 0.31/0.46 semigroup @ a @ inf ).
% 0.31/0.46
% 0.31/0.46 % local.inf.semigroup_axioms
% 0.31/0.46 thf(fact_141_local_Osup_Osemilattice__axioms,axiom,
% 0.31/0.46 semilattice @ a @ sup ).
% 0.31/0.46
% 0.31/0.46 % local.sup.semilattice_axioms
% 0.31/0.46 thf(fact_142_local_Oinf_Osemilattice__axioms,axiom,
% 0.31/0.46 semilattice @ a @ inf ).
% 0.31/0.46
% 0.31/0.46 % local.inf.semilattice_axioms
% 0.31/0.46 thf(fact_143_local_Osup_Oabel__semigroup__axioms,axiom,
% 0.31/0.46 abel_semigroup @ a @ sup ).
% 0.31/0.46
% 0.31/0.46 % local.sup.abel_semigroup_axioms
% 0.31/0.46 thf(fact_144_local_Oinf_Oabel__semigroup__axioms,axiom,
% 0.31/0.46 abel_semigroup @ a @ inf ).
% 0.31/0.46
% 0.31/0.46 % local.inf.abel_semigroup_axioms
% 0.31/0.46 thf(fact_145_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 0.31/0.46 lattic35693393ce_set @ a @ sup ).
% 0.31/0.46
% 0.31/0.46 % local.Sup_fin.semilattice_set_axioms
% 0.31/0.46 thf(fact_146_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 0.31/0.46 lattic35693393ce_set @ a @ inf ).
% 0.31/0.46
% 0.31/0.46 % local.Inf_fin.semilattice_set_axioms
% 0.31/0.46 thf(fact_147_local_Obdd__above__def,axiom,
% 0.31/0.46 ! [A4: set @ a] :
% 0.31/0.46 ( ( condit2040224947_above @ a @ less_eq @ A4 )
% 0.31/0.46 = ( ? [M: a] :
% 0.31/0.46 ! [X2: a] :
% 0.31/0.46 ( ( member @ a @ X2 @ A4 )
% 0.31/0.46 => ( less_eq @ X2 @ M ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.bdd_above_def
% 0.31/0.46 thf(fact_148_local_Obdd__below__def,axiom,
% 0.31/0.46 ! [A4: set @ a] :
% 0.31/0.46 ( ( condit1201339847_below @ a @ less_eq @ A4 )
% 0.31/0.46 = ( ? [M2: a] :
% 0.31/0.46 ! [X2: a] :
% 0.31/0.46 ( ( member @ a @ X2 @ A4 )
% 0.31/0.46 => ( less_eq @ M2 @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.bdd_below_def
% 0.31/0.46 thf(fact_149_local_Obdd__belowI,axiom,
% 0.31/0.46 ! [A4: set @ a,M3: a] :
% 0.31/0.46 ( ! [X3: a] :
% 0.31/0.46 ( ( member @ a @ X3 @ A4 )
% 0.31/0.46 => ( less_eq @ M3 @ X3 ) )
% 0.31/0.46 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.bdd_belowI
% 0.31/0.46 thf(fact_150_local_Obdd__aboveI,axiom,
% 0.31/0.46 ! [A4: set @ a,M4: a] :
% 0.31/0.46 ( ! [X3: a] :
% 0.31/0.46 ( ( member @ a @ X3 @ A4 )
% 0.31/0.46 => ( less_eq @ X3 @ M4 ) )
% 0.31/0.46 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.bdd_aboveI
% 0.31/0.46 thf(fact_151_lattice_Oincomp_Ocong,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( modula1937309406incomp @ A )
% 0.31/0.46 = ( modula1937309406incomp @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lattice.incomp.cong
% 0.31/0.46 thf(fact_152_lattice_Ob__aux_Ocong,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( modula477145868_b_aux @ A )
% 0.31/0.46 = ( modula477145868_b_aux @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % lattice.b_aux.cong
% 0.31/0.46 thf(fact_153_abel__semigroup_Oaxioms_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A] :
% 0.31/0.46 ( ( abel_semigroup @ A @ F )
% 0.31/0.46 => ( semigroup @ A @ F ) ) ).
% 0.31/0.46
% 0.31/0.46 % abel_semigroup.axioms(1)
% 0.31/0.46 thf(fact_154_semilattice__set__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( lattic35693393ce_set @ A )
% 0.31/0.46 = ( semilattice @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % semilattice_set_def
% 0.31/0.46 thf(fact_155_semilattice__set_Ointro,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A] :
% 0.31/0.46 ( ( semilattice @ A @ F )
% 0.31/0.46 => ( lattic35693393ce_set @ A @ F ) ) ).
% 0.31/0.46
% 0.31/0.46 % semilattice_set.intro
% 0.31/0.46 thf(fact_156_abel__semigroup_Oleft__commute,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A,B2: A,A2: A,C: A] :
% 0.31/0.46 ( ( abel_semigroup @ A @ F )
% 0.31/0.46 => ( ( F @ B2 @ ( F @ A2 @ C ) )
% 0.31/0.46 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % abel_semigroup.left_commute
% 0.31/0.46 thf(fact_157_abel__semigroup_Ocommute,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.31/0.46 ( ( abel_semigroup @ A @ F )
% 0.31/0.46 => ( ( F @ A2 @ B2 )
% 0.31/0.46 = ( F @ B2 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % abel_semigroup.commute
% 0.31/0.46 thf(fact_158_semigroup_Ointro,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A] :
% 0.31/0.46 ( ! [A5: A,B4: A,C2: A] :
% 0.31/0.46 ( ( F @ ( F @ A5 @ B4 ) @ C2 )
% 0.31/0.46 = ( F @ A5 @ ( F @ B4 @ C2 ) ) )
% 0.31/0.46 => ( semigroup @ A @ F ) ) ).
% 0.31/0.46
% 0.31/0.46 % semigroup.intro
% 0.31/0.46 thf(fact_159_semigroup_Oassoc,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 0.31/0.46 ( ( semigroup @ A @ F )
% 0.31/0.46 => ( ( F @ ( F @ A2 @ B2 ) @ C )
% 0.31/0.46 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % semigroup.assoc
% 0.31/0.46 thf(fact_160_semigroup__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( semigroup @ A )
% 0.31/0.46 = ( ^ [F2: A > A > A] :
% 0.31/0.46 ! [A3: A,B3: A,C3: A] :
% 0.31/0.46 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 0.31/0.46 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % semigroup_def
% 0.31/0.46 thf(fact_161_semilattice__set_Oaxioms,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A] :
% 0.31/0.46 ( ( lattic35693393ce_set @ A @ F )
% 0.31/0.46 => ( semilattice @ A @ F ) ) ).
% 0.31/0.46
% 0.31/0.46 % semilattice_set.axioms
% 0.31/0.46 thf(fact_162_semilattice_Oaxioms_I1_J,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A] :
% 0.31/0.46 ( ( semilattice @ A @ F )
% 0.31/0.46 => ( abel_semigroup @ A @ F ) ) ).
% 0.31/0.46
% 0.31/0.46 % semilattice.axioms(1)
% 0.31/0.46 thf(fact_163_local_Obdd__above__mono,axiom,
% 0.31/0.46 ! [B5: set @ a,A4: set @ a] :
% 0.31/0.46 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 0.31/0.46 => ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 0.31/0.46 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.bdd_above_mono
% 0.31/0.46 thf(fact_164_local_Obdd__below__mono,axiom,
% 0.31/0.46 ! [B5: set @ a,A4: set @ a] :
% 0.31/0.46 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 0.31/0.46 => ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 0.31/0.46 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.bdd_below_mono
% 0.31/0.46 thf(fact_165_local_Oantimono__def,axiom,
% 0.31/0.46 ! [B: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ! [F: a > B] :
% 0.31/0.46 ( ( antimono @ a @ B @ less_eq @ F )
% 0.31/0.46 = ( ! [X2: a,Y3: a] :
% 0.31/0.46 ( ( less_eq @ X2 @ Y3 )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.antimono_def
% 0.31/0.46 thf(fact_166_local_OantimonoI,axiom,
% 0.31/0.46 ! [B: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ! [F: a > B] :
% 0.31/0.46 ( ! [X3: a,Y4: a] :
% 0.31/0.46 ( ( less_eq @ X3 @ Y4 )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 0.31/0.46 => ( antimono @ a @ B @ less_eq @ F ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.antimonoI
% 0.31/0.46 thf(fact_167_local_OantimonoE,axiom,
% 0.31/0.46 ! [B: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ! [F: a > B,X: a,Y: a] :
% 0.31/0.46 ( ( antimono @ a @ B @ less_eq @ F )
% 0.31/0.46 => ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.antimonoE
% 0.31/0.46 thf(fact_168_local_OantimonoD,axiom,
% 0.31/0.46 ! [B: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ! [F: a > B,X: a,Y: a] :
% 0.31/0.46 ( ( antimono @ a @ B @ less_eq @ F )
% 0.31/0.46 => ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.antimonoD
% 0.31/0.46 thf(fact_169_local_OmonoD,axiom,
% 0.31/0.46 ! [B: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ! [F: a > B,X: a,Y: a] :
% 0.31/0.46 ( ( mono @ a @ B @ less_eq @ F )
% 0.31/0.46 => ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.monoD
% 0.31/0.46 thf(fact_170_local_OmonoE,axiom,
% 0.31/0.46 ! [B: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ! [F: a > B,X: a,Y: a] :
% 0.31/0.46 ( ( mono @ a @ B @ less_eq @ F )
% 0.31/0.46 => ( ( less_eq @ X @ Y )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.monoE
% 0.31/0.46 thf(fact_171_local_OmonoI,axiom,
% 0.31/0.46 ! [B: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ! [F: a > B] :
% 0.31/0.46 ( ! [X3: a,Y4: a] :
% 0.31/0.46 ( ( less_eq @ X3 @ Y4 )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.31/0.46 => ( mono @ a @ B @ less_eq @ F ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.monoI
% 0.31/0.46 thf(fact_172_local_Omono__def,axiom,
% 0.31/0.46 ! [B: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ! [F: a > B] :
% 0.31/0.46 ( ( mono @ a @ B @ less_eq @ F )
% 0.31/0.46 = ( ! [X2: a,Y3: a] :
% 0.31/0.46 ( ( less_eq @ X2 @ Y3 )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % local.mono_def
% 0.31/0.46 thf(fact_173_semilattice_Oidem,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A,A2: A] :
% 0.31/0.46 ( ( semilattice @ A @ F )
% 0.31/0.46 => ( ( F @ A2 @ A2 )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % semilattice.idem
% 0.31/0.46 thf(fact_174_semilattice_Oleft__idem,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.31/0.46 ( ( semilattice @ A @ F )
% 0.31/0.46 => ( ( F @ A2 @ ( F @ A2 @ B2 ) )
% 0.31/0.46 = ( F @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % semilattice.left_idem
% 0.31/0.46 thf(fact_175_semilattice_Oright__idem,axiom,
% 0.31/0.46 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.31/0.46 ( ( semilattice @ A @ F )
% 0.31/0.46 => ( ( F @ ( F @ A2 @ B2 ) @ B2 )
% 0.31/0.46 = ( F @ A2 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % semilattice.right_idem
% 0.31/0.46 thf(fact_176_subsetI,axiom,
% 0.31/0.46 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/0.46 ( ! [X3: A] :
% 0.31/0.46 ( ( member @ A @ X3 @ A4 )
% 0.31/0.46 => ( member @ A @ X3 @ B5 ) )
% 0.31/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.31/0.46
% 0.31/0.46 % subsetI
% 0.31/0.46 thf(fact_177_subset__antisym,axiom,
% 0.31/0.46 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.31/0.46 => ( A4 = B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subset_antisym
% 0.31/0.46 thf(fact_178_preorder__class_Oorder__refl,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( preorder @ A )
% 0.31/0.46 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.31/0.46
% 0.31/0.46 % preorder_class.order_refl
% 0.31/0.46 thf(fact_179_order_Oantimono_Ocong,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ( ( antimono @ A @ B )
% 0.31/0.46 = ( antimono @ A @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order.antimono.cong
% 0.31/0.46 thf(fact_180_order_Omono_Ocong,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( order @ B )
% 0.31/0.46 => ( ( mono @ A @ B )
% 0.31/0.46 = ( mono @ A @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order.mono.cong
% 0.31/0.46 thf(fact_181_order__class_Odual__order_Oantisym,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ! [B2: A,A2: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.dual_order.antisym
% 0.31/0.46 thf(fact_182_order__class_Odual__order_Oeq__iff,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ( ( ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 0.31/0.46 = ( ^ [A3: A,B3: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.31/0.46 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.dual_order.eq_iff
% 0.31/0.46 thf(fact_183_order__class_Odual__order_Otrans,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ! [B2: A,A2: A,C: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/0.46 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.31/0.46 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.dual_order.trans
% 0.31/0.46 thf(fact_184_linorder__wlog,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( linorder @ A )
% 0.31/0.46 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.31/0.46 ( ! [A5: A,B4: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.31/0.46 => ( P @ A5 @ B4 ) )
% 0.31/0.46 => ( ! [A5: A,B4: A] :
% 0.31/0.46 ( ( P @ B4 @ A5 )
% 0.31/0.46 => ( P @ A5 @ B4 ) )
% 0.31/0.46 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % linorder_wlog
% 0.31/0.46 thf(fact_185_order__class_Odual__order_Orefl,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.dual_order.refl
% 0.31/0.46 thf(fact_186_preorder__class_Oorder__trans,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( preorder @ A )
% 0.31/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.46 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.31/0.46 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % preorder_class.order_trans
% 0.31/0.46 thf(fact_187_order__class_Oorder_Oantisym,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ! [A2: A,B2: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/0.46 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.order.antisym
% 0.31/0.46 thf(fact_188_ord__class_Oord__le__eq__trans,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( ord @ A )
% 0.31/0.46 => ! [A2: A,B2: A,C: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/0.46 => ( ( B2 = C )
% 0.31/0.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ord_class.ord_le_eq_trans
% 0.31/0.46 thf(fact_189_ord__class_Oord__eq__le__trans,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( ord @ A )
% 0.31/0.46 => ! [A2: A,B2: A,C: A] :
% 0.31/0.46 ( ( A2 = B2 )
% 0.31/0.46 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.31/0.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ord_class.ord_eq_le_trans
% 0.31/0.46 thf(fact_190_order__class_Oorder_Oeq__iff,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ( ( ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 0.31/0.46 = ( ^ [A3: A,B3: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.31/0.46 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.order.eq_iff
% 0.31/0.46 thf(fact_191_order__class_Oantisym__conv,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ! [Y: A,X: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.46 => ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.46 = ( X = Y ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.antisym_conv
% 0.31/0.46 thf(fact_192_le__cases3,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( linorder @ A )
% 0.31/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.31/0.46 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.46 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.31/0.46 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.46 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.31/0.46 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.31/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.31/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.31/0.46 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.31/0.46 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.31/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.31/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.31/0.46 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_cases3
% 0.31/0.46 thf(fact_193_order__class_Oorder_Otrans,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ! [A2: A,B2: A,C: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/0.46 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.31/0.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.order.trans
% 0.31/0.46 thf(fact_194_le__cases,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( linorder @ A )
% 0.31/0.46 => ! [X: A,Y: A] :
% 0.31/0.46 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.31/0.46 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_cases
% 0.31/0.46 thf(fact_195_preorder__class_Oeq__refl,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( preorder @ A )
% 0.31/0.46 => ! [X: A,Y: A] :
% 0.31/0.46 ( ( X = Y )
% 0.31/0.46 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % preorder_class.eq_refl
% 0.31/0.46 thf(fact_196_linear,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( linorder @ A )
% 0.31/0.46 => ! [X: A,Y: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.46 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % linear
% 0.31/0.46 thf(fact_197_order__class_Oantisym,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ! [X: A,Y: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.46 => ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.46 => ( X = Y ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.antisym
% 0.31/0.46 thf(fact_198_order__class_Oeq__iff,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( order @ A )
% 0.31/0.46 => ( ( ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 0.31/0.46 = ( ^ [X2: A,Y3: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/0.46 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_class.eq_iff
% 0.31/0.46 thf(fact_199_ord__le__eq__subst,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType] :
% 0.31/0.46 ( ( ( ord @ B )
% 0.31/0.46 & ( ord @ A ) )
% 0.31/0.46 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.31/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/0.46 => ( ( ( F @ B2 )
% 0.31/0.46 = C )
% 0.31/0.46 => ( ! [X3: A,Y4: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ord_le_eq_subst
% 0.31/0.46 thf(fact_200_ord__eq__le__subst,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType] :
% 0.31/0.46 ( ( ( ord @ B )
% 0.31/0.46 & ( ord @ A ) )
% 0.31/0.46 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( F @ B2 ) )
% 0.31/0.46 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.31/0.46 => ( ! [X3: B,Y4: B] :
% 0.31/0.46 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.31/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.31/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ord_eq_le_subst
% 0.31/0.46 thf(fact_201_order__subst2,axiom,
% 0.31/0.46 ! [A: $tType,C4: $tType] :
% 0.31/0.46 ( ( ( order @ C4 )
% 0.31/0.46 & ( order @ A ) )
% 0.31/0.46 => ! [A2: A,B2: A,F: A > C4,C: C4] :
% 0.31/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/0.46 => ( ( ord_less_eq @ C4 @ ( F @ B2 ) @ C )
% 0.31/0.46 => ( ! [X3: A,Y4: A] :
% 0.31/0.46 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.31/0.46 => ( ord_less_eq @ C4 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.31/0.46 => ( ord_less_eq @ C4 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_subst2
% 0.31/0.46 thf(fact_202_order__subst1,axiom,
% 0.31/0.46 ! [A: $tType,B: $tType] :
% 0.31/0.46 ( ( ( order @ B )
% 0.31/0.46 & ( order @ A ) )
% 0.31/0.46 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.31/0.46 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.31/0.46 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.31/0.46 => ( ! [X3: B,Y4: B] :
% 0.31/0.46 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.31/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.31/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % order_subst1
% 0.31/0.46 thf(fact_203_le__fun__def,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( ord @ B )
% 0.31/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.31/0.46 = ( ^ [F2: A > B,G2: A > B] :
% 0.31/0.46 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_fun_def
% 0.31/0.46 thf(fact_204_le__funI,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( ord @ B )
% 0.31/0.46 => ! [F: A > B,G: A > B] :
% 0.31/0.46 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.31/0.46 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_funI
% 0.31/0.46 thf(fact_205_le__funE,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( ord @ B )
% 0.31/0.46 => ! [F: A > B,G: A > B,X: A] :
% 0.31/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_funE
% 0.31/0.46 thf(fact_206_le__funD,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( ord @ B )
% 0.31/0.46 => ! [F: A > B,G: A > B,X: A] :
% 0.31/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/0.46 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_funD
% 0.31/0.46 thf(fact_207_Collect__mono__iff,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.31/0.46 = ( ! [X2: A] :
% 0.31/0.46 ( ( P @ X2 )
% 0.31/0.46 => ( Q @ X2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mono_iff
% 0.31/0.46 thf(fact_208_set__eq__subset,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( ^ [Y2: set @ A,Z: set @ A] : ( Y2 = Z ) )
% 0.31/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.31/0.47 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % set_eq_subset
% 0.31/0.47 thf(fact_209_subset__trans,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C5: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C5 )
% 0.31/0.47 => ( ord_less_eq @ ( set @ A ) @ A4 @ C5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_trans
% 0.31/0.47 thf(fact_210_Collect__mono,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.47 ( ! [X3: A] :
% 0.31/0.47 ( ( P @ X3 )
% 0.31/0.47 => ( Q @ X3 ) )
% 0.31/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono
% 0.31/0.47 thf(fact_211_subset__refl,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.31/0.47
% 0.31/0.47 % subset_refl
% 0.31/0.47 thf(fact_212_subset__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.31/0.47 ! [T: A] :
% 0.31/0.47 ( ( member @ A @ T @ A6 )
% 0.31/0.47 => ( member @ A @ T @ B6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_iff
% 0.31/0.47 thf(fact_213_equalityD2,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/0.47 ( ( A4 = B5 )
% 0.31/0.47 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equalityD2
% 0.31/0.47 thf(fact_214_equalityD1,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/0.47 ( ( A4 = B5 )
% 0.31/0.47 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equalityD1
% 0.31/0.47 thf(fact_215_subset__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.31/0.47 ! [X2: A] :
% 0.31/0.47 ( ( member @ A @ X2 @ A6 )
% 0.31/0.47 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_eq
% 0.31/0.47 thf(fact_216_equalityE,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/0.47 ( ( A4 = B5 )
% 0.31/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % equalityE
% 0.31/0.47 thf(fact_217_subsetD,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/0.47 => ( ( member @ A @ C @ A4 )
% 0.31/0.47 => ( member @ A @ C @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetD
% 0.31/0.47 thf(fact_218_in__mono,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/0.47 => ( ( member @ A @ X @ A4 )
% 0.31/0.47 => ( member @ A @ X @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_mono
% 0.31/0.47 thf(fact_219_ord_OLeast_Ocong,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( least @ A )
% 0.31/0.47 = ( least @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.Least.cong
% 0.31/0.47 thf(fact_220_order_OGreatest_Ocong,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( greatest @ A )
% 0.31/0.47 = ( greatest @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.Greatest.cong
% 0.31/0.47 thf(fact_221_ord_Omin_Ocong,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( min @ A )
% 0.31/0.47 = ( min @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.min.cong
% 0.31/0.47 thf(fact_222_ord_Omax_Ocong,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( max @ A )
% 0.31/0.47 = ( max @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.max.cong
% 0.31/0.47 thf(fact_223_ord_Omin__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( min @ A )
% 0.31/0.47 = ( ^ [Less_eq: A > A > $o,A3: A,B3: A] : ( if @ A @ ( Less_eq @ A3 @ B3 ) @ A3 @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.min_def
% 0.31/0.47 thf(fact_224_ord_Omax__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( max @ A )
% 0.31/0.47 = ( ^ [Less_eq: A > A > $o,A3: A,B3: A] : ( if @ A @ ( Less_eq @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.max_def
% 0.31/0.47 thf(fact_225_local_Omono__inf,axiom,
% 0.31/0.47 ! [B: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ B )
% 0.31/0.47 => ! [F: a > B,A4: a,B5: a] :
% 0.31/0.47 ( ( mono @ a @ B @ less_eq @ F )
% 0.31/0.47 => ( ord_less_eq @ B @ ( F @ ( inf @ A4 @ B5 ) ) @ ( inf_inf @ B @ ( F @ A4 ) @ ( F @ B5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.mono_inf
% 0.31/0.47 thf(fact_226_local_Omono__sup,axiom,
% 0.31/0.47 ! [B: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ B )
% 0.31/0.47 => ! [F: a > B,A4: a,B5: a] :
% 0.31/0.47 ( ( mono @ a @ B @ less_eq @ F )
% 0.31/0.47 => ( ord_less_eq @ B @ ( sup_sup @ B @ ( F @ A4 ) @ ( F @ B5 ) ) @ ( F @ ( sup @ A4 @ B5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.mono_sup
% 0.31/0.47 thf(fact_227_local_Obdd__above__finite,axiom,
% 0.31/0.47 ! [A4: set @ a] :
% 0.31/0.47 ( ( finite_finite @ a @ A4 )
% 0.31/0.47 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.bdd_above_finite
% 0.31/0.47 thf(fact_228_local_Ofinite__has__minimal2,axiom,
% 0.31/0.47 ! [A4: set @ a,A2: a] :
% 0.31/0.47 ( ( finite_finite @ a @ A4 )
% 0.31/0.47 => ( ( member @ a @ A2 @ A4 )
% 0.31/0.47 => ? [X3: a] :
% 0.31/0.47 ( ( member @ a @ X3 @ A4 )
% 0.31/0.47 & ( less_eq @ X3 @ A2 )
% 0.31/0.47 & ! [Xa: a] :
% 0.31/0.47 ( ( member @ a @ Xa @ A4 )
% 0.31/0.47 => ( ( less_eq @ Xa @ X3 )
% 0.31/0.47 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.finite_has_minimal2
% 0.31/0.47 thf(fact_229_local_Ofinite__has__maximal2,axiom,
% 0.31/0.47 ! [A4: set @ a,A2: a] :
% 0.31/0.47 ( ( finite_finite @ a @ A4 )
% 0.31/0.47 => ( ( member @ a @ A2 @ A4 )
% 0.31/0.47 => ? [X3: a] :
% 0.31/0.47 ( ( member @ a @ X3 @ A4 )
% 0.31/0.47 & ( less_eq @ A2 @ X3 )
% 0.31/0.47 & ! [Xa: a] :
% 0.31/0.47 ( ( member @ a @ Xa @ A4 )
% 0.31/0.47 => ( ( less_eq @ X3 @ Xa )
% 0.31/0.47 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.finite_has_maximal2
% 0.31/0.47 thf(fact_230_local_Obdd__below__Int2,axiom,
% 0.31/0.47 ! [B5: set @ a,A4: set @ a] :
% 0.31/0.47 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 0.31/0.47 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.bdd_below_Int2
% 0.31/0.47 thf(fact_231_local_Obdd__below__Int1,axiom,
% 0.31/0.47 ! [A4: set @ a,B5: set @ a] :
% 0.31/0.47 ( ( condit1201339847_below @ a @ less_eq @ A4 )
% 0.31/0.47 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.bdd_below_Int1
% 0.31/0.47 thf(fact_232_local_Obdd__above__Int2,axiom,
% 0.31/0.47 ! [B5: set @ a,A4: set @ a] :
% 0.31/0.47 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 0.31/0.47 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.bdd_above_Int2
% 0.31/0.47 thf(fact_233_local_Obdd__above__Int1,axiom,
% 0.31/0.47 ! [A4: set @ a,B5: set @ a] :
% 0.31/0.47 ( ( condit2040224947_above @ a @ less_eq @ A4 )
% 0.31/0.47 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.bdd_above_Int1
% 0.31/0.47 thf(fact_234_local_Obdd__below__finite,axiom,
% 0.31/0.47 ! [A4: set @ a] :
% 0.31/0.47 ( ( finite_finite @ a @ A4 )
% 0.31/0.47 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % local.bdd_below_finite
% 0.31/0.47 thf(fact_235_Un__subset__iff,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C5: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C5 )
% 0.31/0.47 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C5 )
% 0.31/0.47 & ( ord_less_eq @ ( set @ A ) @ B5 @ C5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_subset_iff
% 0.31/0.47 thf(fact_236_Int__subset__iff,axiom,
% 0.31/0.47 ! [A: $tType,C5: set @ A,A4: set @ A,B5: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ C5 @ ( inf_inf @ ( set @ A ) @ A4 @ B5 ) )
% 0.31/0.47 = ( ( ord_less_eq @ ( set @ A ) @ C5 @ A4 )
% 0.31/0.47 & ( ord_less_eq @ ( set @ A ) @ C5 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Int_subset_iff
% 0.31/0.47 thf(fact_237_semilattice__inf__class_Oinf__right__idem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 0.31/0.47 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_inf_class.inf_right_idem
% 0.31/0.47 thf(fact_238_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ A )
% 0.31/0.47 => ! [A2: A,B2: A] :
% 0.31/0.47 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.31/0.47 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_inf_class.inf.right_idem
% 0.31/0.47 thf(fact_239_semilattice__inf__class_Oinf__left__idem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.31/0.47 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_inf_class.inf_left_idem
% 0.31/0.47 thf(fact_240_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ A )
% 0.31/0.47 => ! [A2: A,B2: A] :
% 0.31/0.47 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.31/0.47 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_inf_class.inf.left_idem
% 0.31/0.47 thf(fact_241_semilattice__inf__class_Oinf__idem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( inf_inf @ A @ X @ X )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_inf_class.inf_idem
% 0.31/0.47 thf(fact_242_semilattice__inf__class_Oinf_Oidem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( inf_inf @ A @ A2 @ A2 )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_inf_class.inf.idem
% 0.31/0.47 thf(fact_243_inf__apply,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ B )
% 0.31/0.47 => ( ( inf_inf @ ( A > B ) )
% 0.31/0.47 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( inf_inf @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inf_apply
% 0.31/0.47 thf(fact_244_semilattice__sup__class_Osup_Oright__idem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ A )
% 0.31/0.47 => ! [A2: A,B2: A] :
% 0.31/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ B2 )
% 0.31/0.47 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_sup_class.sup.right_idem
% 0.31/0.47 thf(fact_245_semilattice__sup__class_Osup__left__idem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.31/0.47 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_sup_class.sup_left_idem
% 0.31/0.47 thf(fact_246_semilattice__sup__class_Osup_Oleft__idem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ A )
% 0.31/0.47 => ! [A2: A,B2: A] :
% 0.31/0.47 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) )
% 0.31/0.47 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_sup_class.sup.left_idem
% 0.31/0.47 thf(fact_247_semilattice__sup__class_Osup__idem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( sup_sup @ A @ X @ X )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_sup_class.sup_idem
% 0.31/0.47 thf(fact_248_semilattice__sup__class_Osup_Oidem,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( sup_sup @ A @ A2 @ A2 )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_sup_class.sup.idem
% 0.31/0.47 thf(fact_249_sup__apply,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ B )
% 0.31/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.31/0.47 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_apply
% 0.31/0.47 thf(fact_250_semilattice__inf__class_Ole__inf__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z2 ) )
% 0.31/0.47 = ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 & ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_inf_class.le_inf_iff
% 0.31/0.47 thf(fact_251_semilattice__inf__class_Oinf_Obounded__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ A )
% 0.31/0.47 => ! [A2: A,B2: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 0.31/0.47 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/0.47 & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_inf_class.inf.bounded_iff
% 0.31/0.47 thf(fact_252_semilattice__sup__class_Ole__sup__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z2 )
% 0.31/0.47 = ( ( ord_less_eq @ A @ X @ Z2 )
% 0.31/0.47 & ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_sup_class.le_sup_iff
% 0.31/0.47 thf(fact_253_semilattice__sup__class_Osup_Obounded__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ A )
% 0.31/0.47 => ! [B2: A,C: A,A2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C ) @ A2 )
% 0.31/0.47 = ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/0.47 & ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semilattice_sup_class.sup.bounded_iff
% 0.31/0.47 thf(fact_254_lattice__class_Osup__inf__absorb,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( lattice @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( sup_sup @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % lattice_class.sup_inf_absorb
% 0.31/0.47 thf(fact_255_lattice__class_Oinf__sup__absorb,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( lattice @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( inf_inf @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % lattice_class.inf_sup_absorb
% 0.31/0.47
% 0.31/0.47 % Type constructors (19)
% 0.31/0.47 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.31/0.47 ! [A7: $tType,A8: $tType] :
% 0.31/0.47 ( ( semilattice_sup @ A8 )
% 0.31/0.47 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.31/0.47 ! [A7: $tType,A8: $tType] :
% 0.31/0.47 ( ( semilattice_inf @ A8 )
% 0.31/0.47 => ( semilattice_inf @ ( A7 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/0.47 ! [A7: $tType,A8: $tType] :
% 0.31/0.47 ( ( preorder @ A8 )
% 0.31/0.47 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.31/0.47 ! [A7: $tType,A8: $tType] :
% 0.31/0.47 ( ( lattice @ A8 )
% 0.31/0.47 => ( lattice @ ( A7 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/0.47 ! [A7: $tType,A8: $tType] :
% 0.31/0.47 ( ( order @ A8 )
% 0.31/0.47 => ( order @ ( A7 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/0.47 ! [A7: $tType,A8: $tType] :
% 0.31/0.47 ( ( ord @ A8 )
% 0.31/0.47 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1,axiom,
% 0.31/0.47 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_2,axiom,
% 0.31/0.47 ! [A7: $tType] : ( semilattice_inf @ ( set @ A7 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_3,axiom,
% 0.31/0.47 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Lattices_Olattice_4,axiom,
% 0.31/0.47 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.31/0.47 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 0.31/0.47 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_7,axiom,
% 0.31/0.47 semilattice_sup @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_8,axiom,
% 0.31/0.47 semilattice_inf @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_9,axiom,
% 0.31/0.47 preorder @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.31/0.47 linorder @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Lattices_Olattice_10,axiom,
% 0.31/0.47 lattice @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_11,axiom,
% 0.31/0.47 order @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Oord_12,axiom,
% 0.31/0.47 ord @ $o ).
% 0.31/0.47
% 0.31/0.47 % Helper facts (3)
% 0.31/0.47 thf(help_If_3_1_T,axiom,
% 0.31/0.47 ! [P: $o] :
% 0.31/0.47 ( ( P = $true )
% 0.31/0.47 | ( P = $false ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_2_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X: A,Y: A] :
% 0.31/0.47 ( ( if @ A @ $false @ X @ Y )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_1_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X: A,Y: A] :
% 0.31/0.47 ( ( if @ A @ $true @ X @ Y )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % Conjectures (2)
% 0.31/0.47 thf(conj_0,hypothesis,
% 0.31/0.47 less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ).
% 0.31/0.47
% 0.31/0.47 thf(conj_1,conjecture,
% 0.31/0.47 ( ( inf @ ( modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2 ) @ ( modula849153099_c_aux @ a @ inf @ sup @ a2 @ b @ c ) )
% 0.31/0.47 = ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.37/1.46 ---- Embedded in THF ---
% 2.37/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.37/1.46 %%% Generated on Tue Feb 24 08:27:11 EST 2026
% 2.37/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.37/1.46 %%% Logic specification used:
% 2.37/1.46 %%% thf(spec, logic, $$dhol).
% 2.37/1.46
% 2.37/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2DTF32551.p
% 2.37/1.46 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.37/1.46 thf(ty_tf_a, type, a: $tType).
% 2.37/1.46 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.37/1.46 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.37/1.46 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.37/1.46 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 2.37/1.46 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.37/1.46 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.37/1.46 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 2.37/1.46 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 2.37/1.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above, type, condit2040224947_above: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.37/1.46 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below, type, condit1201339847_below: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.37/1.46 thf(sy_c_Finite__Set_Ocomp__fun__idem, type, finite_comp_fun_idem: (!> [A:$tType,B:$tType]: (((A > (B > B)) > $o)))).
% 2.37/1.46 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.37/1.46 thf(sy_c_Groups_Oabel__semigroup, type, abel_semigroup: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.37/1.46 thf(sy_c_Groups_Osemigroup, type, semigroup: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.37/1.46 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.37/1.46 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.37/1.46 thf(sy_c_Lattices_Osemilattice, type, semilattice: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.37/1.46 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.37/1.46 thf(sy_c_Lattices__Big_Osemilattice__set, type, lattic35693393ce_set: (!> [A:$tType]: (((A > (A > A)) > $o)))).
% 2.37/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oa__aux, type, modula105138637_a_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.37/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Ob__aux, type, modula477145868_b_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.37/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oc__aux, type, modula849153099_c_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.37/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Od__aux, type, modula1221160330_d_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.37/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oe__aux, type, modula1593167561_e_aux: (!> [A:$tType]: (((A > (A > A)) > ((A > (A > A)) > (A > (A > (A > A)))))))).
% 2.37/1.46 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oincomp, type, modula1937309406incomp: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > $o)))))).
% 2.37/1.46 thf(sy_c_Orderings_Oord_OLeast, type, least: (!> [A:$tType]: (((A > (A > $o)) > ((A > $o) > A))))).
% 2.37/1.46 thf(sy_c_Orderings_Oord_Omax, type, max: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > A)))))).
% 2.37/1.46 thf(sy_c_Orderings_Oord_Omin, type, min: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > A)))))).
% 2.37/1.46 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.37/1.46 thf(sy_c_Orderings_Oorder_OGreatest, type, greatest: (!> [A:$tType]: (((A > (A > $o)) > ((A > $o) > A))))).
% 2.37/1.46 thf(sy_c_Orderings_Oorder_Oantimono, type, antimono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.37/1.46 thf(sy_c_Orderings_Oorder_Omono, type, mono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.37/1.46 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.37/1.46 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.37/1.46 thf(sy_v_a, type, a2: a).
% 2.37/1.46 thf(sy_v_b, type, b: a).
% 2.37/1.46 thf(sy_v_c, type, c: a).
% 2.37/1.46 thf(sy_v_inf, type, inf: (a > (a > a))).
% 2.37/1.46 thf(sy_v_less__eq, type, less_eq: (a > (a > $o))).
% 2.37/1.46 thf(sy_v_sup, type, sup: (a > (a > a))).
% 2.37/1.46 thf(fact_0_local_Oantisym, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) => (((less_eq @ Y) @ X) => (X = Y)))))).
% 2.37/1.46 thf(fact_1_local_Oantisym__conv, axiom, (! [Y:a,X:a]: ((((less_eq @ Y) @ X) => (((less_eq @ X) @ Y) = (X = Y)))))).
% 2.37/1.46 thf(fact_2_local_Odual__order_Oantisym, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (((less_eq @ A2) @ B2) => (A2 = B2)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 thf(fact_6_local_Oeq__refl, axiom, (! [X:a,Y:a]: (((X = Y) => ((less_eq @ X) @ Y))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 thf(fact_9_local_Oorder_Oantisym, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (((less_eq @ B2) @ A2) => (A2 = B2)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 thf(fact_13_local_Oinf_Oassoc, axiom, (! [A2:a,B2:a,C:a]: ((((inf @ ((inf @ A2) @ B2)) @ C) = ((inf @ A2) @ ((inf @ B2) @ C)))))).
% 2.37/1.46 thf(fact_14_local_Oinf_Ocommute, axiom, (! [A2:a,B2:a]: ((((inf @ A2) @ B2) = ((inf @ B2) @ A2))))).
% 2.37/1.46 thf(fact_15_local_Oinf_Oleft__commute, axiom, (! [B2:a,A2:a,C:a]: ((((inf @ B2) @ ((inf @ A2) @ C)) = ((inf @ A2) @ ((inf @ B2) @ C)))))).
% 2.37/1.46 thf(fact_16_local_Oinf__assoc, axiom, (! [X:a,Y:a,Z2:a]: ((((inf @ ((inf @ X) @ Y)) @ Z2) = ((inf @ X) @ ((inf @ Y) @ Z2)))))).
% 2.37/1.46 thf(fact_17_local_Oinf__commute, axiom, (! [X:a,Y:a]: ((((inf @ X) @ Y) = ((inf @ Y) @ X))))).
% 2.37/1.46 thf(fact_18_local_Oinf__left__commute, axiom, (! [X:a,Y:a,Z2:a]: ((((inf @ X) @ ((inf @ Y) @ Z2)) = ((inf @ Y) @ ((inf @ X) @ Z2)))))).
% 2.37/1.46 thf(fact_19_local_Osup_Oassoc, axiom, (! [A2:a,B2:a,C:a]: ((((sup @ ((sup @ A2) @ B2)) @ C) = ((sup @ A2) @ ((sup @ B2) @ C)))))).
% 2.37/1.46 thf(fact_20_local_Osup_Ocommute, axiom, (! [A2:a,B2:a]: ((((sup @ A2) @ B2) = ((sup @ B2) @ A2))))).
% 2.37/1.46 thf(fact_21_local_Osup_Oleft__commute, axiom, (! [B2:a,A2:a,C:a]: ((((sup @ B2) @ ((sup @ A2) @ C)) = ((sup @ A2) @ ((sup @ B2) @ C)))))).
% 2.37/1.46 thf(fact_22_local_Osup__assoc, axiom, (! [X:a,Y:a,Z2:a]: ((((sup @ ((sup @ X) @ Y)) @ Z2) = ((sup @ X) @ ((sup @ Y) @ Z2)))))).
% 2.37/1.46 thf(fact_23_local_Osup__commute, axiom, (! [X:a,Y:a]: ((((sup @ X) @ Y) = ((sup @ Y) @ X))))).
% 2.37/1.46 thf(fact_24_local_Osup__left__commute, axiom, (! [X:a,Y:a,Z2:a]: ((((sup @ X) @ ((sup @ Y) @ Z2)) = ((sup @ Y) @ ((sup @ X) @ Z2)))))).
% 2.37/1.46 thf(fact_25_local_Oinf_Oabsorb1, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (((inf @ A2) @ B2) = A2))))).
% 2.37/1.46 thf(fact_26_local_Oinf_Oabsorb2, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (((inf @ A2) @ B2) = B2))))).
% 2.37/1.46 thf(fact_27_local_Oinf_Oabsorb__iff1, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) = (((inf @ A2) @ B2) = A2))))).
% 2.37/1.46 thf(fact_28_local_Oinf_Oabsorb__iff2, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) = (((inf @ A2) @ B2) = B2))))).
% 2.37/1.46 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)))))))))).
% 2.37/1.46 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))))))).
% 2.37/1.46 thf(fact_31_local_Oinf_Ocobounded1, axiom, (! [A2:a,B2:a]: (((less_eq @ ((inf @ A2) @ B2)) @ A2)))).
% 2.37/1.46 thf(fact_32_local_Oinf_Ocobounded2, axiom, (! [A2:a,B2:a]: (((less_eq @ ((inf @ A2) @ B2)) @ B2)))).
% 2.37/1.46 thf(fact_33_local_Oinf_OcoboundedI1, axiom, (! [A2:a,C:a,B2:a]: ((((less_eq @ A2) @ C) => ((less_eq @ ((inf @ A2) @ B2)) @ C))))).
% 2.37/1.46 thf(fact_34_local_Oinf_OcoboundedI2, axiom, (! [B2:a,C:a,A2:a]: ((((less_eq @ B2) @ C) => ((less_eq @ ((inf @ A2) @ B2)) @ C))))).
% 2.37/1.46 thf(fact_35_local_Oinf_OorderE, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (A2 = ((inf @ A2) @ B2)))))).
% 2.37/1.46 thf(fact_36_local_Oinf_OorderI, axiom, (! [A2:a,B2:a]: (((A2 = ((inf @ A2) @ B2)) => ((less_eq @ A2) @ B2))))).
% 2.37/1.46 thf(fact_37_local_Oinf_Oorder__iff, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) = (A2 = ((inf @ A2) @ B2)))))).
% 2.37/1.46 thf(fact_38_local_Oinf__absorb1, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) => (((inf @ X) @ Y) = X))))).
% 2.37/1.46 thf(fact_39_local_Oinf__absorb2, axiom, (! [Y:a,X:a]: ((((less_eq @ Y) @ X) => (((inf @ X) @ Y) = Y))))).
% 2.37/1.46 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))))))).
% 2.37/1.46 thf(fact_41_local_Oinf__le1, axiom, (! [X:a,Y:a]: (((less_eq @ ((inf @ X) @ Y)) @ X)))).
% 2.37/1.46 thf(fact_42_local_Oinf__le2, axiom, (! [X:a,Y:a]: (((less_eq @ ((inf @ X) @ Y)) @ Y)))).
% 2.37/1.46 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))))))).
% 2.37/1.46 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)))))))).
% 2.37/1.46 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.37/1.46 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A4)))) = A4)))).
% 2.37/1.46 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.37/1.46 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.37/1.46 thf(fact_49_local_Ole__iff__inf, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) = (((inf @ X) @ Y) = X))))).
% 2.37/1.46 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)))))))))).
% 2.37/1.46 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))))))).
% 2.37/1.46 thf(fact_52_local_Ole__infI1, axiom, (! [A2:a,X:a,B2:a]: ((((less_eq @ A2) @ X) => ((less_eq @ ((inf @ A2) @ B2)) @ X))))).
% 2.37/1.46 thf(fact_53_local_Ole__infI2, axiom, (! [B2:a,X:a,A2:a]: ((((less_eq @ B2) @ X) => ((less_eq @ ((inf @ A2) @ B2)) @ X))))).
% 2.37/1.46 thf(fact_54_local_Ole__iff__sup, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) = (((sup @ X) @ Y) = Y))))).
% 2.37/1.46 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)))))))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 thf(fact_57_local_Ole__supI1, axiom, (! [X:a,A2:a,B2:a]: ((((less_eq @ X) @ A2) => ((less_eq @ X) @ ((sup @ A2) @ B2)))))).
% 2.37/1.46 thf(fact_58_local_Ole__supI2, axiom, (! [X:a,B2:a,A2:a]: ((((less_eq @ X) @ B2) => ((less_eq @ X) @ ((sup @ A2) @ B2)))))).
% 2.37/1.46 thf(fact_59_local_Osup_Oabsorb1, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (((sup @ A2) @ B2) = A2))))).
% 2.37/1.46 thf(fact_60_local_Osup_Oabsorb2, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) => (((sup @ A2) @ B2) = B2))))).
% 2.37/1.46 thf(fact_61_local_Osup_Oabsorb__iff1, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) = (((sup @ A2) @ B2) = A2))))).
% 2.37/1.46 thf(fact_62_local_Osup_Oabsorb__iff2, axiom, (! [A2:a,B2:a]: ((((less_eq @ A2) @ B2) = (((sup @ A2) @ B2) = B2))))).
% 2.37/1.46 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)))))))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 thf(fact_65_local_Osup_Ocobounded1, axiom, (! [A2:a,B2:a]: (((less_eq @ A2) @ ((sup @ A2) @ B2))))).
% 2.37/1.46 thf(fact_66_local_Osup_Ocobounded2, axiom, (! [B2:a,A2:a]: (((less_eq @ B2) @ ((sup @ A2) @ B2))))).
% 2.37/1.46 thf(fact_67_local_Osup_OcoboundedI1, axiom, (! [C:a,A2:a,B2:a]: ((((less_eq @ C) @ A2) => ((less_eq @ C) @ ((sup @ A2) @ B2)))))).
% 2.37/1.46 thf(fact_68_local_Osup_OcoboundedI2, axiom, (! [C:a,B2:a,A2:a]: ((((less_eq @ C) @ B2) => ((less_eq @ C) @ ((sup @ A2) @ B2)))))).
% 2.37/1.46 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))))))).
% 2.37/1.46 thf(fact_70_local_Osup_OorderE, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) => (A2 = ((sup @ A2) @ B2)))))).
% 2.37/1.46 thf(fact_71_local_Osup_OorderI, axiom, (! [A2:a,B2:a]: (((A2 = ((sup @ A2) @ B2)) => ((less_eq @ B2) @ A2))))).
% 2.37/1.46 thf(fact_72_local_Osup_Oorder__iff, axiom, (! [B2:a,A2:a]: ((((less_eq @ B2) @ A2) = (A2 = ((sup @ A2) @ B2)))))).
% 2.37/1.46 thf(fact_73_local_Osup__absorb1, axiom, (! [Y:a,X:a]: ((((less_eq @ Y) @ X) => (((sup @ X) @ Y) = X))))).
% 2.37/1.46 thf(fact_74_local_Osup__absorb2, axiom, (! [X:a,Y:a]: ((((less_eq @ X) @ Y) => (((sup @ X) @ Y) = Y))))).
% 2.37/1.46 thf(fact_75_local_Osup__ge1, axiom, (! [X:a,Y:a]: (((less_eq @ X) @ ((sup @ X) @ Y))))).
% 2.37/1.46 thf(fact_76_local_Osup__ge2, axiom, (! [Y:a,X:a]: (((less_eq @ Y) @ ((sup @ X) @ Y))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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))))))).
% 2.37/1.46 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)))))))).
% 2.37/1.46 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))))))).
% 2.37/1.46 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))))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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))))).
% 2.37/1.46 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))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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))))).
% 2.37/1.46 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))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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)))))).
% 2.37/1.46 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))))))).
% 2.37/1.46 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)))))))).
% 2.37/1.46 thf(fact_100_local_Oorder_Orefl, axiom, (! [A2:a]: (((less_eq @ A2) @ A2)))).
% 2.37/1.46 thf(fact_101_local_Oorder__refl, axiom, (! [X:a]: (((less_eq @ X) @ X)))).
% 2.37/1.46 thf(fact_102_local_Oinf_Oidem, axiom, (! [A2:a]: ((((inf @ A2) @ A2) = A2)))).
% 2.37/1.46 thf(fact_103_local_Oinf_Oleft__idem, axiom, (! [A2:a,B2:a]: ((((inf @ A2) @ ((inf @ A2) @ B2)) = ((inf @ A2) @ B2))))).
% 2.37/1.46 thf(fact_104_local_Oinf_Oright__idem, axiom, (! [A2:a,B2:a]: ((((inf @ ((inf @ A2) @ B2)) @ B2) = ((inf @ A2) @ B2))))).
% 2.37/1.46 thf(fact_105_local_Oinf__idem, axiom, (! [X:a]: ((((inf @ X) @ X) = X)))).
% 2.37/1.46 thf(fact_106_local_Oinf__left__idem, axiom, (! [X:a,Y:a]: ((((inf @ X) @ ((inf @ X) @ Y)) = ((inf @ X) @ Y))))).
% 2.37/1.46 thf(fact_107_local_Oinf__right__idem, axiom, (! [X:a,Y:a]: ((((inf @ ((inf @ X) @ Y)) @ Y) = ((inf @ X) @ Y))))).
% 2.37/1.46 thf(fact_108_local_Osup_Oidem, axiom, (! [A2:a]: ((((sup @ A2) @ A2) = A2)))).
% 2.37/1.46 thf(fact_109_local_Osup_Oleft__idem, axiom, (! [A2:a,B2:a]: ((((sup @ A2) @ ((sup @ A2) @ B2)) = ((sup @ A2) @ B2))))).
% 2.37/1.46 thf(fact_110_local_Osup_Oright__idem, axiom, (! [A2:a,B2:a]: ((((sup @ ((sup @ A2) @ B2)) @ B2) = ((sup @ A2) @ B2))))).
% 2.37/1.46 thf(fact_111_local_Osup__idem, axiom, (! [X:a]: ((((sup @ X) @ X) = X)))).
% 2.37/1.46 thf(fact_112_local_Osup__left__idem, axiom, (! [X:a,Y:a]: ((((sup @ X) @ ((sup @ X) @ Y)) = ((sup @ X) @ Y))))).
% 2.37/1.46 thf(fact_113_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))))).
% 2.37/1.46 thf(fact_114_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)))))))).
% 2.37/1.46 thf(fact_115_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)))))).
% 2.37/1.46 thf(fact_116_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)))))).
% 2.37/1.46 thf(fact_117_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)))))).
% 2.37/1.46 thf(fact_118_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)))))).
% 2.37/1.46 thf(fact_119_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)))))).
% 2.37/1.46 thf(fact_120_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)))))).
% 2.37/1.46 thf(fact_121_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)))))).
% 2.37/1.46 thf(fact_122_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)))))).
% 2.37/1.46 thf(fact_123_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)))))).
% 2.37/1.46 thf(fact_124_local_Oinf__sup__absorb, axiom, (! [X:a,Y:a]: ((((inf @ X) @ ((sup @ X) @ Y)) = X)))).
% 2.37/1.46 thf(fact_125_local_Osup__inf__absorb, axiom, (! [X:a,Y:a]: ((((sup @ X) @ ((inf @ X) @ Y)) = X)))).
% 2.37/1.46 thf(fact_126_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))))).
% 2.37/1.46 thf(fact_127_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)))))).
% 2.37/1.46 thf(fact_128_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)))))).
% 2.37/1.46 thf(fact_129_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)))))))).
% 2.37/1.46 thf(fact_130_local_OLeast__equality, axiom, (! [P:(a > $o),X:a]: (((P @ X) => ((! [Y4:a]: (((P @ Y4) => ((less_eq @ X) @ Y4)))) => ((((least @ a) @ less_eq) @ P) = X)))))).
% 2.37/1.46 thf(fact_131_local_Ob__aux__def, axiom, (! [A2:a,B2:a,C:a]: ((((((((modula477145868_b_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C) = ((sup @ ((inf @ B2) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C))) @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.37/1.46 thf(fact_132_a__meet__b__eq__d, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) => (((inf @ ((((((modula105138637_a_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) @ ((((((modula477145868_b_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)) = ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ A2) @ B2) @ C)))))).
% 2.37/1.46 thf(fact_133_lattice_Oa__aux_Ocong, axiom, (! [A:$tType]: (((modula105138637_a_aux @ A) = (modula105138637_a_aux @ A))))).
% 2.37/1.46 thf(fact_134_lattice_Oc__aux_Ocong, axiom, (! [A:$tType]: (((modula849153099_c_aux @ A) = (modula849153099_c_aux @ A))))).
% 2.37/1.46 thf(fact_135_lattice_Od__aux_Ocong, axiom, (! [A:$tType]: (((modula1221160330_d_aux @ A) = (modula1221160330_d_aux @ A))))).
% 2.37/1.46 thf(fact_136_lattice_Oe__aux_Ocong, axiom, (! [A:$tType]: (((modula1593167561_e_aux @ A) = (modula1593167561_e_aux @ A))))).
% 2.37/1.46 thf(fact_137_local_Ocomp__fun__idem__sup, axiom, (((finite_comp_fun_idem @ a) @ a) @ sup)).
% 2.37/1.46 thf(fact_138_local_Ocomp__fun__idem__inf, axiom, (((finite_comp_fun_idem @ a) @ a) @ inf)).
% 2.37/1.46 thf(fact_139_local_Osup_Osemigroup__axioms, axiom, ((semigroup @ a) @ sup)).
% 2.37/1.46 thf(fact_140_local_Oinf_Osemigroup__axioms, axiom, ((semigroup @ a) @ inf)).
% 2.37/1.46 thf(fact_141_local_Osup_Osemilattice__axioms, axiom, ((semilattice @ a) @ sup)).
% 2.37/1.46 thf(fact_142_local_Oinf_Osemilattice__axioms, axiom, ((semilattice @ a) @ inf)).
% 2.37/1.46 thf(fact_143_local_Osup_Oabel__semigroup__axioms, axiom, ((abel_semigroup @ a) @ sup)).
% 2.37/1.46 thf(fact_144_local_Oinf_Oabel__semigroup__axioms, axiom, ((abel_semigroup @ a) @ inf)).
% 2.37/1.46 thf(fact_145_local_OSup__fin_Osemilattice__set__axioms, axiom, ((lattic35693393ce_set @ a) @ sup)).
% 2.37/1.46 thf(fact_146_local_OInf__fin_Osemilattice__set__axioms, axiom, ((lattic35693393ce_set @ a) @ inf)).
% 2.37/1.46 thf(fact_147_local_Obdd__above__def, axiom, (! [A4:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ A4) = (? [M:a]: ((! [X2:a]: (((((member @ a) @ X2) @ A4) => ((less_eq @ X2) @ M)))))))))).
% 2.37/1.46 thf(fact_148_local_Obdd__below__def, axiom, (! [A4:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ A4) = (? [M2:a]: ((! [X2:a]: (((((member @ a) @ X2) @ A4) => ((less_eq @ M2) @ X2)))))))))).
% 2.37/1.46 thf(fact_149_local_Obdd__belowI, axiom, (! [A4:(set @ a),M3:a]: (((! [X3:a]: (((((member @ a) @ X3) @ A4) => ((less_eq @ M3) @ X3)))) => (((condit1201339847_below @ a) @ less_eq) @ A4))))).
% 2.37/1.46 thf(fact_150_local_Obdd__aboveI, axiom, (! [A4:(set @ a),M4:a]: (((! [X3:a]: (((((member @ a) @ X3) @ A4) => ((less_eq @ X3) @ M4)))) => (((condit2040224947_above @ a) @ less_eq) @ A4))))).
% 2.37/1.46 thf(fact_151_lattice_Oincomp_Ocong, axiom, (! [A:$tType]: (((modula1937309406incomp @ A) = (modula1937309406incomp @ A))))).
% 2.37/1.46 thf(fact_152_lattice_Ob__aux_Ocong, axiom, (! [A:$tType]: (((modula477145868_b_aux @ A) = (modula477145868_b_aux @ A))))).
% 2.37/1.46 thf(fact_153_abel__semigroup_Oaxioms_I1_J, axiom, (! [A:$tType,F:(A > (A > A))]: ((((abel_semigroup @ A) @ F) => ((semigroup @ A) @ F))))).
% 2.37/1.46 thf(fact_154_semilattice__set__def, axiom, (! [A:$tType]: (((lattic35693393ce_set @ A) = (semilattice @ A))))).
% 2.37/1.46 thf(fact_155_semilattice__set_Ointro, axiom, (! [A:$tType,F:(A > (A > A))]: ((((semilattice @ A) @ F) => ((lattic35693393ce_set @ A) @ F))))).
% 2.37/1.46 thf(fact_156_abel__semigroup_Oleft__commute, axiom, (! [A:$tType,F:(A > (A > A)),B2:A,A2:A,C:A]: ((((abel_semigroup @ A) @ F) => (((F @ B2) @ ((F @ A2) @ C)) = ((F @ A2) @ ((F @ B2) @ C))))))).
% 2.37/1.46 thf(fact_157_abel__semigroup_Ocommute, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A]: ((((abel_semigroup @ A) @ F) => (((F @ A2) @ B2) = ((F @ B2) @ A2)))))).
% 2.37/1.46 thf(fact_158_semigroup_Ointro, axiom, (! [A:$tType,F:(A > (A > A))]: (((! [A5:A,B4:A,C2:A]: ((((F @ ((F @ A5) @ B4)) @ C2) = ((F @ A5) @ ((F @ B4) @ C2))))) => ((semigroup @ A) @ F))))).
% 2.37/1.46 thf(fact_159_semigroup_Oassoc, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A,C:A]: ((((semigroup @ A) @ F) => (((F @ ((F @ A2) @ B2)) @ C) = ((F @ A2) @ ((F @ B2) @ C))))))).
% 2.37/1.46 thf(fact_160_semigroup__def, axiom, (! [A:$tType]: (((semigroup @ A) = (^ [F2:(A > (A > A))]: ((! [A3:A,B3:A,C3:A]: ((((F2 @ ((F2 @ A3) @ B3)) @ C3) = ((F2 @ A3) @ ((F2 @ B3) @ C3))))))))))).
% 2.37/1.46 thf(fact_161_semilattice__set_Oaxioms, axiom, (! [A:$tType,F:(A > (A > A))]: ((((lattic35693393ce_set @ A) @ F) => ((semilattice @ A) @ F))))).
% 2.37/1.46 thf(fact_162_semilattice_Oaxioms_I1_J, axiom, (! [A:$tType,F:(A > (A > A))]: ((((semilattice @ A) @ F) => ((abel_semigroup @ A) @ F))))).
% 2.37/1.46 thf(fact_163_local_Obdd__above__mono, axiom, (! [B5:(set @ a),A4:(set @ a)]: (((((condit2040224947_above @ a) @ less_eq) @ B5) => ((((ord_less_eq @ (set @ a)) @ A4) @ B5) => (((condit2040224947_above @ a) @ less_eq) @ A4)))))).
% 2.37/1.46 thf(fact_164_local_Obdd__below__mono, axiom, (! [B5:(set @ a),A4:(set @ a)]: (((((condit1201339847_below @ a) @ less_eq) @ B5) => ((((ord_less_eq @ (set @ a)) @ A4) @ B5) => (((condit1201339847_below @ a) @ less_eq) @ A4)))))).
% 2.37/1.46 thf(fact_165_local_Oantimono__def, axiom, (! [B:$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)))))))))))).
% 2.37/1.46 thf(fact_166_local_OantimonoI, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: (((! [X3:a,Y4:a]: ((((less_eq @ X3) @ Y4) => (((ord_less_eq @ B) @ (F @ Y4)) @ (F @ X3))))) => ((((antimono @ a) @ B) @ less_eq) @ F)))))))).
% 2.37/1.46 thf(fact_167_local_OantimonoE, axiom, (! [B:$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)))))))))).
% 2.37/1.46 thf(fact_168_local_OantimonoD, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B),X:a,Y:a]: ((((((antimono @ a) @ B) @ less_eq) @ F) => (((less_eq @ X) @ Y) => (((ord_less_eq @ B) @ (F @ Y)) @ (F @ X)))))))))).
% 2.37/1.46 thf(fact_169_local_OmonoD, axiom, (! [B:$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)))))))))).
% 2.37/1.46 thf(fact_170_local_OmonoE, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B),X:a,Y:a]: ((((((mono @ a) @ B) @ less_eq) @ F) => (((less_eq @ X) @ Y) => (((ord_less_eq @ B) @ (F @ X)) @ (F @ Y)))))))))).
% 2.37/1.46 thf(fact_171_local_OmonoI, axiom, (! [B:$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)))))))).
% 2.37/1.46 thf(fact_172_local_Omono__def, axiom, (! [B:$tType]: (((order @ B) => (! [F:(a > B)]: ((((((mono @ a) @ B) @ less_eq) @ F) = (! [X2:a,Y3:a]: ((((less_eq @ X2) @ Y3) => (((ord_less_eq @ B) @ (F @ X2)) @ (F @ Y3)))))))))))).
% 2.37/1.46 thf(fact_173_semilattice_Oidem, axiom, (! [A:$tType,F:(A > (A > A)),A2:A]: ((((semilattice @ A) @ F) => (((F @ A2) @ A2) = A2))))).
% 2.37/1.46 thf(fact_174_semilattice_Oleft__idem, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A]: ((((semilattice @ A) @ F) => (((F @ A2) @ ((F @ A2) @ B2)) = ((F @ A2) @ B2)))))).
% 2.37/1.46 thf(fact_175_semilattice_Oright__idem, axiom, (! [A:$tType,F:(A > (A > A)),A2:A,B2:A]: ((((semilattice @ A) @ F) => (((F @ ((F @ A2) @ B2)) @ B2) = ((F @ A2) @ B2)))))).
% 2.37/1.46 thf(fact_176_subsetI, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A4) => (((member @ A) @ X3) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.37/1.46 thf(fact_177_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A4) => (A4 = B5)))))).
% 2.37/1.46 thf(fact_178_preorder__class_Oorder__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.37/1.46 thf(fact_179_order_Oantimono_Ocong, axiom, (! [B:$tType,A:$tType]: (((order @ B) => (((antimono @ A) @ B) = ((antimono @ A) @ B)))))).
% 2.37/1.46 thf(fact_180_order_Omono_Ocong, axiom, (! [B:$tType,A:$tType]: (((order @ B) => (((mono @ A) @ B) = ((mono @ A) @ B)))))).
% 2.37/1.46 thf(fact_181_order__class_Odual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.37/1.46 thf(fact_182_order__class_Odual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y2:A,Z:A]: ((Y2 = Z))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ B3) @ A3) & (((ord_less_eq @ A) @ A3) @ B3))))))))).
% 2.37/1.46 thf(fact_183_order__class_Odual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 2.37/1.46 thf(fact_184_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A5:A,B4:A]: (((((ord_less_eq @ A) @ A5) @ B4) => ((P @ A5) @ B4)))) => ((! [A5:A,B4:A]: ((((P @ B4) @ A5) => ((P @ A5) @ B4)))) => ((P @ A2) @ B2))))))))).
% 2.37/1.46 thf(fact_185_order__class_Odual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.37/1.46 thf(fact_186_preorder__class_Oorder__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 2.37/1.46 thf(fact_187_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.37/1.46 thf(fact_188_ord__class_Oord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.37/1.46 thf(fact_189_ord__class_Oord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.37/1.46 thf(fact_190_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y2:A,Z:A]: ((Y2 = Z))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) & (((ord_less_eq @ A) @ B3) @ A3))))))))).
% 2.37/1.46 thf(fact_191_order__class_Oantisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 2.37/1.46 thf(fact_192_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 2.37/1.46 thf(fact_193_order__class_Oorder_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.37/1.46 thf(fact_194_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.37/1.46 thf(fact_195_preorder__class_Oeq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.37/1.46 thf(fact_196_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.37/1.46 thf(fact_197_order__class_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.37/1.46 thf(fact_198_order__class_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y2:A,Z:A]: ((Y2 = Z))) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X2))))))))).
% 2.37/1.46 thf(fact_199_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C)))))))))).
% 2.37/1.46 thf(fact_200_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 2.37/1.46 thf(fact_201_order__subst2, axiom, (! [A:$tType,C4:$tType]: ((((order @ C4) & (order @ A)) => (! [A2:A,B2:A,F:(A > C4),C:C4]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C4) @ (F @ B2)) @ C) => ((! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ C4) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ C4) @ (F @ A2)) @ C)))))))))).
% 2.37/1.46 thf(fact_202_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 2.37/1.46 thf(fact_203_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 2.37/1.46 thf(fact_204_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.37/1.46 thf(fact_205_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.37/1.46 thf(fact_206_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.37/1.46 thf(fact_207_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P @ X2) => (Q @ X2)))))))).
% 2.37/1.46 thf(fact_208_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y2:(set @ A),Z:(set @ A)]: ((Y2 = Z))) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))).
% 2.37/1.46 thf(fact_209_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C5) => (((ord_less_eq @ (set @ A)) @ A4) @ C5)))))).
% 2.37/1.46 thf(fact_210_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.37/1.46 thf(fact_211_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 2.37/1.46 thf(fact_212_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A6) => (((member @ A) @ T) @ B6)))))))))).
% 2.37/1.46 thf(fact_213_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A4))))).
% 2.37/1.46 thf(fact_214_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.37/1.46 thf(fact_215_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A6) => (((member @ A) @ X2) @ B6)))))))))).
% 2.37/1.46 thf(fact_216_equalityE, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))))).
% 2.37/1.46 thf(fact_217_subsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C) @ A4) => (((member @ A) @ C) @ B5)))))).
% 2.37/1.46 thf(fact_218_in__mono, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B5)))))).
% 2.37/1.46 thf(fact_219_ord_OLeast_Ocong, axiom, (! [A:$tType]: (((least @ A) = (least @ A))))).
% 2.37/1.46 thf(fact_220_order_OGreatest_Ocong, axiom, (! [A:$tType]: (((greatest @ A) = (greatest @ A))))).
% 2.37/1.46 thf(fact_221_ord_Omin_Ocong, axiom, (! [A:$tType]: (((min @ A) = (min @ A))))).
% 2.37/1.46 thf(fact_222_ord_Omax_Ocong, axiom, (! [A:$tType]: (((max @ A) = (max @ A))))).
% 2.37/1.46 thf(fact_223_ord_Omin__def, axiom, (! [A:$tType]: (((min @ A) = (^ [Less_eq:(A > (A > $o)),A3:A,B3:A]: (((((if @ A) @ ((Less_eq @ A3) @ B3)) @ A3) @ B3))))))).
% 2.37/1.46 thf(fact_224_ord_Omax__def, axiom, (! [A:$tType]: (((max @ A) = (^ [Less_eq:(A > (A > $o)),A3:A,B3:A]: (((((if @ A) @ ((Less_eq @ A3) @ B3)) @ B3) @ A3))))))).
% 2.37/1.46 thf(fact_225_local_Omono__inf, axiom, (! [B:$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)))))))))).
% 2.37/1.46 thf(fact_226_local_Omono__sup, axiom, (! [B:$tType]: (((semilattice_sup @ B) => (! [F:(a > B),A4:a,B5:a]: ((((((mono @ a) @ B) @ less_eq) @ F) => (((ord_less_eq @ B) @ (((sup_sup @ B) @ (F @ A4)) @ (F @ B5))) @ (F @ ((sup @ A4) @ B5)))))))))).
% 2.37/1.46 thf(fact_227_local_Obdd__above__finite, axiom, (! [A4:(set @ a)]: ((((finite_finite @ a) @ A4) => (((condit2040224947_above @ a) @ less_eq) @ A4))))).
% 2.37/1.46 thf(fact_228_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)))))))))))))).
% 2.37/1.46 thf(fact_229_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)))))))))))))).
% 2.37/1.46 thf(fact_230_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)))))).
% 2.37/1.46 thf(fact_231_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)))))).
% 2.37/1.46 thf(fact_232_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)))))).
% 2.37/1.46 thf(fact_233_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)))))).
% 2.37/1.46 thf(fact_234_local_Obdd__below__finite, axiom, (! [A4:(set @ a)]: ((((finite_finite @ a) @ A4) => (((condit1201339847_below @ a) @ less_eq) @ A4))))).
% 2.37/1.46 thf(fact_235_Un__subset__iff, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) @ C5) = ((((ord_less_eq @ (set @ A)) @ A4) @ C5) & (((ord_less_eq @ (set @ A)) @ B5) @ C5)))))).
% 2.37/1.46 thf(fact_236_Int__subset__iff, axiom, (! [A:$tType,C5:(set @ A),A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C5) @ (((inf_inf @ (set @ A)) @ A4) @ B5)) = ((((ord_less_eq @ (set @ A)) @ C5) @ A4) & (((ord_less_eq @ (set @ A)) @ C5) @ B5)))))).
% 2.37/1.46 thf(fact_237_semilattice__inf__class_Oinf__right__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Y) = (((inf_inf @ A) @ X) @ Y)))))))).
% 2.37/1.46 thf(fact_238_semilattice__inf__class_Oinf_Oright__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.37/1.46 thf(fact_239_semilattice__inf__class_Oinf__left__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = (((inf_inf @ A) @ X) @ Y)))))))).
% 2.37/1.46 thf(fact_240_semilattice__inf__class_Oinf_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B2)) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.37/1.46 thf(fact_241_semilattice__inf__class_Oinf__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A]: (((((inf_inf @ A) @ X) @ X) = X))))))).
% 2.37/1.46 thf(fact_242_semilattice__inf__class_Oinf_Oidem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 2.37/1.46 thf(fact_243_inf__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((inf_inf @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 2.37/1.46 thf(fact_244_semilattice__sup__class_Osup_Oright__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ B2) = (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.37/1.46 thf(fact_245_semilattice__sup__class_Osup__left__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.37/1.46 thf(fact_246_semilattice__sup__class_Osup_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: (((((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B2)) = (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.37/1.46 thf(fact_247_semilattice__sup__class_Osup__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 2.37/1.46 thf(fact_248_semilattice__sup__class_Osup_Oidem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ A2) = A2))))))).
% 2.37/1.46 thf(fact_249_sup__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 2.37/1.46 thf(fact_250_semilattice__inf__class_Ole__inf__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z2)) = ((((ord_less_eq @ A) @ X) @ Y) & (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 2.37/1.46 thf(fact_251_semilattice__inf__class_Oinf_Obounded__iff, axiom, (! [A:$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))))))))).
% 2.37/1.46 thf(fact_252_semilattice__sup__class_Ole__sup__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z2) = ((((ord_less_eq @ A) @ X) @ Z2) & (((ord_less_eq @ A) @ Y) @ Z2))))))))).
% 2.37/1.46 thf(fact_253_semilattice__sup__class_Osup_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,C:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C)) @ A2) = ((((ord_less_eq @ A) @ B2) @ A2) & (((ord_less_eq @ A) @ C) @ A2))))))))).
% 2.37/1.46 thf(fact_254_lattice__class_Osup__inf__absorb, axiom, (! [A:$tType]: (((lattice @ A) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = X))))))).
% 2.37/1.46 thf(fact_255_lattice__class_Oinf__sup__absorb, axiom, (! [A:$tType]: (((lattice @ A) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = X))))))).
% 2.37/1.46 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A7:$tType,A8:$tType]: (((semilattice_sup @ A8) => (semilattice_sup @ (A7 > A8)))))).
% 2.37/1.46 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A7:$tType,A8:$tType]: (((semilattice_inf @ A8) => (semilattice_inf @ (A7 > A8)))))).
% 2.37/1.46 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 2.37/1.46 thf(tcon_fun___Lattices_Olattice, axiom, (! [A7:$tType,A8:$tType]: (((lattice @ A8) => (lattice @ (A7 > A8)))))).
% 2.37/1.46 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 2.37/1.46 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.37/1.46 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1, axiom, (! [A7:$tType]: ((semilattice_sup @ (set @ A7))))).
% 2.37/1.46 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_2, axiom, (! [A7:$tType]: ((semilattice_inf @ (set @ A7))))).
% 2.37/1.46 thf(tcon_Set_Oset___Orderings_Opreorder_3, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 2.37/1.46 thf(tcon_Set_Oset___Lattices_Olattice_4, axiom, (! [A7:$tType]: ((lattice @ (set @ A7))))).
% 2.37/1.46 thf(tcon_Set_Oset___Orderings_Oorder_5, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 2.37/1.46 thf(tcon_Set_Oset___Orderings_Oord_6, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.37/1.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_7, axiom, (semilattice_sup @ $o)).
% 2.37/1.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_8, axiom, (semilattice_inf @ $o)).
% 2.37/1.46 thf(tcon_HOL_Obool___Orderings_Opreorder_9, axiom, (preorder @ $o)).
% 2.37/1.46 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.37/1.46 thf(tcon_HOL_Obool___Lattices_Olattice_10, axiom, (lattice @ $o)).
% 2.37/1.46 thf(tcon_HOL_Obool___Orderings_Oorder_11, axiom, (order @ $o)).
% 2.37/1.46 thf(tcon_HOL_Obool___Orderings_Oord_12, axiom, (ord @ $o)).
% 2.37/1.46 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.37/1.46 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.37/1.46 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.37/1.46 thf(conj_0, hypothesis, ((less_eq @ ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)) @ ((((((modula1593167561_e_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))).
% 2.37/1.46 thf(conj_1, conjecture, (((inf @ ((((((modula105138637_a_aux @ a) @ inf) @ sup) @ b) @ c) @ a2)) @ ((((((modula849153099_c_aux @ a) @ inf) @ sup) @ a2) @ b) @ c)) = ((((((modula1221160330_d_aux @ a) @ inf) @ sup) @ a2) @ b) @ c))).
% 2.37/1.46 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2DTF32551.p
% 2.37/1.47 ------------------------
% 2.55/1.50 ---- Cleaned THF ---
% 2.55/1.50 thf(ty_t_Set_Oset,type,
% 2.55/1.50 set: $tType > $tType ).
% 2.55/1.50
% 2.55/1.50 thf(ty_tf_a,type,
% 2.55/1.50 a: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(sy_cl_HOL_Otype,type,
% 2.55/1.50 type:
% 2.55/1.50 !>[A: $tType] : $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_cl_Orderings_Oord,type,
% 2.55/1.50 ord:
% 2.55/1.50 !>[A: $tType] : $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_cl_Orderings_Oorder,type,
% 2.55/1.50 order:
% 2.55/1.50 !>[A: $tType] : $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_cl_Lattices_Olattice,type,
% 2.55/1.50 lattice:
% 2.55/1.50 !>[A: $tType] : $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_cl_Orderings_Olinorder,type,
% 2.55/1.50 linorder:
% 2.55/1.50 !>[A: $tType] : $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_cl_Orderings_Opreorder,type,
% 2.55/1.50 preorder:
% 2.55/1.50 !>[A: $tType] : $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 2.55/1.50 semilattice_inf:
% 2.55/1.50 !>[A: $tType] : $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.55/1.50 semilattice_sup:
% 2.55/1.50 !>[A: $tType] : $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above,type,
% 2.55/1.50 condit2040224947_above:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below,type,
% 2.55/1.50 condit1201339847_below:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Finite__Set_Ocomp__fun__idem,type,
% 2.55/1.50 finite_comp_fun_idem:
% 2.55/1.50 !>[A: $tType,B: $tType] : ( ( A > B > B ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Finite__Set_Ofinite,type,
% 2.55/1.50 finite_finite:
% 2.55/1.50 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Groups_Oabel__semigroup,type,
% 2.55/1.50 abel_semigroup:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Groups_Osemigroup,type,
% 2.55/1.50 semigroup:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_If,type,
% 2.55/1.50 if:
% 2.55/1.50 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 2.55/1.50 inf_inf:
% 2.55/1.50 !>[A: $tType] : ( A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Lattices_Osemilattice,type,
% 2.55/1.50 semilattice:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.55/1.50 sup_sup:
% 2.55/1.50 !>[A: $tType] : ( A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Lattices__Big_Osemilattice__set,type,
% 2.55/1.50 lattic35693393ce_set:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oa__aux,type,
% 2.55/1.50 modula105138637_a_aux:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Ob__aux,type,
% 2.55/1.50 modula477145868_b_aux:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oc__aux,type,
% 2.55/1.50 modula849153099_c_aux:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Od__aux,type,
% 2.55/1.50 modula1221160330_d_aux:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oe__aux,type,
% 2.55/1.50 modula1593167561_e_aux:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > A ) > ( A > A > A ) > A > A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Modular__Distrib__Lattice__Mirabelle__sluygzlgpl_Olattice_Oincomp,type,
% 2.55/1.50 modula1937309406incomp:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oord_OLeast,type,
% 2.55/1.50 least:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oord_Omax,type,
% 2.55/1.50 max:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oord_Omin,type,
% 2.55/1.50 min:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.55/1.50 ord_less_eq:
% 2.55/1.50 !>[A: $tType] : ( A > A > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oorder_OGreatest,type,
% 2.55/1.50 greatest:
% 2.55/1.50 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > A ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oorder_Oantimono,type,
% 2.55/1.50 antimono:
% 2.55/1.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oorder_Omono,type,
% 2.55/1.50 mono:
% 2.55/1.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Set_OCollect,type,
% 2.55/1.50 collect:
% 2.55/1.50 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_member,type,
% 2.55/1.50 member:
% 2.55/1.50 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_a,type,
% 2.55/1.50 a2: a ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_b,type,
% 2.55/1.50 b: a ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_c,type,
% 2.55/1.50 c: a ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_inf,type,
% 2.55/1.50 inf: a > a > a ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_less__eq,type,
% 2.55/1.50 less_eq: a > a > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_sup,type,
% 2.55/1.50 sup: a > a > a ).
% 2.55/1.50
% 2.55/1.50 thf(fact_0_local_Oantisym,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( less_eq @ X @ Y )
% 2.55/1.50 => ( ( less_eq @ Y @ X )
% 2.55/1.50 => ( X = Y ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_1_local_Oantisym__conv,axiom,
% 2.55/1.50 ! [Y: a,X: a] :
% 2.55/1.50 ( ( less_eq @ Y @ X )
% 2.55/1.50 => ( ( less_eq @ X @ Y )
% 2.55/1.50 = ( X = Y ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_2_local_Odual__order_Oantisym,axiom,
% 2.55/1.50 ! [B2: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 => ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( A2 = B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_3_local_Odual__order_Oeq__iff,axiom,
% 2.55/1.50 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.55/1.50 = ( ^ [A3: a,B3: a] :
% 2.55/1.50 ( ( less_eq @ B3 @ A3 )
% 2.55/1.50 & ( less_eq @ A3 @ B3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_4_local_Odual__order_Otrans,axiom,
% 2.55/1.50 ! [B2: a,A2: a,C: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 => ( ( less_eq @ C @ B2 )
% 2.55/1.50 => ( less_eq @ C @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_5_local_Oeq__iff,axiom,
% 2.55/1.50 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.55/1.50 = ( ^ [X2: a,Y3: a] :
% 2.55/1.50 ( ( less_eq @ X2 @ Y3 )
% 2.55/1.50 & ( less_eq @ Y3 @ X2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_6_local_Oeq__refl,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( X = Y )
% 2.55/1.50 => ( less_eq @ X @ Y ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_7_local_Oord__eq__le__trans,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( A2 = B2 )
% 2.55/1.50 => ( ( less_eq @ B2 @ C )
% 2.55/1.50 => ( less_eq @ A2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_8_local_Oord__le__eq__trans,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( B2 = C )
% 2.55/1.50 => ( less_eq @ A2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_9_local_Oorder_Oantisym,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 => ( A2 = B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_10_local_Oorder_Oeq__iff,axiom,
% 2.55/1.50 ( ( ^ [Y2: a,Z: a] : ( Y2 = Z ) )
% 2.55/1.50 = ( ^ [A3: a,B3: a] :
% 2.55/1.50 ( ( less_eq @ A3 @ B3 )
% 2.55/1.50 & ( less_eq @ B3 @ A3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_11_local_Oorder_Otrans,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( less_eq @ B2 @ C )
% 2.55/1.50 => ( less_eq @ A2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_12_local_Oorder__trans,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ( less_eq @ X @ Y )
% 2.55/1.50 => ( ( less_eq @ Y @ Z2 )
% 2.55/1.50 => ( less_eq @ X @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_13_local_Oinf_Oassoc,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( inf @ ( inf @ A2 @ B2 ) @ C )
% 2.55/1.50 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_14_local_Oinf_Ocommute,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( inf @ A2 @ B2 )
% 2.55/1.50 = ( inf @ B2 @ A2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_15_local_Oinf_Oleft__commute,axiom,
% 2.55/1.50 ! [B2: a,A2: a,C: a] :
% 2.55/1.50 ( ( inf @ B2 @ ( inf @ A2 @ C ) )
% 2.55/1.50 = ( inf @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_16_local_Oinf__assoc,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ( inf @ ( inf @ X @ Y ) @ Z2 )
% 2.55/1.50 = ( inf @ X @ ( inf @ Y @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_17_local_Oinf__commute,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( inf @ X @ Y )
% 2.55/1.50 = ( inf @ Y @ X ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_18_local_Oinf__left__commute,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ( inf @ X @ ( inf @ Y @ Z2 ) )
% 2.55/1.50 = ( inf @ Y @ ( inf @ X @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_19_local_Osup_Oassoc,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( sup @ ( sup @ A2 @ B2 ) @ C )
% 2.55/1.50 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_20_local_Osup_Ocommute,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( sup @ A2 @ B2 )
% 2.55/1.50 = ( sup @ B2 @ A2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_21_local_Osup_Oleft__commute,axiom,
% 2.55/1.50 ! [B2: a,A2: a,C: a] :
% 2.55/1.50 ( ( sup @ B2 @ ( sup @ A2 @ C ) )
% 2.55/1.50 = ( sup @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_22_local_Osup__assoc,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ( sup @ ( sup @ X @ Y ) @ Z2 )
% 2.55/1.50 = ( sup @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_23_local_Osup__commute,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( sup @ X @ Y )
% 2.55/1.50 = ( sup @ Y @ X ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_24_local_Osup__left__commute,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ( sup @ X @ ( sup @ Y @ Z2 ) )
% 2.55/1.50 = ( sup @ Y @ ( sup @ X @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_25_local_Oinf_Oabsorb1,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( inf @ A2 @ B2 )
% 2.55/1.50 = A2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_26_local_Oinf_Oabsorb2,axiom,
% 2.55/1.50 ! [B2: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 => ( ( inf @ A2 @ B2 )
% 2.55/1.50 = B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_27_local_Oinf_Oabsorb__iff1,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 = ( ( inf @ A2 @ B2 )
% 2.55/1.50 = A2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_28_local_Oinf_Oabsorb__iff2,axiom,
% 2.55/1.50 ! [B2: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 = ( ( inf @ A2 @ B2 )
% 2.55/1.50 = B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_29_local_Oinf_OboundedE,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 2.55/1.50 => ~ ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ~ ( less_eq @ A2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_30_local_Oinf_OboundedI,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( less_eq @ A2 @ C )
% 2.55/1.50 => ( less_eq @ A2 @ ( inf @ B2 @ C ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_31_local_Oinf_Ocobounded1,axiom,
% 2.55/1.50 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ A2 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_32_local_Oinf_Ocobounded2,axiom,
% 2.55/1.50 ! [A2: a,B2: a] : ( less_eq @ ( inf @ A2 @ B2 ) @ B2 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_33_local_Oinf_OcoboundedI1,axiom,
% 2.55/1.50 ! [A2: a,C: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ C )
% 2.55/1.50 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_34_local_Oinf_OcoboundedI2,axiom,
% 2.55/1.50 ! [B2: a,C: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ C )
% 2.55/1.50 => ( less_eq @ ( inf @ A2 @ B2 ) @ C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_35_local_Oinf_OorderE,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( A2
% 2.55/1.50 = ( inf @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_36_local_Oinf_OorderI,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( A2
% 2.55/1.50 = ( inf @ A2 @ B2 ) )
% 2.55/1.50 => ( less_eq @ A2 @ B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_37_local_Oinf_Oorder__iff,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 = ( A2
% 2.55/1.50 = ( inf @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_38_local_Oinf__absorb1,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( less_eq @ X @ Y )
% 2.55/1.50 => ( ( inf @ X @ Y )
% 2.55/1.50 = X ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_39_local_Oinf__absorb2,axiom,
% 2.55/1.50 ! [Y: a,X: a] :
% 2.55/1.50 ( ( less_eq @ Y @ X )
% 2.55/1.50 => ( ( inf @ X @ Y )
% 2.55/1.50 = Y ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_40_local_Oinf__greatest,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ( less_eq @ X @ Y )
% 2.55/1.50 => ( ( less_eq @ X @ Z2 )
% 2.55/1.50 => ( less_eq @ X @ ( inf @ Y @ Z2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_41_local_Oinf__le1,axiom,
% 2.55/1.50 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ X ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_42_local_Oinf__le2,axiom,
% 2.55/1.50 ! [X: a,Y: a] : ( less_eq @ ( inf @ X @ Y ) @ Y ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_43_local_Oinf__mono,axiom,
% 2.55/1.50 ! [A2: a,C: a,B2: a,D: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ C )
% 2.55/1.50 => ( ( less_eq @ B2 @ D )
% 2.55/1.50 => ( less_eq @ ( inf @ A2 @ B2 ) @ ( inf @ C @ D ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_44_local_Oinf__unique,axiom,
% 2.55/1.50 ! [F: a > a > a,X: a,Y: a] :
% 2.55/1.50 ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ X3 )
% 2.55/1.50 => ( ! [X3: a,Y4: a] : ( less_eq @ ( F @ X3 @ Y4 ) @ Y4 )
% 2.55/1.50 => ( ! [X3: a,Y4: a,Z3: a] :
% 2.55/1.50 ( ( less_eq @ X3 @ Y4 )
% 2.55/1.50 => ( ( less_eq @ X3 @ Z3 )
% 2.55/1.50 => ( less_eq @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 2.55/1.50 => ( ( inf @ X @ Y )
% 2.55/1.50 = ( F @ X @ Y ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_45_mem__Collect__eq,axiom,
% 2.55/1.50 ! [A: $tType,A2: A,P: A > $o] :
% 2.55/1.50 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.55/1.50 = ( P @ A2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_46_Collect__mem__eq,axiom,
% 2.55/1.50 ! [A: $tType,A4: set @ A] :
% 2.55/1.50 ( ( collect @ A
% 2.55/1.50 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 2.55/1.50 = A4 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_47_Collect__cong,axiom,
% 2.55/1.50 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.55/1.50 ( ! [X3: A] :
% 2.55/1.50 ( ( P @ X3 )
% 2.55/1.50 = ( Q @ X3 ) )
% 2.55/1.50 => ( ( collect @ A @ P )
% 2.55/1.50 = ( collect @ A @ Q ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_48_ext,axiom,
% 2.55/1.50 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.55/1.50 ( ! [X3: A] :
% 2.55/1.50 ( ( F @ X3 )
% 2.55/1.50 = ( G @ X3 ) )
% 2.55/1.50 => ( F = G ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_49_local_Ole__iff__inf,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( less_eq @ X @ Y )
% 2.55/1.50 = ( ( inf @ X @ Y )
% 2.55/1.50 = X ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_50_local_Ole__infE,axiom,
% 2.55/1.50 ! [X: a,A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ X @ ( inf @ A2 @ B2 ) )
% 2.55/1.50 => ~ ( ( less_eq @ X @ A2 )
% 2.55/1.50 => ~ ( less_eq @ X @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_51_local_Ole__infI,axiom,
% 2.55/1.50 ! [X: a,A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ X @ A2 )
% 2.55/1.50 => ( ( less_eq @ X @ B2 )
% 2.55/1.50 => ( less_eq @ X @ ( inf @ A2 @ B2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_52_local_Ole__infI1,axiom,
% 2.55/1.50 ! [A2: a,X: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ X )
% 2.55/1.50 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_53_local_Ole__infI2,axiom,
% 2.55/1.50 ! [B2: a,X: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ X )
% 2.55/1.50 => ( less_eq @ ( inf @ A2 @ B2 ) @ X ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_54_local_Ole__iff__sup,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( less_eq @ X @ Y )
% 2.55/1.50 = ( ( sup @ X @ Y )
% 2.55/1.50 = Y ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_55_local_Ole__supE,axiom,
% 2.55/1.50 ! [A2: a,B2: a,X: a] :
% 2.55/1.50 ( ( less_eq @ ( sup @ A2 @ B2 ) @ X )
% 2.55/1.50 => ~ ( ( less_eq @ A2 @ X )
% 2.55/1.50 => ~ ( less_eq @ B2 @ X ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_56_local_Ole__supI,axiom,
% 2.55/1.50 ! [A2: a,X: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ X )
% 2.55/1.50 => ( ( less_eq @ B2 @ X )
% 2.55/1.50 => ( less_eq @ ( sup @ A2 @ B2 ) @ X ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_57_local_Ole__supI1,axiom,
% 2.55/1.50 ! [X: a,A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ X @ A2 )
% 2.55/1.50 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_58_local_Ole__supI2,axiom,
% 2.55/1.50 ! [X: a,B2: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ X @ B2 )
% 2.55/1.50 => ( less_eq @ X @ ( sup @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_59_local_Osup_Oabsorb1,axiom,
% 2.55/1.50 ! [B2: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 => ( ( sup @ A2 @ B2 )
% 2.55/1.50 = A2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_60_local_Osup_Oabsorb2,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( sup @ A2 @ B2 )
% 2.55/1.50 = B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_61_local_Osup_Oabsorb__iff1,axiom,
% 2.55/1.50 ! [B2: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 = ( ( sup @ A2 @ B2 )
% 2.55/1.50 = A2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_62_local_Osup_Oabsorb__iff2,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 = ( ( sup @ A2 @ B2 )
% 2.55/1.50 = B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_63_local_Osup_OboundedE,axiom,
% 2.55/1.50 ! [B2: a,C: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 2.55/1.50 => ~ ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 => ~ ( less_eq @ C @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_64_local_Osup_OboundedI,axiom,
% 2.55/1.50 ! [B2: a,A2: a,C: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 => ( ( less_eq @ C @ A2 )
% 2.55/1.50 => ( less_eq @ ( sup @ B2 @ C ) @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_65_local_Osup_Ocobounded1,axiom,
% 2.55/1.50 ! [A2: a,B2: a] : ( less_eq @ A2 @ ( sup @ A2 @ B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_66_local_Osup_Ocobounded2,axiom,
% 2.55/1.50 ! [B2: a,A2: a] : ( less_eq @ B2 @ ( sup @ A2 @ B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_67_local_Osup_OcoboundedI1,axiom,
% 2.55/1.50 ! [C: a,A2: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ C @ A2 )
% 2.55/1.50 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_68_local_Osup_OcoboundedI2,axiom,
% 2.55/1.50 ! [C: a,B2: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ C @ B2 )
% 2.55/1.50 => ( less_eq @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_69_local_Osup_Omono,axiom,
% 2.55/1.50 ! [C: a,A2: a,D: a,B2: a] :
% 2.55/1.50 ( ( less_eq @ C @ A2 )
% 2.55/1.50 => ( ( less_eq @ D @ B2 )
% 2.55/1.50 => ( less_eq @ ( sup @ C @ D ) @ ( sup @ A2 @ B2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_70_local_Osup_OorderE,axiom,
% 2.55/1.50 ! [B2: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 => ( A2
% 2.55/1.50 = ( sup @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_71_local_Osup_OorderI,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( A2
% 2.55/1.50 = ( sup @ A2 @ B2 ) )
% 2.55/1.50 => ( less_eq @ B2 @ A2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_72_local_Osup_Oorder__iff,axiom,
% 2.55/1.50 ! [B2: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 = ( A2
% 2.55/1.50 = ( sup @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_73_local_Osup__absorb1,axiom,
% 2.55/1.50 ! [Y: a,X: a] :
% 2.55/1.50 ( ( less_eq @ Y @ X )
% 2.55/1.50 => ( ( sup @ X @ Y )
% 2.55/1.50 = X ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_74_local_Osup__absorb2,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( less_eq @ X @ Y )
% 2.55/1.50 => ( ( sup @ X @ Y )
% 2.55/1.50 = Y ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_75_local_Osup__ge1,axiom,
% 2.55/1.50 ! [X: a,Y: a] : ( less_eq @ X @ ( sup @ X @ Y ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_76_local_Osup__ge2,axiom,
% 2.55/1.50 ! [Y: a,X: a] : ( less_eq @ Y @ ( sup @ X @ Y ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_77_local_Osup__least,axiom,
% 2.55/1.50 ! [Y: a,X: a,Z2: a] :
% 2.55/1.50 ( ( less_eq @ Y @ X )
% 2.55/1.50 => ( ( less_eq @ Z2 @ X )
% 2.55/1.50 => ( less_eq @ ( sup @ Y @ Z2 ) @ X ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_78_local_Osup__mono,axiom,
% 2.55/1.50 ! [A2: a,C: a,B2: a,D: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ C )
% 2.55/1.50 => ( ( less_eq @ B2 @ D )
% 2.55/1.50 => ( less_eq @ ( sup @ A2 @ B2 ) @ ( sup @ C @ D ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_79_local_Osup__unique,axiom,
% 2.55/1.50 ! [F: a > a > a,X: a,Y: a] :
% 2.55/1.50 ( ! [X3: a,Y4: a] : ( less_eq @ X3 @ ( F @ X3 @ Y4 ) )
% 2.55/1.50 => ( ! [X3: a,Y4: a] : ( less_eq @ Y4 @ ( F @ X3 @ Y4 ) )
% 2.55/1.50 => ( ! [X3: a,Y4: a,Z3: a] :
% 2.55/1.50 ( ( less_eq @ Y4 @ X3 )
% 2.55/1.50 => ( ( less_eq @ Z3 @ X3 )
% 2.55/1.50 => ( less_eq @ ( F @ Y4 @ Z3 ) @ X3 ) ) )
% 2.55/1.50 => ( ( sup @ X @ Y )
% 2.55/1.50 = ( F @ X @ Y ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_80_local_Odistrib__imp1,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ! [X3: a,Y4: a,Z3: a] :
% 2.55/1.50 ( ( inf @ X3 @ ( sup @ Y4 @ Z3 ) )
% 2.55/1.50 = ( sup @ ( inf @ X3 @ Y4 ) @ ( inf @ X3 @ Z3 ) ) )
% 2.55/1.50 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 2.55/1.50 = ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_81_local_Odistrib__imp2,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ! [X3: a,Y4: a,Z3: a] :
% 2.55/1.50 ( ( sup @ X3 @ ( inf @ Y4 @ Z3 ) )
% 2.55/1.50 = ( inf @ ( sup @ X3 @ Y4 ) @ ( sup @ X3 @ Z3 ) ) )
% 2.55/1.50 => ( ( inf @ X @ ( sup @ Y @ Z2 ) )
% 2.55/1.50 = ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_82_local_Oa__join__d,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( sup @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 = ( sup @ A2 @ ( inf @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_83_a__meet__d,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( inf @ A2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 = ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ C @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_84_local_Ob__join__d,axiom,
% 2.55/1.50 ! [B2: a,A2: a,C: a] :
% 2.55/1.50 ( ( sup @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 = ( sup @ B2 @ ( inf @ C @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_85_b__meet__d,axiom,
% 2.55/1.50 ! [B2: a,A2: a,C: a] :
% 2.55/1.50 ( ( inf @ B2 @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 = ( sup @ ( inf @ B2 @ C ) @ ( inf @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_86_c__meet__d,axiom,
% 2.55/1.50 ! [C: a,A2: a,B2: a] :
% 2.55/1.50 ( ( inf @ C @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 = ( sup @ ( inf @ C @ A2 ) @ ( inf @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_87_local_Od__aux__def,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.55/1.50 = ( sup @ ( sup @ ( inf @ A2 @ B2 ) @ ( inf @ B2 @ C ) ) @ ( inf @ C @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_88_local_Od__b__c__a,axiom,
% 2.55/1.50 ! [B2: a,C: a,A2: a] :
% 2.55/1.50 ( ( modula1221160330_d_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 2.55/1.50 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_89_local_Od__c__a__b,axiom,
% 2.55/1.50 ! [C: a,A2: a,B2: a] :
% 2.55/1.50 ( ( modula1221160330_d_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 2.55/1.50 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_90_local_Oa__meet__e,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 = ( inf @ A2 @ ( sup @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_91_local_Ob__meet__e,axiom,
% 2.55/1.50 ! [B2: a,A2: a,C: a] :
% 2.55/1.50 ( ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 = ( inf @ B2 @ ( sup @ C @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_92_local_Oc__meet__e,axiom,
% 2.55/1.50 ! [C: a,A2: a,B2: a] :
% 2.55/1.50 ( ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 = ( inf @ C @ ( sup @ A2 @ B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_93_local_Oe__aux__def,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.55/1.50 = ( inf @ ( inf @ ( sup @ A2 @ B2 ) @ ( sup @ B2 @ C ) ) @ ( sup @ C @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_94_local_Oe__b__c__a,axiom,
% 2.55/1.50 ! [B2: a,C: a,A2: a] :
% 2.55/1.50 ( ( modula1593167561_e_aux @ a @ inf @ sup @ B2 @ C @ A2 )
% 2.55/1.50 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_95_local_Oe__c__a__b,axiom,
% 2.55/1.50 ! [C: a,A2: a,B2: a] :
% 2.55/1.50 ( ( modula1593167561_e_aux @ a @ inf @ sup @ C @ A2 @ B2 )
% 2.55/1.50 = ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_96_local_Odistrib__inf__le,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ ( inf @ X @ Y ) @ ( inf @ X @ Z2 ) ) @ ( inf @ X @ ( sup @ Y @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_97_local_Odistrib__sup__le,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] : ( less_eq @ ( sup @ X @ ( inf @ Y @ Z2 ) ) @ ( inf @ ( sup @ X @ Y ) @ ( sup @ X @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_98_local_Omodular,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ( less_eq @ X @ Y )
% 2.55/1.50 => ( ( sup @ X @ ( inf @ Y @ Z2 ) )
% 2.55/1.50 = ( inf @ Y @ ( sup @ X @ Z2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_99_local_Oincomp__def,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( modula1937309406incomp @ a @ less_eq @ X @ Y )
% 2.55/1.50 = ( ~ ( less_eq @ X @ Y )
% 2.55/1.50 & ~ ( less_eq @ Y @ X ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_100_local_Oorder_Orefl,axiom,
% 2.55/1.50 ! [A2: a] : ( less_eq @ A2 @ A2 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_101_local_Oorder__refl,axiom,
% 2.55/1.50 ! [X: a] : ( less_eq @ X @ X ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_102_local_Oinf_Oidem,axiom,
% 2.55/1.50 ! [A2: a] :
% 2.55/1.50 ( ( inf @ A2 @ A2 )
% 2.55/1.50 = A2 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_103_local_Oinf_Oleft__idem,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( inf @ A2 @ ( inf @ A2 @ B2 ) )
% 2.55/1.50 = ( inf @ A2 @ B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_104_local_Oinf_Oright__idem,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( inf @ ( inf @ A2 @ B2 ) @ B2 )
% 2.55/1.50 = ( inf @ A2 @ B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_105_local_Oinf__idem,axiom,
% 2.55/1.50 ! [X: a] :
% 2.55/1.50 ( ( inf @ X @ X )
% 2.55/1.50 = X ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_106_local_Oinf__left__idem,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( inf @ X @ ( inf @ X @ Y ) )
% 2.55/1.50 = ( inf @ X @ Y ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_107_local_Oinf__right__idem,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( inf @ ( inf @ X @ Y ) @ Y )
% 2.55/1.50 = ( inf @ X @ Y ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_108_local_Osup_Oidem,axiom,
% 2.55/1.50 ! [A2: a] :
% 2.55/1.50 ( ( sup @ A2 @ A2 )
% 2.55/1.50 = A2 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_109_local_Osup_Oleft__idem,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( sup @ A2 @ ( sup @ A2 @ B2 ) )
% 2.55/1.50 = ( sup @ A2 @ B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_110_local_Osup_Oright__idem,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( sup @ ( sup @ A2 @ B2 ) @ B2 )
% 2.55/1.50 = ( sup @ A2 @ B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_111_local_Osup__idem,axiom,
% 2.55/1.50 ! [X: a] :
% 2.55/1.50 ( ( sup @ X @ X )
% 2.55/1.50 = X ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_112_local_Osup__left__idem,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( sup @ X @ ( sup @ X @ Y ) )
% 2.55/1.50 = ( sup @ X @ Y ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_113_local_Oc__a,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.55/1.50 = ( modula105138637_a_aux @ a @ inf @ sup @ C @ A2 @ B2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_114_local_OGreatestI2__order,axiom,
% 2.55/1.50 ! [P: a > $o,X: a,Q: a > $o] :
% 2.55/1.50 ( ( P @ X )
% 2.55/1.50 => ( ! [Y4: a] :
% 2.55/1.50 ( ( P @ Y4 )
% 2.55/1.50 => ( less_eq @ Y4 @ X ) )
% 2.55/1.50 => ( ! [X3: a] :
% 2.55/1.50 ( ( P @ X3 )
% 2.55/1.50 => ( ! [Y5: a] :
% 2.55/1.50 ( ( P @ Y5 )
% 2.55/1.50 => ( less_eq @ Y5 @ X3 ) )
% 2.55/1.50 => ( Q @ X3 ) ) )
% 2.55/1.50 => ( Q @ ( greatest @ a @ less_eq @ P ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_115_local_OGreatest__equality,axiom,
% 2.55/1.50 ! [P: a > $o,X: a] :
% 2.55/1.50 ( ( P @ X )
% 2.55/1.50 => ( ! [Y4: a] :
% 2.55/1.50 ( ( P @ Y4 )
% 2.55/1.50 => ( less_eq @ Y4 @ X ) )
% 2.55/1.50 => ( ( greatest @ a @ less_eq @ P )
% 2.55/1.50 = X ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_116_local_Omax__def,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 2.55/1.50 = B2 ) )
% 2.55/1.50 & ( ~ ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 2.55/1.50 = A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_117_local_Omin__def,axiom,
% 2.55/1.50 ! [A2: a,B2: a] :
% 2.55/1.50 ( ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 2.55/1.50 = A2 ) )
% 2.55/1.50 & ( ~ ( less_eq @ A2 @ B2 )
% 2.55/1.50 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 2.55/1.50 = B2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_118_local_Oa__aux__def,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.55/1.50 = ( sup @ ( inf @ A2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_119_local_Oc__aux__def,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( modula849153099_c_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.55/1.50 = ( sup @ ( inf @ C @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_120_local_Oinf_Obounded__iff,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( less_eq @ A2 @ ( inf @ B2 @ C ) )
% 2.55/1.50 = ( ( less_eq @ A2 @ B2 )
% 2.55/1.50 & ( less_eq @ A2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_121_local_Ole__inf__iff,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ( less_eq @ X @ ( inf @ Y @ Z2 ) )
% 2.55/1.50 = ( ( less_eq @ X @ Y )
% 2.55/1.50 & ( less_eq @ X @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_122_local_Ole__sup__iff,axiom,
% 2.55/1.50 ! [X: a,Y: a,Z2: a] :
% 2.55/1.50 ( ( less_eq @ ( sup @ X @ Y ) @ Z2 )
% 2.55/1.50 = ( ( less_eq @ X @ Z2 )
% 2.55/1.50 & ( less_eq @ Y @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_123_local_Osup_Obounded__iff,axiom,
% 2.55/1.50 ! [B2: a,C: a,A2: a] :
% 2.55/1.50 ( ( less_eq @ ( sup @ B2 @ C ) @ A2 )
% 2.55/1.50 = ( ( less_eq @ B2 @ A2 )
% 2.55/1.50 & ( less_eq @ C @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_124_local_Oinf__sup__absorb,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( inf @ X @ ( sup @ X @ Y ) )
% 2.55/1.50 = X ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_125_local_Osup__inf__absorb,axiom,
% 2.55/1.50 ! [X: a,Y: a] :
% 2.55/1.50 ( ( sup @ X @ ( inf @ X @ Y ) )
% 2.55/1.50 = X ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_126_local_Ob__a,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.55/1.50 = ( modula105138637_a_aux @ a @ inf @ sup @ B2 @ C @ A2 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_127_local_OLeast1I,axiom,
% 2.55/1.50 ! [P: a > $o] :
% 2.55/1.50 ( ? [X4: a] :
% 2.55/1.50 ( ( P @ X4 )
% 2.55/1.50 & ! [Y4: a] :
% 2.55/1.50 ( ( P @ Y4 )
% 2.55/1.50 => ( less_eq @ X4 @ Y4 ) )
% 2.55/1.50 & ! [Y4: a] :
% 2.55/1.50 ( ( ( P @ Y4 )
% 2.55/1.50 & ! [Ya: a] :
% 2.55/1.50 ( ( P @ Ya )
% 2.55/1.50 => ( less_eq @ Y4 @ Ya ) ) )
% 2.55/1.50 => ( Y4 = X4 ) ) )
% 2.55/1.50 => ( P @ ( least @ a @ less_eq @ P ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_128_local_OLeast1__le,axiom,
% 2.55/1.50 ! [P: a > $o,Z2: a] :
% 2.55/1.50 ( ? [X4: a] :
% 2.55/1.50 ( ( P @ X4 )
% 2.55/1.50 & ! [Y4: a] :
% 2.55/1.50 ( ( P @ Y4 )
% 2.55/1.50 => ( less_eq @ X4 @ Y4 ) )
% 2.55/1.50 & ! [Y4: a] :
% 2.55/1.50 ( ( ( P @ Y4 )
% 2.55/1.50 & ! [Ya: a] :
% 2.55/1.50 ( ( P @ Ya )
% 2.55/1.50 => ( less_eq @ Y4 @ Ya ) ) )
% 2.55/1.50 => ( Y4 = X4 ) ) )
% 2.55/1.50 => ( ( P @ Z2 )
% 2.55/1.50 => ( less_eq @ ( least @ a @ less_eq @ P ) @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_129_local_OLeastI2__order,axiom,
% 2.55/1.50 ! [P: a > $o,X: a,Q: a > $o] :
% 2.55/1.50 ( ( P @ X )
% 2.55/1.50 => ( ! [Y4: a] :
% 2.55/1.50 ( ( P @ Y4 )
% 2.55/1.50 => ( less_eq @ X @ Y4 ) )
% 2.55/1.50 => ( ! [X3: a] :
% 2.55/1.50 ( ( P @ X3 )
% 2.55/1.50 => ( ! [Y5: a] :
% 2.55/1.50 ( ( P @ Y5 )
% 2.55/1.50 => ( less_eq @ X3 @ Y5 ) )
% 2.55/1.50 => ( Q @ X3 ) ) )
% 2.55/1.50 => ( Q @ ( least @ a @ less_eq @ P ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_130_local_OLeast__equality,axiom,
% 2.55/1.50 ! [P: a > $o,X: a] :
% 2.55/1.50 ( ( P @ X )
% 2.55/1.50 => ( ! [Y4: a] :
% 2.55/1.50 ( ( P @ Y4 )
% 2.55/1.50 => ( less_eq @ X @ Y4 ) )
% 2.55/1.50 => ( ( least @ a @ less_eq @ P )
% 2.55/1.50 = X ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_131_local_Ob__aux__def,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C )
% 2.55/1.50 = ( sup @ ( inf @ B2 @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_132_a__meet__b__eq__d,axiom,
% 2.55/1.50 ! [A2: a,B2: a,C: a] :
% 2.55/1.50 ( ( less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 => ( ( inf @ ( modula105138637_a_aux @ a @ inf @ sup @ A2 @ B2 @ C ) @ ( modula477145868_b_aux @ a @ inf @ sup @ A2 @ B2 @ C ) )
% 2.55/1.50 = ( modula1221160330_d_aux @ a @ inf @ sup @ A2 @ B2 @ C ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_133_lattice_Oa__aux_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( modula105138637_a_aux @ A )
% 2.55/1.51 = ( modula105138637_a_aux @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_134_lattice_Oc__aux_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( modula849153099_c_aux @ A )
% 2.55/1.51 = ( modula849153099_c_aux @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_135_lattice_Od__aux_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( modula1221160330_d_aux @ A )
% 2.55/1.51 = ( modula1221160330_d_aux @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_136_lattice_Oe__aux_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( modula1593167561_e_aux @ A )
% 2.55/1.51 = ( modula1593167561_e_aux @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_137_local_Ocomp__fun__idem__sup,axiom,
% 2.55/1.51 finite_comp_fun_idem @ a @ a @ sup ).
% 2.55/1.51
% 2.55/1.51 thf(fact_138_local_Ocomp__fun__idem__inf,axiom,
% 2.55/1.51 finite_comp_fun_idem @ a @ a @ inf ).
% 2.55/1.51
% 2.55/1.51 thf(fact_139_local_Osup_Osemigroup__axioms,axiom,
% 2.55/1.51 semigroup @ a @ sup ).
% 2.55/1.51
% 2.55/1.51 thf(fact_140_local_Oinf_Osemigroup__axioms,axiom,
% 2.55/1.51 semigroup @ a @ inf ).
% 2.55/1.51
% 2.55/1.51 thf(fact_141_local_Osup_Osemilattice__axioms,axiom,
% 2.55/1.51 semilattice @ a @ sup ).
% 2.55/1.51
% 2.55/1.51 thf(fact_142_local_Oinf_Osemilattice__axioms,axiom,
% 2.55/1.51 semilattice @ a @ inf ).
% 2.55/1.51
% 2.55/1.51 thf(fact_143_local_Osup_Oabel__semigroup__axioms,axiom,
% 2.55/1.51 abel_semigroup @ a @ sup ).
% 2.55/1.51
% 2.55/1.51 thf(fact_144_local_Oinf_Oabel__semigroup__axioms,axiom,
% 2.55/1.51 abel_semigroup @ a @ inf ).
% 2.55/1.51
% 2.55/1.51 thf(fact_145_local_OSup__fin_Osemilattice__set__axioms,axiom,
% 2.55/1.51 lattic35693393ce_set @ a @ sup ).
% 2.55/1.51
% 2.55/1.51 thf(fact_146_local_OInf__fin_Osemilattice__set__axioms,axiom,
% 2.55/1.51 lattic35693393ce_set @ a @ inf ).
% 2.55/1.51
% 2.55/1.51 thf(fact_147_local_Obdd__above__def,axiom,
% 2.55/1.51 ! [A4: set @ a] :
% 2.55/1.51 ( ( condit2040224947_above @ a @ less_eq @ A4 )
% 2.55/1.51 = ( ? [M: a] :
% 2.55/1.51 ! [X2: a] :
% 2.55/1.51 ( ( member @ a @ X2 @ A4 )
% 2.55/1.51 => ( less_eq @ X2 @ M ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_148_local_Obdd__below__def,axiom,
% 2.55/1.51 ! [A4: set @ a] :
% 2.55/1.51 ( ( condit1201339847_below @ a @ less_eq @ A4 )
% 2.55/1.51 = ( ? [M2: a] :
% 2.55/1.51 ! [X2: a] :
% 2.55/1.51 ( ( member @ a @ X2 @ A4 )
% 2.55/1.51 => ( less_eq @ M2 @ X2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_149_local_Obdd__belowI,axiom,
% 2.55/1.51 ! [A4: set @ a,M3: a] :
% 2.55/1.51 ( ! [X3: a] :
% 2.55/1.51 ( ( member @ a @ X3 @ A4 )
% 2.55/1.51 => ( less_eq @ M3 @ X3 ) )
% 2.55/1.51 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_150_local_Obdd__aboveI,axiom,
% 2.55/1.51 ! [A4: set @ a,M4: a] :
% 2.55/1.51 ( ! [X3: a] :
% 2.55/1.51 ( ( member @ a @ X3 @ A4 )
% 2.55/1.51 => ( less_eq @ X3 @ M4 ) )
% 2.55/1.51 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_151_lattice_Oincomp_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( modula1937309406incomp @ A )
% 2.55/1.51 = ( modula1937309406incomp @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_152_lattice_Ob__aux_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( modula477145868_b_aux @ A )
% 2.55/1.51 = ( modula477145868_b_aux @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_153_abel__semigroup_Oaxioms_I1_J,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A] :
% 2.55/1.51 ( ( abel_semigroup @ A @ F )
% 2.55/1.51 => ( semigroup @ A @ F ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_154_semilattice__set__def,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( lattic35693393ce_set @ A )
% 2.55/1.51 = ( semilattice @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_155_semilattice__set_Ointro,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A] :
% 2.55/1.51 ( ( semilattice @ A @ F )
% 2.55/1.51 => ( lattic35693393ce_set @ A @ F ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_156_abel__semigroup_Oleft__commute,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A,B2: A,A2: A,C: A] :
% 2.55/1.51 ( ( abel_semigroup @ A @ F )
% 2.55/1.51 => ( ( F @ B2 @ ( F @ A2 @ C ) )
% 2.55/1.51 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_157_abel__semigroup_Ocommute,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 2.55/1.51 ( ( abel_semigroup @ A @ F )
% 2.55/1.51 => ( ( F @ A2 @ B2 )
% 2.55/1.51 = ( F @ B2 @ A2 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_158_semigroup_Ointro,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A] :
% 2.55/1.51 ( ! [A5: A,B4: A,C2: A] :
% 2.55/1.51 ( ( F @ ( F @ A5 @ B4 ) @ C2 )
% 2.55/1.51 = ( F @ A5 @ ( F @ B4 @ C2 ) ) )
% 2.55/1.51 => ( semigroup @ A @ F ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_159_semigroup_Oassoc,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 2.55/1.51 ( ( semigroup @ A @ F )
% 2.55/1.51 => ( ( F @ ( F @ A2 @ B2 ) @ C )
% 2.55/1.51 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_160_semigroup__def,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semigroup @ A )
% 2.55/1.51 = ( ^ [F2: A > A > A] :
% 2.55/1.51 ! [A3: A,B3: A,C3: A] :
% 2.55/1.51 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 2.55/1.51 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_161_semilattice__set_Oaxioms,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A] :
% 2.55/1.51 ( ( lattic35693393ce_set @ A @ F )
% 2.55/1.51 => ( semilattice @ A @ F ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_162_semilattice_Oaxioms_I1_J,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A] :
% 2.55/1.51 ( ( semilattice @ A @ F )
% 2.55/1.51 => ( abel_semigroup @ A @ F ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_163_local_Obdd__above__mono,axiom,
% 2.55/1.51 ! [B5: set @ a,A4: set @ a] :
% 2.55/1.51 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 2.55/1.51 => ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 2.55/1.51 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_164_local_Obdd__below__mono,axiom,
% 2.55/1.51 ! [B5: set @ a,A4: set @ a] :
% 2.55/1.51 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 2.55/1.51 => ( ( ord_less_eq @ ( set @ a ) @ A4 @ B5 )
% 2.55/1.51 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_165_local_Oantimono__def,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ! [F: a > B] :
% 2.55/1.51 ( ( antimono @ a @ B @ less_eq @ F )
% 2.55/1.51 = ( ! [X2: a,Y3: a] :
% 2.55/1.51 ( ( less_eq @ X2 @ Y3 )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_166_local_OantimonoI,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ! [F: a > B] :
% 2.55/1.51 ( ! [X3: a,Y4: a] :
% 2.55/1.51 ( ( less_eq @ X3 @ Y4 )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 2.55/1.51 => ( antimono @ a @ B @ less_eq @ F ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_167_local_OantimonoE,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ! [F: a > B,X: a,Y: a] :
% 2.55/1.51 ( ( antimono @ a @ B @ less_eq @ F )
% 2.55/1.51 => ( ( less_eq @ X @ Y )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_168_local_OantimonoD,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ! [F: a > B,X: a,Y: a] :
% 2.55/1.51 ( ( antimono @ a @ B @ less_eq @ F )
% 2.55/1.51 => ( ( less_eq @ X @ Y )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_169_local_OmonoD,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ! [F: a > B,X: a,Y: a] :
% 2.55/1.51 ( ( mono @ a @ B @ less_eq @ F )
% 2.55/1.51 => ( ( less_eq @ X @ Y )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_170_local_OmonoE,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ! [F: a > B,X: a,Y: a] :
% 2.55/1.51 ( ( mono @ a @ B @ less_eq @ F )
% 2.55/1.51 => ( ( less_eq @ X @ Y )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_171_local_OmonoI,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ! [F: a > B] :
% 2.55/1.51 ( ! [X3: a,Y4: a] :
% 2.55/1.51 ( ( less_eq @ X3 @ Y4 )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.55/1.51 => ( mono @ a @ B @ less_eq @ F ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_172_local_Omono__def,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ! [F: a > B] :
% 2.55/1.51 ( ( mono @ a @ B @ less_eq @ F )
% 2.55/1.51 = ( ! [X2: a,Y3: a] :
% 2.55/1.51 ( ( less_eq @ X2 @ Y3 )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_173_semilattice_Oidem,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A,A2: A] :
% 2.55/1.51 ( ( semilattice @ A @ F )
% 2.55/1.51 => ( ( F @ A2 @ A2 )
% 2.55/1.51 = A2 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_174_semilattice_Oleft__idem,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 2.55/1.51 ( ( semilattice @ A @ F )
% 2.55/1.51 => ( ( F @ A2 @ ( F @ A2 @ B2 ) )
% 2.55/1.51 = ( F @ A2 @ B2 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_175_semilattice_Oright__idem,axiom,
% 2.55/1.51 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 2.55/1.51 ( ( semilattice @ A @ F )
% 2.55/1.51 => ( ( F @ ( F @ A2 @ B2 ) @ B2 )
% 2.55/1.51 = ( F @ A2 @ B2 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_176_subsetI,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.51 ( ! [X3: A] :
% 2.55/1.51 ( ( member @ A @ X3 @ A4 )
% 2.55/1.51 => ( member @ A @ X3 @ B5 ) )
% 2.55/1.51 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_177_subset__antisym,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.51 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 2.55/1.51 => ( A4 = B5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_178_preorder__class_Oorder__refl,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( preorder @ A )
% 2.55/1.51 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_179_order_Oantimono_Ocong,axiom,
% 2.55/1.51 ! [B: $tType,A: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ( ( antimono @ A @ B )
% 2.55/1.51 = ( antimono @ A @ B ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_180_order_Omono_Ocong,axiom,
% 2.55/1.51 ! [B: $tType,A: $tType] :
% 2.55/1.51 ( ( order @ B )
% 2.55/1.51 => ( ( mono @ A @ B )
% 2.55/1.51 = ( mono @ A @ B ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_181_order__class_Odual__order_Oantisym,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ! [B2: A,A2: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.55/1.51 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.55/1.51 => ( A2 = B2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_182_order__class_Odual__order_Oeq__iff,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ( ( ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 2.55/1.51 = ( ^ [A3: A,B3: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ B3 @ A3 )
% 2.55/1.51 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_183_order__class_Odual__order_Otrans,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ! [B2: A,A2: A,C: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.55/1.51 => ( ( ord_less_eq @ A @ C @ B2 )
% 2.55/1.51 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_184_linorder__wlog,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( linorder @ A )
% 2.55/1.51 => ! [P: A > A > $o,A2: A,B2: A] :
% 2.55/1.51 ( ! [A5: A,B4: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ A5 @ B4 )
% 2.55/1.51 => ( P @ A5 @ B4 ) )
% 2.55/1.51 => ( ! [A5: A,B4: A] :
% 2.55/1.51 ( ( P @ B4 @ A5 )
% 2.55/1.51 => ( P @ A5 @ B4 ) )
% 2.55/1.51 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_185_order__class_Odual__order_Orefl,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_186_preorder__class_Oorder__trans,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( preorder @ A )
% 2.55/1.51 => ! [X: A,Y: A,Z2: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ X @ Y )
% 2.55/1.51 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.55/1.51 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_187_order__class_Oorder_Oantisym,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ! [A2: A,B2: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.55/1.51 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.55/1.51 => ( A2 = B2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_188_ord__class_Oord__le__eq__trans,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( ord @ A )
% 2.55/1.51 => ! [A2: A,B2: A,C: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.55/1.51 => ( ( B2 = C )
% 2.55/1.51 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_189_ord__class_Oord__eq__le__trans,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( ord @ A )
% 2.55/1.51 => ! [A2: A,B2: A,C: A] :
% 2.55/1.51 ( ( A2 = B2 )
% 2.55/1.51 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.55/1.51 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_190_order__class_Oorder_Oeq__iff,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ( ( ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 2.55/1.51 = ( ^ [A3: A,B3: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.55/1.51 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_191_order__class_Oantisym__conv,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ! [Y: A,X: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ Y @ X )
% 2.55/1.51 => ( ( ord_less_eq @ A @ X @ Y )
% 2.55/1.51 = ( X = Y ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_192_le__cases3,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( linorder @ A )
% 2.55/1.51 => ! [X: A,Y: A,Z2: A] :
% 2.55/1.51 ( ( ( ord_less_eq @ A @ X @ Y )
% 2.55/1.51 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 2.55/1.51 => ( ( ( ord_less_eq @ A @ Y @ X )
% 2.55/1.51 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 2.55/1.51 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 2.55/1.51 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 2.55/1.51 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 2.55/1.51 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 2.55/1.51 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.55/1.51 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 2.55/1.51 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 2.55/1.51 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_193_order__class_Oorder_Otrans,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ! [A2: A,B2: A,C: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.55/1.51 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.55/1.51 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_194_le__cases,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( linorder @ A )
% 2.55/1.51 => ! [X: A,Y: A] :
% 2.55/1.51 ( ~ ( ord_less_eq @ A @ X @ Y )
% 2.55/1.51 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_195_preorder__class_Oeq__refl,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( preorder @ A )
% 2.55/1.51 => ! [X: A,Y: A] :
% 2.55/1.51 ( ( X = Y )
% 2.55/1.51 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_196_linear,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( linorder @ A )
% 2.55/1.51 => ! [X: A,Y: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ X @ Y )
% 2.55/1.51 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_197_order__class_Oantisym,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ! [X: A,Y: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ X @ Y )
% 2.55/1.51 => ( ( ord_less_eq @ A @ Y @ X )
% 2.55/1.51 => ( X = Y ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_198_order__class_Oeq__iff,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( order @ A )
% 2.55/1.51 => ( ( ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 2.55/1.51 = ( ^ [X2: A,Y3: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 2.55/1.51 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_199_ord__le__eq__subst,axiom,
% 2.55/1.51 ! [A: $tType,B: $tType] :
% 2.55/1.51 ( ( ( ord @ B )
% 2.55/1.51 & ( ord @ A ) )
% 2.55/1.51 => ! [A2: A,B2: A,F: A > B,C: B] :
% 2.55/1.51 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.55/1.51 => ( ( ( F @ B2 )
% 2.55/1.51 = C )
% 2.55/1.51 => ( ! [X3: A,Y4: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_200_ord__eq__le__subst,axiom,
% 2.55/1.51 ! [A: $tType,B: $tType] :
% 2.55/1.51 ( ( ( ord @ B )
% 2.55/1.51 & ( ord @ A ) )
% 2.55/1.51 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.55/1.51 ( ( A2
% 2.55/1.51 = ( F @ B2 ) )
% 2.55/1.51 => ( ( ord_less_eq @ B @ B2 @ C )
% 2.55/1.51 => ( ! [X3: B,Y4: B] :
% 2.55/1.51 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 2.55/1.51 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.55/1.51 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_201_order__subst2,axiom,
% 2.55/1.51 ! [A: $tType,C4: $tType] :
% 2.55/1.51 ( ( ( order @ C4 )
% 2.55/1.51 & ( order @ A ) )
% 2.55/1.51 => ! [A2: A,B2: A,F: A > C4,C: C4] :
% 2.55/1.51 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.55/1.51 => ( ( ord_less_eq @ C4 @ ( F @ B2 ) @ C )
% 2.55/1.51 => ( ! [X3: A,Y4: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 2.55/1.51 => ( ord_less_eq @ C4 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.55/1.51 => ( ord_less_eq @ C4 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_202_order__subst1,axiom,
% 2.55/1.51 ! [A: $tType,B: $tType] :
% 2.55/1.51 ( ( ( order @ B )
% 2.55/1.51 & ( order @ A ) )
% 2.55/1.51 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.55/1.51 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 2.55/1.51 => ( ( ord_less_eq @ B @ B2 @ C )
% 2.55/1.51 => ( ! [X3: B,Y4: B] :
% 2.55/1.51 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 2.55/1.51 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.55/1.51 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_203_le__fun__def,axiom,
% 2.55/1.51 ! [B: $tType,A: $tType] :
% 2.55/1.51 ( ( ord @ B )
% 2.55/1.51 => ( ( ord_less_eq @ ( A > B ) )
% 2.55/1.51 = ( ^ [F2: A > B,G2: A > B] :
% 2.55/1.51 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_204_le__funI,axiom,
% 2.55/1.51 ! [B: $tType,A: $tType] :
% 2.55/1.51 ( ( ord @ B )
% 2.55/1.51 => ! [F: A > B,G: A > B] :
% 2.55/1.51 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 2.55/1.51 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_205_le__funE,axiom,
% 2.55/1.51 ! [B: $tType,A: $tType] :
% 2.55/1.51 ( ( ord @ B )
% 2.55/1.51 => ! [F: A > B,G: A > B,X: A] :
% 2.55/1.51 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_206_le__funD,axiom,
% 2.55/1.51 ! [B: $tType,A: $tType] :
% 2.55/1.51 ( ( ord @ B )
% 2.55/1.51 => ! [F: A > B,G: A > B,X: A] :
% 2.55/1.51 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_207_Collect__mono__iff,axiom,
% 2.55/1.51 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.55/1.51 = ( ! [X2: A] :
% 2.55/1.51 ( ( P @ X2 )
% 2.55/1.51 => ( Q @ X2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_208_set__eq__subset,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( ^ [Y2: set @ A,Z: set @ A] : ( Y2 = Z ) )
% 2.55/1.51 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.55/1.51 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_209_subset__trans,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A,B5: set @ A,C5: set @ A] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.51 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C5 )
% 2.55/1.51 => ( ord_less_eq @ ( set @ A ) @ A4 @ C5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_210_Collect__mono,axiom,
% 2.55/1.51 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.55/1.51 ( ! [X3: A] :
% 2.55/1.51 ( ( P @ X3 )
% 2.55/1.51 => ( Q @ X3 ) )
% 2.55/1.51 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_211_subset__refl,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_212_subset__iff,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) )
% 2.55/1.51 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.55/1.51 ! [T: A] :
% 2.55/1.51 ( ( member @ A @ T @ A6 )
% 2.55/1.51 => ( member @ A @ T @ B6 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_213_equalityD2,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.51 ( ( A4 = B5 )
% 2.55/1.51 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_214_equalityD1,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.51 ( ( A4 = B5 )
% 2.55/1.51 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_215_subset__eq,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) )
% 2.55/1.51 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.55/1.51 ! [X2: A] :
% 2.55/1.51 ( ( member @ A @ X2 @ A6 )
% 2.55/1.51 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_216_equalityE,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.51 ( ( A4 = B5 )
% 2.55/1.51 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.51 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_217_subsetD,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A,B5: set @ A,C: A] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.51 => ( ( member @ A @ C @ A4 )
% 2.55/1.51 => ( member @ A @ C @ B5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_218_in__mono,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.51 => ( ( member @ A @ X @ A4 )
% 2.55/1.51 => ( member @ A @ X @ B5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_219_ord_OLeast_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( least @ A )
% 2.55/1.51 = ( least @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_220_order_OGreatest_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( greatest @ A )
% 2.55/1.51 = ( greatest @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_221_ord_Omin_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( min @ A )
% 2.55/1.51 = ( min @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_222_ord_Omax_Ocong,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( max @ A )
% 2.55/1.51 = ( max @ A ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_223_ord_Omin__def,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( min @ A )
% 2.55/1.51 = ( ^ [Less_eq: A > A > $o,A3: A,B3: A] : ( if @ A @ ( Less_eq @ A3 @ B3 ) @ A3 @ B3 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_224_ord_Omax__def,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( max @ A )
% 2.55/1.51 = ( ^ [Less_eq: A > A > $o,A3: A,B3: A] : ( if @ A @ ( Less_eq @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_225_local_Omono__inf,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ B )
% 2.55/1.51 => ! [F: a > B,A4: a,B5: a] :
% 2.55/1.51 ( ( mono @ a @ B @ less_eq @ F )
% 2.55/1.51 => ( ord_less_eq @ B @ ( F @ ( inf @ A4 @ B5 ) ) @ ( inf_inf @ B @ ( F @ A4 ) @ ( F @ B5 ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_226_local_Omono__sup,axiom,
% 2.55/1.51 ! [B: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ B )
% 2.55/1.51 => ! [F: a > B,A4: a,B5: a] :
% 2.55/1.51 ( ( mono @ a @ B @ less_eq @ F )
% 2.55/1.51 => ( ord_less_eq @ B @ ( sup_sup @ B @ ( F @ A4 ) @ ( F @ B5 ) ) @ ( F @ ( sup @ A4 @ B5 ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_227_local_Obdd__above__finite,axiom,
% 2.55/1.51 ! [A4: set @ a] :
% 2.55/1.51 ( ( finite_finite @ a @ A4 )
% 2.55/1.51 => ( condit2040224947_above @ a @ less_eq @ A4 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_228_local_Ofinite__has__minimal2,axiom,
% 2.55/1.51 ! [A4: set @ a,A2: a] :
% 2.55/1.51 ( ( finite_finite @ a @ A4 )
% 2.55/1.51 => ( ( member @ a @ A2 @ A4 )
% 2.55/1.51 => ? [X3: a] :
% 2.55/1.51 ( ( member @ a @ X3 @ A4 )
% 2.55/1.51 & ( less_eq @ X3 @ A2 )
% 2.55/1.51 & ! [Xa: a] :
% 2.55/1.51 ( ( member @ a @ Xa @ A4 )
% 2.55/1.51 => ( ( less_eq @ Xa @ X3 )
% 2.55/1.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_229_local_Ofinite__has__maximal2,axiom,
% 2.55/1.51 ! [A4: set @ a,A2: a] :
% 2.55/1.51 ( ( finite_finite @ a @ A4 )
% 2.55/1.51 => ( ( member @ a @ A2 @ A4 )
% 2.55/1.51 => ? [X3: a] :
% 2.55/1.51 ( ( member @ a @ X3 @ A4 )
% 2.55/1.51 & ( less_eq @ A2 @ X3 )
% 2.55/1.51 & ! [Xa: a] :
% 2.55/1.51 ( ( member @ a @ Xa @ A4 )
% 2.55/1.51 => ( ( less_eq @ X3 @ Xa )
% 2.55/1.51 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_230_local_Obdd__below__Int2,axiom,
% 2.55/1.51 ! [B5: set @ a,A4: set @ a] :
% 2.55/1.51 ( ( condit1201339847_below @ a @ less_eq @ B5 )
% 2.55/1.51 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_231_local_Obdd__below__Int1,axiom,
% 2.55/1.51 ! [A4: set @ a,B5: set @ a] :
% 2.55/1.51 ( ( condit1201339847_below @ a @ less_eq @ A4 )
% 2.55/1.51 => ( condit1201339847_below @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_232_local_Obdd__above__Int2,axiom,
% 2.55/1.51 ! [B5: set @ a,A4: set @ a] :
% 2.55/1.51 ( ( condit2040224947_above @ a @ less_eq @ B5 )
% 2.55/1.51 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_233_local_Obdd__above__Int1,axiom,
% 2.55/1.51 ! [A4: set @ a,B5: set @ a] :
% 2.55/1.51 ( ( condit2040224947_above @ a @ less_eq @ A4 )
% 2.55/1.51 => ( condit2040224947_above @ a @ less_eq @ ( inf_inf @ ( set @ a ) @ A4 @ B5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_234_local_Obdd__below__finite,axiom,
% 2.55/1.51 ! [A4: set @ a] :
% 2.55/1.51 ( ( finite_finite @ a @ A4 )
% 2.55/1.51 => ( condit1201339847_below @ a @ less_eq @ A4 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_235_Un__subset__iff,axiom,
% 2.55/1.51 ! [A: $tType,A4: set @ A,B5: set @ A,C5: set @ A] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C5 )
% 2.55/1.51 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C5 )
% 2.55/1.51 & ( ord_less_eq @ ( set @ A ) @ B5 @ C5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_236_Int__subset__iff,axiom,
% 2.55/1.51 ! [A: $tType,C5: set @ A,A4: set @ A,B5: set @ A] :
% 2.55/1.51 ( ( ord_less_eq @ ( set @ A ) @ C5 @ ( inf_inf @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.51 = ( ( ord_less_eq @ ( set @ A ) @ C5 @ A4 )
% 2.55/1.51 & ( ord_less_eq @ ( set @ A ) @ C5 @ B5 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_237_semilattice__inf__class_Oinf__right__idem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ A )
% 2.55/1.51 => ! [X: A,Y: A] :
% 2.55/1.51 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 2.55/1.51 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_238_semilattice__inf__class_Oinf_Oright__idem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ A )
% 2.55/1.51 => ! [A2: A,B2: A] :
% 2.55/1.51 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 2.55/1.51 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_239_semilattice__inf__class_Oinf__left__idem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ A )
% 2.55/1.51 => ! [X: A,Y: A] :
% 2.55/1.51 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 2.55/1.51 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_240_semilattice__inf__class_Oinf_Oleft__idem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ A )
% 2.55/1.51 => ! [A2: A,B2: A] :
% 2.55/1.51 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 2.55/1.51 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_241_semilattice__inf__class_Oinf__idem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ A )
% 2.55/1.51 => ! [X: A] :
% 2.55/1.51 ( ( inf_inf @ A @ X @ X )
% 2.55/1.51 = X ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_242_semilattice__inf__class_Oinf_Oidem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ A )
% 2.55/1.51 => ! [A2: A] :
% 2.55/1.51 ( ( inf_inf @ A @ A2 @ A2 )
% 2.55/1.51 = A2 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_243_inf__apply,axiom,
% 2.55/1.51 ! [B: $tType,A: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ B )
% 2.55/1.51 => ( ( inf_inf @ ( A > B ) )
% 2.55/1.51 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( inf_inf @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_244_semilattice__sup__class_Osup_Oright__idem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ A )
% 2.55/1.51 => ! [A2: A,B2: A] :
% 2.55/1.51 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ B2 )
% 2.55/1.51 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_245_semilattice__sup__class_Osup__left__idem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ A )
% 2.55/1.51 => ! [X: A,Y: A] :
% 2.55/1.51 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.55/1.51 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_246_semilattice__sup__class_Osup_Oleft__idem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ A )
% 2.55/1.51 => ! [A2: A,B2: A] :
% 2.55/1.51 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) )
% 2.55/1.51 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_247_semilattice__sup__class_Osup__idem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ A )
% 2.55/1.51 => ! [X: A] :
% 2.55/1.51 ( ( sup_sup @ A @ X @ X )
% 2.55/1.51 = X ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_248_semilattice__sup__class_Osup_Oidem,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ A )
% 2.55/1.51 => ! [A2: A] :
% 2.55/1.51 ( ( sup_sup @ A @ A2 @ A2 )
% 2.55/1.51 = A2 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_249_sup__apply,axiom,
% 2.55/1.51 ! [B: $tType,A: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ B )
% 2.55/1.51 => ( ( sup_sup @ ( A > B ) )
% 2.55/1.51 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_250_semilattice__inf__class_Ole__inf__iff,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ A )
% 2.55/1.51 => ! [X: A,Y: A,Z2: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z2 ) )
% 2.55/1.51 = ( ( ord_less_eq @ A @ X @ Y )
% 2.55/1.51 & ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_251_semilattice__inf__class_Oinf_Obounded__iff,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ A )
% 2.55/1.51 => ! [A2: A,B2: A,C: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 2.55/1.51 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.55/1.51 & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_252_semilattice__sup__class_Ole__sup__iff,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ A )
% 2.55/1.51 => ! [X: A,Y: A,Z2: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z2 )
% 2.55/1.51 = ( ( ord_less_eq @ A @ X @ Z2 )
% 2.55/1.51 & ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_253_semilattice__sup__class_Osup_Obounded__iff,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ A )
% 2.55/1.51 => ! [B2: A,C: A,A2: A] :
% 2.55/1.51 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C ) @ A2 )
% 2.55/1.51 = ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.55/1.51 & ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_254_lattice__class_Osup__inf__absorb,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( lattice @ A )
% 2.55/1.51 => ! [X: A,Y: A] :
% 2.55/1.51 ( ( sup_sup @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 2.55/1.51 = X ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(fact_255_lattice__class_Oinf__sup__absorb,axiom,
% 2.55/1.51 ! [A: $tType] :
% 2.55/1.51 ( ( lattice @ A )
% 2.55/1.51 => ! [X: A,Y: A] :
% 2.55/1.51 ( ( inf_inf @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.55/1.51 = X ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.55/1.51 ! [A7: $tType,A8: $tType] :
% 2.55/1.51 ( ( semilattice_sup @ A8 )
% 2.55/1.51 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 2.55/1.51 ! [A7: $tType,A8: $tType] :
% 2.55/1.51 ( ( semilattice_inf @ A8 )
% 2.55/1.51 => ( semilattice_inf @ ( A7 > A8 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.55/1.51 ! [A7: $tType,A8: $tType] :
% 2.55/1.51 ( ( preorder @ A8 )
% 2.55/1.51 => ( preorder @ ( A7 > A8 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.55/1.51 ! [A7: $tType,A8: $tType] :
% 2.55/1.51 ( ( lattice @ A8 )
% 2.55/1.51 => ( lattice @ ( A7 > A8 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.55/1.51 ! [A7: $tType,A8: $tType] :
% 2.55/1.51 ( ( order @ A8 )
% 2.55/1.51 => ( order @ ( A7 > A8 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_fun___Orderings_Oord,axiom,
% 2.55/1.51 ! [A7: $tType,A8: $tType] :
% 2.55/1.51 ( ( ord @ A8 )
% 2.55/1.51 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1,axiom,
% 2.55/1.51 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_2,axiom,
% 2.55/1.51 ! [A7: $tType] : ( semilattice_inf @ ( set @ A7 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_Set_Oset___Orderings_Opreorder_3,axiom,
% 2.55/1.51 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_Set_Oset___Lattices_Olattice_4,axiom,
% 2.55/1.51 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 2.55/1.51 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 2.55/1.51 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_7,axiom,
% 2.55/1.51 semilattice_sup @ $o ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_8,axiom,
% 2.55/1.51 semilattice_inf @ $o ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_HOL_Obool___Orderings_Opreorder_9,axiom,
% 2.55/1.51 preorder @ $o ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.55/1.51 linorder @ $o ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_HOL_Obool___Lattices_Olattice_10,axiom,
% 2.55/1.51 lattice @ $o ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_HOL_Obool___Orderings_Oorder_11,axiom,
% 2.55/1.51 order @ $o ).
% 2.55/1.51
% 2.55/1.51 thf(tcon_HOL_Obool___Orderings_Oord_12,axiom,
% 2.55/1.51 ord @ $o ).
% 2.55/1.51
% 2.55/1.51 thf(help_If_3_1_T,axiom,
% 2.55/1.51 ! [P: $o] :
% 2.55/1.51 ( ( P = $true )
% 2.55/1.51 | ( P = $false ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(help_If_2_1_T,axiom,
% 2.55/1.51 ! [A: $tType,X: A,Y: A] :
% 2.55/1.51 ( ( if @ A @ $false @ X @ Y )
% 2.55/1.51 = Y ) ).
% 2.55/1.51
% 2.55/1.51 thf(help_If_1_1_T,axiom,
% 2.55/1.51 ! [A: $tType,X: A,Y: A] :
% 2.55/1.51 ( ( if @ A @ $true @ X @ Y )
% 2.55/1.51 = X ) ).
% 2.55/1.51
% 2.55/1.51 thf(conj_0,hypothesis,
% 2.55/1.51 less_eq @ ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) @ ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ).
% 2.55/1.51
% 2.55/1.51 thf(conj_1,conjecture,
% 2.55/1.51 ( ( inf @ ( modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2 ) @ ( modula849153099_c_aux @ a @ inf @ sup @ a2 @ b @ c ) )
% 2.55/1.51 = ( modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c ) ) ).
% 2.55/1.51 ------------------------
% 2.55/1.53 % (32728)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/183Mi)
% 2.55/1.53 % (32729)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_32551 for (2999ds/4Mi)
% 2.55/1.53 % (32730)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_32551 for (2999ds/27Mi)
% 2.55/1.53 % (32734)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/18Mi)
% 2.55/1.53 % (32729)Instruction limit reached!
% 2.55/1.53 % (32729)------------------------------
% 2.55/1.53 % (32729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.53 % (32729)Termination reason: Unknown
% 2.55/1.53 % (32729)Termination phase: shuffling
% 2.55/1.53
% 2.55/1.53 % (32729)Memory used [KB]: 1279
% 2.55/1.53 % (32729)Time elapsed: 0.003 s
% 2.55/1.53 % (32729)Instructions burned: 4 (million)
% 2.55/1.53 % (32729)------------------------------
% 2.55/1.53 % (32729)------------------------------
% 2.55/1.53 % (32731)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/2Mi)
% 2.55/1.53 % (32733)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_32551 for (2999ds/275Mi)
% 2.55/1.53 % (32732)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_32551 for (2999ds/2Mi)
% 2.55/1.54 % (32731)Instruction limit reached!
% 2.55/1.54 % (32731)------------------------------
% 2.55/1.54 % (32731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.54 % (32732)Instruction limit reached!
% 2.55/1.54 % (32732)------------------------------
% 2.55/1.54 % (32732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.54 % (32731)Termination reason: Unknown
% 2.55/1.54 % (32731)Termination phase: shuffling
% 2.55/1.54
% 2.55/1.54 % (32731)Memory used [KB]: 1279
% 2.55/1.54 % (32731)Time elapsed: 0.003 s
% 2.55/1.54 % (32731)Instructions burned: 2 (million)
% 2.55/1.54 % (32731)------------------------------
% 2.55/1.54 % (32731)------------------------------
% 2.55/1.54 % (32732)Termination reason: Unknown
% 2.55/1.54 % (32732)Termination phase: shuffling
% 2.55/1.54
% 2.55/1.54 % (32732)Memory used [KB]: 1279
% 2.55/1.54 % (32732)Time elapsed: 0.003 s
% 2.55/1.54 % (32732)Instructions burned: 2 (million)
% 2.55/1.54 % (32732)------------------------------
% 2.55/1.54 % (32732)------------------------------
% 2.55/1.54 % (32734)Instruction limit reached!
% 2.55/1.54 % (32734)------------------------------
% 2.55/1.54 % (32734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.54 % (32734)Termination reason: Unknown
% 2.55/1.54 % (32734)Termination phase: Property scanning
% 2.55/1.54
% 2.55/1.54 % (32734)Memory used [KB]: 1535
% 2.55/1.54 % (32734)Time elapsed: 0.011 s
% 2.55/1.54 % (32734)Instructions burned: 19 (million)
% 2.55/1.54 % (32734)------------------------------
% 2.55/1.54 % (32734)------------------------------
% 2.55/1.55 % (32730)Instruction limit reached!
% 2.55/1.55 % (32730)------------------------------
% 2.55/1.55 % (32730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.55 % (32730)Termination reason: Unknown
% 2.55/1.55 % (32730)Termination phase: Preprocessing 1
% 2.55/1.55
% 2.55/1.55 % (32730)Memory used [KB]: 1535
% 2.55/1.55 % (32730)Time elapsed: 0.015 s
% 2.55/1.55 % (32730)Instructions burned: 28 (million)
% 2.55/1.55 % (32730)------------------------------
% 2.55/1.55 % (32730)------------------------------
% 2.55/1.55 % (32737)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/3Mi)
% 2.55/1.55 % (32737)Instruction limit reached!
% 2.55/1.55 % (32737)------------------------------
% 2.55/1.55 % (32737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.55 % (32737)Termination reason: Unknown
% 2.55/1.55 % (32737)Termination phase: shuffling
% 2.55/1.55
% 2.55/1.55 % (32737)Memory used [KB]: 1279
% 2.55/1.55 % (32737)Time elapsed: 0.003 s
% 2.55/1.55 % (32737)Instructions burned: 3 (million)
% 2.55/1.55 % (32737)------------------------------
% 2.55/1.55 % (32737)------------------------------
% 2.55/1.55 % (32739)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_32551 for (2999ds/15Mi)
% 2.55/1.55 % (32738)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_32551 for (2999ds/37Mi)
% 2.55/1.56 % (32739)Instruction limit reached!
% 2.55/1.56 % (32739)------------------------------
% 2.55/1.56 % (32739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.56 % (32739)Termination reason: Unknown
% 2.55/1.56 % (32739)Termination phase: shuffling
% 2.55/1.56
% 2.55/1.56 % (32739)Memory used [KB]: 1535
% 2.55/1.56 % (32739)Time elapsed: 0.009 s
% 2.55/1.56 % (32739)Instructions burned: 15 (million)
% 2.55/1.56 % (32739)------------------------------
% 2.55/1.56 % (32739)------------------------------
% 2.55/1.56 % (32741)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_32551 for (2999ds/1041Mi)
% 2.55/1.56 % (32740)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_32551 for (2999ds/3Mi)
% 2.55/1.56 % (32740)Instruction limit reached!
% 2.55/1.56 % (32740)------------------------------
% 2.55/1.56 % (32740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.56 % (32740)Termination reason: Unknown
% 2.55/1.56 % (32740)Termination phase: shuffling
% 2.55/1.56
% 2.55/1.56 % (32740)Memory used [KB]: 1279
% 2.55/1.56 % (32740)Time elapsed: 0.003 s
% 2.55/1.56 % (32740)Instructions burned: 3 (million)
% 2.55/1.56 % (32740)------------------------------
% 2.55/1.56 % (32740)------------------------------
% 2.55/1.57 % (32744)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/7Mi)
% 2.55/1.57 % (32738)Instruction limit reached!
% 2.55/1.57 % (32738)------------------------------
% 2.55/1.57 % (32738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.57 % (32738)Termination reason: Unknown
% 2.55/1.57 % (32738)Termination phase: Property scanning
% 2.55/1.57
% 2.55/1.57 % (32738)Memory used [KB]: 1918
% 2.55/1.57 % (32738)Time elapsed: 0.020 s
% 2.55/1.57 % (32738)Instructions burned: 38 (million)
% 2.55/1.57 % (32738)------------------------------
% 2.55/1.57 % (32738)------------------------------
% 2.55/1.57 % (32744)Instruction limit reached!
% 2.55/1.57 % (32744)------------------------------
% 2.55/1.57 % (32744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.57 % (32744)Termination reason: Unknown
% 2.55/1.57 % (32744)Termination phase: shuffling
% 2.55/1.57
% 2.55/1.57 % (32744)Memory used [KB]: 1407
% 2.55/1.57 % (32744)Time elapsed: 0.006 s
% 2.55/1.57 % (32744)Instructions burned: 8 (million)
% 2.55/1.57 % (32744)------------------------------
% 2.55/1.57 % (32744)------------------------------
% 2.55/1.58 % (32746)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_32551 for (2999ds/3Mi)
% 2.55/1.58 % (32746)Instruction limit reached!
% 2.55/1.58 % (32746)------------------------------
% 2.55/1.58 % (32746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.58 % (32746)Termination reason: Unknown
% 2.55/1.58 % (32746)Termination phase: shuffling
% 2.55/1.58
% 2.55/1.58 % (32746)Memory used [KB]: 1279
% 2.55/1.58 % (32746)Time elapsed: 0.003 s
% 2.55/1.58 % (32746)Instructions burned: 3 (million)
% 2.55/1.58 % (32746)------------------------------
% 2.55/1.58 % (32746)------------------------------
% 2.55/1.58 % (32728)Instruction limit reached!
% 2.55/1.58 % (32728)------------------------------
% 2.55/1.58 % (32728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.58 % (32728)Termination reason: Unknown
% 2.55/1.58 % (32728)Termination phase: Saturation
% 2.55/1.58
% 2.55/1.58 % (32728)Memory used [KB]: 6908
% 2.55/1.58 % (32728)Time elapsed: 0.058 s
% 2.55/1.58 % (32728)Instructions burned: 183 (million)
% 2.55/1.58 % (32728)------------------------------
% 2.55/1.58 % (32728)------------------------------
% 2.55/1.59 % (32747)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_32551 for (2999ds/3Mi)
% 2.55/1.59 % (32748)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/7Mi)
% 2.55/1.59 % (32747)Instruction limit reached!
% 2.55/1.59 % (32747)------------------------------
% 2.55/1.59 % (32747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.59 % (32747)Termination reason: Unknown
% 2.55/1.59 % (32747)Termination phase: shuffling
% 2.55/1.59
% 2.55/1.59 % (32747)Memory used [KB]: 1279
% 2.55/1.59 % (32747)Time elapsed: 0.003 s
% 2.55/1.59 % (32747)Instructions burned: 4 (million)
% 2.55/1.59 % (32747)------------------------------
% 2.55/1.59 % (32747)------------------------------
% 2.55/1.59 % (32745)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/16Mi)
% 2.55/1.59 % (32748)Instruction limit reached!
% 2.55/1.59 % (32748)------------------------------
% 2.55/1.59 % (32748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.59 % (32748)Termination reason: Unknown
% 2.55/1.59 % (32748)Termination phase: shuffling
% 2.55/1.59
% 2.55/1.59 % (32748)Memory used [KB]: 1407
% 2.55/1.59 % (32748)Time elapsed: 0.005 s
% 2.55/1.59 % (32748)Instructions burned: 7 (million)
% 2.55/1.59 % (32748)------------------------------
% 2.55/1.59 % (32748)------------------------------
% 2.55/1.59 % (32750)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/3Mi)
% 2.55/1.59 % (32750)Instruction limit reached!
% 2.55/1.59 % (32750)------------------------------
% 2.55/1.59 % (32750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.59 % (32750)Termination reason: Unknown
% 2.55/1.59 % (32750)Termination phase: shuffling
% 2.55/1.59
% 2.55/1.59 % (32750)Memory used [KB]: 1279
% 2.55/1.59 % (32750)Time elapsed: 0.002 s
% 2.55/1.59 % (32750)Instructions burned: 4 (million)
% 2.55/1.59 % (32750)------------------------------
% 2.55/1.59 % (32750)------------------------------
% 2.59/1.60 % (32745)Instruction limit reached!
% 2.59/1.60 % (32745)------------------------------
% 2.59/1.60 % (32745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.60 % (32745)Termination reason: Unknown
% 2.59/1.60 % (32745)Termination phase: Property scanning
% 2.59/1.60
% 2.59/1.60 % (32745)Memory used [KB]: 1535
% 2.59/1.60 % (32745)Time elapsed: 0.011 s
% 2.59/1.60 % (32745)Instructions burned: 16 (million)
% 2.59/1.60 % (32745)------------------------------
% 2.59/1.60 % (32745)------------------------------
% 2.59/1.60 % (32751)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/4Mi)
% 2.59/1.60 % (32751)Instruction limit reached!
% 2.59/1.60 % (32751)------------------------------
% 2.59/1.60 % (32751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.60 % (32751)Termination reason: Unknown
% 2.59/1.60 % (32751)Termination phase: shuffling
% 2.59/1.60
% 2.59/1.60 % (32751)Memory used [KB]: 1407
% 2.59/1.60 % (32751)Time elapsed: 0.004 s
% 2.59/1.60 % (32751)Instructions burned: 5 (million)
% 2.59/1.60 % (32751)------------------------------
% 2.59/1.60 % (32751)------------------------------
% 2.59/1.60 % (32753)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/710Mi)
% 2.59/1.61 % (32752)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/18Mi)
% 2.59/1.61 % (32754)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/6Mi)
% 2.59/1.61 % (32754)Instruction limit reached!
% 2.59/1.61 % (32754)------------------------------
% 2.59/1.61 % (32754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.61 % (32754)Termination reason: Unknown
% 2.59/1.61 % (32754)Termination phase: shuffling
% 2.59/1.61
% 2.59/1.61 % (32754)Memory used [KB]: 1407
% 2.59/1.61 % (32754)Time elapsed: 0.005 s
% 2.59/1.61 % (32754)Instructions burned: 7 (million)
% 2.59/1.61 % (32754)------------------------------
% 2.59/1.61 % (32754)------------------------------
% 2.59/1.62 % (32752)Instruction limit reached!
% 2.59/1.62 % (32752)------------------------------
% 2.59/1.62 % (32752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.62 % (32752)Termination reason: Unknown
% 2.59/1.62 % (32752)Termination phase: Property scanning
% 2.59/1.62
% 2.59/1.62 % (32752)Memory used [KB]: 1535
% 2.59/1.62 % (32752)Time elapsed: 0.011 s
% 2.59/1.62 % (32752)Instructions burned: 18 (million)
% 2.59/1.62 % (32752)------------------------------
% 2.59/1.62 % (32752)------------------------------
% 2.59/1.62 % (32756)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_32551 for (2999ds/902Mi)
% 2.59/1.62 % (32757)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_32551 for (2999ds/21Mi)
% 2.59/1.63 % (32758)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32551 for (2999ds/5Mi)
% 2.59/1.63 % (32758)Instruction limit reached!
% 2.59/1.63 % (32758)------------------------------
% 2.59/1.63 % (32758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.63 % (32758)Termination reason: Unknown
% 2.59/1.63 % (32758)Termination phase: shuffling
% 2.59/1.63
% 2.59/1.63 % (32758)Memory used [KB]: 1407
% 2.59/1.63 % (32758)Time elapsed: 0.003 s
% 2.59/1.63 % (32758)Instructions burned: 8 (million)
% 2.59/1.63 % (32758)------------------------------
% 2.59/1.63 % (32758)------------------------------
% 2.59/1.63 % (32757)Instruction limit reached!
% 2.59/1.63 % (32757)------------------------------
% 2.59/1.63 % (32757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.63 % (32757)Termination reason: Unknown
% 2.59/1.63 % (32757)Termination phase: Property scanning
% 2.59/1.63
% 2.59/1.63 % (32757)Memory used [KB]: 1535
% 2.59/1.63 % (32757)Time elapsed: 0.014 s
% 2.59/1.63 % (32757)Instructions burned: 22 (million)
% 2.59/1.63 % (32757)------------------------------
% 2.59/1.63 % (32757)------------------------------
% 2.59/1.63 % (32759)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_32551 for (2999ds/6Mi)
% 2.59/1.63 % (32759)Instruction limit reached!
% 2.59/1.63 % (32759)------------------------------
% 2.59/1.63 % (32759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.63 % (32759)Termination reason: Unknown
% 2.59/1.63 % (32759)Termination phase: shuffling
% 2.59/1.63
% 2.59/1.63 % (32759)Memory used [KB]: 1407
% 2.59/1.63 % (32759)Time elapsed: 0.004 s
% 2.59/1.63 % (32759)Instructions burned: 6 (million)
% 2.59/1.63 % (32759)------------------------------
% 2.59/1.63 % (32759)------------------------------
% 2.59/1.64 % (32761)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32551 for (2998ds/377Mi)
% 2.59/1.65 % (32762)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_32551 for (2998ds/779Mi)
% 2.59/1.65 % (32763)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_32551 for (2998ds/19Mi)
% 2.59/1.66 % (32763)Instruction limit reached!
% 2.59/1.66 % (32763)------------------------------
% 2.59/1.66 % (32763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.66 % (32763)Termination reason: Unknown
% 2.59/1.66 % (32763)Termination phase: shuffling
% 2.59/1.66
% 2.59/1.66 % (32763)Memory used [KB]: 1663
% 2.59/1.66 % (32763)Time elapsed: 0.010 s
% 2.59/1.66 % (32763)Instructions burned: 19 (million)
% 2.59/1.66 % (32763)------------------------------
% 2.59/1.66 % (32763)------------------------------
% 2.59/1.67 % (32733)Instruction limit reached!
% 2.59/1.67 % (32733)------------------------------
% 2.59/1.67 % (32733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.67 % (32733)Termination reason: Unknown
% 2.59/1.67 % (32733)Termination phase: Saturation
% 2.59/1.67
% 2.59/1.67 % (32733)Memory used [KB]: 6524
% 2.59/1.67 % (32733)Time elapsed: 0.134 s
% 2.59/1.67 % (32733)Instructions burned: 276 (million)
% 2.59/1.67 % (32733)------------------------------
% 2.59/1.67 % (32733)------------------------------
% 2.59/1.67 % (32764)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32551 for (2998ds/879Mi)
% 2.59/1.68 % (32765)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32551 for (2998ds/17Mi)
% 2.59/1.68 % (32765)Instruction limit reached!
% 2.59/1.68 % (32765)------------------------------
% 2.59/1.68 % (32765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.68 % (32765)Termination reason: Unknown
% 2.59/1.68 % (32765)Termination phase: Property scanning
% 2.59/1.68
% 2.59/1.68 % (32765)Memory used [KB]: 1535
% 2.59/1.68 % (32765)Time elapsed: 0.008 s
% 2.59/1.68 % (32765)Instructions burned: 20 (million)
% 2.59/1.69 % (32765)------------------------------
% 2.59/1.69 % (32765)------------------------------
% 2.59/1.70 % (32766)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32551 for (2998ds/3Mi)
% 2.59/1.70 % (32766)Instruction limit reached!
% 2.59/1.70 % (32766)------------------------------
% 2.59/1.70 % (32766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.70 % (32766)Termination reason: Unknown
% 2.59/1.70 % (32766)Termination phase: shuffling
% 2.59/1.70
% 2.59/1.70 % (32766)Memory used [KB]: 1279
% 2.59/1.70 % (32766)Time elapsed: 0.004 s
% 2.59/1.70 % (32766)Instructions burned: 4 (million)
% 2.59/1.70 % (32766)------------------------------
% 2.59/1.70 % (32766)------------------------------
% 2.59/1.72 % (302)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_32551 for (2998ds/30Mi)
% 2.59/1.73 % (302)Instruction limit reached!
% 2.59/1.73 % (302)------------------------------
% 2.59/1.73 % (302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.73 % (302)Termination reason: Unknown
% 2.59/1.73 % (302)Termination phase: Preprocessing 1
% 2.59/1.73
% 2.59/1.73 % (302)Memory used [KB]: 1663
% 2.59/1.73 % (302)Time elapsed: 0.011 s
% 2.59/1.73 % (302)Instructions burned: 33 (million)
% 2.59/1.73 % (302)------------------------------
% 2.59/1.73 % (302)------------------------------
% 2.59/1.74 % (304)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_32551 for (2997ds/127Mi)
% 2.59/1.78 % (304)Instruction limit reached!
% 2.59/1.78 % (304)------------------------------
% 2.59/1.78 % (304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.78 % (304)Termination reason: Unknown
% 2.59/1.78 % (304)Termination phase: Saturation
% 2.59/1.78
% 2.59/1.78 % (304)Memory used [KB]: 6780
% 2.59/1.78 % (304)Time elapsed: 0.044 s
% 2.59/1.78 % (304)Instructions burned: 127 (million)
% 2.59/1.78 % (304)------------------------------
% 2.59/1.78 % (304)------------------------------
% 2.59/1.80 % (308)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_32551 for (2997ds/100Mi)
% 2.59/1.80 % (32761)Instruction limit reached!
% 2.59/1.80 % (32761)------------------------------
% 2.59/1.80 % (32761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.80 % (32761)Termination reason: Unknown
% 2.59/1.80 % (32761)Termination phase: Saturation
% 2.59/1.80
% 2.59/1.80 % (32761)Memory used [KB]: 7291
% 2.59/1.80 % (32761)Time elapsed: 0.167 s
% 2.59/1.80 % (32761)Instructions burned: 378 (million)
% 2.59/1.80 % (32761)------------------------------
% 2.59/1.80 % (32761)------------------------------
% 2.59/1.82 % (310)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_32551 for (2997ds/3Mi)
% 2.59/1.82 % (310)Instruction limit reached!
% 2.59/1.82 % (310)------------------------------
% 2.59/1.82 % (310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.82 % (310)Termination reason: Unknown
% 2.59/1.82 % (310)Termination phase: shuffling
% 2.59/1.82
% 2.59/1.82 % (310)Memory used [KB]: 1279
% 2.59/1.82 % (310)Time elapsed: 0.003 s
% 2.59/1.82 % (310)Instructions burned: 3 (million)
% 2.59/1.82 % (310)------------------------------
% 2.59/1.82 % (310)------------------------------
% 2.59/1.84 % (308)Instruction limit reached!
% 2.59/1.84 % (308)------------------------------
% 2.59/1.84 % (308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.84 % (308)Termination reason: Unknown
% 2.59/1.84 % (308)Termination phase: Saturation
% 2.59/1.84
% 2.59/1.84 % (308)Memory used [KB]: 6652
% 2.59/1.84 % (308)Time elapsed: 0.047 s
% 2.59/1.84 % (308)Instructions burned: 101 (million)
% 2.59/1.84 % (308)------------------------------
% 2.59/1.84 % (308)------------------------------
% 2.59/1.85 % (312)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_32551 for (2997ds/20Mi)
% 2.59/1.86 % (312)Instruction limit reached!
% 2.59/1.86 % (312)------------------------------
% 2.59/1.86 % (312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.86 % (312)Termination reason: Unknown
% 2.59/1.86 % (312)Termination phase: Property scanning
% 2.59/1.86
% 2.59/1.86 % (312)Memory used [KB]: 1535
% 2.59/1.86 % (312)Time elapsed: 0.011 s
% 2.59/1.86 % (312)Instructions burned: 22 (million)
% 2.59/1.86 % (312)------------------------------
% 2.59/1.86 % (312)------------------------------
% 2.59/1.86 % (314)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_32551 for (2996ds/86Mi)
% 2.59/1.89 % (316)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_32551 for (2996ds/107Mi)
% 2.59/1.89 % (314)Instruction limit reached!
% 2.59/1.89 % (314)------------------------------
% 2.59/1.89 % (314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.89 % (314)Termination reason: Unknown
% 2.59/1.89 % (314)Termination phase: Saturation
% 2.59/1.89
% 2.59/1.89 % (314)Memory used [KB]: 6524
% 2.59/1.89 % (314)Time elapsed: 0.059 s
% 2.59/1.89 % (314)Instructions burned: 88 (million)
% 2.59/1.89 % (314)------------------------------
% 2.59/1.89 % (314)------------------------------
% 2.59/1.90 % (317)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_32551 for (2996ds/39Mi)
% 2.59/1.90 % (32753)Instruction limit reached!
% 2.59/1.90 % (32753)------------------------------
% 2.59/1.90 % (32753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.90 % (32753)Termination reason: Unknown
% 2.59/1.90 % (32753)Termination phase: Saturation
% 2.59/1.90
% 2.59/1.90 % (32753)Memory used [KB]: 7164
% 2.59/1.90 % (32753)Time elapsed: 0.296 s
% 2.59/1.90 % (32753)Instructions burned: 710 (million)
% 2.59/1.90 % (32753)------------------------------
% 2.59/1.90 % (32753)------------------------------
% 2.59/1.91 % (317)Instruction limit reached!
% 2.59/1.91 % (317)------------------------------
% 2.59/1.91 % (317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.91 % (317)Termination reason: Unknown
% 2.59/1.91 % (317)Termination phase: Property scanning
% 2.59/1.91
% 2.59/1.91 % (317)Memory used [KB]: 1918
% 2.59/1.91 % (317)Time elapsed: 0.012 s
% 2.59/1.91 % (317)Instructions burned: 42 (million)
% 2.59/1.91 % (317)------------------------------
% 2.59/1.91 % (317)------------------------------
% 2.59/1.92 % (319)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_32551 for (2996ds/448Mi)
% 2.59/1.93 % (316)Instruction limit reached!
% 2.59/1.93 % (316)------------------------------
% 2.59/1.93 % (316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.93 % (316)Termination reason: Unknown
% 2.59/1.93 % (316)Termination phase: Saturation
% 2.59/1.93
% 2.59/1.93 % (316)Memory used [KB]: 6524
% 2.59/1.93 % (316)Time elapsed: 0.039 s
% 2.59/1.93 % (316)Instructions burned: 107 (million)
% 2.59/1.93 % (316)------------------------------
% 2.59/1.93 % (316)------------------------------
% 2.59/1.94 % (321)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_32551 for (2995ds/46Mi)
% 2.59/1.95 % (323)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_32551 for (2995ds/98Mi)
% 2.59/1.96 % (321)Instruction limit reached!
% 2.59/1.96 % (321)------------------------------
% 2.59/1.96 % (321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.96 % (321)Termination reason: Unknown
% 2.59/1.96 % (321)Termination phase: Saturation
% 2.59/1.96
% 2.59/1.96 % (321)Memory used [KB]: 6140
% 2.59/1.96 % (321)Time elapsed: 0.024 s
% 2.59/1.96 % (321)Instructions burned: 47 (million)
% 2.59/1.96 % (321)------------------------------
% 2.59/1.96 % (321)------------------------------
% 2.59/1.98 % (327)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_32551 for (2995ds/507Mi)
% 2.59/1.98 % (323)Instruction limit reached!
% 2.59/1.98 % (323)------------------------------
% 2.59/1.98 % (323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.98 % (323)Termination reason: Unknown
% 2.59/1.98 % (323)Termination phase: Saturation
% 2.59/1.98
% 2.59/1.98 % (323)Memory used [KB]: 2174
% 2.59/1.98 % (323)Time elapsed: 0.033 s
% 2.59/1.98 % (323)Instructions burned: 99 (million)
% 2.59/1.98 % (323)------------------------------
% 2.59/1.98 % (323)------------------------------
% 2.59/1.99 % (331)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_32551 for (2995ds/149Mi)
% 2.59/2.00 % (32756)Instruction limit reached!
% 2.59/2.00 % (32756)------------------------------
% 2.59/2.00 % (32756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/2.00 % (32756)Termination reason: Unknown
% 2.59/2.00 % (32756)Termination phase: Saturation
% 2.59/2.00
% 2.59/2.00 % (32756)Memory used [KB]: 7803
% 2.59/2.00 % (32756)Time elapsed: 0.390 s
% 2.59/2.00 % (32756)Instructions burned: 904 (million)
% 2.59/2.00 % (32756)------------------------------
% 2.59/2.00 % (32756)------------------------------
% 2.59/2.01 % (32762)Instruction limit reached!
% 2.59/2.01 % (32762)------------------------------
% 2.59/2.01 % (32762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/2.01 % (32762)Termination reason: Unknown
% 2.59/2.01 % (32762)Termination phase: Saturation
% 2.59/2.01
% 2.59/2.01 % (32762)Memory used [KB]: 7291
% 2.59/2.01 % (32762)Time elapsed: 0.369 s
% 2.59/2.01 % (32762)Instructions burned: 779 (million)
% 2.59/2.01 % (32762)------------------------------
% 2.59/2.01 % (32762)------------------------------
% 5.88/2.03 % (335)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_32551 for (2994ds/6Mi)
% 5.88/2.03 % (335)Instruction limit reached!
% 5.88/2.03 % (335)------------------------------
% 5.88/2.03 % (335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.03 % (335)Termination reason: Unknown
% 5.88/2.03 % (335)Termination phase: shuffling
% 5.88/2.03
% 5.88/2.03 % (335)Memory used [KB]: 1407
% 5.88/2.03 % (335)Time elapsed: 0.005 s
% 5.88/2.03 % (335)Instructions burned: 7 (million)
% 5.88/2.03 % (335)------------------------------
% 5.88/2.03 % (335)------------------------------
% 5.88/2.04 % (32741)Instruction limit reached!
% 5.88/2.04 % (32741)------------------------------
% 5.88/2.04 % (32741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.04 % (32741)Termination reason: Unknown
% 5.88/2.04 % (32741)Termination phase: Saturation
% 5.88/2.04
% 5.88/2.04 % (32741)Memory used [KB]: 9466
% 5.88/2.04 % (32741)Time elapsed: 0.476 s
% 5.88/2.04 % (32741)Instructions burned: 1041 (million)
% 5.88/2.04 % (32741)------------------------------
% 5.88/2.04 % (32741)------------------------------
% 5.88/2.04 % (333)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_32551 for (2995ds/39Mi)
% 5.88/2.04 % (331)Instruction limit reached!
% 5.88/2.04 % (331)------------------------------
% 5.88/2.04 % (331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.04 % (331)Termination reason: Unknown
% 5.88/2.04 % (331)Termination phase: Saturation
% 5.88/2.04
% 5.88/2.04 % (331)Memory used [KB]: 6780
% 5.88/2.04 % (331)Time elapsed: 0.051 s
% 5.88/2.04 % (331)Instructions burned: 150 (million)
% 5.88/2.04 % (331)------------------------------
% 5.88/2.04 % (331)------------------------------
% 5.88/2.05 % (338)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_32551 for (2994ds/1087Mi)
% 5.88/2.05 % (340)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_32551 for (2994ds/44Mi)
% 5.88/2.05 % (339)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_32551 for (2994ds/47Mi)
% 5.88/2.06 % (333)Instruction limit reached!
% 5.88/2.06 % (333)------------------------------
% 5.88/2.06 % (333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.06 % (333)Termination reason: Unknown
% 5.88/2.06 % (333)Termination phase: Property scanning
% 5.88/2.06
% 5.88/2.06 % (333)Memory used [KB]: 1791
% 5.88/2.06 % (333)Time elapsed: 0.021 s
% 5.88/2.06 % (333)Instructions burned: 39 (million)
% 5.88/2.06 % (333)------------------------------
% 5.88/2.06 % (333)------------------------------
% 5.88/2.06 % (340)Instruction limit reached!
% 5.88/2.06 % (340)------------------------------
% 5.88/2.06 % (340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.06 % (340)Termination reason: Unknown
% 5.88/2.06 % (340)Termination phase: Property scanning
% 5.88/2.06
% 5.88/2.06 % (340)Memory used [KB]: 1918
% 5.88/2.06 % (340)Time elapsed: 0.013 s
% 5.88/2.06 % (340)Instructions burned: 44 (million)
% 5.88/2.06 % (340)------------------------------
% 5.88/2.06 % (340)------------------------------
% 5.88/2.07 % (344)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_32551 for (2994ds/62Mi)
% 5.88/2.07 % (343)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_32551 for (2994ds/432Mi)
% 5.88/2.08 % (339)Instruction limit reached!
% 5.88/2.08 % (339)------------------------------
% 5.88/2.08 % (339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.08 % (339)Termination reason: Unknown
% 5.88/2.08 % (339)Termination phase: Property scanning
% 5.88/2.08
% 5.88/2.08 % (339)Memory used [KB]: 1791
% 5.88/2.08 % (339)Time elapsed: 0.024 s
% 5.88/2.08 % (339)Instructions burned: 47 (million)
% 5.88/2.08 % (339)------------------------------
% 5.88/2.08 % (339)------------------------------
% 5.88/2.09 % (344)Instruction limit reached!
% 5.88/2.09 % (344)------------------------------
% 5.88/2.09 % (344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.09 % (344)Termination reason: Unknown
% 5.88/2.09 % (344)Termination phase: Property scanning
% 5.88/2.09
% 5.88/2.09 % (344)Memory used [KB]: 2046
% 5.88/2.09 % (344)Time elapsed: 0.023 s
% 5.88/2.09 % (344)Instructions burned: 62 (million)
% 5.88/2.09 % (344)------------------------------
% 5.88/2.09 % (344)------------------------------
% 5.88/2.10 % (346)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_32551 for (2994ds/31Mi)
% 5.88/2.10 % (32764)Instruction limit reached!
% 5.88/2.10 % (32764)------------------------------
% 5.88/2.10 % (32764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.10 % (32764)Termination reason: Unknown
% 5.88/2.10 % (32764)Termination phase: Saturation
% 5.88/2.10
% 5.88/2.10 % (32764)Memory used [KB]: 7675
% 5.88/2.10 % (32764)Time elapsed: 0.426 s
% 5.88/2.10 % (32764)Instructions burned: 879 (million)
% 5.88/2.10 % (32764)------------------------------
% 5.88/2.10 % (32764)------------------------------
% 5.88/2.11 % (350)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_32551 for (2994ds/96Mi)
% 5.88/2.11 % (346)Instruction limit reached!
% 5.88/2.11 % (346)------------------------------
% 5.88/2.11 % (346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.11 % (346)Termination reason: Unknown
% 5.88/2.11 % (346)Termination phase: Preprocessing 3
% 5.88/2.11
% 5.88/2.11 % (346)Memory used [KB]: 1663
% 5.88/2.11 % (346)Time elapsed: 0.017 s
% 5.88/2.11 % (346)Instructions burned: 31 (million)
% 5.88/2.11 % (346)------------------------------
% 5.88/2.11 % (346)------------------------------
% 5.88/2.12 % (351)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_32551 for (2994ds/453Mi)
% 5.88/2.12 % (319)Instruction limit reached!
% 5.88/2.12 % (319)------------------------------
% 5.88/2.12 % (319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.12 % (319)Termination reason: Unknown
% 5.88/2.12 % (319)Termination phase: Saturation
% 5.88/2.12
% 5.88/2.12 % (319)Memory used [KB]: 7291
% 5.88/2.12 % (319)Time elapsed: 0.191 s
% 5.88/2.12 % (319)Instructions burned: 449 (million)
% 5.88/2.12 % (319)------------------------------
% 5.88/2.12 % (319)------------------------------
% 6.44/2.13 % (353)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_32551 for (2994ds/71Mi)
% 6.44/2.14 % (354)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_32551 for (2993ds/83Mi)
% 6.44/2.16 % (350)Instruction limit reached!
% 6.44/2.16 % (350)------------------------------
% 6.44/2.16 % (350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.16 % (350)Termination reason: Unknown
% 6.44/2.16 % (350)Termination phase: Saturation
% 6.44/2.16
% 6.44/2.16 % (350)Memory used [KB]: 6652
% 6.44/2.16 % (350)Time elapsed: 0.048 s
% 6.44/2.16 % (350)Instructions burned: 96 (million)
% 6.44/2.16 % (350)------------------------------
% 6.44/2.16 % (350)------------------------------
% 6.44/2.16 % (353)Instruction limit reached!
% 6.44/2.16 % (353)------------------------------
% 6.44/2.16 % (353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.16 % (353)Termination reason: Unknown
% 6.44/2.16 % (353)Termination phase: Property scanning
% 6.44/2.16
% 6.44/2.16 % (353)Memory used [KB]: 1918
% 6.44/2.16 % (353)Time elapsed: 0.035 s
% 6.44/2.16 % (353)Instructions burned: 71 (million)
% 6.44/2.16 % (353)------------------------------
% 6.44/2.16 % (353)------------------------------
% 6.44/2.17 % (354)Instruction limit reached!
% 6.44/2.17 % (354)------------------------------
% 6.44/2.17 % (354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.17 % (354)Termination reason: Unknown
% 6.44/2.17 % (354)Termination phase: Saturation
% 6.44/2.17
% 6.44/2.17 % (354)Memory used [KB]: 6268
% 6.44/2.17 % (354)Time elapsed: 0.039 s
% 6.44/2.17 % (354)Instructions burned: 84 (million)
% 6.44/2.17 % (354)------------------------------
% 6.44/2.17 % (354)------------------------------
% 6.44/2.17 % (357)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_32551 for (2993ds/11Mi)
% 6.44/2.18 % (357)Instruction limit reached!
% 6.44/2.18 % (357)------------------------------
% 6.44/2.18 % (357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.18 % (357)Termination reason: Unknown
% 6.44/2.18 % (357)Termination phase: shuffling
% 6.44/2.18
% 6.44/2.18 % (357)Memory used [KB]: 1535
% 6.44/2.18 % (357)Time elapsed: 0.007 s
% 6.44/2.18 % (357)Instructions burned: 11 (million)
% 6.44/2.18 % (357)------------------------------
% 6.44/2.18 % (357)------------------------------
% 6.44/2.18 % (358)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_32551 for (2993ds/41Mi)
% 6.44/2.18 % (360)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32551 for (2993ds/6Mi)
% 6.44/2.19 % (360)Instruction limit reached!
% 6.44/2.19 % (360)------------------------------
% 6.44/2.19 % (360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.19 % (360)Termination reason: Unknown
% 6.44/2.19 % (360)Termination phase: shuffling
% 6.44/2.19
% 6.44/2.19 % (360)Memory used [KB]: 1407
% 6.44/2.19 % (360)Time elapsed: 0.003 s
% 6.44/2.19 % (360)Instructions burned: 6 (million)
% 6.44/2.19 % (360)------------------------------
% 6.44/2.19 % (360)------------------------------
% 6.44/2.19 % (362)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_32551 for (2993ds/343Mi)
% 6.44/2.20 % (361)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_32551 for (2993ds/150Mi)
% 6.70/2.20 % (358)Instruction limit reached!
% 6.70/2.20 % (358)------------------------------
% 6.70/2.20 % (358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.20 % (358)Termination reason: Unknown
% 6.70/2.20 % (358)Termination phase: Property scanning
% 6.70/2.20
% 6.70/2.20 % (358)Memory used [KB]: 1918
% 6.70/2.20 % (358)Time elapsed: 0.020 s
% 6.70/2.20 % (358)Instructions burned: 41 (million)
% 6.70/2.20 % (358)------------------------------
% 6.70/2.20 % (358)------------------------------
% 6.70/2.21 % (363)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_32551 for (2993ds/109Mi)
% 6.70/2.22 % (327)Instruction limit reached!
% 6.70/2.22 % (327)------------------------------
% 6.70/2.22 % (327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.22 % (327)Termination reason: Unknown
% 6.70/2.22 % (327)Termination phase: Saturation
% 6.70/2.22
% 6.70/2.22 % (327)Memory used [KB]: 7547
% 6.70/2.22 % (327)Time elapsed: 0.242 s
% 6.70/2.22 % (327)Instructions burned: 507 (million)
% 6.70/2.22 % (327)------------------------------
% 6.70/2.22 % (327)------------------------------
% 6.70/2.23 % (365)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_32551 for (2993ds/253Mi)
% 6.70/2.26 % (343)Instruction limit reached!
% 6.70/2.26 % (343)------------------------------
% 6.70/2.26 % (343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.26 % (343)Termination reason: Unknown
% 6.70/2.26 % (343)Termination phase: Saturation
% 6.70/2.26
% 6.70/2.26 % (343)Memory used [KB]: 3582
% 6.70/2.26 % (343)Time elapsed: 0.184 s
% 6.70/2.26 % (343)Instructions burned: 432 (million)
% 6.70/2.26 % (343)------------------------------
% 6.70/2.26 % (343)------------------------------
% 6.70/2.27 % (363)Instruction limit reached!
% 6.70/2.27 % (363)------------------------------
% 6.70/2.27 % (363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.27 % (363)Termination reason: Unknown
% 6.70/2.27 % (363)Termination phase: Saturation
% 6.70/2.27
% 6.70/2.27 % (363)Memory used [KB]: 6652
% 6.70/2.27 % (363)Time elapsed: 0.055 s
% 6.70/2.27 % (363)Instructions burned: 110 (million)
% 6.70/2.27 % (363)------------------------------
% 6.70/2.27 % (363)------------------------------
% 6.70/2.27 % (361)Instruction limit reached!
% 6.70/2.27 % (361)------------------------------
% 6.70/2.27 % (361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.27 % (361)Termination reason: Unknown
% 6.70/2.27 % (361)Termination phase: Saturation
% 6.70/2.27
% 6.70/2.27 % (361)Memory used [KB]: 6780
% 6.70/2.27 % (361)Time elapsed: 0.076 s
% 6.70/2.27 % (361)Instructions burned: 150 (million)
% 6.70/2.27 % (361)------------------------------
% 6.70/2.27 % (361)------------------------------
% 6.70/2.27 % (368)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_32551 for (2992ds/140Mi)
% 6.70/2.28 % (369)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_32551 for (2992ds/614Mi)
% 6.70/2.29 % (370)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_32551 for (2992ds/202Mi)
% 7.13/2.32 % (362)Instruction limit reached!
% 7.13/2.32 % (362)------------------------------
% 7.13/2.32 % (362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.32 % (362)Termination reason: Unknown
% 7.13/2.32 % (362)Termination phase: Saturation
% 7.13/2.32
% 7.13/2.32 % (362)Memory used [KB]: 6908
% 7.13/2.32 % (362)Time elapsed: 0.123 s
% 7.13/2.32 % (362)Instructions burned: 344 (million)
% 7.13/2.32 % (362)------------------------------
% 7.13/2.32 % (362)------------------------------
% 7.13/2.32 % (351)Instruction limit reached!
% 7.13/2.32 % (351)------------------------------
% 7.13/2.32 % (351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.32 % (351)Termination reason: Unknown
% 7.13/2.32 % (351)Termination phase: Saturation
% 7.13/2.32
% 7.13/2.32 % (351)Memory used [KB]: 7419
% 7.13/2.32 % (351)Time elapsed: 0.202 s
% 7.13/2.32 % (351)Instructions burned: 455 (million)
% 7.13/2.32 % (351)------------------------------
% 7.13/2.32 % (351)------------------------------
% 7.13/2.33 % (375)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_32551 for (2992ds/283Mi)
% 7.13/2.33 % (374)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_32551 for (2992ds/339Mi)
% 7.13/2.34 % (368)Instruction limit reached!
% 7.13/2.34 % (368)------------------------------
% 7.13/2.34 % (368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.34 % (368)Termination reason: Unknown
% 7.13/2.34 % (368)Termination phase: Saturation
% 7.13/2.34
% 7.13/2.34 % (368)Memory used [KB]: 6524
% 7.13/2.34 % (368)Time elapsed: 0.071 s
% 7.13/2.34 % (368)Instructions burned: 141 (million)
% 7.13/2.34 % (368)------------------------------
% 7.13/2.34 % (368)------------------------------
% 7.13/2.35 % (365)Instruction limit reached!
% 7.13/2.35 % (365)------------------------------
% 7.13/2.35 % (365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.35 % (365)Termination reason: Unknown
% 7.13/2.35 % (365)Termination phase: Saturation
% 7.13/2.35
% 7.13/2.35 % (365)Memory used [KB]: 6652
% 7.13/2.35 % (365)Time elapsed: 0.119 s
% 7.13/2.35 % (365)Instructions burned: 254 (million)
% 7.13/2.35 % (365)------------------------------
% 7.13/2.35 % (365)------------------------------
% 7.13/2.35 % (376)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_32551 for (2991ds/134Mi)
% 7.13/2.37 % (379)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_32551 for (2991ds/298Mi)
% 7.13/2.38 % (370)Instruction limit reached!
% 7.13/2.38 % (370)------------------------------
% 7.13/2.38 % (370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.38 % (370)Termination reason: Unknown
% 7.13/2.38 % (370)Termination phase: Saturation
% 7.13/2.38
% 7.13/2.38 % (370)Memory used [KB]: 6652
% 7.13/2.38 % (370)Time elapsed: 0.097 s
% 7.13/2.38 % (370)Instructions burned: 202 (million)
% 7.13/2.38 % (370)------------------------------
% 7.13/2.38 % (370)------------------------------
% 7.13/2.39 % (380)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_32551 for (2991ds/192Mi)
% 7.81/2.41 % (376)Instruction limit reached!
% 7.81/2.41 % (376)------------------------------
% 7.81/2.41 % (376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.41 % (376)Termination reason: Unknown
% 7.81/2.41 % (376)Termination phase: Saturation
% 7.81/2.41
% 7.81/2.41 % (376)Memory used [KB]: 6652
% 7.81/2.41 % (376)Time elapsed: 0.062 s
% 7.81/2.41 % (376)Instructions burned: 134 (million)
% 7.81/2.42 % (376)------------------------------
% 7.81/2.42 % (376)------------------------------
% 7.81/2.43 % (385)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_32551 for (2991ds/258Mi)
% 7.81/2.45 % (375)Instruction limit reached!
% 7.81/2.45 % (375)------------------------------
% 7.81/2.45 % (375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.45 % (375)Termination reason: Unknown
% 7.81/2.45 % (375)Termination phase: Saturation
% 7.81/2.45
% 7.81/2.45 % (375)Memory used [KB]: 7419
% 7.81/2.45 % (375)Time elapsed: 0.126 s
% 7.81/2.45 % (375)Instructions burned: 285 (million)
% 7.81/2.45 % (375)------------------------------
% 7.81/2.45 % (375)------------------------------
% 7.81/2.47 % (388)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_32551 for (2990ds/90Mi)
% 7.81/2.47 % (380)Instruction limit reached!
% 7.81/2.47 % (380)------------------------------
% 7.81/2.47 % (380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.47 % (380)Termination reason: Unknown
% 7.81/2.47 % (380)Termination phase: Saturation
% 7.81/2.47
% 7.81/2.47 % (380)Memory used [KB]: 7419
% 7.81/2.47 % (380)Time elapsed: 0.080 s
% 7.81/2.47 % (380)Instructions burned: 193 (million)
% 7.81/2.47 % (380)------------------------------
% 7.81/2.47 % (380)------------------------------
% 7.81/2.48 % (374)Instruction limit reached!
% 7.81/2.48 % (374)------------------------------
% 7.81/2.48 % (374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.48 % (374)Termination reason: Unknown
% 7.81/2.48 % (374)Termination phase: Saturation
% 7.81/2.48
% 7.81/2.48 % (374)Memory used [KB]: 6652
% 7.81/2.48 % (374)Time elapsed: 0.146 s
% 7.81/2.48 % (374)Instructions burned: 341 (million)
% 7.81/2.48 % (374)------------------------------
% 7.81/2.48 % (374)------------------------------
% 7.81/2.49 % (389)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_32551 for (2990ds/231Mi)
% 7.81/2.49 % (390)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_32551 for (2990ds/458Mi)
% 8.27/2.50 % (379)Instruction limit reached!
% 8.27/2.50 % (379)------------------------------
% 8.27/2.50 % (379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.50 % (379)Termination reason: Unknown
% 8.27/2.50 % (379)Termination phase: Saturation
% 8.27/2.50
% 8.27/2.50 % (379)Memory used [KB]: 7803
% 8.27/2.50 % (379)Time elapsed: 0.134 s
% 8.27/2.50 % (379)Instructions burned: 298 (million)
% 8.27/2.50 % (379)------------------------------
% 8.27/2.50 % (379)------------------------------
% 8.27/2.51 % (388)Instruction limit reached!
% 8.27/2.51 % (388)------------------------------
% 8.27/2.51 % (388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.51 % (388)Termination reason: Unknown
% 8.27/2.51 % (388)Termination phase: Saturation
% 8.27/2.51
% 8.27/2.51 % (388)Memory used [KB]: 6524
% 8.27/2.51 % (388)Time elapsed: 0.045 s
% 8.27/2.51 % (388)Instructions burned: 90 (million)
% 8.27/2.51 % (388)------------------------------
% 8.27/2.51 % (388)------------------------------
% 8.27/2.52 % (394)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_32551 for (2990ds/31Mi)
% 8.27/2.52 % (385)Instruction limit reached!
% 8.27/2.52 % (385)------------------------------
% 8.27/2.52 % (385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.52 % (385)Termination reason: Unknown
% 8.27/2.52 % (385)Termination phase: Saturation
% 8.27/2.52
% 8.27/2.52 % (385)Memory used [KB]: 6524
% 8.27/2.52 % (385)Time elapsed: 0.094 s
% 8.27/2.52 % (385)Instructions burned: 260 (million)
% 8.27/2.52 % (385)------------------------------
% 8.27/2.52 % (385)------------------------------
% 8.27/2.53 % (338)Instruction limit reached!
% 8.27/2.53 % (338)------------------------------
% 8.27/2.53 % (338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.53 % (338)Termination reason: Unknown
% 8.27/2.53 % (338)Termination phase: Saturation
% 8.27/2.53
% 8.27/2.53 % (338)Memory used [KB]: 7675
% 8.27/2.53 % (338)Time elapsed: 0.477 s
% 8.27/2.53 % (338)Instructions burned: 1088 (million)
% 8.27/2.53 % (338)------------------------------
% 8.27/2.53 % (338)------------------------------
% 8.27/2.53 % (395)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_32551 for (2990ds/297Mi)
% 8.27/2.53 % (394)Instruction limit reached!
% 8.27/2.53 % (394)------------------------------
% 8.27/2.53 % (394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.53 % (394)Termination reason: Unknown
% 8.27/2.53 % (394)Termination phase: Preprocessing 3
% 8.27/2.53
% 8.27/2.53 % (394)Memory used [KB]: 1663
% 8.27/2.53 % (394)Time elapsed: 0.017 s
% 8.27/2.53 % (394)Instructions burned: 31 (million)
% 8.27/2.53 % (394)------------------------------
% 8.27/2.53 % (394)------------------------------
% 8.27/2.54 % (396)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_32551 for (2990ds/987Mi)
% 8.27/2.54 % (397)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_32551 for (2989ds/182Mi)
% 8.27/2.55 % (398)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_32551 for (2989ds/182Mi)
% 8.27/2.56 % (390)First to succeed.
% 8.27/2.56 % (390)Refutation found. Thanks to Tanya!
% 8.27/2.56 % SZS status Theorem for DTF2THF_32551
% 8.27/2.56 % SZS output start Proof for DTF2THF_32551
% 8.27/2.56 thf(type_def_6, type, set: ($tType) > $tType).
% 8.27/2.56 thf(type_def_7, type, a: $tType).
% 8.27/2.56 thf(func_def_0, type, set: ($tType) > $tType).
% 8.27/2.56 thf(func_def_1, type, a: $tType).
% 8.27/2.56 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 8.27/2.56 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 8.27/2.56 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 8.27/2.56 thf(func_def_5, type, lattice: !>[X0: $tType]:($o)).
% 8.27/2.56 thf(func_def_6, type, linorder: !>[X0: $tType]:($o)).
% 8.27/2.56 thf(func_def_7, type, preorder: !>[X0: $tType]:($o)).
% 8.27/2.56 thf(func_def_8, type, semilattice_inf: !>[X0: $tType]:($o)).
% 8.27/2.56 thf(func_def_9, type, semilattice_sup: !>[X0: $tType]:($o)).
% 8.27/2.56 thf(func_def_10, type, condit2040224947_above: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 8.27/2.56 thf(func_def_11, type, condit1201339847_below: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 8.27/2.56 thf(func_def_12, type, finite_comp_fun_idem: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > $o)).
% 8.27/2.56 thf(func_def_13, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 8.27/2.56 thf(func_def_14, type, abel_semigroup: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 8.27/2.56 thf(func_def_15, type, semigroup: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 8.27/2.56 thf(func_def_16, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_17, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_18, type, semilattice: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 8.27/2.56 thf(func_def_19, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_20, type, lattic35693393ce_set: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 8.27/2.56 thf(func_def_21, type, modula105138637_a_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_22, type, modula477145868_b_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_23, type, modula849153099_c_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_24, type, modula1221160330_d_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_25, type, modula1593167561_e_aux: !>[X0: $tType]:((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_26, type, modula1937309406incomp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 8.27/2.56 thf(func_def_27, type, least: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 8.27/2.56 thf(func_def_28, type, max: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_29, type, min: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 8.27/2.56 thf(func_def_30, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 8.27/2.56 thf(func_def_31, type, greatest: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 8.27/2.56 thf(func_def_32, type, antimono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 8.27/2.56 thf(func_def_33, type, mono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 8.27/2.56 thf(func_def_34, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 8.27/2.56 thf(func_def_35, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 8.27/2.56 thf(func_def_36, type, a2: a).
% 8.27/2.56 thf(func_def_37, type, b: a).
% 8.27/2.56 thf(func_def_38, type, c: a).
% 8.27/2.56 thf(func_def_39, type, inf: a > a > a).
% 8.27/2.56 thf(func_def_40, type, less_eq: a > a > $o).
% 8.27/2.56 thf(func_def_41, type, sup: a > a > a).
% 8.27/2.56 thf(func_def_56, type, sK0: a).
% 8.27/2.56 thf(func_def_57, type, sK1: a).
% 8.27/2.56 thf(func_def_58, type, sK2: a).
% 8.27/2.56 thf(func_def_59, type, sK3: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 8.27/2.56 thf(func_def_60, type, sK4: (a > a > a) > a).
% 8.27/2.56 thf(func_def_61, type, sK5: (a > a > a) > a).
% 8.27/2.56 thf(func_def_62, type, sK6: (a > a > a) > a).
% 8.27/2.56 thf(func_def_63, type, sK7: (a > a > a) > a).
% 8.27/2.56 thf(func_def_64, type, sK8: (a > a > a) > a).
% 8.27/2.56 thf(func_def_65, type, sK9: (a > a > a) > a).
% 8.27/2.56 thf(func_def_66, type, sK10: (a > a > a) > a).
% 8.27/2.56 thf(func_def_67, type, sK11: a).
% 8.27/2.56 thf(func_def_68, type, sK12: a).
% 8.27/2.56 thf(func_def_69, type, sK13: a).
% 8.27/2.56 thf(func_def_70, type, sK14: (a > a > a) > a).
% 8.27/2.56 thf(func_def_71, type, sK15: (a > a > a) > a).
% 8.27/2.56 thf(func_def_72, type, sK16: (a > a > a) > a).
% 8.27/2.56 thf(func_def_73, type, sK17: (a > a > a) > a).
% 8.27/2.56 thf(func_def_74, type, sK18: (a > a > a) > a).
% 8.27/2.56 thf(func_def_75, type, sK19: (a > a > a) > a).
% 8.27/2.56 thf(func_def_76, type, sK20: (a > a > a) > a).
% 8.27/2.56 thf(func_def_78, type, ph22: !>[X0: $tType]:(X0)).
% 8.27/2.56 thf(f1040,plain,(
% 8.27/2.56 $false),
% 8.27/2.56 inference(subsumption_resolution,[status(thm)],[f1039,f1015])).
% 8.27/2.56 thf(f1015,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1014,f896])).
% 8.27/2.56 thf(f896,plain,(
% 8.27/2.56 ( ! [X0 : a,X1 : a] : (((inf @ X1 @ X0) = (inf @ X0 @ X1))) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f748])).
% 8.27/2.56 thf(f748,plain,(
% 8.27/2.56 ! [X0 : a,X1 : a] : ((inf @ X1 @ X0) = (inf @ X0 @ X1))),
% 8.27/2.56 inference(rectify,[status(thm)],[f15])).
% 8.27/2.56 thf(f15,axiom,(
% 8.27/2.56 ! [X5 : a,X4 : a] : ((inf @ X5 @ X4) = (inf @ X4 @ X5))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_14_local_Oinf_Ocommute)).
% 8.27/2.56 thf(f1014,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1013,f898])).
% 8.27/2.56 thf(f898,plain,(
% 8.27/2.56 ( ! [X0 : a,X1 : a] : (((sup @ X0 @ X1) = (sup @ X1 @ X0))) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f760])).
% 8.27/2.56 thf(f760,plain,(
% 8.27/2.56 ! [X0 : a,X1 : a] : ((sup @ X0 @ X1) = (sup @ X1 @ X0))),
% 8.27/2.56 inference(rectify,[status(thm)],[f21])).
% 8.27/2.56 thf(f21,axiom,(
% 8.27/2.56 ! [X5 : a,X4 : a] : ((sup @ X5 @ X4) = (sup @ X4 @ X5))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_20_local_Osup_Ocommute)).
% 8.27/2.56 thf(f1013,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1012,f896])).
% 8.27/2.56 thf(f1012,plain,(
% 8.27/2.56 ($true = (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ c @ a2) @ (sup @ b @ c)))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1011,f957])).
% 8.27/2.56 thf(f957,plain,(
% 8.27/2.56 ( ! [X2 : a,X0 : a,X1 : a] : (((inf @ X1 @ (inf @ X0 @ X2)) = (inf @ X0 @ (inf @ X1 @ X2)))) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f756])).
% 8.27/2.56 thf(f756,plain,(
% 8.27/2.56 ! [X0 : a,X1 : a,X2 : a] : ((inf @ X1 @ (inf @ X0 @ X2)) = (inf @ X0 @ (inf @ X1 @ X2)))),
% 8.27/2.56 inference(rectify,[status(thm)],[f19])).
% 8.27/2.56 thf(f19,axiom,(
% 8.27/2.56 ! [X2 : a,X3 : a,X13 : a] : ((inf @ X2 @ (inf @ X3 @ X13)) = (inf @ X3 @ (inf @ X2 @ X13)))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_18_local_Oinf__left__commute)).
% 8.27/2.56 thf(f1011,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ c @ a2) @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)))) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1010,f896])).
% 8.27/2.56 thf(f1010,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2))) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1009,f934])).
% 8.27/2.56 thf(f934,plain,(
% 8.27/2.56 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (inf @ (inf @ (sup @ X0 @ X1) @ (sup @ X1 @ X2)) @ (sup @ X2 @ X0)))) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f738])).
% 8.27/2.56 thf(f738,plain,(
% 8.27/2.56 ! [X0 : a,X1 : a,X2 : a] : ((modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (inf @ (inf @ (sup @ X0 @ X1) @ (sup @ X1 @ X2)) @ (sup @ X2 @ X0)))),
% 8.27/2.56 inference(rectify,[status(thm)],[f94])).
% 8.27/2.56 thf(f94,axiom,(
% 8.27/2.56 ! [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)))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_93_local_Oe__aux__def)).
% 8.27/2.56 thf(f1009,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1008,f898])).
% 8.27/2.56 thf(f1008,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1007,f896])).
% 8.27/2.56 thf(f1007,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1006,f898])).
% 8.27/2.56 thf(f1006,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ c @ a2) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1005,f862])).
% 8.27/2.56 thf(f862,plain,(
% 8.27/2.56 ( ! [X2 : a,X0 : a,X1 : a] : (((sup @ X1 @ (sup @ X0 @ X2)) = (sup @ X0 @ (sup @ X1 @ X2)))) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f764])).
% 8.27/2.56 thf(f764,plain,(
% 8.27/2.56 ! [X0 : a,X1 : a,X2 : a] : ((sup @ X1 @ (sup @ X0 @ X2)) = (sup @ X0 @ (sup @ X1 @ X2)))),
% 8.27/2.56 inference(rectify,[status(thm)],[f22])).
% 8.27/2.56 thf(f22,axiom,(
% 8.27/2.56 ! [X4 : a,X5 : a,X10 : a] : ((sup @ X5 @ (sup @ X4 @ X10)) = (sup @ X4 @ (sup @ X5 @ X10)))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_21_local_Osup_Oleft__commute)).
% 8.27/2.56 thf(f1005,plain,(
% 8.27/2.56 ($true = (less_eq @ (sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1004,f898])).
% 8.27/2.56 thf(f1004,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f864,f869])).
% 8.27/2.56 thf(f869,plain,(
% 8.27/2.56 ( ! [X2 : a,X0 : a,X1 : a] : (((sup @ (sup @ (inf @ X0 @ X1) @ (inf @ X1 @ X2)) @ (inf @ X2 @ X0)) = (modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2))) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f730])).
% 8.27/2.56 thf(f730,plain,(
% 8.27/2.56 ! [X0 : a,X1 : a,X2 : a] : ((sup @ (sup @ (inf @ X0 @ X1) @ (inf @ X1 @ X2)) @ (inf @ X2 @ X0)) = (modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2))),
% 8.27/2.56 inference(rectify,[status(thm)],[f88])).
% 8.27/2.56 thf(f88,axiom,(
% 8.27/2.56 ! [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)))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_87_local_Od__aux__def)).
% 8.27/2.56 thf(f864,plain,(
% 8.27/2.56 ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f322])).
% 8.27/2.56 thf(f322,plain,(
% 8.27/2.56 ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) = $true)),
% 8.27/2.56 inference(fool_elimination,[status(thm)],[f321])).
% 8.27/2.56 thf(f321,plain,(
% 8.27/2.56 (less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c))),
% 8.27/2.56 inference(rectify,[status(thm)],[f279])).
% 8.27/2.56 thf(f279,axiom,(
% 8.27/2.56 (less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) @ (modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',conj_0)).
% 8.27/2.56 thf(f1039,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) != $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1038,f896])).
% 8.27/2.56 thf(f1038,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))) != $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1037,f898])).
% 8.27/2.56 thf(f1037,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))) != $true)),
% 8.27/2.56 inference(trivial_inequality_removal,[status(thm)],[f1036])).
% 8.27/2.56 thf(f1036,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))) != $true) | ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1035,f898])).
% 8.27/2.56 thf(f1035,plain,(
% 8.27/2.56 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))) | ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))) != $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1034,f896])).
% 8.27/2.56 thf(f1034,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (inf @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)) @ (sup @ a2 @ b))) != $true) | ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1033,f934])).
% 8.27/2.56 thf(f1033,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true) | ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1032,f896])).
% 8.27/2.56 thf(f1032,plain,(
% 8.27/2.56 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))) | ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1031,f898])).
% 8.27/2.56 thf(f1031,plain,(
% 8.27/2.56 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ c @ a2) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))) | ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1030,f862])).
% 8.27/2.56 thf(f1030,plain,(
% 8.27/2.56 ((sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))) | ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1029,f898])).
% 8.27/2.56 thf(f1029,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true) | ((sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1028,f896])).
% 8.27/2.56 thf(f1028,plain,(
% 8.27/2.56 ($true != (less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ c @ a2))) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2))) | ((sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1027,f898])).
% 8.27/2.56 thf(f1027,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ c @ a2) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true) | ((sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1026,f862])).
% 8.27/2.56 thf(f1026,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true) | ((sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1025,f898])).
% 8.27/2.56 thf(f1025,plain,(
% 8.27/2.56 ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true) | ((sup @ (inf @ c @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1024,f898])).
% 8.27/2.56 thf(f1024,plain,(
% 8.27/2.56 ((sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))) | ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1023,f869])).
% 8.27/2.56 thf(f1023,plain,(
% 8.27/2.56 ((modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))) | ((less_eq @ (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true)),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1022,f869])).
% 8.27/2.56 thf(f1022,plain,(
% 8.27/2.56 ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true) | ((modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1021,f966])).
% 8.27/2.56 thf(f966,plain,(
% 8.27/2.56 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (modula1221160330_d_aux @ a @ inf @ sup @ X1 @ X2 @ X0))) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f723])).
% 8.27/2.56 thf(f723,plain,(
% 8.27/2.56 ! [X0 : a,X1 : a,X2 : a] : ((modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (modula1221160330_d_aux @ a @ inf @ sup @ X1 @ X2 @ X0))),
% 8.27/2.56 inference(rectify,[status(thm)],[f90])).
% 8.27/2.56 thf(f90,axiom,(
% 8.27/2.56 ! [X10 : a,X5 : a,X4 : a] : ((modula1221160330_d_aux @ a @ inf @ sup @ X5 @ X4 @ X10) = (modula1221160330_d_aux @ a @ inf @ sup @ X10 @ X5 @ X4))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_89_local_Od__c__a__b)).
% 8.27/2.56 thf(f1021,plain,(
% 8.27/2.56 ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true) | ((modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f1020,f966])).
% 8.27/2.56 thf(f1020,plain,(
% 8.27/2.56 ((modula1221160330_d_aux @ a @ inf @ sup @ b @ c @ a2) != (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))) | ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != $true)),
% 8.27/2.56 inference(superposition,[status(thm)],[f993,f1016])).
% 8.27/2.56 thf(f1016,plain,(
% 8.27/2.56 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (inf @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula105138637_a_aux @ a @ inf @ sup @ X1 @ X2 @ X0))) | ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) != $true)) )),
% 8.27/2.56 inference(superposition,[status(thm)],[f968,f886])).
% 8.27/2.56 thf(f886,plain,(
% 8.27/2.56 ( ! [X2 : a,X0 : a,X1 : a] : (((modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (modula105138637_a_aux @ a @ inf @ sup @ X1 @ X2 @ X0))) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f771])).
% 8.27/2.56 thf(f771,plain,(
% 8.27/2.56 ! [X0 : a,X1 : a,X2 : a] : ((modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (modula105138637_a_aux @ a @ inf @ sup @ X1 @ X2 @ X0))),
% 8.27/2.56 inference(rectify,[status(thm)],[f127])).
% 8.27/2.56 thf(f127,axiom,(
% 8.27/2.56 ! [X5 : a,X4 : a,X10 : a] : ((modula477145868_b_aux @ a @ inf @ sup @ X5 @ X4 @ X10) = (modula105138637_a_aux @ a @ inf @ sup @ X4 @ X10 @ X5))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_126_local_Ob__a)).
% 8.27/2.56 thf(f968,plain,(
% 8.27/2.56 ( ! [X2 : a,X0 : a,X1 : a] : (((modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (inf @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2))) | ((less_eq @ (modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) != $true)) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f812])).
% 8.27/2.56 thf(f812,plain,(
% 8.27/2.56 ! [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)) != $true) | ((modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (inf @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2))))),
% 8.27/2.56 inference(ennf_transformation,[status(thm)],[f680])).
% 8.27/2.56 thf(f680,plain,(
% 8.27/2.56 ! [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)) = $true) => ((modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (inf @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2))))),
% 8.27/2.56 inference(fool_elimination,[status(thm)],[f679])).
% 8.27/2.56 thf(f679,plain,(
% 8.27/2.56 ! [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)) => ((modula1221160330_d_aux @ a @ inf @ sup @ X0 @ X1 @ X2) = (inf @ (modula105138637_a_aux @ a @ inf @ sup @ X0 @ X1 @ X2) @ (modula477145868_b_aux @ a @ inf @ sup @ X0 @ X1 @ X2))))),
% 8.27/2.56 inference(rectify,[status(thm)],[f133])).
% 8.27/2.56 thf(f133,axiom,(
% 8.27/2.56 ! [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)) => ((modula1221160330_d_aux @ a @ inf @ sup @ X5 @ X4 @ X10) = (inf @ (modula105138637_a_aux @ a @ inf @ sup @ X5 @ X4 @ X10) @ (modula477145868_b_aux @ a @ inf @ sup @ X5 @ X4 @ X10))))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_132_a__meet__b__eq__d)).
% 8.27/2.56 thf(f993,plain,(
% 8.27/2.56 ((sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))) != (inf @ (modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b)))),
% 8.27/2.56 inference(backward_demodulation,[status(thm)],[f983,f862])).
% 8.27/2.56 thf(f983,plain,(
% 8.27/2.56 ((sup @ (inf @ a2 @ c) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))) != (inf @ (modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b)))),
% 8.27/2.56 inference(backward_demodulation,[status(thm)],[f982,f898])).
% 8.27/2.56 thf(f982,plain,(
% 8.27/2.56 ((inf @ (modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b)) != (sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ a2 @ c)))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f981,f896])).
% 8.27/2.56 thf(f981,plain,(
% 8.27/2.56 ((sup @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c)) @ (inf @ c @ a2)) != (inf @ (modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b)))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f980,f869])).
% 8.27/2.56 thf(f980,plain,(
% 8.27/2.56 ((modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) != (inf @ (modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula105138637_a_aux @ a @ inf @ sup @ c @ a2 @ b)))),
% 8.27/2.56 inference(forward_demodulation,[status(thm)],[f863,f890])).
% 8.27/2.56 thf(f890,plain,(
% 8.27/2.56 ( ! [X2 : a,X0 : a,X1 : a] : (((modula105138637_a_aux @ a @ inf @ sup @ X2 @ X0 @ X1) = (modula849153099_c_aux @ a @ inf @ sup @ X0 @ X1 @ X2))) )),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f772])).
% 8.27/2.56 thf(f772,plain,(
% 8.27/2.56 ! [X0 : a,X1 : a,X2 : a] : ((modula105138637_a_aux @ a @ inf @ sup @ X2 @ X0 @ X1) = (modula849153099_c_aux @ a @ inf @ sup @ X0 @ X1 @ X2))),
% 8.27/2.56 inference(rectify,[status(thm)],[f114])).
% 8.27/2.56 thf(f114,axiom,(
% 8.27/2.56 ! [X5 : a,X4 : a,X10 : a] : ((modula849153099_c_aux @ a @ inf @ sup @ X5 @ X4 @ X10) = (modula105138637_a_aux @ a @ inf @ sup @ X10 @ X5 @ X4))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',fact_113_local_Oc__a)).
% 8.27/2.56 thf(f863,plain,(
% 8.27/2.56 ((modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) != (inf @ (modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula849153099_c_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.27/2.56 inference(cnf_transformation,[status(thm)],[f721])).
% 8.27/2.56 thf(f721,plain,(
% 8.27/2.56 ((modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) != (inf @ (modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula849153099_c_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.27/2.56 inference(flattening,[status(thm)],[f281])).
% 8.27/2.56 thf(f281,negated_conjecture,(
% 8.27/2.56 ~((modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) = (inf @ (modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula849153099_c_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.27/2.56 inference(negated_conjecture,[status(cth)],[f280])).
% 8.27/2.56 thf(f280,conjecture,(
% 8.27/2.56 ((modula1221160330_d_aux @ a @ inf @ sup @ a2 @ b @ c) = (inf @ (modula105138637_a_aux @ a @ inf @ sup @ b @ c @ a2) @ (modula849153099_c_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 8.27/2.56 file('/export/starexec/sandbox2/tmp/tmp.Ng7iUKOhs2/DTF2THF_32551.p',conj_1)).
% 8.27/2.56 % SZS output end Proof for DTF2THF_32551
% 8.27/2.56 % (390)------------------------------
% 8.27/2.56 % (390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.56 % (390)Termination reason: Refutation
% 8.27/2.56
% 8.27/2.56 % (390)Memory used [KB]: 6524
% 8.27/2.56 % (390)Time elapsed: 0.091 s
% 8.27/2.56 % (390)Instructions burned: 132 (million)
% 8.27/2.56 % (390)------------------------------
% 8.27/2.56 % (390)------------------------------
% 8.27/2.56 % (32725)Success in time 1.054 s
%------------------------------------------------------------------------------