%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP079^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.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 08:55:22 AM UTC 2026
% Result : Theorem 15.92s 3.51s
% Output : Refutation 15.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP079^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:25:42 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : ITP079^2 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.46 % Domain : Interactive Theorem Proving
% 0.19/0.46 % Problem : Sledgehammer Irreducible problem prob_209__6623758_1
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Des21]
% 0.19/0.46 % Names : Irreducible/prob_209__6623758_1 [Des21]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.19/0.46 % Syntax : Number of formulae : 337 ( 49 unt; 48 typ; 0 def)
% 0.19/0.46 % Number of atoms : 1027 ( 179 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.19/0.46 % Number of connectives : 3347 ( 79 ~; 21 |; 72 &;2652 @)
% 0.19/0.46 % ( 0 <=>; 523 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 28 ( 8 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 185 ( 185 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 50 ( 47 usr; 4 con; 0-6 aty)
% 0.19/0.46 % Number of variables : 1105 ( 68 ^; 974 !; 10 ?;1105 :)
% 0.19/0.46 % ( 53 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.46 % SPC : TH1_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:21:39.550
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % Could-be-implicit typings (3)
% 0.19/0.46 thf(ty_t_List_Olist,type,
% 0.19/0.46 list: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Set_Oset,type,
% 0.19/0.46 set: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_tf_val,type,
% 0.19/0.46 val: $tType ).
% 0.19/0.46
% 0.19/0.46 % Explicit typings (45)
% 0.19/0.46 thf(sy_cl_HOL_Otype,type,
% 0.19/0.46 type:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Obot,type,
% 0.19/0.46 bot:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.19/0.46 ord:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.46 order:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.19/0.46 group_add:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Ono__bot,type,
% 0.19/0.46 no_bot:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Ono__top,type,
% 0.19/0.46 no_top:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.19/0.46 linorder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.19/0.46 preorder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Owellorder,type,
% 0.19/0.46 wellorder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Complete__Lattices_OSup,type,
% 0.19/0.46 complete_Sup:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Odense__order,type,
% 0.19/0.46 dense_order:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.19/0.46 boolean_algebra:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.19/0.46 semilattice_sup:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.19/0.46 dense_linorder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.19/0.46 ordered_ab_group_add:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 0.19/0.46 comple187826305attice:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.19/0.46 condit1037483654norder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.19/0.46 uminus_uminus:
% 0.19/0.46 !>[A: $tType] : ( A > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_If,type,
% 0.19/0.46 if:
% 0.19/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.19/0.46 sup_sup:
% 0.19/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist_Orec__list,type,
% 0.19/0.46 rec_list:
% 0.19/0.46 !>[C: $tType,A: $tType] : ( C > ( A > ( list @ A ) > C > C ) > ( list @ A ) > C ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Misc_Oswap__args2,type,
% 0.19/0.46 swap_args2:
% 0.19/0.46 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C > A ) > C > B > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.19/0.46 ord_less:
% 0.19/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.19/0.46 ord_less_eq:
% 0.19/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.19/0.46 order_Greatest:
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oorder__class_Oantimono,type,
% 0.19/0.46 order_antimono:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oorder__class_Ostrict__mono,type,
% 0.19/0.46 order_strict_mono:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN,type,
% 0.19/0.46 refine111645177_ALIGN:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP,type,
% 0.19/0.46 refine574149253T_SIMP:
% 0.19/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Refine__Misc_Ocont,type,
% 0.19/0.46 refine_cont:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Refine__Misc_Ogalois__connection,type,
% 0.19/0.46 refine1150083786ection:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( B > A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Refine__Misc_Oinf__distrib,type,
% 0.19/0.46 refine_inf_distrib:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Refine__Misc_Ostrict,type,
% 0.19/0.46 refine_strict:
% 0.19/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc,type,
% 0.19/0.46 refine551993528up_loc:
% 0.19/0.46 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OCollect,type,
% 0.19/0.46 collect:
% 0.19/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set__Interval_Oord__class_OatLeast,type,
% 0.19/0.46 set_ord_atLeast:
% 0.19/0.46 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost,type,
% 0.19/0.46 set_or331188842AtMost:
% 0.19/0.46 !>[A: $tType] : ( A > A > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set__Interval_Oord__class_OatMost,type,
% 0.19/0.46 set_ord_atMost:
% 0.19/0.46 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThan,type,
% 0.19/0.46 set_ord_greaterThan:
% 0.19/0.46 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan,type,
% 0.19/0.46 set_or578182835ssThan:
% 0.19/0.46 !>[A: $tType] : ( A > A > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set__Interval_Oord__class_OlessThan,type,
% 0.19/0.46 set_ord_lessThan:
% 0.19/0.46 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member,type,
% 0.19/0.46 member:
% 0.19/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_P,type,
% 0.19/0.46 p: set @ val ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_scc,type,
% 0.19/0.46 scc: set @ val ).
% 0.19/0.46
% 0.19/0.46 % Relevant facts (255)
% 0.19/0.46 thf(fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062,axiom,
% 0.19/0.46 ! [X: val] :
% 0.19/0.46 ( ( member @ val @ X @ scc )
% 0.19/0.46 => ( member @ val @ X @ p ) ) ).
% 0.19/0.46
% 0.19/0.46 % \<open>\<And>x. x \<in> scc \<Longrightarrow> x \<in> P\<close>
% 0.19/0.46 thf(fact_1_subsetI,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.19/0.46 ( ! [X2: A] :
% 0.19/0.46 ( ( member @ A @ X2 @ A2 )
% 0.19/0.46 => ( member @ A @ X2 @ B2 ) )
% 0.19/0.46 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % subsetI
% 0.19/0.46 thf(fact_2_subset__antisym,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.19/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.19/0.46 => ( A2 = B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subset_antisym
% 0.19/0.46 thf(fact_3_order__mono__setup_Orefl,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( preorder @ A )
% 0.19/0.46 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % order_mono_setup.refl
% 0.19/0.46 thf(fact_4_relprop__triggers_I6_J,axiom,
% 0.19/0.46 ! [I: $tType,R: set @ I,R2: set @ I] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ I ) @ R @ R2 )
% 0.19/0.46 => ( ord_less_eq @ ( set @ I ) @ R @ R2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % relprop_triggers(6)
% 0.19/0.46 thf(fact_5_in__mono,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,X3: A] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.19/0.46 => ( ( member @ A @ X3 @ A2 )
% 0.19/0.46 => ( member @ A @ X3 @ B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_mono
% 0.19/0.46 thf(fact_6_subsetD,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,C2: A] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.19/0.46 => ( ( member @ A @ C2 @ A2 )
% 0.19/0.46 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subsetD
% 0.19/0.46 thf(fact_7_equalityE,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.19/0.46 ( ( A2 = B2 )
% 0.19/0.46 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.19/0.46 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % equalityE
% 0.19/0.46 thf(fact_8_subset__eq,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.46 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.19/0.46 ! [X4: A] :
% 0.19/0.46 ( ( member @ A @ X4 @ A3 )
% 0.19/0.46 => ( member @ A @ X4 @ B3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subset_eq
% 0.19/0.46 thf(fact_9_equalityD1,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.19/0.46 ( ( A2 = B2 )
% 0.19/0.46 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % equalityD1
% 0.19/0.46 thf(fact_10_equalityD2,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.19/0.46 ( ( A2 = B2 )
% 0.19/0.46 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % equalityD2
% 0.19/0.46 thf(fact_11_subset__iff,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.46 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.19/0.46 ! [T: A] :
% 0.19/0.46 ( ( member @ A @ T @ A3 )
% 0.19/0.46 => ( member @ A @ T @ B3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subset_iff
% 0.19/0.46 thf(fact_12_subset__refl,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.19/0.46
% 0.19/0.46 % subset_refl
% 0.19/0.46 thf(fact_13_order__mono__setup_Omono__let,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType] :
% 0.19/0.46 ( ( preorder @ A )
% 0.19/0.46 => ! [F: B > A,F2: B > A,X3: B] :
% 0.19/0.46 ( ! [X2: B] : ( ord_less_eq @ A @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.19/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F2 @ X3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % order_mono_setup.mono_let
% 0.19/0.46 thf(fact_14_order__mono__setup_Omono__if,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( preorder @ A )
% 0.19/0.46 => ! [T2: A,T3: A,E: A,E2: A,B4: $o] :
% 0.19/0.46 ( ( ord_less_eq @ A @ T2 @ T3 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ E @ E2 )
% 0.19/0.46 => ( ord_less_eq @ A @ ( if @ A @ B4 @ T2 @ E ) @ ( if @ A @ B4 @ T3 @ E2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % order_mono_setup.mono_if
% 0.19/0.46 thf(fact_15_Collect__mono__iff,axiom,
% 0.19/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.19/0.46 = ( ! [X4: A] :
% 0.19/0.46 ( ( P @ X4 )
% 0.19/0.46 => ( Q @ X4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mono_iff
% 0.19/0.46 thf(fact_16_set__eq__subset,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ^ [Y: set @ A,Z: set @ A] : ( Y = Z ) )
% 0.19/0.46 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.19/0.46 & ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % set_eq_subset
% 0.19/0.46 thf(fact_17_subset__trans,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.19/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.19/0.46 => ( ord_less_eq @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subset_trans
% 0.19/0.46 thf(fact_18_Collect__mono,axiom,
% 0.19/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.46 ( ! [X2: A] :
% 0.19/0.46 ( ( P @ X2 )
% 0.19/0.46 => ( Q @ X2 ) )
% 0.19/0.46 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mono
% 0.19/0.46 thf(fact_19_subset__Collect__conv,axiom,
% 0.19/0.46 ! [A: $tType,S: set @ A,P: A > $o] :
% 0.19/0.46 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 0.19/0.46 = ( ! [X4: A] :
% 0.19/0.46 ( ( member @ A @ X4 @ S )
% 0.19/0.46 => ( P @ X4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subset_Collect_conv
% 0.19/0.46 thf(fact_20_dual__order_Oantisym,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [B4: A,A4: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.46 => ( A4 = B4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % dual_order.antisym
% 0.19/0.46 thf(fact_21_dual__order_Oeq__iff,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.19/0.46 = ( ^ [A5: A,B5: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.19/0.46 & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % dual_order.eq_iff
% 0.19/0.46 thf(fact_22_transfer_Otransfer__Let,axiom,
% 0.19/0.46 ! [C: $tType,A: $tType,B: $tType] :
% 0.19/0.46 ( ( comple187826305attice @ A )
% 0.19/0.46 => ! [Alpha: C > A,F: B > C,F3: B > A,X3: B] :
% 0.19/0.46 ( ! [X2: B] : ( ord_less_eq @ A @ ( Alpha @ ( F @ X2 ) ) @ ( F3 @ X2 ) )
% 0.19/0.46 => ( ord_less_eq @ A @ ( Alpha @ ( F @ X3 ) ) @ ( F3 @ X3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transfer.transfer_Let
% 0.19/0.46 thf(fact_23_dual__order_Otrans,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [B4: A,A4: A,C2: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.19/0.46 => ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % dual_order.trans
% 0.19/0.46 thf(fact_24_linorder__wlog,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( linorder @ A )
% 0.19/0.46 => ! [P: A > A > $o,A4: A,B4: A] :
% 0.19/0.46 ( ! [A6: A,B6: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.19/0.46 => ( P @ A6 @ B6 ) )
% 0.19/0.46 => ( ! [A6: A,B6: A] :
% 0.19/0.46 ( ( P @ B6 @ A6 )
% 0.19/0.46 => ( P @ A6 @ B6 ) )
% 0.19/0.46 => ( P @ A4 @ B4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % linorder_wlog
% 0.19/0.46 thf(fact_25_transfer_Otransfer__if,axiom,
% 0.19/0.46 ! [C: $tType,A: $tType] :
% 0.19/0.46 ( ( comple187826305attice @ A )
% 0.19/0.46 => ! [B4: $o,Alpha: C > A,S1: C,S12: A,S2: C,S22: A] :
% 0.19/0.46 ( ( B4
% 0.19/0.46 => ( ord_less_eq @ A @ ( Alpha @ S1 ) @ S12 ) )
% 0.19/0.46 => ( ( ~ B4
% 0.19/0.46 => ( ord_less_eq @ A @ ( Alpha @ S2 ) @ S22 ) )
% 0.19/0.46 => ( ord_less_eq @ A @ ( Alpha @ ( if @ C @ B4 @ S1 @ S2 ) ) @ ( if @ A @ B4 @ S12 @ S22 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transfer.transfer_if
% 0.19/0.46 thf(fact_26_dual__order_Orefl,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 0.19/0.46
% 0.19/0.46 % dual_order.refl
% 0.19/0.46 thf(fact_27_order__trans,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( preorder @ A )
% 0.19/0.46 => ! [X3: A,Y2: A,Z2: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.19/0.46 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % order_trans
% 0.19/0.46 thf(fact_28_order__class_Oorder_Oantisym,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [A4: A,B4: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.19/0.46 => ( A4 = B4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % order_class.order.antisym
% 0.19/0.46 thf(fact_29_ord__le__eq__trans,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ord @ A )
% 0.19/0.46 => ! [A4: A,B4: A,C2: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.46 => ( ( B4 = C2 )
% 0.19/0.46 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord_le_eq_trans
% 0.19/0.46 thf(fact_30_le__funD,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( ord @ B )
% 0.19/0.46 => ! [F: A > B,G: A > B,X3: A] :
% 0.19/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.19/0.46 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_funD
% 0.19/0.46 thf(fact_31_le__funE,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( ord @ B )
% 0.19/0.46 => ! [F: A > B,G: A > B,X3: A] :
% 0.19/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.19/0.46 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_funE
% 0.19/0.46 thf(fact_32_le__funI,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( ord @ B )
% 0.19/0.46 => ! [F: A > B,G: A > B] :
% 0.19/0.46 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.19/0.46 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_funI
% 0.19/0.46 thf(fact_33_le__fun__def,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( ord @ B )
% 0.19/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.19/0.46 = ( ^ [F4: A > B,G2: A > B] :
% 0.19/0.46 ! [X4: A] : ( ord_less_eq @ B @ ( F4 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_fun_def
% 0.19/0.46 thf(fact_34_order__subst1,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType] :
% 0.19/0.46 ( ( ( order @ B )
% 0.19/0.46 & ( order @ A ) )
% 0.19/0.46 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A4 @ ( F @ B4 ) )
% 0.19/0.46 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.19/0.46 => ( ! [X2: B,Y3: B] :
% 0.19/0.46 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.19/0.46 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.19/0.46 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % order_subst1
% 0.19/0.46 thf(fact_35_order__subst2,axiom,
% 0.19/0.46 ! [A: $tType,C: $tType] :
% 0.19/0.46 ( ( ( order @ C )
% 0.19/0.46 & ( order @ A ) )
% 0.19/0.46 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.46 => ( ( ord_less_eq @ C @ ( F @ B4 ) @ C2 )
% 0.19/0.46 => ( ! [X2: A,Y3: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.19/0.46 => ( ord_less_eq @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.19/0.46 => ( ord_less_eq @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % order_subst2
% 0.19/0.46 thf(fact_36_ord__eq__le__eq__trans,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ord @ A )
% 0.19/0.46 => ! [A4: A,B4: A,C2: A,D: A] :
% 0.19/0.46 ( ( A4 = B4 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.19/0.46 => ( ( C2 = D )
% 0.19/0.46 => ( ord_less_eq @ A @ A4 @ D ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord_eq_le_eq_trans
% 0.19/0.46 thf(fact_37_ord__eq__le__subst,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType] :
% 0.19/0.46 ( ( ( ord @ B )
% 0.19/0.46 & ( ord @ A ) )
% 0.19/0.46 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.19/0.46 ( ( A4
% 0.19/0.46 = ( F @ B4 ) )
% 0.19/0.46 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.19/0.46 => ( ! [X2: B,Y3: B] :
% 0.19/0.46 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.19/0.46 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.19/0.46 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord_eq_le_subst
% 0.19/0.46 thf(fact_38_ord__le__eq__subst,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType] :
% 0.19/0.46 ( ( ( ord @ B )
% 0.19/0.46 & ( ord @ A ) )
% 0.19/0.46 => ! [A4: A,B4: A,F: A > B,C2: B] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.46 => ( ( ( F @ B4 )
% 0.19/0.46 = C2 )
% 0.19/0.46 => ( ! [X2: A,Y3: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.19/0.46 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.19/0.46 => ( ord_less_eq @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord_le_eq_subst
% 0.19/0.46 thf(fact_39_eq__iff,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.19/0.46 = ( ^ [X4: A,Y4: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.19/0.46 & ( ord_less_eq @ A @ Y4 @ X4 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_iff
% 0.19/0.46 thf(fact_40_antisym,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [X3: A,Y2: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.19/0.46 => ( X3 = Y2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % antisym
% 0.19/0.46 thf(fact_41_linear,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( linorder @ A )
% 0.19/0.46 => ! [X3: A,Y2: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.46 | ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % linear
% 0.19/0.46 thf(fact_42_eq__refl,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( preorder @ A )
% 0.19/0.46 => ! [X3: A,Y2: A] :
% 0.19/0.46 ( ( X3 = Y2 )
% 0.19/0.46 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_refl
% 0.19/0.46 thf(fact_43_le__cases,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( linorder @ A )
% 0.19/0.46 => ! [X3: A,Y2: A] :
% 0.19/0.46 ( ~ ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.46 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_cases
% 0.19/0.46 thf(fact_44_order_Otrans,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [A4: A,B4: A,C2: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.19/0.46 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % order.trans
% 0.19/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: $tType,A4: A,P: A > $o] :
% 0.19/0.46 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.19/0.46 = ( P @ A4 ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A: $tType,A2: set @ A] :
% 0.19/0.46 ( ( collect @ A
% 0.19/0.46 @ ^ [X4: A] : ( member @ A @ X4 @ A2 ) )
% 0.19/0.46 = A2 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_47_Collect__cong,axiom,
% 0.19/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.46 ( ! [X2: A] :
% 0.19/0.46 ( ( P @ X2 )
% 0.19/0.46 = ( Q @ X2 ) )
% 0.19/0.46 => ( ( collect @ A @ P )
% 0.19/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_cong
% 0.19/0.46 thf(fact_48_ext,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.19/0.46 ( ! [X2: A] :
% 0.19/0.46 ( ( F @ X2 )
% 0.19/0.46 = ( G @ X2 ) )
% 0.19/0.46 => ( F = G ) ) ).
% 0.19/0.46
% 0.19/0.46 % ext
% 0.19/0.46 thf(fact_49_le__cases3,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( linorder @ A )
% 0.19/0.46 => ! [X3: A,Y2: A,Z2: A] :
% 0.19/0.46 ( ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.46 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 0.19/0.46 => ( ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.19/0.46 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.19/0.46 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.19/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 0.19/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 0.19/0.46 => ~ ( ord_less_eq @ A @ Y2 @ X3 ) )
% 0.19/0.46 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.19/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.19/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.19/0.46 => ~ ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_cases3
% 0.19/0.46 thf(fact_50_antisym__conv,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [Y2: A,X3: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.46 = ( X3 = Y2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % antisym_conv
% 0.19/0.46 thf(fact_51_order__class_Oorder_Oeq__iff,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.19/0.46 = ( ^ [A5: A,B5: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.19/0.46 & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % order_class.order.eq_iff
% 0.19/0.46 thf(fact_52_ord__eq__le__trans,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ord @ A )
% 0.19/0.46 => ! [A4: A,B4: A,C2: A] :
% 0.19/0.46 ( ( A4 = B4 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.19/0.46 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord_eq_le_trans
% 0.19/0.46 thf(fact_53_GreatestI2__order,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [P: A > $o,X3: A,Q: A > $o] :
% 0.19/0.46 ( ( P @ X3 )
% 0.19/0.46 => ( ! [Y3: A] :
% 0.19/0.46 ( ( P @ Y3 )
% 0.19/0.46 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.19/0.46 => ( ! [X2: A] :
% 0.19/0.46 ( ( P @ X2 )
% 0.19/0.46 => ( ! [Y5: A] :
% 0.19/0.46 ( ( P @ Y5 )
% 0.19/0.46 => ( ord_less_eq @ A @ Y5 @ X2 ) )
% 0.19/0.46 => ( Q @ X2 ) ) )
% 0.19/0.46 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % GreatestI2_order
% 0.19/0.46 thf(fact_54_Greatest__equality,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [P: A > $o,X3: A] :
% 0.19/0.46 ( ( P @ X3 )
% 0.19/0.46 => ( ! [Y3: A] :
% 0.19/0.46 ( ( P @ Y3 )
% 0.19/0.46 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.19/0.47 => ( ( order_Greatest @ A @ P )
% 0.19/0.47 = X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Greatest_equality
% 0.19/0.47 thf(fact_55_Refine__Misc_Oif__mono,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [B4: $o,M1: A,M12: A,M2: A,M22: A] :
% 0.19/0.47 ( ( B4
% 0.19/0.47 => ( ord_less_eq @ A @ M1 @ M12 ) )
% 0.19/0.47 => ( ( ~ B4
% 0.19/0.47 => ( ord_less_eq @ A @ M2 @ M22 ) )
% 0.19/0.47 => ( ord_less_eq @ A @ ( if @ A @ B4 @ M1 @ M2 ) @ ( if @ A @ B4 @ M12 @ M22 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Refine_Misc.if_mono
% 0.19/0.47 thf(fact_56_lhs__step__If,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [B4: $o,T2: A,M: A,E: A] :
% 0.19/0.47 ( ( B4
% 0.19/0.47 => ( ord_less_eq @ A @ T2 @ M ) )
% 0.19/0.47 => ( ( ~ B4
% 0.19/0.47 => ( ord_less_eq @ A @ E @ M ) )
% 0.19/0.47 => ( ord_less_eq @ A @ ( if @ A @ B4 @ T2 @ E ) @ M ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % lhs_step_If
% 0.19/0.47 thf(fact_57_verit__la__disequality,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [A4: A,B4: A] :
% 0.19/0.47 ( ( A4 = B4 )
% 0.19/0.47 | ~ ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.47 | ~ ( ord_less_eq @ A @ B4 @ A4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % verit_la_disequality
% 0.19/0.47 thf(fact_58_le__rel__bool__arg__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ( ( ord_less_eq @ ( $o > A ) )
% 0.19/0.47 = ( ^ [X5: $o > A,Y6: $o > A] :
% 0.19/0.47 ( ( ord_less_eq @ A @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 0.19/0.47 & ( ord_less_eq @ A @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_rel_bool_arg_iff
% 0.19/0.47 thf(fact_59_antimonoD,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( order @ A )
% 0.19/0.47 & ( order @ B ) )
% 0.19/0.47 => ! [F: A > B,X3: A,Y2: A] :
% 0.19/0.47 ( ( order_antimono @ A @ B @ F )
% 0.19/0.47 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.47 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antimonoD
% 0.19/0.47 thf(fact_60_antimonoE,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( order @ A )
% 0.19/0.47 & ( order @ B ) )
% 0.19/0.47 => ! [F: A > B,X3: A,Y2: A] :
% 0.19/0.47 ( ( order_antimono @ A @ B @ F )
% 0.19/0.47 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.47 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antimonoE
% 0.19/0.47 thf(fact_61_antimono__def,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( order @ A )
% 0.19/0.47 & ( order @ B ) )
% 0.19/0.47 => ( ( order_antimono @ A @ B )
% 0.19/0.47 = ( ^ [F4: A > B] :
% 0.19/0.47 ! [X4: A,Y4: A] :
% 0.19/0.47 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.19/0.47 => ( ord_less_eq @ B @ ( F4 @ Y4 ) @ ( F4 @ X4 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antimono_def
% 0.19/0.47 thf(fact_62_antimonoI,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( order @ A )
% 0.19/0.47 & ( order @ B ) )
% 0.19/0.47 => ! [F: A > B] :
% 0.19/0.47 ( ! [X2: A,Y3: A] :
% 0.19/0.47 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.19/0.47 => ( ord_less_eq @ B @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.19/0.47 => ( order_antimono @ A @ B @ F ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antimonoI
% 0.19/0.47 thf(fact_63_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ( refine551993528up_loc @ A @ ( ord_less_eq @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_mono_setup.mono_setup_loc_axioms
% 0.19/0.47 thf(fact_64_swap__args2__def,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType,B: $tType] :
% 0.19/0.47 ( ( swap_args2 @ B @ C @ A )
% 0.19/0.47 = ( ^ [F4: B > C > A,X4: C,Y4: B] : ( F4 @ Y4 @ X4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % swap_args2_def
% 0.19/0.47 thf(fact_65_galois__connection_O_092_060gamma_062_092_060alpha_062__infl,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( comple187826305attice @ A )
% 0.19/0.47 & ( comple187826305attice @ B ) )
% 0.19/0.47 => ! [Alpha: A > B,Gamma: B > A,X3: A] :
% 0.19/0.47 ( ( refine1150083786ection @ A @ B @ Alpha @ Gamma )
% 0.19/0.47 => ( ord_less_eq @ A @ X3 @ ( Gamma @ ( Alpha @ X3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % galois_connection.\<gamma>\<alpha>_infl
% 0.19/0.47 thf(fact_66_galois__connection_O_092_060alpha_062_092_060gamma_062__defl,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( ( comple187826305attice @ B )
% 0.19/0.47 & ( comple187826305attice @ A ) )
% 0.19/0.47 => ! [Alpha: A > B,Gamma: B > A,X3: B] :
% 0.19/0.47 ( ( refine1150083786ection @ A @ B @ Alpha @ Gamma )
% 0.19/0.47 => ( ord_less_eq @ B @ ( Alpha @ ( Gamma @ X3 ) ) @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % galois_connection.\<alpha>\<gamma>_defl
% 0.19/0.47 thf(fact_67_galois__connection_Ogalois,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( ( comple187826305attice @ B )
% 0.19/0.47 & ( comple187826305attice @ A ) )
% 0.19/0.47 => ! [Alpha: A > B,Gamma: B > A,C2: A,A4: B] :
% 0.19/0.47 ( ( refine1150083786ection @ A @ B @ Alpha @ Gamma )
% 0.19/0.47 => ( ( ord_less_eq @ A @ C2 @ ( Gamma @ A4 ) )
% 0.19/0.47 = ( ord_less_eq @ B @ ( Alpha @ C2 ) @ A4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % galois_connection.galois
% 0.19/0.47 thf(fact_68_galois__connection_Ointro,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( ( comple187826305attice @ B )
% 0.19/0.47 & ( comple187826305attice @ A ) )
% 0.19/0.47 => ! [Gamma: B > A,Alpha: A > B] :
% 0.19/0.47 ( ! [C4: A,A6: B] :
% 0.19/0.47 ( ( ord_less_eq @ A @ C4 @ ( Gamma @ A6 ) )
% 0.19/0.47 = ( ord_less_eq @ B @ ( Alpha @ C4 ) @ A6 ) )
% 0.19/0.47 => ( refine1150083786ection @ A @ B @ Alpha @ Gamma ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % galois_connection.intro
% 0.19/0.47 thf(fact_69_galois__connection__def,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( comple187826305attice @ A )
% 0.19/0.47 & ( comple187826305attice @ B ) )
% 0.19/0.47 => ( ( refine1150083786ection @ A @ B )
% 0.19/0.47 = ( ^ [Alpha2: A > B,Gamma2: B > A] :
% 0.19/0.47 ! [C5: A,A5: B] :
% 0.19/0.47 ( ( ord_less_eq @ A @ C5 @ ( Gamma2 @ A5 ) )
% 0.19/0.47 = ( ord_less_eq @ B @ ( Alpha2 @ C5 ) @ A5 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % galois_connection_def
% 0.19/0.47 thf(fact_70_mono__setup__loc__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( refine551993528up_loc @ A )
% 0.19/0.47 = ( ^ [Le: A > A > $o] :
% 0.19/0.47 ! [X4: A] : ( Le @ X4 @ X4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % mono_setup_loc_def
% 0.19/0.47 thf(fact_71_mono__setup__loc_Orefl,axiom,
% 0.19/0.47 ! [A: $tType,Le2: A > A > $o,X3: A] :
% 0.19/0.47 ( ( refine551993528up_loc @ A @ Le2 )
% 0.19/0.47 => ( Le2 @ X3 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % mono_setup_loc.refl
% 0.19/0.47 thf(fact_72_mono__setup__loc_Ointro,axiom,
% 0.19/0.47 ! [A: $tType,Le2: A > A > $o] :
% 0.19/0.47 ( ! [X2: A] : ( Le2 @ X2 @ X2 )
% 0.19/0.47 => ( refine551993528up_loc @ A @ Le2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % mono_setup_loc.intro
% 0.19/0.47 thf(fact_73_mono__setup__loc_Omono__if,axiom,
% 0.19/0.47 ! [A: $tType,Le2: A > A > $o,T2: A,T3: A,E: A,E2: A,B4: $o] :
% 0.19/0.47 ( ( refine551993528up_loc @ A @ Le2 )
% 0.19/0.47 => ( ( Le2 @ T2 @ T3 )
% 0.19/0.47 => ( ( Le2 @ E @ E2 )
% 0.19/0.47 => ( Le2 @ ( if @ A @ B4 @ T2 @ E ) @ ( if @ A @ B4 @ T3 @ E2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % mono_setup_loc.mono_if
% 0.19/0.47 thf(fact_74_mono__setup__loc_Omono__let,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,Le2: A > A > $o,F: B > A,F2: B > A,X3: B] :
% 0.19/0.47 ( ( refine551993528up_loc @ A @ Le2 )
% 0.19/0.47 => ( ! [X2: B] : ( Le2 @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.19/0.47 => ( Le2 @ ( F @ X3 ) @ ( F2 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % mono_setup_loc.mono_let
% 0.19/0.47 thf(fact_75_galois__connection_Oinf__dist___092_060alpha_062,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( comple187826305attice @ A )
% 0.19/0.47 & ( comple187826305attice @ B ) )
% 0.19/0.47 => ! [Alpha: A > B,Gamma: B > A] :
% 0.19/0.47 ( ( refine1150083786ection @ A @ B @ Alpha @ Gamma )
% 0.19/0.47 => ( refine_inf_distrib @ A @ B @ Alpha ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % galois_connection.inf_dist_\<alpha>
% 0.19/0.47 thf(fact_76_strict__mono__less__eq,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( linorder @ A )
% 0.19/0.47 & ( order @ B ) )
% 0.19/0.47 => ! [F: A > B,X3: A,Y2: A] :
% 0.19/0.47 ( ( order_strict_mono @ A @ B @ F )
% 0.19/0.47 => ( ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y2 ) )
% 0.19/0.47 = ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % strict_mono_less_eq
% 0.19/0.47 thf(fact_77_greaterThan__subset__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_greaterThan @ A @ X3 ) @ ( set_ord_greaterThan @ A @ Y2 ) )
% 0.19/0.47 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % greaterThan_subset_iff
% 0.19/0.47 thf(fact_78_START__REFINEG__TRANSFER,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [D: A,C2: A,A4: A] :
% 0.19/0.47 ( ( refine111645177_ALIGN @ A @ A @ D @ C2 )
% 0.19/0.47 => ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.19/0.47 => ( ( refine574149253T_SIMP @ A @ C2 @ D )
% 0.19/0.47 => ( ord_less_eq @ A @ D @ A4 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % START_REFINEG_TRANSFER
% 0.19/0.47 thf(fact_79_lessThan__subset__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_lessThan @ A @ X3 ) @ ( set_ord_lessThan @ A @ Y2 ) )
% 0.19/0.47 = ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % lessThan_subset_iff
% 0.19/0.47 thf(fact_80_transfer_Otransfer__rec__list,axiom,
% 0.19/0.47 ! [C: $tType,D2: $tType,A: $tType,B: $tType] :
% 0.19/0.47 ( ( comple187826305attice @ A )
% 0.19/0.47 => ! [Alpha: C > A,Fn: B > C,Fn2: B > A,Fc: D2 > ( list @ D2 ) > ( B > C ) > B > C,Fc2: D2 > ( list @ D2 ) > ( B > A ) > B > A,L: list @ D2,S3: B] :
% 0.19/0.47 ( ! [S4: B] : ( ord_less_eq @ A @ ( Alpha @ ( Fn @ S4 ) ) @ ( Fn2 @ S4 ) )
% 0.19/0.47 => ( ! [X2: D2,L2: list @ D2,Rec: B > C,Rec2: B > A,S4: B] :
% 0.19/0.47 ( ! [Sa: B] : ( ord_less_eq @ A @ ( Alpha @ ( Rec @ Sa ) ) @ ( Rec2 @ Sa ) )
% 0.19/0.47 => ( ord_less_eq @ A @ ( Alpha @ ( Fc @ X2 @ L2 @ Rec @ S4 ) ) @ ( Fc2 @ X2 @ L2 @ Rec2 @ S4 ) ) )
% 0.19/0.47 => ( ord_less_eq @ A @ ( Alpha @ ( rec_list @ ( B > C ) @ D2 @ Fn @ Fc @ L @ S3 ) ) @ ( rec_list @ ( B > A ) @ D2 @ Fn2 @ Fc2 @ L @ S3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transfer.transfer_rec_list
% 0.19/0.47 thf(fact_81_atLeast__subset__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atLeast @ A @ X3 ) @ ( set_ord_atLeast @ A @ Y2 ) )
% 0.19/0.47 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % atLeast_subset_iff
% 0.19/0.47 thf(fact_82_lessThan__eq__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ( set_ord_lessThan @ A @ X3 )
% 0.19/0.47 = ( set_ord_lessThan @ A @ Y2 ) )
% 0.19/0.47 = ( X3 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % lessThan_eq_iff
% 0.19/0.47 thf(fact_83_atLeast__eq__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ( set_ord_atLeast @ A @ X3 )
% 0.19/0.47 = ( set_ord_atLeast @ A @ Y2 ) )
% 0.19/0.47 = ( X3 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % atLeast_eq_iff
% 0.19/0.47 thf(fact_84_greaterThan__eq__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ( set_ord_greaterThan @ A @ X3 )
% 0.19/0.47 = ( set_ord_greaterThan @ A @ Y2 ) )
% 0.19/0.47 = ( X3 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % greaterThan_eq_iff
% 0.19/0.47 thf(fact_85_atLeast__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [I2: A,K: A] :
% 0.19/0.47 ( ( member @ A @ I2 @ ( set_ord_atLeast @ A @ K ) )
% 0.19/0.47 = ( ord_less_eq @ A @ K @ I2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % atLeast_iff
% 0.19/0.47 thf(fact_86_strict__mono__eq,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( linorder @ A )
% 0.19/0.47 & ( order @ B ) )
% 0.19/0.47 => ! [F: A > B,X3: A,Y2: A] :
% 0.19/0.47 ( ( order_strict_mono @ A @ B @ F )
% 0.19/0.47 => ( ( ( F @ X3 )
% 0.19/0.47 = ( F @ Y2 ) )
% 0.19/0.47 = ( X3 = Y2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % strict_mono_eq
% 0.19/0.47 thf(fact_87_Ioi__le__Ico,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [A4: A] : ( ord_less_eq @ ( set @ A ) @ ( set_ord_greaterThan @ A @ A4 ) @ ( set_ord_atLeast @ A @ A4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Ioi_le_Ico
% 0.19/0.47 thf(fact_88_STOP__REFINEG__TRANSFER,axiom,
% 0.19/0.47 ! [A: $tType,C2: A] : ( refine574149253T_SIMP @ A @ C2 @ C2 ) ).
% 0.19/0.47
% 0.19/0.47 % STOP_REFINEG_TRANSFER
% 0.19/0.47 thf(fact_89_REFINEG__TRANSFER__ALIGNI,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType,X3: A,Y2: B] : ( refine111645177_ALIGN @ A @ B @ X3 @ Y2 ) ).
% 0.19/0.47
% 0.19/0.47 % REFINEG_TRANSFER_ALIGNI
% 0.19/0.47 thf(fact_90_REFINEG__TRANSFER__ALIGN__def,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( refine111645177_ALIGN @ A @ B )
% 0.19/0.47 = ( ^ [X4: A,Y4: B] : $true ) ) ).
% 0.19/0.47
% 0.19/0.47 % REFINEG_TRANSFER_ALIGN_def
% 0.19/0.47 thf(fact_91_REFINEG__TRANSFER__POST__SIMP__def,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( refine574149253T_SIMP @ A )
% 0.19/0.47 = ( ^ [Y: A,Z: A] : ( Y = Z ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % REFINEG_TRANSFER_POST_SIMP_def
% 0.19/0.47 thf(fact_92_Ici__subset__Ioi__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [A4: A,B4: A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atLeast @ A @ A4 ) @ ( set_ord_greaterThan @ A @ B4 ) )
% 0.19/0.47 = ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Ici_subset_Ioi_iff
% 0.19/0.47 thf(fact_93_Icc__subset__Ici__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [L: A,H: A,L3: A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_or331188842AtMost @ A @ L @ H ) @ ( set_ord_atLeast @ A @ L3 ) )
% 0.19/0.47 = ( ~ ( ord_less_eq @ A @ L @ H )
% 0.19/0.47 | ( ord_less_eq @ A @ L3 @ L ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Icc_subset_Ici_iff
% 0.19/0.47 thf(fact_94_inf__distribD_I1_J,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( ( complete_Sup @ A )
% 0.19/0.47 & ( bot @ A )
% 0.19/0.47 & ( complete_Sup @ B )
% 0.19/0.47 & ( bot @ B ) )
% 0.19/0.47 => ! [F: A > B] :
% 0.19/0.47 ( ( refine_inf_distrib @ A @ B @ F )
% 0.19/0.47 => ( refine_strict @ A @ B @ F ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % inf_distribD(1)
% 0.19/0.47 thf(fact_95_Compl__atLeast,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [K: A] :
% 0.19/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( set_ord_atLeast @ A @ K ) )
% 0.19/0.47 = ( set_ord_lessThan @ A @ K ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Compl_atLeast
% 0.19/0.47 thf(fact_96_Compl__lessThan,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [K: A] :
% 0.19/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( set_ord_lessThan @ A @ K ) )
% 0.19/0.47 = ( set_ord_atLeast @ A @ K ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Compl_lessThan
% 0.19/0.47 thf(fact_97_atMost__subset__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ X3 ) @ ( set_ord_atMost @ A @ Y2 ) )
% 0.19/0.47 = ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % atMost_subset_iff
% 0.19/0.47 thf(fact_98_psubsetI,axiom,
% 0.19/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.19/0.47 => ( ( A2 != B2 )
% 0.19/0.47 => ( ord_less @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % psubsetI
% 0.19/0.47 thf(fact_99_verit__minus__simplify_I4_J,axiom,
% 0.19/0.47 ! [B: $tType] :
% 0.19/0.47 ( ( group_add @ B )
% 0.19/0.47 => ! [B4: B] :
% 0.19/0.47 ( ( uminus_uminus @ B @ ( uminus_uminus @ B @ B4 ) )
% 0.19/0.47 = B4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % verit_minus_simplify(4)
% 0.19/0.47 thf(fact_100_atMost__eq__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ( set_ord_atMost @ A @ X3 )
% 0.19/0.47 = ( set_ord_atMost @ A @ Y2 ) )
% 0.19/0.47 = ( X3 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % atMost_eq_iff
% 0.19/0.47 thf(fact_101_ComplI,axiom,
% 0.19/0.47 ! [A: $tType,C2: A,A2: set @ A] :
% 0.19/0.47 ( ~ ( member @ A @ C2 @ A2 )
% 0.19/0.47 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ComplI
% 0.19/0.47 thf(fact_102_Compl__iff,axiom,
% 0.19/0.47 ! [A: $tType,C2: A,A2: set @ A] :
% 0.19/0.47 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.19/0.47 = ( ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Compl_iff
% 0.19/0.47 thf(fact_103_Compl__eq__Compl__iff,axiom,
% 0.19/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.19/0.47 ( ( ( uminus_uminus @ ( set @ A ) @ A2 )
% 0.19/0.47 = ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.19/0.47 = ( A2 = B2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Compl_eq_Compl_iff
% 0.19/0.47 thf(fact_104_atLeastAtMost__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [I2: A,L: A,U: A] :
% 0.19/0.47 ( ( member @ A @ I2 @ ( set_or331188842AtMost @ A @ L @ U ) )
% 0.19/0.47 = ( ( ord_less_eq @ A @ L @ I2 )
% 0.19/0.47 & ( ord_less_eq @ A @ I2 @ U ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % atLeastAtMost_iff
% 0.19/0.47 thf(fact_105_Icc__eq__Icc,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [L: A,H: A,L3: A,H2: A] :
% 0.19/0.47 ( ( ( set_or331188842AtMost @ A @ L @ H )
% 0.19/0.47 = ( set_or331188842AtMost @ A @ L3 @ H2 ) )
% 0.19/0.47 = ( ( ( L = L3 )
% 0.19/0.47 & ( H = H2 ) )
% 0.19/0.47 | ( ~ ( ord_less_eq @ A @ L @ H )
% 0.19/0.47 & ~ ( ord_less_eq @ A @ L3 @ H2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Icc_eq_Icc
% 0.19/0.47 thf(fact_106_atMost__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [I2: A,K: A] :
% 0.19/0.47 ( ( member @ A @ I2 @ ( set_ord_atMost @ A @ K ) )
% 0.19/0.47 = ( ord_less_eq @ A @ I2 @ K ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % atMost_iff
% 0.19/0.47 thf(fact_107_lessThan__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [I2: A,K: A] :
% 0.19/0.47 ( ( member @ A @ I2 @ ( set_ord_lessThan @ A @ K ) )
% 0.19/0.47 = ( ord_less @ A @ I2 @ K ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % lessThan_iff
% 0.19/0.47 thf(fact_108_Compl__anti__mono,axiom,
% 0.19/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.19/0.47 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Compl_anti_mono
% 0.19/0.47 thf(fact_109_Compl__subset__Compl__iff,axiom,
% 0.19/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.19/0.47 = ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Compl_subset_Compl_iff
% 0.19/0.47 thf(fact_110_greaterThan__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [I2: A,K: A] :
% 0.19/0.47 ( ( member @ A @ I2 @ ( set_ord_greaterThan @ A @ K ) )
% 0.19/0.47 = ( ord_less @ A @ K @ I2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % greaterThan_iff
% 0.19/0.47 thf(fact_111_atLeastatMost__subset__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [A4: A,B4: A,C2: A,D: A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_or331188842AtMost @ A @ A4 @ B4 ) @ ( set_or331188842AtMost @ A @ C2 @ D ) )
% 0.19/0.47 = ( ~ ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.47 | ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.19/0.47 & ( ord_less_eq @ A @ B4 @ D ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % atLeastatMost_subset_iff
% 0.19/0.47 thf(fact_112_Compl__atMost,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [K: A] :
% 0.19/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( set_ord_atMost @ A @ K ) )
% 0.19/0.47 = ( set_ord_greaterThan @ A @ K ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Compl_atMost
% 0.19/0.47 thf(fact_113_Compl__greaterThan,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [K: A] :
% 0.19/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( set_ord_greaterThan @ A @ K ) )
% 0.19/0.47 = ( set_ord_atMost @ A @ K ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Compl_greaterThan
% 0.19/0.47 thf(fact_114_Icc__subset__Iic__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [L: A,H: A,H2: A] :
% 0.19/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_or331188842AtMost @ A @ L @ H ) @ ( set_ord_atMost @ A @ H2 ) )
% 0.19/0.47 = ( ~ ( ord_less_eq @ A @ L @ H )
% 0.19/0.47 | ( ord_less_eq @ A @ H @ H2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Icc_subset_Iic_iff
% 0.19/0.47 thf(fact_115_lessThan__strict__subset__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [M: A,N: A] :
% 0.19/0.47 ( ( ord_less @ ( set @ A ) @ ( set_ord_lessThan @ A @ M ) @ ( set_ord_lessThan @ A @ N ) )
% 0.19/0.47 = ( ord_less @ A @ M @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % lessThan_strict_subset_iff
% 0.19/0.47 thf(fact_116_not__Iic__eq__Icc,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( no_bot @ A )
% 0.19/0.47 => ! [H2: A,L: A,H: A] :
% 0.19/0.47 ( ( set_ord_atMost @ A @ H2 )
% 0.19/0.47 != ( set_or331188842AtMost @ A @ L @ H ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % not_Iic_eq_Icc
% 0.19/0.47 thf(fact_117_not__Iic__le__Icc,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( no_bot @ A )
% 0.19/0.47 => ! [H: A,L3: A,H2: A] :
% 0.19/0.47 ~ ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ H ) @ ( set_or331188842AtMost @ A @ L3 @ H2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % not_Iic_le_Icc
% 0.19/0.47 thf(fact_118_atLeastatMost__psubset__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [A4: A,B4: A,C2: A,D: A] :
% 0.19/0.47 ( ( ord_less @ ( set @ A ) @ ( set_or331188842AtMost @ A @ A4 @ B4 ) @ ( set_or331188842AtMost @ A @ C2 @ D ) )
% 0.19/0.47 = ( ( ~ ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.47 | ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.19/0.47 & ( ord_less_eq @ A @ B4 @ D )
% 0.19/0.47 & ( ( ord_less @ A @ C2 @ A4 )
% 0.19/0.47 | ( ord_less @ A @ B4 @ D ) ) ) )
% 0.19/0.47 & ( ord_less_eq @ A @ C2 @ D ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % atLeastatMost_psubset_iff
% 0.19/0.47 thf(fact_119_verit__comp__simplify1_I1_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [A4: A] :
% 0.19/0.47 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % verit_comp_simplify1(1)
% 0.19/0.47 thf(fact_120_verit__negate__coefficient_I3_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ordered_ab_group_add @ A )
% 0.19/0.47 => ! [A4: A,B4: A] :
% 0.19/0.47 ( ( A4 = B4 )
% 0.19/0.47 => ( ( uminus_uminus @ A @ A4 )
% 0.19/0.47 = ( uminus_uminus @ A @ B4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % verit_negate_coefficient(3)
% 0.19/0.47 thf(fact_121_verit__negate__coefficient_I2_J,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ordered_ab_group_add @ A )
% 0.19/0.47 => ! [A4: A,B4: A] :
% 0.19/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.19/0.47 => ( ord_less @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % verit_negate_coefficient(2)
% 0.19/0.47 thf(fact_122_all__nat__split__at,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [K: A,P: A > $o] :
% 0.19/0.47 ( ! [I3: A] :
% 0.19/0.47 ( ( ord_less @ A @ I3 @ K )
% 0.19/0.47 => ( P @ I3 ) )
% 0.19/0.47 => ( ( P @ K )
% 0.19/0.47 => ( ! [I3: A] :
% 0.19/0.47 ( ( ord_less @ A @ K @ I3 )
% 0.19/0.47 => ( P @ I3 ) )
% 0.19/0.47 => ! [X_1: A] : ( P @ X_1 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % all_nat_split_at
% 0.19/0.47 thf(fact_123_ComplD,axiom,
% 0.19/0.47 ! [A: $tType,C2: A,A2: set @ A] :
% 0.19/0.47 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.19/0.47 => ~ ( member @ A @ C2 @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % ComplD
% 0.19/0.47 thf(fact_124_double__complement,axiom,
% 0.19/0.47 ! [A: $tType,A2: set @ A] :
% 0.19/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.19/0.47 = A2 ) ).
% 0.19/0.47
% 0.19/0.47 % double_complement
% 0.19/0.47 thf(fact_125_ord__eq__less__subst,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( ( ord @ B )
% 0.19/0.47 & ( ord @ A ) )
% 0.19/0.47 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.19/0.47 ( ( A4
% 0.19/0.47 = ( F @ B4 ) )
% 0.19/0.47 => ( ( ord_less @ B @ B4 @ C2 )
% 0.19/0.47 => ( ! [X2: B,Y3: B] :
% 0.19/0.47 ( ( ord_less @ B @ X2 @ Y3 )
% 0.19/0.47 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.19/0.47 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_eq_less_subst
% 0.19/0.47 thf(fact_126_ord__less__eq__subst,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( ( ord @ B )
% 0.19/0.47 & ( ord @ A ) )
% 0.19/0.47 => ! [A4: A,B4: A,F: A > B,C2: B] :
% 0.19/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.19/0.47 => ( ( ( F @ B4 )
% 0.19/0.47 = C2 )
% 0.19/0.47 => ( ! [X2: A,Y3: A] :
% 0.19/0.47 ( ( ord_less @ A @ X2 @ Y3 )
% 0.19/0.47 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.19/0.47 => ( ord_less @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_less_eq_subst
% 0.19/0.47 thf(fact_127_order__less__subst1,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( ( order @ B )
% 0.19/0.47 & ( order @ A ) )
% 0.19/0.47 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.19/0.47 ( ( ord_less @ A @ A4 @ ( F @ B4 ) )
% 0.19/0.47 => ( ( ord_less @ B @ B4 @ C2 )
% 0.19/0.47 => ( ! [X2: B,Y3: B] :
% 0.19/0.47 ( ( ord_less @ B @ X2 @ Y3 )
% 0.19/0.47 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.19/0.47 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_less_subst1
% 0.19/0.47 thf(fact_128_order__less__subst2,axiom,
% 0.19/0.47 ! [A: $tType,C: $tType] :
% 0.19/0.47 ( ( ( order @ C )
% 0.19/0.47 & ( order @ A ) )
% 0.19/0.47 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.19/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.19/0.47 => ( ( ord_less @ C @ ( F @ B4 ) @ C2 )
% 0.19/0.47 => ( ! [X2: A,Y3: A] :
% 0.19/0.47 ( ( ord_less @ A @ X2 @ Y3 )
% 0.19/0.47 => ( ord_less @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.19/0.47 => ( ord_less @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_less_subst2
% 0.19/0.47 thf(fact_129_lt__ex,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( no_bot @ A )
% 0.19/0.47 => ! [X3: A] :
% 0.19/0.47 ? [Y3: A] : ( ord_less @ A @ Y3 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % lt_ex
% 0.19/0.47 thf(fact_130_gt__ex,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( no_top @ A )
% 0.19/0.47 => ! [X3: A] :
% 0.19/0.47 ? [X_12: A] : ( ord_less @ A @ X3 @ X_12 ) ) ).
% 0.19/0.47
% 0.19/0.47 % gt_ex
% 0.19/0.47 thf(fact_131_neqE,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( X3 != Y2 )
% 0.19/0.47 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % neqE
% 0.19/0.47 thf(fact_132_neq__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( X3 != Y2 )
% 0.19/0.47 = ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 | ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % neq_iff
% 0.19/0.47 thf(fact_133_order_Oasym,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [A4: A,B4: A] :
% 0.19/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.19/0.47 => ~ ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.asym
% 0.19/0.47 thf(fact_134_dense,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( dense_order @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ? [Z3: A] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Z3 )
% 0.19/0.47 & ( ord_less @ A @ Z3 @ Y2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dense
% 0.19/0.47 thf(fact_135_less__imp__neq,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ( X3 != Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_neq
% 0.19/0.47 thf(fact_136_less__asym,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_asym
% 0.19/0.47 thf(fact_137_less__asym_H,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [A4: A,B4: A] :
% 0.19/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.19/0.47 => ~ ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_asym'
% 0.19/0.47 thf(fact_138_less__trans,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A,Z2: A] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ( ( ord_less @ A @ Y2 @ Z2 )
% 0.19/0.47 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_trans
% 0.19/0.47 thf(fact_139_less__linear,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 | ( X3 = Y2 )
% 0.19/0.47 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_linear
% 0.19/0.47 thf(fact_140_less__irrefl,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [X3: A] :
% 0.19/0.47 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_irrefl
% 0.19/0.47 thf(fact_141_ord__eq__less__trans,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [A4: A,B4: A,C2: A] :
% 0.19/0.47 ( ( A4 = B4 )
% 0.19/0.47 => ( ( ord_less @ A @ B4 @ C2 )
% 0.19/0.47 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_eq_less_trans
% 0.19/0.47 thf(fact_142_ord__less__eq__trans,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ord @ A )
% 0.19/0.47 => ! [A4: A,B4: A,C2: A] :
% 0.19/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.19/0.47 => ( ( B4 = C2 )
% 0.19/0.47 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_less_eq_trans
% 0.19/0.47 thf(fact_143_dual__order_Oasym,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [B4: A,A4: A] :
% 0.19/0.47 ( ( ord_less @ A @ B4 @ A4 )
% 0.19/0.47 => ~ ( ord_less @ A @ A4 @ B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.asym
% 0.19/0.47 thf(fact_144_less__imp__not__eq,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ( X3 != Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_not_eq
% 0.19/0.47 thf(fact_145_less__not__sym,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_not_sym
% 0.19/0.47 thf(fact_146_less__induct,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( wellorder @ A )
% 0.19/0.47 => ! [P: A > $o,A4: A] :
% 0.19/0.47 ( ! [X2: A] :
% 0.19/0.47 ( ! [Y5: A] :
% 0.19/0.47 ( ( ord_less @ A @ Y5 @ X2 )
% 0.19/0.47 => ( P @ Y5 ) )
% 0.19/0.47 => ( P @ X2 ) )
% 0.19/0.47 => ( P @ A4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_induct
% 0.19/0.47 thf(fact_147_antisym__conv3,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [Y2: A,X3: A] :
% 0.19/0.47 ( ~ ( ord_less @ A @ Y2 @ X3 )
% 0.19/0.47 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.19/0.47 = ( X3 = Y2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antisym_conv3
% 0.19/0.47 thf(fact_148_less__imp__not__eq2,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ( Y2 != X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_not_eq2
% 0.19/0.47 thf(fact_149_less__imp__triv,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( preorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A,P: $o] :
% 0.19/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ( ( ord_less @ A @ Y2 @ X3 )
% 0.19/0.47 => P ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_triv
% 0.19/0.47 thf(fact_150_linorder__cases,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linorder @ A )
% 0.19/0.47 => ! [X3: A,Y2: A] :
% 0.19/0.47 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.47 => ( ( X3 != Y2 )
% 0.19/0.47 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % linorder_cases
% 0.19/0.47 thf(fact_151_dual__order_Oirrefl,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [A4: A] :
% 0.19/0.47 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.irrefl
% 0.19/0.47 thf(fact_152_order_Ostrict__trans,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( order @ A )
% 0.19/0.47 => ! [A4: A,B4: A,C2: A] :
% 0.19/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.19/0.47 => ( ( ord_less @ A @ B4 @ C2 )
% 0.19/0.47 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.strict_trans
% 0.19/0.47 thf(fact_153_less__imp__not__less,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.30/0.47 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_less
% 0.30/0.47 thf(fact_154_exists__least__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( wellorder @ A )
% 0.30/0.47 => ( ( ^ [P2: A > $o] :
% 0.30/0.47 ? [X6: A] : ( P2 @ X6 ) )
% 0.30/0.47 = ( ^ [P3: A > $o] :
% 0.30/0.47 ? [N2: A] :
% 0.30/0.47 ( ( P3 @ N2 )
% 0.30/0.47 & ! [M3: A] :
% 0.30/0.47 ( ( ord_less @ A @ M3 @ N2 )
% 0.30/0.47 => ~ ( P3 @ M3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % exists_least_iff
% 0.30/0.47 thf(fact_155_linorder__less__wlog,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > A > $o,A4: A,B4: A] :
% 0.30/0.47 ( ! [A6: A,B6: A] :
% 0.30/0.47 ( ( ord_less @ A @ A6 @ B6 )
% 0.30/0.47 => ( P @ A6 @ B6 ) )
% 0.30/0.47 => ( ! [A6: A] : ( P @ A6 @ A6 )
% 0.30/0.47 => ( ! [A6: A,B6: A] :
% 0.30/0.47 ( ( P @ B6 @ A6 )
% 0.30/0.47 => ( P @ A6 @ B6 ) )
% 0.30/0.47 => ( P @ A4 @ B4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_less_wlog
% 0.30/0.47 thf(fact_156_dual__order_Ostrict__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A4: A,C2: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A4 )
% 0.30/0.47 => ( ( ord_less @ A @ C2 @ B4 )
% 0.30/0.47 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans
% 0.30/0.47 thf(fact_157_not__less__iff__gr__or__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.30/0.47 = ( ( ord_less @ A @ Y2 @ X3 )
% 0.30/0.47 | ( X3 = Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_less_iff_gr_or_eq
% 0.30/0.47 thf(fact_158_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.30/0.47 => ( A4 != B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_implies_not_eq
% 0.30/0.47 thf(fact_159_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A4: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A4 )
% 0.30/0.47 => ( A4 != B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_implies_not_eq
% 0.30/0.47 thf(fact_160_Iic__subset__Iio__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ A4 ) @ ( set_ord_lessThan @ A @ B4 ) )
% 0.30/0.47 = ( ord_less @ A @ A4 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Iic_subset_Iio_iff
% 0.30/0.47 thf(fact_161_leD,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [Y2: A,X3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.30/0.47 => ~ ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % leD
% 0.30/0.47 thf(fact_162_leI,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % leI
% 0.30/0.47 thf(fact_163_le__less,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ( ( ord_less_eq @ A )
% 0.30/0.47 = ( ^ [X4: A,Y4: A] :
% 0.30/0.47 ( ( ord_less @ A @ X4 @ Y4 )
% 0.30/0.47 | ( X4 = Y4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_less
% 0.30/0.47 thf(fact_164_less__le,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ( ( ord_less @ A )
% 0.30/0.47 = ( ^ [X4: A,Y4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.30/0.47 & ( X4 != Y4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_le
% 0.30/0.47 thf(fact_165_order__le__less__subst1,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( order @ B )
% 0.30/0.47 & ( order @ A ) )
% 0.30/0.47 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A4 @ ( F @ B4 ) )
% 0.30/0.47 => ( ( ord_less @ B @ B4 @ C2 )
% 0.30/0.47 => ( ! [X2: B,Y3: B] :
% 0.30/0.47 ( ( ord_less @ B @ X2 @ Y3 )
% 0.30/0.47 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.30/0.47 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_le_less_subst1
% 0.30/0.47 thf(fact_166_order__le__less__subst2,axiom,
% 0.30/0.47 ! [A: $tType,C: $tType] :
% 0.30/0.47 ( ( ( order @ C )
% 0.30/0.47 & ( order @ A ) )
% 0.30/0.47 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.30/0.47 => ( ( ord_less @ C @ ( F @ B4 ) @ C2 )
% 0.30/0.47 => ( ! [X2: A,Y3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.30/0.47 => ( ord_less_eq @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.30/0.47 => ( ord_less @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_le_less_subst2
% 0.30/0.47 thf(fact_167_order__less__le__subst1,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( order @ B )
% 0.30/0.47 & ( order @ A ) )
% 0.30/0.47 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.30/0.47 ( ( ord_less @ A @ A4 @ ( F @ B4 ) )
% 0.30/0.47 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.30/0.47 => ( ! [X2: B,Y3: B] :
% 0.30/0.47 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.30/0.47 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_le_subst1
% 0.30/0.47 thf(fact_168_order__less__le__subst2,axiom,
% 0.30/0.47 ! [A: $tType,C: $tType] :
% 0.30/0.47 ( ( ( order @ C )
% 0.30/0.47 & ( order @ A ) )
% 0.30/0.47 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.30/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.30/0.47 => ( ( ord_less_eq @ C @ ( F @ B4 ) @ C2 )
% 0.30/0.47 => ( ! [X2: A,Y3: A] :
% 0.30/0.47 ( ( ord_less @ A @ X2 @ Y3 )
% 0.30/0.47 => ( ord_less @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.30/0.47 => ( ord_less @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_le_subst2
% 0.30/0.47 thf(fact_169_not__le,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ~ ( ord_less_eq @ A @ X3 @ Y2 ) )
% 0.30/0.47 = ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_le
% 0.30/0.47 thf(fact_170_not__less,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_less
% 0.30/0.47 thf(fact_171_le__neq__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.30/0.47 => ( ( A4 != B4 )
% 0.30/0.47 => ( ord_less @ A @ A4 @ B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_neq_trans
% 0.30/0.47 thf(fact_172_antisym__conv1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.30/0.47 = ( X3 = Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym_conv1
% 0.30/0.47 thf(fact_173_antisym__conv2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.30/0.47 = ( X3 = Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym_conv2
% 0.30/0.47 thf(fact_174_less__imp__le,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_le
% 0.30/0.47 thf(fact_175_le__less__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A,Z2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ( ord_less @ A @ Y2 @ Z2 )
% 0.30/0.47 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_less_trans
% 0.30/0.47 thf(fact_176_less__le__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A,Z2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.30/0.47 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_le_trans
% 0.30/0.47 thf(fact_177_dense__ge,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( dense_linorder @ A )
% 0.30/0.47 => ! [Z2: A,Y2: A] :
% 0.30/0.47 ( ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X2 )
% 0.30/0.47 => ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.30/0.47 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dense_ge
% 0.30/0.47 thf(fact_178_dense__le,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( dense_linorder @ A )
% 0.30/0.47 => ! [Y2: A,Z2: A] :
% 0.30/0.47 ( ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less_eq @ A @ X2 @ Z2 ) )
% 0.30/0.47 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dense_le
% 0.30/0.47 thf(fact_179_le__less__linear,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.30/0.47 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_less_linear
% 0.30/0.47 thf(fact_180_le__imp__less__or__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ( ord_less @ A @ X3 @ Y2 )
% 0.30/0.47 | ( X3 = Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_imp_less_or_eq
% 0.30/0.47 thf(fact_181_less__le__not__le,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ( ( ord_less @ A )
% 0.30/0.47 = ( ^ [X4: A,Y4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.30/0.47 & ~ ( ord_less_eq @ A @ Y4 @ X4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_le_not_le
% 0.30/0.47 thf(fact_182_not__le__imp__less,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Y2: A,X3: A] :
% 0.30/0.47 ( ~ ( ord_less_eq @ A @ Y2 @ X3 )
% 0.30/0.47 => ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_le_imp_less
% 0.30/0.47 thf(fact_183_order_Ostrict__trans1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A4: A,B4: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.30/0.47 => ( ( ord_less @ A @ B4 @ C2 )
% 0.30/0.47 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_trans1
% 0.30/0.47 thf(fact_184_order_Ostrict__trans2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A4: A,B4: A,C2: A] :
% 0.30/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.30/0.47 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_trans2
% 0.30/0.47 thf(fact_185_order_Oorder__iff__strict,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ( ( ord_less_eq @ A )
% 0.30/0.47 = ( ^ [A5: A,B5: A] :
% 0.30/0.47 ( ( ord_less @ A @ A5 @ B5 )
% 0.30/0.47 | ( A5 = B5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.order_iff_strict
% 0.30/0.47 thf(fact_186_order_Ostrict__iff__order,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ( ( ord_less @ A )
% 0.30/0.47 = ( ^ [A5: A,B5: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.30/0.47 & ( A5 != B5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_iff_order
% 0.30/0.47 thf(fact_187_dual__order_Ostrict__trans1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A4: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.30/0.47 => ( ( ord_less @ A @ C2 @ B4 )
% 0.30/0.47 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans1
% 0.30/0.47 thf(fact_188_dual__order_Ostrict__trans2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A4: A,C2: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A4 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.30/0.47 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans2
% 0.30/0.47 thf(fact_189_dense__ge__bounded,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( dense_linorder @ A )
% 0.30/0.47 => ! [Z2: A,X3: A,Y2: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X3 )
% 0.30/0.47 => ( ! [W: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ W )
% 0.30/0.47 => ( ( ord_less @ A @ W @ X3 )
% 0.30/0.47 => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 0.30/0.47 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dense_ge_bounded
% 0.30/0.47 thf(fact_190_dense__le__bounded,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( dense_linorder @ A )
% 0.30/0.47 => ! [X3: A,Y2: A,Z2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ! [W: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ W )
% 0.30/0.47 => ( ( ord_less @ A @ W @ Y2 )
% 0.30/0.47 => ( ord_less_eq @ A @ W @ Z2 ) ) )
% 0.30/0.47 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dense_le_bounded
% 0.30/0.47 thf(fact_191_order_Ostrict__implies__order,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.30/0.47 => ( ord_less_eq @ A @ A4 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_implies_order
% 0.30/0.47 thf(fact_192_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ( ( ord_less_eq @ A )
% 0.30/0.47 = ( ^ [B5: A,A5: A] :
% 0.30/0.47 ( ( ord_less @ A @ B5 @ A5 )
% 0.30/0.47 | ( A5 = B5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.order_iff_strict
% 0.30/0.47 thf(fact_193_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ( ( ord_less @ A )
% 0.30/0.47 = ( ^ [B5: A,A5: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.30/0.47 & ( A5 != B5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_iff_order
% 0.30/0.47 thf(fact_194_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A4: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A4 )
% 0.30/0.47 => ( ord_less_eq @ A @ B4 @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_implies_order
% 0.30/0.47 thf(fact_195_order_Onot__eq__order__implies__strict,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( A4 != B4 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.30/0.47 => ( ord_less @ A @ A4 @ B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.not_eq_order_implies_strict
% 0.30/0.47 thf(fact_196_verit__comp__simplify1_I3_J,axiom,
% 0.30/0.47 ! [B: $tType] :
% 0.30/0.47 ( ( linorder @ B )
% 0.30/0.47 => ! [B7: B,A7: B] :
% 0.30/0.47 ( ( ~ ( ord_less_eq @ B @ B7 @ A7 ) )
% 0.30/0.47 = ( ord_less @ B @ A7 @ B7 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % verit_comp_simplify1(3)
% 0.30/0.47 thf(fact_197_psubsetE,axiom,
% 0.30/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubsetE
% 0.30/0.47 thf(fact_198_psubset__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.30/0.47 & ( A3 != B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubset_eq
% 0.30/0.47 thf(fact_199_psubset__imp__subset,axiom,
% 0.30/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.47 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubset_imp_subset
% 0.30/0.47 thf(fact_200_psubset__subset__trans,axiom,
% 0.30/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.30/0.47 => ( ord_less @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubset_subset_trans
% 0.30/0.47 thf(fact_201_subset__not__subset__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.30/0.47 & ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_not_subset_eq
% 0.30/0.47 thf(fact_202_subset__psubset__trans,axiom,
% 0.30/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less @ ( set @ A ) @ B2 @ C3 )
% 0.30/0.47 => ( ord_less @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_psubset_trans
% 0.30/0.47 thf(fact_203_subset__iff__psubset__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A3 @ B3 )
% 0.30/0.47 | ( A3 = B3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % subset_iff_psubset_eq
% 0.30/0.47 thf(fact_204_less__fun__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( ord @ B )
% 0.30/0.47 => ( ( ord_less @ ( A > B ) )
% 0.30/0.47 = ( ^ [F4: A > B,G2: A > B] :
% 0.30/0.47 ( ( ord_less_eq @ ( A > B ) @ F4 @ G2 )
% 0.30/0.47 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_fun_def
% 0.30/0.47 thf(fact_205_not__Ici__eq__Icc,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( no_top @ A )
% 0.30/0.47 => ! [L3: A,L: A,H: A] :
% 0.30/0.47 ( ( set_ord_atLeast @ A @ L3 )
% 0.30/0.47 != ( set_or331188842AtMost @ A @ L @ H ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_Ici_eq_Icc
% 0.30/0.47 thf(fact_206_not__Iic__eq__Ici,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( no_top @ A )
% 0.30/0.47 => ! [H: A,L3: A] :
% 0.30/0.47 ( ( set_ord_atMost @ A @ H )
% 0.30/0.47 != ( set_ord_atLeast @ A @ L3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_Iic_eq_Ici
% 0.30/0.47 thf(fact_207_strict__monoD,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( ( order @ A )
% 0.30/0.47 & ( order @ B ) )
% 0.30/0.47 => ! [F: A > B,X3: A,Y2: A] :
% 0.30/0.47 ( ( order_strict_mono @ A @ B @ F )
% 0.30/0.47 => ( ( ord_less @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % strict_monoD
% 0.30/0.47 thf(fact_208_strict__monoI,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( ( order @ A )
% 0.30/0.47 & ( order @ B ) )
% 0.30/0.47 => ! [F: A > B] :
% 0.30/0.47 ( ! [X2: A,Y3: A] :
% 0.30/0.47 ( ( ord_less @ A @ X2 @ Y3 )
% 0.30/0.47 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.30/0.47 => ( order_strict_mono @ A @ B @ F ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % strict_monoI
% 0.30/0.47 thf(fact_209_strict__mono__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( ( order @ A )
% 0.30/0.47 & ( order @ B ) )
% 0.30/0.47 => ( ( order_strict_mono @ A @ B )
% 0.30/0.47 = ( ^ [F4: A > B] :
% 0.30/0.47 ! [X4: A,Y4: A] :
% 0.30/0.47 ( ( ord_less @ A @ X4 @ Y4 )
% 0.30/0.47 => ( ord_less @ B @ ( F4 @ X4 ) @ ( F4 @ Y4 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % strict_mono_def
% 0.30/0.47 thf(fact_210_strict__mono__less,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( ( linorder @ A )
% 0.30/0.47 & ( order @ B ) )
% 0.30/0.47 => ! [F: A > B,X3: A,Y2: A] :
% 0.30/0.47 ( ( order_strict_mono @ A @ B @ F )
% 0.30/0.47 => ( ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y2 ) )
% 0.30/0.47 = ( ord_less @ A @ X3 @ Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % strict_mono_less
% 0.30/0.47 thf(fact_211_not__Ici__le__Icc,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( no_top @ A )
% 0.30/0.47 => ! [L: A,L3: A,H2: A] :
% 0.30/0.47 ~ ( ord_less_eq @ ( set @ A ) @ ( set_ord_atLeast @ A @ L ) @ ( set_or331188842AtMost @ A @ L3 @ H2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_Ici_le_Icc
% 0.30/0.47 thf(fact_212_not__Ici__le__Iic,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( no_top @ A )
% 0.30/0.47 => ! [L: A,H2: A] :
% 0.30/0.47 ~ ( ord_less_eq @ ( set @ A ) @ ( set_ord_atLeast @ A @ L ) @ ( set_ord_atMost @ A @ H2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_Ici_le_Iic
% 0.30/0.47 thf(fact_213_not__Iic__le__Ici,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( no_bot @ A )
% 0.30/0.47 => ! [H: A,L3: A] :
% 0.30/0.47 ~ ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ H ) @ ( set_ord_atLeast @ A @ L3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_Iic_le_Ici
% 0.30/0.47 thf(fact_214_compl__le__compl__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( boolean_algebra @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ ( uminus_uminus @ A @ Y2 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % compl_le_compl_iff
% 0.30/0.47 thf(fact_215_neg__le__iff__le,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordered_ab_group_add @ A )
% 0.30/0.47 => ! [B4: A,A4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A4 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ A4 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neg_le_iff_le
% 0.30/0.47 thf(fact_216_compl__mono,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( boolean_algebra @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y2 ) @ ( uminus_uminus @ A @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % compl_mono
% 0.30/0.47 thf(fact_217_compl__le__swap1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( boolean_algebra @ A )
% 0.30/0.47 => ! [Y2: A,X3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ Y2 @ ( uminus_uminus @ A @ X3 ) )
% 0.30/0.47 => ( ord_less_eq @ A @ X3 @ ( uminus_uminus @ A @ Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % compl_le_swap1
% 0.30/0.47 thf(fact_218_compl__le__swap2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( boolean_algebra @ A )
% 0.30/0.47 => ! [Y2: A,X3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y2 ) @ X3 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % compl_le_swap2
% 0.30/0.47 thf(fact_219_psubsetD,axiom,
% 0.30/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C2: A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.47 => ( ( member @ A @ C2 @ A2 )
% 0.30/0.47 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubsetD
% 0.30/0.47 thf(fact_220_psubset__trans,axiom,
% 0.30/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.30/0.47 => ( ( ord_less @ ( set @ A ) @ B2 @ C3 )
% 0.30/0.47 => ( ord_less @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubset_trans
% 0.30/0.47 thf(fact_221_le__imp__neg__le,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordered_ab_group_add @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_imp_neg_le
% 0.30/0.47 thf(fact_222_minus__le__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordered_ab_group_add @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A4 ) @ B4 )
% 0.30/0.47 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minus_le_iff
% 0.30/0.47 thf(fact_223_le__minus__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ordered_ab_group_add @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A4 @ ( uminus_uminus @ A @ B4 ) )
% 0.30/0.47 = ( ord_less_eq @ A @ B4 @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_minus_iff
% 0.30/0.47 thf(fact_224_complete__interval,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( condit1037483654norder @ A )
% 0.30/0.47 => ! [A4: A,B4: A,P: A > $o] :
% 0.30/0.47 ( ( ord_less @ A @ A4 @ B4 )
% 0.30/0.47 => ( ( P @ A4 )
% 0.30/0.47 => ( ~ ( P @ B4 )
% 0.30/0.47 => ? [C4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A4 @ C4 )
% 0.30/0.47 & ( ord_less_eq @ A @ C4 @ B4 )
% 0.30/0.47 & ! [X7: A] :
% 0.30/0.47 ( ( ( ord_less_eq @ A @ A4 @ X7 )
% 0.30/0.47 & ( ord_less @ A @ X7 @ C4 ) )
% 0.30/0.47 => ( P @ X7 ) )
% 0.30/0.47 & ! [D3: A] :
% 0.30/0.47 ( ! [X2: A] :
% 0.30/0.47 ( ( ( ord_less_eq @ A @ A4 @ X2 )
% 0.30/0.47 & ( ord_less @ A @ X2 @ D3 ) )
% 0.30/0.47 => ( P @ X2 ) )
% 0.30/0.47 => ( ord_less_eq @ A @ D3 @ C4 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % complete_interval
% 0.30/0.47 thf(fact_225_pinf_I6_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T2: A] :
% 0.30/0.47 ? [Z3: A] :
% 0.30/0.47 ! [X7: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z3 @ X7 )
% 0.30/0.47 => ~ ( ord_less_eq @ A @ X7 @ T2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(6)
% 0.30/0.47 thf(fact_226_minf_I8_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T2: A] :
% 0.30/0.47 ? [Z3: A] :
% 0.30/0.47 ! [X7: A] :
% 0.30/0.47 ( ( ord_less @ A @ X7 @ Z3 )
% 0.30/0.47 => ~ ( ord_less_eq @ A @ T2 @ X7 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(8)
% 0.30/0.47 thf(fact_227_minf_I6_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T2: A] :
% 0.30/0.47 ? [Z3: A] :
% 0.30/0.47 ! [X7: A] :
% 0.30/0.47 ( ( ord_less @ A @ X7 @ Z3 )
% 0.30/0.47 => ( ord_less_eq @ A @ X7 @ T2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(6)
% 0.30/0.47 thf(fact_228_pinf_I8_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T2: A] :
% 0.30/0.47 ? [Z3: A] :
% 0.30/0.47 ! [X7: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z3 @ X7 )
% 0.30/0.47 => ( ord_less_eq @ A @ T2 @ X7 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(8)
% 0.30/0.47 thf(fact_229_inf__distribI,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( ( complete_Sup @ A )
% 0.30/0.47 & ( bot @ A )
% 0.30/0.47 & ( complete_Sup @ B )
% 0.30/0.47 & ( bot @ B ) )
% 0.30/0.47 => ! [F: A > B] :
% 0.30/0.47 ( ( refine_strict @ A @ B @ F )
% 0.30/0.47 => ( ( refine_cont @ A @ B @ F )
% 0.30/0.47 => ( refine_inf_distrib @ A @ B @ F ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_distribI
% 0.30/0.47 thf(fact_230_inf__distrib__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( ( complete_Sup @ A )
% 0.30/0.47 & ( bot @ A )
% 0.30/0.47 & ( complete_Sup @ B )
% 0.30/0.47 & ( bot @ B ) )
% 0.30/0.47 => ( ( refine_inf_distrib @ A @ B )
% 0.30/0.47 = ( ^ [F4: A > B] :
% 0.30/0.47 ( ( refine_strict @ A @ B @ F4 )
% 0.30/0.47 & ( refine_cont @ A @ B @ F4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_distrib_def
% 0.30/0.47 thf(fact_231_inf__distribD_I2_J,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( ( complete_Sup @ A )
% 0.30/0.47 & ( bot @ A )
% 0.30/0.47 & ( complete_Sup @ B )
% 0.30/0.47 & ( bot @ B ) )
% 0.30/0.47 => ! [F: A > B] :
% 0.30/0.47 ( ( refine_inf_distrib @ A @ B @ F )
% 0.30/0.47 => ( refine_cont @ A @ B @ F ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_distribD(2)
% 0.30/0.47 thf(fact_232_greaterThanLessThan__subseteq__atLeastAtMost__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( dense_linorder @ A )
% 0.30/0.47 => ! [A4: A,B4: A,C2: A,D: A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_or578182835ssThan @ A @ A4 @ B4 ) @ ( set_or331188842AtMost @ A @ C2 @ D ) )
% 0.30/0.47 = ( ( ord_less @ A @ A4 @ B4 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.30/0.47 & ( ord_less_eq @ A @ B4 @ D ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % greaterThanLessThan_subseteq_atLeastAtMost_iff
% 0.30/0.47 thf(fact_233_ivl__disj__un__one_I7_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [L: A,U: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ L @ U )
% 0.30/0.47 => ( ( sup_sup @ ( set @ A ) @ ( set_or331188842AtMost @ A @ L @ U ) @ ( set_ord_greaterThan @ A @ U ) )
% 0.30/0.47 = ( set_ord_atLeast @ A @ L ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ivl_disj_un_one(7)
% 0.30/0.47 thf(fact_234_UnCI,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.30/0.47 ( ( ~ ( member @ A @ C2 @ B2 )
% 0.30/0.47 => ( member @ A @ C2 @ A2 ) )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnCI
% 0.30/0.47 thf(fact_235_Un__iff,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.30/0.47 = ( ( member @ A @ C2 @ A2 )
% 0.30/0.47 | ( member @ A @ C2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_iff
% 0.30/0.47 thf(fact_236_le__sup__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X3: A,Y2: A,Z2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X3 @ Y2 ) @ Z2 )
% 0.30/0.47 = ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.30/0.47 & ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % le_sup_iff
% 0.30/0.47 thf(fact_237_sup_Obounded__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [B4: A,C2: A,A4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A4 )
% 0.30/0.47 = ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.30/0.47 & ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.bounded_iff
% 0.30/0.47 thf(fact_238_Un__subset__iff,axiom,
% 0.30/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.30/0.47 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C3 )
% 0.30/0.47 & ( ord_less_eq @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_subset_iff
% 0.30/0.47 thf(fact_239_greaterThanLessThan__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord @ A )
% 0.30/0.47 => ! [I2: A,L: A,U: A] :
% 0.30/0.47 ( ( member @ A @ I2 @ ( set_or578182835ssThan @ A @ L @ U ) )
% 0.30/0.47 = ( ( ord_less @ A @ L @ I2 )
% 0.30/0.47 & ( ord_less @ A @ I2 @ U ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % greaterThanLessThan_iff
% 0.30/0.47 thf(fact_240_sup_OcoboundedI2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [C2: A,B4: A,A4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.30/0.47 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.coboundedI2
% 0.30/0.47 thf(fact_241_sup_OcoboundedI1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [C2: A,A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.30/0.47 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.coboundedI1
% 0.30/0.47 thf(fact_242_sup_Oabsorb__iff2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ( ( ord_less_eq @ A )
% 0.30/0.47 = ( ^ [A5: A,B5: A] :
% 0.30/0.47 ( ( sup_sup @ A @ A5 @ B5 )
% 0.30/0.47 = B5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.absorb_iff2
% 0.30/0.47 thf(fact_243_sup_Oabsorb__iff1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ( ( ord_less_eq @ A )
% 0.30/0.47 = ( ^ [B5: A,A5: A] :
% 0.30/0.47 ( ( sup_sup @ A @ A5 @ B5 )
% 0.30/0.47 = A5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.absorb_iff1
% 0.30/0.47 thf(fact_244_sup_Ocobounded2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [B4: A,A4: A] : ( ord_less_eq @ A @ B4 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.cobounded2
% 0.30/0.47 thf(fact_245_sup_Ocobounded1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A4: A,B4: A] : ( ord_less_eq @ A @ A4 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.cobounded1
% 0.30/0.47 thf(fact_246_sup_Oorder__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ( ( ord_less_eq @ A )
% 0.30/0.47 = ( ^ [B5: A,A5: A] :
% 0.30/0.47 ( A5
% 0.30/0.47 = ( sup_sup @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.order_iff
% 0.30/0.47 thf(fact_247_sup_OboundedI,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [B4: A,A4: A,C2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.boundedI
% 0.30/0.47 thf(fact_248_sup_OboundedE,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [B4: A,C2: A,A4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A4 )
% 0.30/0.47 => ~ ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.30/0.47 => ~ ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.boundedE
% 0.30/0.47 thf(fact_249_sup__absorb2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X3: A,Y2: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.30/0.47 => ( ( sup_sup @ A @ X3 @ Y2 )
% 0.30/0.47 = Y2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_absorb2
% 0.30/0.47 thf(fact_250_sup__absorb1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [Y2: A,X3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.30/0.47 => ( ( sup_sup @ A @ X3 @ Y2 )
% 0.30/0.47 = X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_absorb1
% 0.30/0.47 thf(fact_251_sup_Oabsorb2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.30/0.47 => ( ( sup_sup @ A @ A4 @ B4 )
% 0.30/0.47 = B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.absorb2
% 0.30/0.47 thf(fact_252_sup_Oabsorb1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [B4: A,A4: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.30/0.47 => ( ( sup_sup @ A @ A4 @ B4 )
% 0.30/0.47 = A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.absorb1
% 0.30/0.47 thf(fact_253_sup__unique,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [F: A > A > A,X3: A,Y2: A] :
% 0.30/0.47 ( ! [X2: A,Y3: A] : ( ord_less_eq @ A @ X2 @ ( F @ X2 @ Y3 ) )
% 0.30/0.47 => ( ! [X2: A,Y3: A] : ( ord_less_eq @ A @ Y3 @ ( F @ X2 @ Y3 ) )
% 0.30/0.47 => ( ! [X2: A,Y3: A,Z3: A] :
% 0.30/0.47 ( ( ord_less_eq @ A @ Y3 @ X2 )
% 0.30/0.47 => ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.30/0.47 => ( ord_less_eq @ A @ ( F @ Y3 @ Z3 ) @ X2 ) ) )
% 0.30/0.47 => ( ( sup_sup @ A @ X3 @ Y2 )
% 0.30/0.47 = ( F @ X3 @ Y2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_unique
% 0.30/0.47 thf(fact_254_sup_OorderI,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A4: A,B4: A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 = ( sup_sup @ A @ A4 @ B4 ) )
% 0.30/0.47 => ( ord_less_eq @ A @ B4 @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.orderI
% 0.30/0.47
% 0.30/0.47 % Subclasses (4)
% 0.30/0.47 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( type @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( ord @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( order @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ( preorder @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % Type constructors (25)
% 0.30/0.47 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( comple187826305attice @ A9 )
% 0.30/0.47 => ( comple187826305attice @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A9 )
% 0.30/0.47 => ( semilattice_sup @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( boolean_algebra @ A9 )
% 0.30/0.47 => ( boolean_algebra @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Complete__Lattices_OSup,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( complete_Sup @ A9 )
% 0.30/0.47 => ( complete_Sup @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( preorder @ A9 )
% 0.30/0.47 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( order @ A9 )
% 0.30/0.47 => ( order @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( ord @ A9 )
% 0.30/0.47 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.47 ! [A8: $tType,A9: $tType] :
% 0.30/0.47 ( ( bot @ A9 )
% 0.30/0.47 => ( bot @ ( A8 > A9 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1,axiom,
% 0.30/0.47 ! [A8: $tType] : ( comple187826305attice @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_2,axiom,
% 0.30/0.47 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_3,axiom,
% 0.30/0.47 ! [A8: $tType] : ( boolean_algebra @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Complete__Lattices_OSup_4,axiom,
% 0.30/0.47 ! [A8: $tType] : ( complete_Sup @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.30/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.30/0.47 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Oord_7,axiom,
% 0.30/0.47 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Obot_8,axiom,
% 0.30/0.47 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_9,axiom,
% 0.30/0.47 comple187826305attice @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_10,axiom,
% 0.30/0.47 semilattice_sup @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_11,axiom,
% 0.30/0.47 boolean_algebra @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Complete__Lattices_OSup_12,axiom,
% 0.30/0.47 complete_Sup @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 0.30/0.47 preorder @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.30/0.47 linorder @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_14,axiom,
% 0.30/0.47 order @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Oord_15,axiom,
% 0.30/0.47 ord @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Obot_16,axiom,
% 0.30/0.47 bot @ $o ).
% 0.30/0.47
% 0.30/0.47 % Helper facts (3)
% 0.30/0.47 thf(help_If_3_1_T,axiom,
% 0.30/0.47 ! [P: $o] :
% 0.30/0.47 ( ( P = $true )
% 0.30/0.47 | ( P = $false ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_2_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,Y2: A] :
% 0.30/0.47 ( ( if @ A @ $false @ X3 @ Y2 )
% 0.30/0.47 = Y2 ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_1_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,Y2: A] :
% 0.30/0.47 ( ( if @ A @ $true @ X3 @ Y2 )
% 0.30/0.47 = X3 ) ).
% 0.30/0.47
% 0.30/0.47 % Free types (1)
% 0.30/0.47 thf(tfree_0,hypothesis,
% 0.30/0.47 linorder @ val ).
% 0.30/0.47
% 0.30/0.47 % Conjectures (1)
% 0.30/0.47 thf(conj_0,conjecture,
% 0.30/0.47 ord_less_eq @ ( set @ val ) @ scc @ p ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 0.31/1.50 ---- Embedded in THF ---
% 0.31/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.50 %%% Generated on Tue Feb 24 08:25:43 EST 2026
% 0.31/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.50 %%% Logic specification used:
% 0.31/1.50 %%% thf(spec, logic, $$dhol).
% 0.31/1.50
% 0.31/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Kpz0KHslZL/DTF2DTF17623.p
% 0.31/1.50 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 0.31/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.31/1.50 thf(ty_tf_val, type, val: $tType).
% 0.31/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Complete__Lattices_OSup, type, complete_Sup: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Complete__Lattices_Ocomplete__lattice, type, comple187826305attice: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 0.31/1.50 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.31/1.50 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 0.31/1.50 thf(sy_c_List_Olist_Orec__list, type, rec_list: (!> [C:$tType,A:$tType]: ((C > ((A > ((list @ A) > (C > C))) > ((list @ A) > C)))))).
% 0.31/1.50 thf(sy_c_Misc_Oswap__args2, type, swap_args2: (!> [B:$tType,C:$tType,A:$tType]: (((B > (C > A)) > (C > (B > A)))))).
% 0.31/1.50 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_Orderings_Oorder__class_OGreatest, type, order_Greatest: (!> [A:$tType]: (((A > $o) > A)))).
% 0.31/1.50 thf(sy_c_Orderings_Oorder__class_Oantimono, type, order_antimono: (!> [A:$tType,B:$tType]: (((A > B) > $o)))).
% 0.31/1.50 thf(sy_c_Orderings_Oorder__class_Ostrict__mono, type, order_strict_mono: (!> [A:$tType,B:$tType]: (((A > B) > $o)))).
% 0.31/1.50 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN, type, refine111645177_ALIGN: (!> [A:$tType,B:$tType]: ((A > (B > $o))))).
% 0.31/1.50 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP, type, refine574149253T_SIMP: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_Refine__Misc_Ocont, type, refine_cont: (!> [A:$tType,B:$tType]: (((A > B) > $o)))).
% 0.31/1.50 thf(sy_c_Refine__Misc_Ogalois__connection, type, refine1150083786ection: (!> [A:$tType,B:$tType]: (((A > B) > ((B > A) > $o))))).
% 0.31/1.50 thf(sy_c_Refine__Misc_Oinf__distrib, type, refine_inf_distrib: (!> [A:$tType,B:$tType]: (((A > B) > $o)))).
% 0.31/1.50 thf(sy_c_Refine__Misc_Ostrict, type, refine_strict: (!> [A:$tType,B:$tType]: (((A > B) > $o)))).
% 0.31/1.50 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc, type, refine551993528up_loc: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 0.31/1.50 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.31/1.50 thf(sy_c_Set__Interval_Oord__class_OatLeast, type, set_ord_atLeast: (!> [A:$tType]: ((A > (set @ A))))).
% 0.31/1.50 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost, type, set_or331188842AtMost: (!> [A:$tType]: ((A > (A > (set @ A)))))).
% 0.31/1.50 thf(sy_c_Set__Interval_Oord__class_OatMost, type, set_ord_atMost: (!> [A:$tType]: ((A > (set @ A))))).
% 0.31/1.50 thf(sy_c_Set__Interval_Oord__class_OgreaterThan, type, set_ord_greaterThan: (!> [A:$tType]: ((A > (set @ A))))).
% 0.31/1.50 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan, type, set_or578182835ssThan: (!> [A:$tType]: ((A > (A > (set @ A)))))).
% 0.31/1.50 thf(sy_c_Set__Interval_Oord__class_OlessThan, type, set_ord_lessThan: (!> [A:$tType]: ((A > (set @ A))))).
% 0.31/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.31/1.50 thf(sy_v_P, type, p: (set @ val)).
% 0.31/1.50 thf(sy_v_scc, type, scc: (set @ val)).
% 0.31/1.50 thf(fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062, axiom, (! [X:val]: (((((member @ val) @ X) @ scc) => (((member @ val) @ X) @ p))))).
% 0.31/1.50 thf(fact_1_subsetI, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A2) => (((member @ A) @ X2) @ B2)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 0.31/1.50 thf(fact_2_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ A2) => (A2 = B2)))))).
% 0.31/1.50 thf(fact_3_order__mono__setup_Orefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 0.31/1.50 thf(fact_4_relprop__triggers_I6_J, axiom, (! [I:$tType,R:(set @ I),R2:(set @ I)]: (((((ord_less_eq @ (set @ I)) @ R) @ R2) => (((ord_less_eq @ (set @ I)) @ R) @ R2))))).
% 0.31/1.50 thf(fact_5_in__mono, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B2)))))).
% 0.31/1.50 thf(fact_6_subsetD, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B2)))))).
% 0.31/1.50 thf(fact_7_equalityE, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => (~ ((((ord_less_eq @ (set @ A)) @ B2) @ A2)))))))))).
% 0.31/1.50 thf(fact_8_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: ((! [X4:A]: (((((member @ A) @ X4) @ A3) => (((member @ A) @ X4) @ B3)))))))))).
% 0.31/1.50 thf(fact_9_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 0.31/1.50 thf(fact_10_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((A2 = B2) => (((ord_less_eq @ (set @ A)) @ B2) @ A2))))).
% 0.31/1.50 thf(fact_11_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A3) => (((member @ A) @ T) @ B3)))))))))).
% 0.31/1.50 thf(fact_12_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 0.31/1.50 thf(fact_13_order__mono__setup_Omono__let, axiom, (! [A:$tType,B:$tType]: (((preorder @ A) => (! [F:(B > A),F2:(B > A),X3:B]: (((! [X2:B]: ((((ord_less_eq @ A) @ (F @ X2)) @ (F2 @ X2)))) => (((ord_less_eq @ A) @ (F @ X3)) @ (F2 @ X3))))))))).
% 0.31/1.50 thf(fact_14_order__mono__setup_Omono__if, axiom, (! [A:$tType]: (((preorder @ A) => (! [T2:A,T3:A,E:A,E2:A,B4:$o]: (((((ord_less_eq @ A) @ T2) @ T3) => ((((ord_less_eq @ A) @ E) @ E2) => (((ord_less_eq @ A) @ ((((if @ A) @ B4) @ T2) @ E)) @ ((((if @ A) @ B4) @ T3) @ E2)))))))))).
% 0.31/1.50 thf(fact_15_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X4:A]: (((P @ X4) => (Q @ X4)))))))).
% 0.31/1.50 thf(fact_16_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y:(set @ A),Z:(set @ A)]: ((Y = Z))) = (^ [A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) & (((ord_less_eq @ (set @ A)) @ B3) @ A3)))))))).
% 0.31/1.50 thf(fact_17_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C3) => (((ord_less_eq @ (set @ A)) @ A2) @ C3)))))).
% 0.31/1.50 thf(fact_18_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) => (Q @ X2)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 0.31/1.50 thf(fact_19_subset__Collect__conv, axiom, (! [A:$tType,S:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ S) @ ((collect @ A) @ P)) = (! [X4:A]: (((((member @ A) @ X4) @ S) => (P @ X4)))))))).
% 0.31/1.50 thf(fact_20_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A]: (((((ord_less_eq @ A) @ B4) @ A4) => ((((ord_less_eq @ A) @ A4) @ B4) => (A4 = B4))))))))).
% 0.31/1.50 thf(fact_21_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ B5) @ A5) & (((ord_less_eq @ A) @ A5) @ B5))))))))).
% 0.31/1.50 thf(fact_22_transfer_Otransfer__Let, axiom, (! [C:$tType,A:$tType,B:$tType]: (((comple187826305attice @ A) => (! [Alpha:(C > A),F:(B > C),F3:(B > A),X3:B]: (((! [X2:B]: ((((ord_less_eq @ A) @ (Alpha @ (F @ X2))) @ (F3 @ X2)))) => (((ord_less_eq @ A) @ (Alpha @ (F @ X3))) @ (F3 @ X3))))))))).
% 0.31/1.50 thf(fact_23_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A,C2:A]: (((((ord_less_eq @ A) @ B4) @ A4) => ((((ord_less_eq @ A) @ C2) @ B4) => (((ord_less_eq @ A) @ C2) @ A4))))))))).
% 0.31/1.50 thf(fact_24_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A4:A,B4:A]: (((! [A6:A,B6:A]: (((((ord_less_eq @ A) @ A6) @ B6) => ((P @ A6) @ B6)))) => ((! [A6:A,B6:A]: ((((P @ B6) @ A6) => ((P @ A6) @ B6)))) => ((P @ A4) @ B4))))))))).
% 0.31/1.50 thf(fact_25_transfer_Otransfer__if, axiom, (! [C:$tType,A:$tType]: (((comple187826305attice @ A) => (! [B4:$o,Alpha:(C > A),S1:C,S12:A,S2:C,S22:A]: (((B4 => (((ord_less_eq @ A) @ (Alpha @ S1)) @ S12)) => (((~ (B4)) => (((ord_less_eq @ A) @ (Alpha @ S2)) @ S22)) => (((ord_less_eq @ A) @ (Alpha @ ((((if @ C) @ B4) @ S1) @ S2))) @ ((((if @ A) @ B4) @ S12) @ S22)))))))))).
% 0.31/1.50 thf(fact_26_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A]: ((((ord_less_eq @ A) @ A4) @ A4))))))).
% 0.31/1.50 thf(fact_27_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 0.31/1.50 thf(fact_28_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((((ord_less_eq @ A) @ B4) @ A4) => (A4 = B4))))))))).
% 0.31/1.50 thf(fact_29_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((B4 = C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 0.31/1.50 thf(fact_30_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3))))))))).
% 0.31/1.50 thf(fact_31_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3))))))))).
% 0.31/1.50 thf(fact_32_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X2:A]: ((((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 0.31/1.50 thf(fact_33_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F4:(A > B),G2:(A > B)]: ((! [X4:A]: ((((ord_less_eq @ B) @ (F4 @ X4)) @ (G2 @ X4))))))))))).
% 0.31/1.50 thf(fact_34_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((((ord_less_eq @ A) @ A4) @ (F @ B4)) => ((((ord_less_eq @ B) @ B4) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A4) @ (F @ C2))))))))))).
% 0.31/1.50 thf(fact_35_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A4:A,B4:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A4) @ B4) => ((((ord_less_eq @ C) @ (F @ B4)) @ C2) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ C) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ C) @ (F @ A4)) @ C2)))))))))).
% 0.31/1.50 thf(fact_36_ord__eq__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B4:A,C2:A,D:A]: (((A4 = B4) => ((((ord_less_eq @ A) @ B4) @ C2) => ((C2 = D) => (((ord_less_eq @ A) @ A4) @ D)))))))))).
% 0.31/1.50 thf(fact_37_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((A4 = (F @ B4)) => ((((ord_less_eq @ B) @ B4) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A4) @ (F @ C2))))))))))).
% 0.31/1.50 thf(fact_38_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,B4:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A4) @ B4) => (((F @ B4) = C2) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ B) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ B) @ (F @ A4)) @ C2)))))))))).
% 0.31/1.50 thf(fact_39_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) & (((ord_less_eq @ A) @ Y4) @ X4))))))))).
% 0.31/1.50 thf(fact_40_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X3) => (X3 = Y2))))))))).
% 0.31/1.50 thf(fact_41_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.31/1.50 thf(fact_42_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((X3 = Y2) => (((ord_less_eq @ A) @ X3) @ Y2)))))))).
% 0.31/1.50 thf(fact_43_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.31/1.50 thf(fact_44_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((((ord_less_eq @ A) @ B4) @ C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 0.31/1.50 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 0.31/1.50 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A2)))) = A2)))).
% 0.31/1.50 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.31/1.50 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 0.31/1.50 thf(fact_49_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z2)))) => (((((ord_less_eq @ A) @ Y2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y2)))) => (((((ord_less_eq @ A) @ Z2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X3)))) => (((((ord_less_eq @ A) @ Y2) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y2))))))))))))))))).
% 0.31/1.50 thf(fact_50_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X3:A]: (((((ord_less_eq @ A) @ Y2) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y2) = (X3 = Y2))))))))).
% 0.31/1.50 thf(fact_51_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) & (((ord_less_eq @ A) @ B5) @ A5))))))))).
% 0.31/1.50 thf(fact_52_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B4:A,C2:A]: (((A4 = B4) => ((((ord_less_eq @ A) @ B4) @ C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 0.31/1.50 thf(fact_53_GreatestI2__order, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X3:A,Q:(A > $o)]: (((P @ X3) => ((! [Y3:A]: (((P @ Y3) => (((ord_less_eq @ A) @ Y3) @ X3)))) => ((! [X2:A]: (((P @ X2) => ((! [Y5:A]: (((P @ Y5) => (((ord_less_eq @ A) @ Y5) @ X2)))) => (Q @ X2))))) => (Q @ ((order_Greatest @ A) @ P))))))))))).
% 0.31/1.50 thf(fact_54_Greatest__equality, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X3:A]: (((P @ X3) => ((! [Y3:A]: (((P @ Y3) => (((ord_less_eq @ A) @ Y3) @ X3)))) => (((order_Greatest @ A) @ P) = X3))))))))).
% 0.31/1.50 thf(fact_55_Refine__Misc_Oif__mono, axiom, (! [A:$tType]: (((ord @ A) => (! [B4:$o,M1:A,M12:A,M2:A,M22:A]: (((B4 => (((ord_less_eq @ A) @ M1) @ M12)) => (((~ (B4)) => (((ord_less_eq @ A) @ M2) @ M22)) => (((ord_less_eq @ A) @ ((((if @ A) @ B4) @ M1) @ M2)) @ ((((if @ A) @ B4) @ M12) @ M22)))))))))).
% 0.31/1.50 thf(fact_56_lhs__step__If, axiom, (! [A:$tType]: (((ord @ A) => (! [B4:$o,T2:A,M:A,E:A]: (((B4 => (((ord_less_eq @ A) @ T2) @ M)) => (((~ (B4)) => (((ord_less_eq @ A) @ E) @ M)) => (((ord_less_eq @ A) @ ((((if @ A) @ B4) @ T2) @ E)) @ M))))))))).
% 0.31/1.50 thf(fact_57_verit__la__disequality, axiom, (! [A:$tType]: (((linorder @ A) => (! [A4:A,B4:A]: (((A4 = B4) | ((~ ((((ord_less_eq @ A) @ A4) @ B4))) | (~ ((((ord_less_eq @ A) @ B4) @ A4))))))))))).
% 0.31/1.50 thf(fact_58_le__rel__bool__arg__iff, axiom, (! [A:$tType]: (((ord @ A) => ((ord_less_eq @ ($o > A)) = (^ [X5:($o > A),Y6:($o > A)]: (((((ord_less_eq @ A) @ (X5 @ $false)) @ (Y6 @ $false)) & (((ord_less_eq @ A) @ (X5 @ $true)) @ (Y6 @ $true)))))))))).
% 0.31/1.50 thf(fact_59_antimonoD, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (! [F:(A > B),X3:A,Y2:A]: (((((order_antimono @ A) @ B) @ F) => ((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ B) @ (F @ Y2)) @ (F @ X3)))))))))).
% 0.31/1.50 thf(fact_60_antimonoE, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (! [F:(A > B),X3:A,Y2:A]: (((((order_antimono @ A) @ B) @ F) => ((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ B) @ (F @ Y2)) @ (F @ X3)))))))))).
% 0.31/1.50 thf(fact_61_antimono__def, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (((order_antimono @ A) @ B) = (^ [F4:(A > B)]: ((! [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) => (((ord_less_eq @ B) @ (F4 @ Y4)) @ (F4 @ X4)))))))))))).
% 0.31/1.50 thf(fact_62_antimonoI, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (! [F:(A > B)]: (((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ B) @ (F @ Y3)) @ (F @ X2))))) => (((order_antimono @ A) @ B) @ F)))))))).
% 0.31/1.50 thf(fact_63_order__mono__setup_Omono__setup__loc__axioms, axiom, (! [A:$tType]: (((preorder @ A) => ((refine551993528up_loc @ A) @ (ord_less_eq @ A)))))).
% 0.31/1.50 thf(fact_64_swap__args2__def, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((swap_args2 @ B) @ C) @ A) = (^ [F4:(B > (C > A)),X4:C,Y4:B]: (((F4 @ Y4) @ X4))))))).
% 0.31/1.50 thf(fact_65_galois__connection_O_092_060gamma_062_092_060alpha_062__infl, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) & (comple187826305attice @ B)) => (! [Alpha:(A > B),Gamma:(B > A),X3:A]: ((((((refine1150083786ection @ A) @ B) @ Alpha) @ Gamma) => (((ord_less_eq @ A) @ X3) @ (Gamma @ (Alpha @ X3)))))))))).
% 0.31/1.50 thf(fact_66_galois__connection_O_092_060alpha_062_092_060gamma_062__defl, axiom, (! [A:$tType,B:$tType]: ((((comple187826305attice @ B) & (comple187826305attice @ A)) => (! [Alpha:(A > B),Gamma:(B > A),X3:B]: ((((((refine1150083786ection @ A) @ B) @ Alpha) @ Gamma) => (((ord_less_eq @ B) @ (Alpha @ (Gamma @ X3))) @ X3)))))))).
% 0.31/1.50 thf(fact_67_galois__connection_Ogalois, axiom, (! [A:$tType,B:$tType]: ((((comple187826305attice @ B) & (comple187826305attice @ A)) => (! [Alpha:(A > B),Gamma:(B > A),C2:A,A4:B]: ((((((refine1150083786ection @ A) @ B) @ Alpha) @ Gamma) => ((((ord_less_eq @ A) @ C2) @ (Gamma @ A4)) = (((ord_less_eq @ B) @ (Alpha @ C2)) @ A4))))))))).
% 0.31/1.50 thf(fact_68_galois__connection_Ointro, axiom, (! [A:$tType,B:$tType]: ((((comple187826305attice @ B) & (comple187826305attice @ A)) => (! [Gamma:(B > A),Alpha:(A > B)]: (((! [C4:A,A6:B]: (((((ord_less_eq @ A) @ C4) @ (Gamma @ A6)) = (((ord_less_eq @ B) @ (Alpha @ C4)) @ A6)))) => ((((refine1150083786ection @ A) @ B) @ Alpha) @ Gamma)))))))).
% 0.31/1.50 thf(fact_69_galois__connection__def, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) & (comple187826305attice @ B)) => (((refine1150083786ection @ A) @ B) = (^ [Alpha2:(A > B),Gamma2:(B > A)]: ((! [C5:A,A5:B]: (((((ord_less_eq @ A) @ C5) @ (Gamma2 @ A5)) = (((ord_less_eq @ B) @ (Alpha2 @ C5)) @ A5))))))))))).
% 0.31/1.50 thf(fact_70_mono__setup__loc__def, axiom, (! [A:$tType]: (((refine551993528up_loc @ A) = (^ [Le:(A > (A > $o))]: ((! [X4:A]: (((Le @ X4) @ X4))))))))).
% 0.31/1.50 thf(fact_71_mono__setup__loc_Orefl, axiom, (! [A:$tType,Le2:(A > (A > $o)),X3:A]: ((((refine551993528up_loc @ A) @ Le2) => ((Le2 @ X3) @ X3))))).
% 0.31/1.50 thf(fact_72_mono__setup__loc_Ointro, axiom, (! [A:$tType,Le2:(A > (A > $o))]: (((! [X2:A]: (((Le2 @ X2) @ X2))) => ((refine551993528up_loc @ A) @ Le2))))).
% 0.31/1.50 thf(fact_73_mono__setup__loc_Omono__if, axiom, (! [A:$tType,Le2:(A > (A > $o)),T2:A,T3:A,E:A,E2:A,B4:$o]: ((((refine551993528up_loc @ A) @ Le2) => (((Le2 @ T2) @ T3) => (((Le2 @ E) @ E2) => ((Le2 @ ((((if @ A) @ B4) @ T2) @ E)) @ ((((if @ A) @ B4) @ T3) @ E2)))))))).
% 0.31/1.50 thf(fact_74_mono__setup__loc_Omono__let, axiom, (! [A:$tType,B:$tType,Le2:(A > (A > $o)),F:(B > A),F2:(B > A),X3:B]: ((((refine551993528up_loc @ A) @ Le2) => ((! [X2:B]: (((Le2 @ (F @ X2)) @ (F2 @ X2)))) => ((Le2 @ (F @ X3)) @ (F2 @ X3))))))).
% 0.31/1.50 thf(fact_75_galois__connection_Oinf__dist___092_060alpha_062, axiom, (! [B:$tType,A:$tType]: ((((comple187826305attice @ A) & (comple187826305attice @ B)) => (! [Alpha:(A > B),Gamma:(B > A)]: ((((((refine1150083786ection @ A) @ B) @ Alpha) @ Gamma) => (((refine_inf_distrib @ A) @ B) @ Alpha)))))))).
% 0.31/1.50 thf(fact_76_strict__mono__less__eq, axiom, (! [B:$tType,A:$tType]: ((((linorder @ A) & (order @ B)) => (! [F:(A > B),X3:A,Y2:A]: (((((order_strict_mono @ A) @ B) @ F) => ((((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y2)) = (((ord_less_eq @ A) @ X3) @ Y2))))))))).
% 0.31/1.50 thf(fact_77_greaterThan__subset__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ (set @ A)) @ ((set_ord_greaterThan @ A) @ X3)) @ ((set_ord_greaterThan @ A) @ Y2)) = (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.31/1.50 thf(fact_78_START__REFINEG__TRANSFER, axiom, (! [A:$tType]: (((ord @ A) => (! [D:A,C2:A,A4:A]: ((((((refine111645177_ALIGN @ A) @ A) @ D) @ C2) => ((((ord_less_eq @ A) @ C2) @ A4) => ((((refine574149253T_SIMP @ A) @ C2) @ D) => (((ord_less_eq @ A) @ D) @ A4)))))))))).
% 0.31/1.50 thf(fact_79_lessThan__subset__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ (set @ A)) @ ((set_ord_lessThan @ A) @ X3)) @ ((set_ord_lessThan @ A) @ Y2)) = (((ord_less_eq @ A) @ X3) @ Y2)))))))).
% 0.31/1.50 thf(fact_80_transfer_Otransfer__rec__list, axiom, (! [C:$tType,D2:$tType,A:$tType,B:$tType]: (((comple187826305attice @ A) => (! [Alpha:(C > A),Fn:(B > C),Fn2:(B > A),Fc:(D2 > ((list @ D2) > ((B > C) > (B > C)))),Fc2:(D2 > ((list @ D2) > ((B > A) > (B > A)))),L:(list @ D2),S3:B]: (((! [S4:B]: ((((ord_less_eq @ A) @ (Alpha @ (Fn @ S4))) @ (Fn2 @ S4)))) => ((! [X2:D2,L2:(list @ D2),Rec:(B > C),Rec2:(B > A),S4:B]: (((! [Sa:B]: ((((ord_less_eq @ A) @ (Alpha @ (Rec @ Sa))) @ (Rec2 @ Sa)))) => (((ord_less_eq @ A) @ (Alpha @ ((((Fc @ X2) @ L2) @ Rec) @ S4))) @ ((((Fc2 @ X2) @ L2) @ Rec2) @ S4))))) => (((ord_less_eq @ A) @ (Alpha @ ((((((rec_list @ (B > C)) @ D2) @ Fn) @ Fc) @ L) @ S3))) @ ((((((rec_list @ (B > A)) @ D2) @ Fn2) @ Fc2) @ L) @ S3)))))))))).
% 0.31/1.50 thf(fact_81_atLeast__subset__iff, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ (set @ A)) @ ((set_ord_atLeast @ A) @ X3)) @ ((set_ord_atLeast @ A) @ Y2)) = (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.31/1.50 thf(fact_82_lessThan__eq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((set_ord_lessThan @ A) @ X3) = ((set_ord_lessThan @ A) @ Y2)) = (X3 = Y2)))))))).
% 0.31/1.50 thf(fact_83_atLeast__eq__iff, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((set_ord_atLeast @ A) @ X3) = ((set_ord_atLeast @ A) @ Y2)) = (X3 = Y2)))))))).
% 0.31/1.50 thf(fact_84_greaterThan__eq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((set_ord_greaterThan @ A) @ X3) = ((set_ord_greaterThan @ A) @ Y2)) = (X3 = Y2)))))))).
% 0.31/1.50 thf(fact_85_atLeast__iff, axiom, (! [A:$tType]: (((ord @ A) => (! [I2:A,K:A]: (((((member @ A) @ I2) @ ((set_ord_atLeast @ A) @ K)) = (((ord_less_eq @ A) @ K) @ I2)))))))).
% 0.31/1.50 thf(fact_86_strict__mono__eq, axiom, (! [B:$tType,A:$tType]: ((((linorder @ A) & (order @ B)) => (! [F:(A > B),X3:A,Y2:A]: (((((order_strict_mono @ A) @ B) @ F) => (((F @ X3) = (F @ Y2)) = (X3 = Y2))))))))).
% 0.31/1.50 thf(fact_87_Ioi__le__Ico, axiom, (! [A:$tType]: (((preorder @ A) => (! [A4:A]: ((((ord_less_eq @ (set @ A)) @ ((set_ord_greaterThan @ A) @ A4)) @ ((set_ord_atLeast @ A) @ A4)))))))).
% 0.31/1.50 thf(fact_88_STOP__REFINEG__TRANSFER, axiom, (! [A:$tType,C2:A]: ((((refine574149253T_SIMP @ A) @ C2) @ C2)))).
% 0.31/1.50 thf(fact_89_REFINEG__TRANSFER__ALIGNI, axiom, (! [A:$tType,B:$tType,X3:A,Y2:B]: (((((refine111645177_ALIGN @ A) @ B) @ X3) @ Y2)))).
% 0.31/1.50 thf(fact_90_REFINEG__TRANSFER__ALIGN__def, axiom, (! [B:$tType,A:$tType]: ((((refine111645177_ALIGN @ A) @ B) = (^ [X4:A,Y4:B]: ($true)))))).
% 0.31/1.50 thf(fact_91_REFINEG__TRANSFER__POST__SIMP__def, axiom, (! [A:$tType]: (((refine574149253T_SIMP @ A) = (^ [Y:A,Z:A]: ((Y = Z))))))).
% 0.31/1.50 thf(fact_92_Ici__subset__Ioi__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [A4:A,B4:A]: (((((ord_less_eq @ (set @ A)) @ ((set_ord_atLeast @ A) @ A4)) @ ((set_ord_greaterThan @ A) @ B4)) = (((ord_less @ A) @ B4) @ A4)))))))).
% 0.31/1.50 thf(fact_93_Icc__subset__Ici__iff, axiom, (! [A:$tType]: (((preorder @ A) => (! [L:A,H:A,L3:A]: (((((ord_less_eq @ (set @ A)) @ (((set_or331188842AtMost @ A) @ L) @ H)) @ ((set_ord_atLeast @ A) @ L3)) = ((~ ((((ord_less_eq @ A) @ L) @ H))) | (((ord_less_eq @ A) @ L3) @ L))))))))).
% 0.31/1.50 thf(fact_94_inf__distribD_I1_J, axiom, (! [B:$tType,A:$tType]: ((((complete_Sup @ A) & ((bot @ A) & ((complete_Sup @ B) & (bot @ B)))) => (! [F:(A > B)]: (((((refine_inf_distrib @ A) @ B) @ F) => (((refine_strict @ A) @ B) @ F)))))))).
% 0.31/1.50 thf(fact_95_Compl__atLeast, axiom, (! [A:$tType]: (((linorder @ A) => (! [K:A]: ((((uminus_uminus @ (set @ A)) @ ((set_ord_atLeast @ A) @ K)) = ((set_ord_lessThan @ A) @ K)))))))).
% 0.31/1.50 thf(fact_96_Compl__lessThan, axiom, (! [A:$tType]: (((linorder @ A) => (! [K:A]: ((((uminus_uminus @ (set @ A)) @ ((set_ord_lessThan @ A) @ K)) = ((set_ord_atLeast @ A) @ K)))))))).
% 0.31/1.50 thf(fact_97_atMost__subset__iff, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ (set @ A)) @ ((set_ord_atMost @ A) @ X3)) @ ((set_ord_atMost @ A) @ Y2)) = (((ord_less_eq @ A) @ X3) @ Y2)))))))).
% 0.31/1.50 thf(fact_98_psubsetI, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((A2 != B2) => (((ord_less @ (set @ A)) @ A2) @ B2)))))).
% 0.31/1.50 thf(fact_99_verit__minus__simplify_I4_J, axiom, (! [B:$tType]: (((group_add @ B) => (! [B4:B]: ((((uminus_uminus @ B) @ ((uminus_uminus @ B) @ B4)) = B4))))))).
% 0.31/1.50 thf(fact_100_atMost__eq__iff, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((set_ord_atMost @ A) @ X3) = ((set_ord_atMost @ A) @ Y2)) = (X3 = Y2)))))))).
% 0.31/1.50 thf(fact_101_ComplI, axiom, (! [A:$tType,C2:A,A2:(set @ A)]: (((~ ((((member @ A) @ C2) @ A2))) => (((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A2)))))).
% 0.31/1.50 thf(fact_102_Compl__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A2)) = (~ ((((member @ A) @ C2) @ A2))))))).
% 0.31/1.50 thf(fact_103_Compl__eq__Compl__iff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A2) = ((uminus_uminus @ (set @ A)) @ B2)) = (A2 = B2))))).
% 0.31/1.50 thf(fact_104_atLeastAtMost__iff, axiom, (! [A:$tType]: (((ord @ A) => (! [I2:A,L:A,U:A]: (((((member @ A) @ I2) @ (((set_or331188842AtMost @ A) @ L) @ U)) = ((((ord_less_eq @ A) @ L) @ I2) & (((ord_less_eq @ A) @ I2) @ U))))))))).
% 0.31/1.50 thf(fact_105_Icc__eq__Icc, axiom, (! [A:$tType]: (((order @ A) => (! [L:A,H:A,L3:A,H2:A]: ((((((set_or331188842AtMost @ A) @ L) @ H) = (((set_or331188842AtMost @ A) @ L3) @ H2)) = (((L = L3) & (H = H2)) | ((~ ((((ord_less_eq @ A) @ L) @ H))) & (~ ((((ord_less_eq @ A) @ L3) @ H2)))))))))))).
% 0.31/1.50 thf(fact_106_atMost__iff, axiom, (! [A:$tType]: (((ord @ A) => (! [I2:A,K:A]: (((((member @ A) @ I2) @ ((set_ord_atMost @ A) @ K)) = (((ord_less_eq @ A) @ I2) @ K)))))))).
% 0.31/1.50 thf(fact_107_lessThan__iff, axiom, (! [A:$tType]: (((ord @ A) => (! [I2:A,K:A]: (((((member @ A) @ I2) @ ((set_ord_lessThan @ A) @ K)) = (((ord_less @ A) @ I2) @ K)))))))).
% 0.31/1.50 thf(fact_108_Compl__anti__mono, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => (((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ B2)) @ ((uminus_uminus @ (set @ A)) @ A2)))))).
% 0.31/1.50 thf(fact_109_Compl__subset__Compl__iff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) @ ((uminus_uminus @ (set @ A)) @ B2)) = (((ord_less_eq @ (set @ A)) @ B2) @ A2))))).
% 0.31/1.50 thf(fact_110_greaterThan__iff, axiom, (! [A:$tType]: (((ord @ A) => (! [I2:A,K:A]: (((((member @ A) @ I2) @ ((set_ord_greaterThan @ A) @ K)) = (((ord_less @ A) @ K) @ I2)))))))).
% 0.31/1.50 thf(fact_111_atLeastatMost__subset__iff, axiom, (! [A:$tType]: (((preorder @ A) => (! [A4:A,B4:A,C2:A,D:A]: (((((ord_less_eq @ (set @ A)) @ (((set_or331188842AtMost @ A) @ A4) @ B4)) @ (((set_or331188842AtMost @ A) @ C2) @ D)) = ((~ ((((ord_less_eq @ A) @ A4) @ B4))) | ((((ord_less_eq @ A) @ C2) @ A4) & (((ord_less_eq @ A) @ B4) @ D)))))))))).
% 0.31/1.50 thf(fact_112_Compl__atMost, axiom, (! [A:$tType]: (((linorder @ A) => (! [K:A]: ((((uminus_uminus @ (set @ A)) @ ((set_ord_atMost @ A) @ K)) = ((set_ord_greaterThan @ A) @ K)))))))).
% 0.31/1.50 thf(fact_113_Compl__greaterThan, axiom, (! [A:$tType]: (((linorder @ A) => (! [K:A]: ((((uminus_uminus @ (set @ A)) @ ((set_ord_greaterThan @ A) @ K)) = ((set_ord_atMost @ A) @ K)))))))).
% 0.31/1.50 thf(fact_114_Icc__subset__Iic__iff, axiom, (! [A:$tType]: (((preorder @ A) => (! [L:A,H:A,H2:A]: (((((ord_less_eq @ (set @ A)) @ (((set_or331188842AtMost @ A) @ L) @ H)) @ ((set_ord_atMost @ A) @ H2)) = ((~ ((((ord_less_eq @ A) @ L) @ H))) | (((ord_less_eq @ A) @ H) @ H2))))))))).
% 0.31/1.50 thf(fact_115_lessThan__strict__subset__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [M:A,N:A]: (((((ord_less @ (set @ A)) @ ((set_ord_lessThan @ A) @ M)) @ ((set_ord_lessThan @ A) @ N)) = (((ord_less @ A) @ M) @ N)))))))).
% 0.31/1.50 thf(fact_116_not__Iic__eq__Icc, axiom, (! [A:$tType]: (((no_bot @ A) => (! [H2:A,L:A,H:A]: ((((set_ord_atMost @ A) @ H2) != (((set_or331188842AtMost @ A) @ L) @ H)))))))).
% 0.31/1.50 thf(fact_117_not__Iic__le__Icc, axiom, (! [A:$tType]: (((no_bot @ A) => (! [H:A,L3:A,H2:A]: ((~ ((((ord_less_eq @ (set @ A)) @ ((set_ord_atMost @ A) @ H)) @ (((set_or331188842AtMost @ A) @ L3) @ H2)))))))))).
% 0.31/1.50 thf(fact_118_atLeastatMost__psubset__iff, axiom, (! [A:$tType]: (((preorder @ A) => (! [A4:A,B4:A,C2:A,D:A]: (((((ord_less @ (set @ A)) @ (((set_or331188842AtMost @ A) @ A4) @ B4)) @ (((set_or331188842AtMost @ A) @ C2) @ D)) = (((~ ((((ord_less_eq @ A) @ A4) @ B4))) | ((((ord_less_eq @ A) @ C2) @ A4) & ((((ord_less_eq @ A) @ B4) @ D) & ((((ord_less @ A) @ C2) @ A4) | (((ord_less @ A) @ B4) @ D))))) & (((ord_less_eq @ A) @ C2) @ D))))))))).
% 0.31/1.50 thf(fact_119_verit__comp__simplify1_I1_J, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A]: ((~ ((((ord_less @ A) @ A4) @ A4))))))))).
% 0.31/1.50 thf(fact_120_verit__negate__coefficient_I3_J, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B4:A]: (((A4 = B4) => (((uminus_uminus @ A) @ A4) = ((uminus_uminus @ A) @ B4))))))))).
% 0.31/1.50 thf(fact_121_verit__negate__coefficient_I2_J, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B4:A]: (((((ord_less @ A) @ A4) @ B4) => (((ord_less @ A) @ ((uminus_uminus @ A) @ B4)) @ ((uminus_uminus @ A) @ A4))))))))).
% 0.31/1.50 thf(fact_122_all__nat__split__at, axiom, (! [A:$tType]: (((linorder @ A) => (! [K:A,P:(A > $o)]: (((! [I3:A]: (((((ord_less @ A) @ I3) @ K) => (P @ I3)))) => ((P @ K) => ((! [I3:A]: (((((ord_less @ A) @ K) @ I3) => (P @ I3)))) => (! [X_1:A]: ((P @ X_1)))))))))))).
% 0.31/1.50 thf(fact_123_ComplD, axiom, (! [A:$tType,C2:A,A2:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A2)) => (~ ((((member @ A) @ C2) @ A2))))))).
% 0.31/1.50 thf(fact_124_double__complement, axiom, (! [A:$tType,A2:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) = A2)))).
% 0.31/1.50 thf(fact_125_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((A4 = (F @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less @ B) @ X2) @ Y3) => (((ord_less @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 0.31/1.50 thf(fact_126_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,B4:A,F:(A > B),C2:B]: (((((ord_less @ A) @ A4) @ B4) => (((F @ B4) = C2) => ((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ B) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ B) @ (F @ A4)) @ C2)))))))))).
% 0.31/1.50 thf(fact_127_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((((ord_less @ A) @ A4) @ (F @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less @ B) @ X2) @ Y3) => (((ord_less @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 0.31/1.50 thf(fact_128_order__less__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A4:A,B4:A,F:(A > C),C2:C]: (((((ord_less @ A) @ A4) @ B4) => ((((ord_less @ C) @ (F @ B4)) @ C2) => ((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ C) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ C) @ (F @ A4)) @ C2)))))))))).
% 0.31/1.50 thf(fact_129_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X3:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X3))))))))).
% 0.31/1.50 thf(fact_130_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X3:A]: ((? [X_12:A]: ((((ord_less @ A) @ X3) @ X_12))))))))).
% 0.31/1.50 thf(fact_131_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((X3 != Y2) => ((~ ((((ord_less @ A) @ X3) @ Y2))) => (((ord_less @ A) @ Y2) @ X3))))))))).
% 0.31/1.50 thf(fact_132_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((X3 != Y2) = ((((ord_less @ A) @ X3) @ Y2) | (((ord_less @ A) @ Y2) @ X3))))))))).
% 0.31/1.50 thf(fact_133_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A]: (((((ord_less @ A) @ A4) @ B4) => (~ ((((ord_less @ A) @ B4) @ A4)))))))))).
% 0.31/1.50 thf(fact_134_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (? [Z3:A]: (((((ord_less @ A) @ X3) @ Z3) & (((ord_less @ A) @ Z3) @ Y2))))))))))).
% 0.31/1.50 thf(fact_135_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (X3 != Y2)))))))).
% 0.31/1.50 thf(fact_136_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 0.31/1.50 thf(fact_137_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A4:A,B4:A]: (((((ord_less @ A) @ A4) @ B4) => (~ ((((ord_less @ A) @ B4) @ A4)))))))))).
% 0.31/1.50 thf(fact_138_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ Z2) => (((ord_less @ A) @ X3) @ Z2))))))))).
% 0.31/1.50 thf(fact_139_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) | ((X3 = Y2) | (((ord_less @ A) @ Y2) @ X3))))))))).
% 0.31/1.50 thf(fact_140_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((~ ((((ord_less @ A) @ X3) @ X3))))))))).
% 0.31/1.50 thf(fact_141_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B4:A,C2:A]: (((A4 = B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 0.31/1.50 thf(fact_142_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B4:A,C2:A]: (((((ord_less @ A) @ A4) @ B4) => ((B4 = C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 0.31/1.50 thf(fact_143_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A]: (((((ord_less @ A) @ B4) @ A4) => (~ ((((ord_less @ A) @ A4) @ B4)))))))))).
% 0.31/1.50 thf(fact_144_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (X3 != Y2)))))))).
% 0.31/1.50 thf(fact_145_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 0.31/1.50 thf(fact_146_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A4:A]: (((! [X2:A]: (((! [Y5:A]: (((((ord_less @ A) @ Y5) @ X2) => (P @ Y5)))) => (P @ X2)))) => (P @ A4)))))))).
% 0.31/1.50 thf(fact_147_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y2:A,X3:A]: (((~ ((((ord_less @ A) @ Y2) @ X3))) => ((~ ((((ord_less @ A) @ X3) @ Y2))) = (X3 = Y2))))))))).
% 0.31/1.50 thf(fact_148_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (Y2 != X3)))))))).
% 0.31/1.50 thf(fact_149_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,P:$o]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ X3) => P)))))))).
% 0.31/1.50 thf(fact_150_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => ((X3 != Y2) => (((ord_less @ A) @ Y2) @ X3))))))))).
% 0.31/1.50 thf(fact_151_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A]: ((~ ((((ord_less @ A) @ A4) @ A4))))))))).
% 0.31/1.50 thf(fact_152_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A,C2:A]: (((((ord_less @ A) @ A4) @ B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 0.31/1.50 thf(fact_153_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 0.31/1.50 thf(fact_154_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P2:(A > $o)]: ((? [X6:A]: ((P2 @ X6))))) = (^ [P3:(A > $o)]: ((? [N2:A]: (((P3 @ N2) & (! [M3:A]: (((((ord_less @ A) @ M3) @ N2) => (~ ((P3 @ M3)))))))))))))))).
% 0.31/1.50 thf(fact_155_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A4:A,B4:A]: (((! [A6:A,B6:A]: (((((ord_less @ A) @ A6) @ B6) => ((P @ A6) @ B6)))) => ((! [A6:A]: (((P @ A6) @ A6))) => ((! [A6:A,B6:A]: ((((P @ B6) @ A6) => ((P @ A6) @ B6)))) => ((P @ A4) @ B4)))))))))).
% 0.31/1.50 thf(fact_156_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A,C2:A]: (((((ord_less @ A) @ B4) @ A4) => ((((ord_less @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ A4))))))))).
% 0.31/1.50 thf(fact_157_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) = ((((ord_less @ A) @ Y2) @ X3) | (X3 = Y2))))))))).
% 0.31/1.50 thf(fact_158_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A]: (((((ord_less @ A) @ A4) @ B4) => (A4 != B4)))))))).
% 0.31/1.50 thf(fact_159_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A]: (((((ord_less @ A) @ B4) @ A4) => (A4 != B4)))))))).
% 0.31/1.50 thf(fact_160_Iic__subset__Iio__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [A4:A,B4:A]: (((((ord_less_eq @ (set @ A)) @ ((set_ord_atMost @ A) @ A4)) @ ((set_ord_lessThan @ A) @ B4)) = (((ord_less @ A) @ A4) @ B4)))))))).
% 0.31/1.50 thf(fact_161_leD, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X3:A]: (((((ord_less_eq @ A) @ Y2) @ X3) => (~ ((((ord_less @ A) @ X3) @ Y2)))))))))).
% 0.31/1.50 thf(fact_162_leI, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.31/1.50 thf(fact_163_le__less, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [X4:A,Y4:A]: (((((ord_less @ A) @ X4) @ Y4) | (X4 = Y4))))))))).
% 0.31/1.50 thf(fact_164_less__le, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) & (X4 != Y4))))))))).
% 0.31/1.50 thf(fact_165_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((((ord_less_eq @ A) @ A4) @ (F @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less @ B) @ X2) @ Y3) => (((ord_less @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 0.31/1.50 thf(fact_166_order__le__less__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A4:A,B4:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A4) @ B4) => ((((ord_less @ C) @ (F @ B4)) @ C2) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ C) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ C) @ (F @ A4)) @ C2)))))))))).
% 0.31/1.50 thf(fact_167_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A4:A,F:(B > A),B4:B,C2:B]: (((((ord_less @ A) @ A4) @ (F @ B4)) => ((((ord_less_eq @ B) @ B4) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 0.31/1.50 thf(fact_168_order__less__le__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A4:A,B4:A,F:(A > C),C2:C]: (((((ord_less @ A) @ A4) @ B4) => ((((ord_less_eq @ C) @ (F @ B4)) @ C2) => ((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ C) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ C) @ (F @ A4)) @ C2)))))))))).
% 0.31/1.50 thf(fact_169_not__le, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y2))) = (((ord_less @ A) @ Y2) @ X3)))))))).
% 0.31/1.50 thf(fact_170_not__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) = (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.31/1.50 thf(fact_171_le__neq__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((A4 != B4) => (((ord_less @ A) @ A4) @ B4))))))))).
% 0.31/1.50 thf(fact_172_antisym__conv1, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => ((((ord_less_eq @ A) @ X3) @ Y2) = (X3 = Y2))))))))).
% 0.31/1.50 thf(fact_173_antisym__conv2, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((~ ((((ord_less @ A) @ X3) @ Y2))) = (X3 = Y2))))))))).
% 0.31/1.50 thf(fact_174_less__imp__le, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (((ord_less_eq @ A) @ X3) @ Y2)))))))).
% 0.31/1.50 thf(fact_175_le__less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ Z2) => (((ord_less @ A) @ X3) @ Z2))))))))).
% 0.31/1.50 thf(fact_176_less__le__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z2) => (((ord_less @ A) @ X3) @ Z2))))))))).
% 0.31/1.50 thf(fact_177_dense__ge, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z2:A,Y2:A]: (((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => (((ord_less_eq @ A) @ Y2) @ X2)))) => (((ord_less_eq @ A) @ Y2) @ Z2)))))))).
% 0.31/1.50 thf(fact_178_dense__le, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Y2:A,Z2:A]: (((! [X2:A]: (((((ord_less @ A) @ X2) @ Y2) => (((ord_less_eq @ A) @ X2) @ Z2)))) => (((ord_less_eq @ A) @ Y2) @ Z2)))))))).
% 0.31/1.50 thf(fact_179_le__less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) | (((ord_less @ A) @ Y2) @ X3)))))))).
% 0.31/1.50 thf(fact_180_le__imp__less__or__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less @ A) @ X3) @ Y2) | (X3 = Y2))))))))).
% 0.31/1.50 thf(fact_181_less__le__not__le, axiom, (! [A:$tType]: (((preorder @ A) => ((ord_less @ A) = (^ [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) & (~ ((((ord_less_eq @ A) @ Y4) @ X4))))))))))).
% 0.31/1.50 thf(fact_182_not__le__imp__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y2:A,X3:A]: (((~ ((((ord_less_eq @ A) @ Y2) @ X3))) => (((ord_less @ A) @ X3) @ Y2)))))))).
% 0.31/1.50 thf(fact_183_order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 0.31/1.50 thf(fact_184_order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A,C2:A]: (((((ord_less @ A) @ A4) @ B4) => ((((ord_less_eq @ A) @ B4) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 0.31/1.50 thf(fact_185_order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [A5:A,B5:A]: (((((ord_less @ A) @ A5) @ B5) | (A5 = B5))))))))).
% 0.31/1.50 thf(fact_186_order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) & (A5 != B5))))))))).
% 0.31/1.50 thf(fact_187_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A,C2:A]: (((((ord_less_eq @ A) @ B4) @ A4) => ((((ord_less @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ A4))))))))).
% 0.31/1.50 thf(fact_188_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A,C2:A]: (((((ord_less @ A) @ B4) @ A4) => ((((ord_less_eq @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ A4))))))))).
% 0.31/1.50 thf(fact_189_dense__ge__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z2:A,X3:A,Y2:A]: (((((ord_less @ A) @ Z2) @ X3) => ((! [W:A]: (((((ord_less @ A) @ Z2) @ W) => ((((ord_less @ A) @ W) @ X3) => (((ord_less_eq @ A) @ Y2) @ W))))) => (((ord_less_eq @ A) @ Y2) @ Z2))))))))).
% 0.31/1.50 thf(fact_190_dense__le__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less @ A) @ X3) @ Y2) => ((! [W:A]: (((((ord_less @ A) @ X3) @ W) => ((((ord_less @ A) @ W) @ Y2) => (((ord_less_eq @ A) @ W) @ Z2))))) => (((ord_less_eq @ A) @ Y2) @ Z2))))))))).
% 0.31/1.50 thf(fact_191_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A]: (((((ord_less @ A) @ A4) @ B4) => (((ord_less_eq @ A) @ A4) @ B4)))))))).
% 0.31/1.50 thf(fact_192_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B5:A,A5:A]: (((((ord_less @ A) @ B5) @ A5) | (A5 = B5))))))))).
% 0.31/1.50 thf(fact_193_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B5:A,A5:A]: (((((ord_less_eq @ A) @ B5) @ A5) & (A5 != B5))))))))).
% 0.31/1.50 thf(fact_194_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A4:A]: (((((ord_less @ A) @ B4) @ A4) => (((ord_less_eq @ A) @ B4) @ A4)))))))).
% 0.31/1.50 thf(fact_195_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B4:A]: (((A4 != B4) => ((((ord_less_eq @ A) @ A4) @ B4) => (((ord_less @ A) @ A4) @ B4))))))))).
% 0.31/1.50 thf(fact_196_verit__comp__simplify1_I3_J, axiom, (! [B:$tType]: (((linorder @ B) => (! [B7:B,A7:B]: (((~ ((((ord_less_eq @ B) @ B7) @ A7))) = (((ord_less @ B) @ A7) @ B7)))))))).
% 0.31/1.50 thf(fact_197_psubsetE, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B2) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => (((ord_less_eq @ (set @ A)) @ B2) @ A2)))))))).
% 0.31/1.50 thf(fact_198_psubset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) & (A3 != B3)))))))).
% 0.31/1.50 thf(fact_199_psubset__imp__subset, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B2) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 0.31/1.50 thf(fact_200_psubset__subset__trans, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C3) => (((ord_less @ (set @ A)) @ A2) @ C3)))))).
% 0.31/1.50 thf(fact_201_subset__not__subset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) & (~ ((((ord_less_eq @ (set @ A)) @ B3) @ A3)))))))))).
% 0.31/1.50 thf(fact_202_subset__psubset__trans, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less @ (set @ A)) @ B2) @ C3) => (((ord_less @ (set @ A)) @ A2) @ C3)))))).
% 0.31/1.50 thf(fact_203_subset__iff__psubset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B3:(set @ A)]: (((((ord_less @ (set @ A)) @ A3) @ B3) | (A3 = B3)))))))).
% 0.31/1.50 thf(fact_204_less__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less @ (A > B)) = (^ [F4:(A > B),G2:(A > B)]: (((((ord_less_eq @ (A > B)) @ F4) @ G2) & (~ ((((ord_less_eq @ (A > B)) @ G2) @ F4))))))))))).
% 0.31/1.50 thf(fact_205_not__Ici__eq__Icc, axiom, (! [A:$tType]: (((no_top @ A) => (! [L3:A,L:A,H:A]: ((((set_ord_atLeast @ A) @ L3) != (((set_or331188842AtMost @ A) @ L) @ H)))))))).
% 0.31/1.50 thf(fact_206_not__Iic__eq__Ici, axiom, (! [A:$tType]: (((no_top @ A) => (! [H:A,L3:A]: ((((set_ord_atMost @ A) @ H) != ((set_ord_atLeast @ A) @ L3)))))))).
% 0.31/1.50 thf(fact_207_strict__monoD, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (! [F:(A > B),X3:A,Y2:A]: (((((order_strict_mono @ A) @ B) @ F) => ((((ord_less @ A) @ X3) @ Y2) => (((ord_less @ B) @ (F @ X3)) @ (F @ Y2)))))))))).
% 0.31/1.50 thf(fact_208_strict__monoI, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (! [F:(A > B)]: (((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ B) @ (F @ X2)) @ (F @ Y3))))) => (((order_strict_mono @ A) @ B) @ F)))))))).
% 0.31/1.50 thf(fact_209_strict__mono__def, axiom, (! [B:$tType,A:$tType]: ((((order @ A) & (order @ B)) => (((order_strict_mono @ A) @ B) = (^ [F4:(A > B)]: ((! [X4:A,Y4:A]: (((((ord_less @ A) @ X4) @ Y4) => (((ord_less @ B) @ (F4 @ X4)) @ (F4 @ Y4)))))))))))).
% 0.31/1.50 thf(fact_210_strict__mono__less, axiom, (! [B:$tType,A:$tType]: ((((linorder @ A) & (order @ B)) => (! [F:(A > B),X3:A,Y2:A]: (((((order_strict_mono @ A) @ B) @ F) => ((((ord_less @ B) @ (F @ X3)) @ (F @ Y2)) = (((ord_less @ A) @ X3) @ Y2))))))))).
% 0.31/1.50 thf(fact_211_not__Ici__le__Icc, axiom, (! [A:$tType]: (((no_top @ A) => (! [L:A,L3:A,H2:A]: ((~ ((((ord_less_eq @ (set @ A)) @ ((set_ord_atLeast @ A) @ L)) @ (((set_or331188842AtMost @ A) @ L3) @ H2)))))))))).
% 0.31/1.50 thf(fact_212_not__Ici__le__Iic, axiom, (! [A:$tType]: (((no_top @ A) => (! [L:A,H2:A]: ((~ ((((ord_less_eq @ (set @ A)) @ ((set_ord_atLeast @ A) @ L)) @ ((set_ord_atMost @ A) @ H2)))))))))).
% 0.31/1.50 thf(fact_213_not__Iic__le__Ici, axiom, (! [A:$tType]: (((no_bot @ A) => (! [H:A,L3:A]: ((~ ((((ord_less_eq @ (set @ A)) @ ((set_ord_atMost @ A) @ H)) @ ((set_ord_atLeast @ A) @ L3)))))))))).
% 0.31/1.50 thf(fact_214_compl__le__compl__iff, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X3)) @ ((uminus_uminus @ A) @ Y2)) = (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 0.31/1.50 thf(fact_215_neg__le__iff__le, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B4:A,A4:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B4)) @ ((uminus_uminus @ A) @ A4)) = (((ord_less_eq @ A) @ A4) @ B4)))))))).
% 0.31/1.50 thf(fact_216_compl__mono, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y2)) @ ((uminus_uminus @ A) @ X3))))))))).
% 0.31/1.50 thf(fact_217_compl__le__swap1, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y2:A,X3:A]: (((((ord_less_eq @ A) @ Y2) @ ((uminus_uminus @ A) @ X3)) => (((ord_less_eq @ A) @ X3) @ ((uminus_uminus @ A) @ Y2))))))))).
% 0.31/1.50 thf(fact_218_compl__le__swap2, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y2:A,X3:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y2)) @ X3) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X3)) @ Y2)))))))).
% 0.31/1.50 thf(fact_219_psubsetD, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C2:A]: (((((ord_less @ (set @ A)) @ A2) @ B2) => ((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B2)))))).
% 0.31/1.50 thf(fact_220_psubset__trans, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B2) => ((((ord_less @ (set @ A)) @ B2) @ C3) => (((ord_less @ (set @ A)) @ A2) @ C3)))))).
% 0.31/1.50 thf(fact_221_le__imp__neg__le, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B4)) @ ((uminus_uminus @ A) @ A4))))))))).
% 0.31/1.50 thf(fact_222_minus__le__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B4:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ A4)) @ B4) = (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B4)) @ A4)))))))).
% 0.31/1.50 thf(fact_223_le__minus__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ ((uminus_uminus @ A) @ B4)) = (((ord_less_eq @ A) @ B4) @ ((uminus_uminus @ A) @ A4))))))))).
% 0.31/1.50 thf(fact_224_complete__interval, axiom, (! [A:$tType]: (((condit1037483654norder @ A) => (! [A4:A,B4:A,P:(A > $o)]: (((((ord_less @ A) @ A4) @ B4) => ((P @ A4) => ((~ ((P @ B4))) => (? [C4:A]: (((((ord_less_eq @ A) @ A4) @ C4) & ((((ord_less_eq @ A) @ C4) @ B4) & ((! [X7:A]: ((((((ord_less_eq @ A) @ A4) @ X7) & (((ord_less @ A) @ X7) @ C4)) => (P @ X7)))) & (! [D3:A]: (((! [X2:A]: ((((((ord_less_eq @ A) @ A4) @ X2) & (((ord_less @ A) @ X2) @ D3)) => (P @ X2)))) => (((ord_less_eq @ A) @ D3) @ C4)))))))))))))))))).
% 0.31/1.50 thf(fact_225_pinf_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z3:A]: ((! [X7:A]: (((((ord_less @ A) @ Z3) @ X7) => (~ ((((ord_less_eq @ A) @ X7) @ T2)))))))))))))).
% 0.31/1.50 thf(fact_226_minf_I8_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z3:A]: ((! [X7:A]: (((((ord_less @ A) @ X7) @ Z3) => (~ ((((ord_less_eq @ A) @ T2) @ X7)))))))))))))).
% 0.31/1.50 thf(fact_227_minf_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z3:A]: ((! [X7:A]: (((((ord_less @ A) @ X7) @ Z3) => (((ord_less_eq @ A) @ X7) @ T2)))))))))))).
% 0.31/1.50 thf(fact_228_pinf_I8_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z3:A]: ((! [X7:A]: (((((ord_less @ A) @ Z3) @ X7) => (((ord_less_eq @ A) @ T2) @ X7)))))))))))).
% 0.31/1.50 thf(fact_229_inf__distribI, axiom, (! [B:$tType,A:$tType]: ((((complete_Sup @ A) & ((bot @ A) & ((complete_Sup @ B) & (bot @ B)))) => (! [F:(A > B)]: (((((refine_strict @ A) @ B) @ F) => ((((refine_cont @ A) @ B) @ F) => (((refine_inf_distrib @ A) @ B) @ F))))))))).
% 0.31/1.50 thf(fact_230_inf__distrib__def, axiom, (! [B:$tType,A:$tType]: ((((complete_Sup @ A) & ((bot @ A) & ((complete_Sup @ B) & (bot @ B)))) => (((refine_inf_distrib @ A) @ B) = (^ [F4:(A > B)]: (((((refine_strict @ A) @ B) @ F4) & (((refine_cont @ A) @ B) @ F4))))))))).
% 0.31/1.50 thf(fact_231_inf__distribD_I2_J, axiom, (! [B:$tType,A:$tType]: ((((complete_Sup @ A) & ((bot @ A) & ((complete_Sup @ B) & (bot @ B)))) => (! [F:(A > B)]: (((((refine_inf_distrib @ A) @ B) @ F) => (((refine_cont @ A) @ B) @ F)))))))).
% 0.31/1.50 thf(fact_232_greaterThanLessThan__subseteq__atLeastAtMost__iff, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [A4:A,B4:A,C2:A,D:A]: (((((ord_less_eq @ (set @ A)) @ (((set_or578182835ssThan @ A) @ A4) @ B4)) @ (((set_or331188842AtMost @ A) @ C2) @ D)) = ((((ord_less @ A) @ A4) @ B4) => ((((ord_less_eq @ A) @ C2) @ A4) & (((ord_less_eq @ A) @ B4) @ D)))))))))).
% 0.31/1.50 thf(fact_233_ivl__disj__un__one_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [L:A,U:A]: (((((ord_less_eq @ A) @ L) @ U) => ((((sup_sup @ (set @ A)) @ (((set_or331188842AtMost @ A) @ L) @ U)) @ ((set_ord_greaterThan @ A) @ U)) = ((set_ord_atLeast @ A) @ L))))))))).
% 0.31/1.50 thf(fact_234_UnCI, axiom, (! [A:$tType,C2:A,B2:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ A2)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 0.31/1.50 thf(fact_235_Un__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C2) @ A2) | (((member @ A) @ C2) @ B2)))))).
% 0.31/1.50 thf(fact_236_le__sup__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ X3) @ Y2)) @ Z2) = ((((ord_less_eq @ A) @ X3) @ Z2) & (((ord_less_eq @ A) @ Y2) @ Z2))))))))).
% 0.31/1.50 thf(fact_237_sup_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B4:A,C2:A,A4:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B4) @ C2)) @ A4) = ((((ord_less_eq @ A) @ B4) @ A4) & (((ord_less_eq @ A) @ C2) @ A4))))))))).
% 0.31/1.50 thf(fact_238_Un__subset__iff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C3) = ((((ord_less_eq @ (set @ A)) @ A2) @ C3) & (((ord_less_eq @ (set @ A)) @ B2) @ C3)))))).
% 0.31/1.50 thf(fact_239_greaterThanLessThan__iff, axiom, (! [A:$tType]: (((ord @ A) => (! [I2:A,L:A,U:A]: (((((member @ A) @ I2) @ (((set_or578182835ssThan @ A) @ L) @ U)) = ((((ord_less @ A) @ L) @ I2) & (((ord_less @ A) @ I2) @ U))))))))).
% 0.31/1.50 thf(fact_240_sup_OcoboundedI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C2:A,B4:A,A4:A]: (((((ord_less_eq @ A) @ C2) @ B4) => (((ord_less_eq @ A) @ C2) @ (((sup_sup @ A) @ A4) @ B4))))))))).
% 0.31/1.50 thf(fact_241_sup_OcoboundedI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C2:A,A4:A,B4:A]: (((((ord_less_eq @ A) @ C2) @ A4) => (((ord_less_eq @ A) @ C2) @ (((sup_sup @ A) @ A4) @ B4))))))))).
% 0.31/1.50 thf(fact_242_sup_Oabsorb__iff2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [A5:A,B5:A]: (((((sup_sup @ A) @ A5) @ B5) = B5)))))))).
% 0.31/1.50 thf(fact_243_sup_Oabsorb__iff1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B5:A,A5:A]: (((((sup_sup @ A) @ A5) @ B5) = A5)))))))).
% 0.31/1.50 thf(fact_244_sup_Ocobounded2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B4:A,A4:A]: ((((ord_less_eq @ A) @ B4) @ (((sup_sup @ A) @ A4) @ B4)))))))).
% 0.31/1.50 thf(fact_245_sup_Ocobounded1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A4:A,B4:A]: ((((ord_less_eq @ A) @ A4) @ (((sup_sup @ A) @ A4) @ B4)))))))).
% 0.31/1.50 thf(fact_246_sup_Oorder__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B5:A,A5:A]: ((A5 = (((sup_sup @ A) @ A5) @ B5))))))))).
% 0.31/1.50 thf(fact_247_sup_OboundedI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B4:A,A4:A,C2:A]: (((((ord_less_eq @ A) @ B4) @ A4) => ((((ord_less_eq @ A) @ C2) @ A4) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ B4) @ C2)) @ A4))))))))).
% 0.31/1.50 thf(fact_248_sup_OboundedE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B4:A,C2:A,A4:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B4) @ C2)) @ A4) => (~ (((((ord_less_eq @ A) @ B4) @ A4) => (~ ((((ord_less_eq @ A) @ C2) @ A4))))))))))))).
% 0.31/1.50 thf(fact_249_sup__absorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((sup_sup @ A) @ X3) @ Y2) = Y2)))))))).
% 0.31/1.50 thf(fact_250_sup__absorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y2:A,X3:A]: (((((ord_less_eq @ A) @ Y2) @ X3) => ((((sup_sup @ A) @ X3) @ Y2) = X3)))))))).
% 0.31/1.50 thf(fact_251_sup_Oabsorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((((sup_sup @ A) @ A4) @ B4) = B4)))))))).
% 0.31/1.50 thf(fact_252_sup_Oabsorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B4:A,A4:A]: (((((ord_less_eq @ A) @ B4) @ A4) => ((((sup_sup @ A) @ A4) @ B4) = A4)))))))).
% 0.31/1.50 thf(fact_253_sup__unique, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [F:(A > (A > A)),X3:A,Y2:A]: (((! [X2:A,Y3:A]: ((((ord_less_eq @ A) @ X2) @ ((F @ X2) @ Y3)))) => ((! [X2:A,Y3:A]: ((((ord_less_eq @ A) @ Y3) @ ((F @ X2) @ Y3)))) => ((! [X2:A,Y3:A,Z3:A]: (((((ord_less_eq @ A) @ Y3) @ X2) => ((((ord_less_eq @ A) @ Z3) @ X2) => (((ord_less_eq @ A) @ ((F @ Y3) @ Z3)) @ X2))))) => ((((sup_sup @ A) @ X3) @ Y2) = ((F @ X3) @ Y2))))))))))).
% 0.31/1.50 thf(fact_254_sup_OorderI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A4:A,B4:A]: (((A4 = (((sup_sup @ A) @ A4) @ B4)) => (((ord_less_eq @ A) @ B4) @ A4)))))))).
% 0.31/1.50 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: (((linorder @ A) => (type @ A))))).
% 0.31/1.50 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: (((linorder @ A) => (ord @ A))))).
% 0.31/1.50 thf(subcl_Orderings_Olinorder___Orderings_Oorder, axiom, (! [A:$tType]: (((linorder @ A) => (order @ A))))).
% 0.31/1.50 thf(subcl_Orderings_Olinorder___Orderings_Opreorder, axiom, (! [A:$tType]: (((linorder @ A) => (preorder @ A))))).
% 0.31/1.51 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice, axiom, (! [A8:$tType,A9:$tType]: (((comple187826305attice @ A9) => (comple187826305attice @ (A8 > A9)))))).
% 0.31/1.51 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A8:$tType,A9:$tType]: (((semilattice_sup @ A9) => (semilattice_sup @ (A8 > A9)))))).
% 0.31/1.51 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A8:$tType,A9:$tType]: (((boolean_algebra @ A9) => (boolean_algebra @ (A8 > A9)))))).
% 0.31/1.51 thf(tcon_fun___Complete__Lattices_OSup, axiom, (! [A8:$tType,A9:$tType]: (((complete_Sup @ A9) => (complete_Sup @ (A8 > A9)))))).
% 0.31/1.51 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 0.31/1.51 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 0.31/1.51 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 0.31/1.51 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: (((bot @ A9) => (bot @ (A8 > A9)))))).
% 0.31/1.51 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1, axiom, (! [A8:$tType]: ((comple187826305attice @ (set @ A8))))).
% 0.31/1.51 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_2, axiom, (! [A8:$tType]: ((semilattice_sup @ (set @ A8))))).
% 0.31/1.51 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_3, axiom, (! [A8:$tType]: ((boolean_algebra @ (set @ A8))))).
% 0.31/1.51 thf(tcon_Set_Oset___Complete__Lattices_OSup_4, axiom, (! [A8:$tType]: ((complete_Sup @ (set @ A8))))).
% 0.31/1.51 thf(tcon_Set_Oset___Orderings_Opreorder_5, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 0.31/1.51 thf(tcon_Set_Oset___Orderings_Oorder_6, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 0.31/1.51 thf(tcon_Set_Oset___Orderings_Oord_7, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 0.31/1.51 thf(tcon_Set_Oset___Orderings_Obot_8, axiom, (! [A8:$tType]: ((bot @ (set @ A8))))).
% 0.31/1.51 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_9, axiom, (comple187826305attice @ $o)).
% 0.31/1.51 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_10, axiom, (semilattice_sup @ $o)).
% 0.31/1.51 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_11, axiom, (boolean_algebra @ $o)).
% 0.31/1.51 thf(tcon_HOL_Obool___Complete__Lattices_OSup_12, axiom, (complete_Sup @ $o)).
% 0.31/1.51 thf(tcon_HOL_Obool___Orderings_Opreorder_13, axiom, (preorder @ $o)).
% 0.31/1.51 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 0.31/1.51 thf(tcon_HOL_Obool___Orderings_Oorder_14, axiom, (order @ $o)).
% 0.31/1.51 thf(tcon_HOL_Obool___Orderings_Oord_15, axiom, (ord @ $o)).
% 0.31/1.51 thf(tcon_HOL_Obool___Orderings_Obot_16, axiom, (bot @ $o)).
% 0.31/1.51 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.31/1.51 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y2:A]: ((((((if @ A) @ $false) @ X3) @ Y2) = Y2)))).
% 0.31/1.51 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y2:A]: ((((((if @ A) @ $true) @ X3) @ Y2) = X3)))).
% 0.31/1.51 thf(tfree_0, hypothesis, (linorder @ val)).
% 0.31/1.51 thf(conj_0, conjecture, (((ord_less_eq @ (set @ val)) @ scc) @ p)).
% 0.31/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.Kpz0KHslZL/DTF2DTF17623.p
% 0.31/1.51 ------------------------
% 0.31/1.54 ---- Cleaned THF ---
% 0.31/1.54 thf(ty_t_List_Olist,type,
% 0.31/1.54 list: $tType > $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_t_Set_Oset,type,
% 0.31/1.54 set: $tType > $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_tf_val,type,
% 0.31/1.54 val: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_HOL_Otype,type,
% 0.31/1.54 type:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Obot,type,
% 0.31/1.54 bot:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Oord,type,
% 0.31/1.54 ord:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Oorder,type,
% 0.31/1.54 order:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Ogroup__add,type,
% 0.31/1.54 group_add:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Ono__bot,type,
% 0.31/1.54 no_bot:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Ono__top,type,
% 0.31/1.54 no_top:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/1.54 linorder:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Opreorder,type,
% 0.31/1.54 preorder:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Owellorder,type,
% 0.31/1.54 wellorder:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Complete__Lattices_OSup,type,
% 0.31/1.54 complete_Sup:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Odense__order,type,
% 0.31/1.54 dense_order:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.31/1.54 boolean_algebra:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.31/1.54 semilattice_sup:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.31/1.54 dense_linorder:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.31/1.54 ordered_ab_group_add:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 0.31/1.54 comple187826305attice:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.31/1.54 condit1037483654norder:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.31/1.54 uminus_uminus:
% 0.31/1.54 !>[A: $tType] : ( A > A ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_If,type,
% 0.31/1.54 if:
% 0.31/1.54 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.31/1.54 sup_sup:
% 0.31/1.54 !>[A: $tType] : ( A > A > A ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_List_Olist_Orec__list,type,
% 0.31/1.54 rec_list:
% 0.31/1.54 !>[C: $tType,A: $tType] : ( C > ( A > ( list @ A ) > C > C ) > ( list @ A ) > C ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Misc_Oswap__args2,type,
% 0.31/1.54 swap_args2:
% 0.31/1.54 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C > A ) > C > B > A ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.31/1.54 ord_less:
% 0.31/1.54 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/1.54 ord_less_eq:
% 0.31/1.54 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.31/1.54 order_Greatest:
% 0.31/1.54 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oorder__class_Oantimono,type,
% 0.31/1.54 order_antimono:
% 0.31/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oorder__class_Ostrict__mono,type,
% 0.31/1.54 order_strict_mono:
% 0.31/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN,type,
% 0.31/1.54 refine111645177_ALIGN:
% 0.31/1.54 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP,type,
% 0.31/1.54 refine574149253T_SIMP:
% 0.31/1.54 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Refine__Misc_Ocont,type,
% 0.31/1.54 refine_cont:
% 0.31/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Refine__Misc_Ogalois__connection,type,
% 0.31/1.54 refine1150083786ection:
% 0.31/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > ( B > A ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Refine__Misc_Oinf__distrib,type,
% 0.31/1.54 refine_inf_distrib:
% 0.31/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Refine__Misc_Ostrict,type,
% 0.31/1.54 refine_strict:
% 0.31/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc,type,
% 0.31/1.54 refine551993528up_loc:
% 0.31/1.54 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Set_OCollect,type,
% 0.31/1.54 collect:
% 0.31/1.54 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Set__Interval_Oord__class_OatLeast,type,
% 0.31/1.54 set_ord_atLeast:
% 0.31/1.54 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost,type,
% 0.31/1.54 set_or331188842AtMost:
% 0.31/1.54 !>[A: $tType] : ( A > A > ( set @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Set__Interval_Oord__class_OatMost,type,
% 0.31/1.54 set_ord_atMost:
% 0.31/1.54 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Set__Interval_Oord__class_OgreaterThan,type,
% 0.31/1.54 set_ord_greaterThan:
% 0.31/1.54 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan,type,
% 0.31/1.54 set_or578182835ssThan:
% 0.31/1.54 !>[A: $tType] : ( A > A > ( set @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Set__Interval_Oord__class_OlessThan,type,
% 0.31/1.54 set_ord_lessThan:
% 0.31/1.54 !>[A: $tType] : ( A > ( set @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_member,type,
% 0.31/1.54 member:
% 0.31/1.54 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_P,type,
% 0.31/1.54 p: set @ val ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_scc,type,
% 0.31/1.54 scc: set @ val ).
% 0.31/1.54
% 0.31/1.54 thf(fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062,axiom,
% 0.31/1.54 ! [X: val] :
% 0.31/1.54 ( ( member @ val @ X @ scc )
% 0.31/1.54 => ( member @ val @ X @ p ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_1_subsetI,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ! [X2: A] :
% 0.31/1.54 ( ( member @ A @ X2 @ A2 )
% 0.31/1.54 => ( member @ A @ X2 @ B2 ) )
% 0.31/1.54 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_2_subset__antisym,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.31/1.54 => ( A2 = B2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_3_order__mono__setup_Orefl,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_4_relprop__triggers_I6_J,axiom,
% 0.31/1.54 ! [I: $tType,R: set @ I,R2: set @ I] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ I ) @ R @ R2 )
% 0.31/1.54 => ( ord_less_eq @ ( set @ I ) @ R @ R2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_5_in__mono,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A,X3: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ( member @ A @ X3 @ A2 )
% 0.31/1.54 => ( member @ A @ X3 @ B2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_6_subsetD,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A,C2: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ( member @ A @ C2 @ A2 )
% 0.31/1.54 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_7_equalityE,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( A2 = B2 )
% 0.31/1.54 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_8_subset__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.54 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.54 ! [X4: A] :
% 0.31/1.54 ( ( member @ A @ X4 @ A3 )
% 0.31/1.54 => ( member @ A @ X4 @ B3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_9_equalityD1,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( A2 = B2 )
% 0.31/1.54 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_10_equalityD2,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( A2 = B2 )
% 0.31/1.54 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_11_subset__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.54 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.54 ! [T: A] :
% 0.31/1.54 ( ( member @ A @ T @ A3 )
% 0.31/1.54 => ( member @ A @ T @ B3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_12_subset__refl,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_13_order__mono__setup_Omono__let,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [F: B > A,F2: B > A,X3: B] :
% 0.31/1.54 ( ! [X2: B] : ( ord_less_eq @ A @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.31/1.54 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F2 @ X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_14_order__mono__setup_Omono__if,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [T2: A,T3: A,E: A,E2: A,B4: $o] :
% 0.31/1.54 ( ( ord_less_eq @ A @ T2 @ T3 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ E @ E2 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( if @ A @ B4 @ T2 @ E ) @ ( if @ A @ B4 @ T3 @ E2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_15_Collect__mono__iff,axiom,
% 0.31/1.54 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.31/1.54 = ( ! [X4: A] :
% 0.31/1.54 ( ( P @ X4 )
% 0.31/1.54 => ( Q @ X4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_16_set__eq__subset,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ^ [Y: set @ A,Z: set @ A] : ( Y = Z ) )
% 0.31/1.54 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.54 & ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_17_subset__trans,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.31/1.54 => ( ord_less_eq @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_18_Collect__mono,axiom,
% 0.31/1.54 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.54 ( ! [X2: A] :
% 0.31/1.54 ( ( P @ X2 )
% 0.31/1.54 => ( Q @ X2 ) )
% 0.31/1.54 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_19_subset__Collect__conv,axiom,
% 0.31/1.54 ! [A: $tType,S: set @ A,P: A > $o] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 0.31/1.54 = ( ! [X4: A] :
% 0.31/1.54 ( ( member @ A @ X4 @ S )
% 0.31/1.54 => ( P @ X4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_20_dual__order_Oantisym,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [B4: A,A4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( A4 = B4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_21_dual__order_Oeq__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.31/1.54 = ( ^ [A5: A,B5: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.31/1.54 & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_22_transfer_Otransfer__Let,axiom,
% 0.31/1.54 ! [C: $tType,A: $tType,B: $tType] :
% 0.31/1.54 ( ( comple187826305attice @ A )
% 0.31/1.54 => ! [Alpha: C > A,F: B > C,F3: B > A,X3: B] :
% 0.31/1.54 ( ! [X2: B] : ( ord_less_eq @ A @ ( Alpha @ ( F @ X2 ) ) @ ( F3 @ X2 ) )
% 0.31/1.54 => ( ord_less_eq @ A @ ( Alpha @ ( F @ X3 ) ) @ ( F3 @ X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_23_dual__order_Otrans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [B4: A,A4: A,C2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.31/1.54 => ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_24_linorder__wlog,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [P: A > A > $o,A4: A,B4: A] :
% 0.31/1.54 ( ! [A6: A,B6: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.31/1.54 => ( P @ A6 @ B6 ) )
% 0.31/1.54 => ( ! [A6: A,B6: A] :
% 0.31/1.54 ( ( P @ B6 @ A6 )
% 0.31/1.54 => ( P @ A6 @ B6 ) )
% 0.31/1.54 => ( P @ A4 @ B4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_25_transfer_Otransfer__if,axiom,
% 0.31/1.54 ! [C: $tType,A: $tType] :
% 0.31/1.54 ( ( comple187826305attice @ A )
% 0.31/1.54 => ! [B4: $o,Alpha: C > A,S1: C,S12: A,S2: C,S22: A] :
% 0.31/1.54 ( ( B4
% 0.31/1.54 => ( ord_less_eq @ A @ ( Alpha @ S1 ) @ S12 ) )
% 0.31/1.54 => ( ( ~ B4
% 0.31/1.54 => ( ord_less_eq @ A @ ( Alpha @ S2 ) @ S22 ) )
% 0.31/1.54 => ( ord_less_eq @ A @ ( Alpha @ ( if @ C @ B4 @ S1 @ S2 ) ) @ ( if @ A @ B4 @ S12 @ S22 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_26_dual__order_Orefl,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_27_order__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A,Z2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.31/1.54 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_28_order__class_Oorder_Oantisym,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.54 => ( A4 = B4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_29_ord__le__eq__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( B4 = C2 )
% 0.31/1.54 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_30_le__funD,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ord @ B )
% 0.31/1.54 => ! [F: A > B,G: A > B,X3: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/1.54 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_31_le__funE,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ord @ B )
% 0.31/1.54 => ! [F: A > B,G: A > B,X3: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/1.54 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_32_le__funI,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ord @ B )
% 0.31/1.54 => ! [F: A > B,G: A > B] :
% 0.31/1.54 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.31/1.54 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_33_le__fun__def,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ord @ B )
% 0.31/1.54 => ( ( ord_less_eq @ ( A > B ) )
% 0.31/1.54 = ( ^ [F4: A > B,G2: A > B] :
% 0.31/1.54 ! [X4: A] : ( ord_less_eq @ B @ ( F4 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_34_order__subst1,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( order @ B )
% 0.31/1.54 & ( order @ A ) )
% 0.31/1.54 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ ( F @ B4 ) )
% 0.31/1.54 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.31/1.54 => ( ! [X2: B,Y3: B] :
% 0.31/1.54 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_35_order__subst2,axiom,
% 0.31/1.54 ! [A: $tType,C: $tType] :
% 0.31/1.54 ( ( ( order @ C )
% 0.31/1.54 & ( order @ A ) )
% 0.31/1.54 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less_eq @ C @ ( F @ B4 ) @ C2 )
% 0.31/1.54 => ( ! [X2: A,Y3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less_eq @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less_eq @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_36_ord__eq__le__eq__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A,D: A] :
% 0.31/1.54 ( ( A4 = B4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.31/1.54 => ( ( C2 = D )
% 0.31/1.54 => ( ord_less_eq @ A @ A4 @ D ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_37_ord__eq__le__subst,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( ord @ B )
% 0.31/1.54 & ( ord @ A ) )
% 0.31/1.54 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.31/1.54 ( ( A4
% 0.31/1.54 = ( F @ B4 ) )
% 0.31/1.54 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.31/1.54 => ( ! [X2: B,Y3: B] :
% 0.31/1.54 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_38_ord__le__eq__subst,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( ord @ B )
% 0.31/1.54 & ( ord @ A ) )
% 0.31/1.54 => ! [A4: A,B4: A,F: A > B,C2: B] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ( F @ B4 )
% 0.31/1.54 = C2 )
% 0.31/1.54 => ( ! [X2: A,Y3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less_eq @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_39_eq__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.31/1.54 = ( ^ [X4: A,Y4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.31/1.54 & ( ord_less_eq @ A @ Y4 @ X4 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_40_antisym,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.31/1.54 => ( X3 = Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_41_linear,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 | ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_42_eq__refl,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( X3 = Y2 )
% 0.31/1.54 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_43_le__cases,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ~ ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_44_order_Otrans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.31/1.54 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_45_mem__Collect__eq,axiom,
% 0.31/1.54 ! [A: $tType,A4: A,P: A > $o] :
% 0.31/1.54 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.31/1.54 = ( P @ A4 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_46_Collect__mem__eq,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A] :
% 0.31/1.54 ( ( collect @ A
% 0.31/1.54 @ ^ [X4: A] : ( member @ A @ X4 @ A2 ) )
% 0.31/1.54 = A2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_47_Collect__cong,axiom,
% 0.31/1.54 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.54 ( ! [X2: A] :
% 0.31/1.54 ( ( P @ X2 )
% 0.31/1.54 = ( Q @ X2 ) )
% 0.31/1.54 => ( ( collect @ A @ P )
% 0.31/1.54 = ( collect @ A @ Q ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_48_ext,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.31/1.54 ( ! [X2: A] :
% 0.31/1.54 ( ( F @ X2 )
% 0.31/1.54 = ( G @ X2 ) )
% 0.31/1.54 => ( F = G ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_49_le__cases3,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A,Z2: A] :
% 0.31/1.54 ( ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 0.31/1.54 => ( ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.31/1.54 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.31/1.54 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.31/1.54 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 0.31/1.54 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 0.31/1.54 => ~ ( ord_less_eq @ A @ Y2 @ X3 ) )
% 0.31/1.54 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.31/1.54 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.31/1.54 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.31/1.54 => ~ ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_50_antisym__conv,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [Y2: A,X3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 = ( X3 = Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_51_order__class_Oorder_Oeq__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.31/1.54 = ( ^ [A5: A,B5: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.31/1.54 & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_52_ord__eq__le__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.54 ( ( A4 = B4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.31/1.54 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_53_GreatestI2__order,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [P: A > $o,X3: A,Q: A > $o] :
% 0.31/1.54 ( ( P @ X3 )
% 0.31/1.54 => ( ! [Y3: A] :
% 0.31/1.54 ( ( P @ Y3 )
% 0.31/1.54 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.31/1.54 => ( ! [X2: A] :
% 0.31/1.54 ( ( P @ X2 )
% 0.31/1.54 => ( ! [Y5: A] :
% 0.31/1.54 ( ( P @ Y5 )
% 0.31/1.54 => ( ord_less_eq @ A @ Y5 @ X2 ) )
% 0.31/1.54 => ( Q @ X2 ) ) )
% 0.31/1.54 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_54_Greatest__equality,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [P: A > $o,X3: A] :
% 0.31/1.54 ( ( P @ X3 )
% 0.31/1.54 => ( ! [Y3: A] :
% 0.31/1.54 ( ( P @ Y3 )
% 0.31/1.54 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.31/1.54 => ( ( order_Greatest @ A @ P )
% 0.31/1.54 = X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_55_Refine__Misc_Oif__mono,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [B4: $o,M1: A,M12: A,M2: A,M22: A] :
% 0.31/1.54 ( ( B4
% 0.31/1.54 => ( ord_less_eq @ A @ M1 @ M12 ) )
% 0.31/1.54 => ( ( ~ B4
% 0.31/1.54 => ( ord_less_eq @ A @ M2 @ M22 ) )
% 0.31/1.54 => ( ord_less_eq @ A @ ( if @ A @ B4 @ M1 @ M2 ) @ ( if @ A @ B4 @ M12 @ M22 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_56_lhs__step__If,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [B4: $o,T2: A,M: A,E: A] :
% 0.31/1.54 ( ( B4
% 0.31/1.54 => ( ord_less_eq @ A @ T2 @ M ) )
% 0.31/1.54 => ( ( ~ B4
% 0.31/1.54 => ( ord_less_eq @ A @ E @ M ) )
% 0.31/1.54 => ( ord_less_eq @ A @ ( if @ A @ B4 @ T2 @ E ) @ M ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_57_verit__la__disequality,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( A4 = B4 )
% 0.31/1.54 | ~ ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 | ~ ( ord_less_eq @ A @ B4 @ A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_58_le__rel__bool__arg__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ( ( ord_less_eq @ ( $o > A ) )
% 0.31/1.54 = ( ^ [X5: $o > A,Y6: $o > A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 0.31/1.54 & ( ord_less_eq @ A @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_59_antimonoD,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( order @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ! [F: A > B,X3: A,Y2: A] :
% 0.31/1.54 ( ( order_antimono @ A @ B @ F )
% 0.31/1.54 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_60_antimonoE,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( order @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ! [F: A > B,X3: A,Y2: A] :
% 0.31/1.54 ( ( order_antimono @ A @ B @ F )
% 0.31/1.54 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ord_less_eq @ B @ ( F @ Y2 ) @ ( F @ X3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_61_antimono__def,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( order @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ( ( order_antimono @ A @ B )
% 0.31/1.54 = ( ^ [F4: A > B] :
% 0.31/1.54 ! [X4: A,Y4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.31/1.54 => ( ord_less_eq @ B @ ( F4 @ Y4 ) @ ( F4 @ X4 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_62_antimonoI,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( order @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ! [F: A > B] :
% 0.31/1.54 ( ! [X2: A,Y3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less_eq @ B @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.31/1.54 => ( order_antimono @ A @ B @ F ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_63_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ( refine551993528up_loc @ A @ ( ord_less_eq @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_64_swap__args2__def,axiom,
% 0.31/1.54 ! [A: $tType,C: $tType,B: $tType] :
% 0.31/1.54 ( ( swap_args2 @ B @ C @ A )
% 0.31/1.54 = ( ^ [F4: B > C > A,X4: C,Y4: B] : ( F4 @ Y4 @ X4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_65_galois__connection_O_092_060gamma_062_092_060alpha_062__infl,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( comple187826305attice @ A )
% 0.31/1.54 & ( comple187826305attice @ B ) )
% 0.31/1.54 => ! [Alpha: A > B,Gamma: B > A,X3: A] :
% 0.31/1.54 ( ( refine1150083786ection @ A @ B @ Alpha @ Gamma )
% 0.31/1.54 => ( ord_less_eq @ A @ X3 @ ( Gamma @ ( Alpha @ X3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_66_galois__connection_O_092_060alpha_062_092_060gamma_062__defl,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( comple187826305attice @ B )
% 0.31/1.54 & ( comple187826305attice @ A ) )
% 0.31/1.54 => ! [Alpha: A > B,Gamma: B > A,X3: B] :
% 0.31/1.54 ( ( refine1150083786ection @ A @ B @ Alpha @ Gamma )
% 0.31/1.54 => ( ord_less_eq @ B @ ( Alpha @ ( Gamma @ X3 ) ) @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_67_galois__connection_Ogalois,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( comple187826305attice @ B )
% 0.31/1.54 & ( comple187826305attice @ A ) )
% 0.31/1.54 => ! [Alpha: A > B,Gamma: B > A,C2: A,A4: B] :
% 0.31/1.54 ( ( refine1150083786ection @ A @ B @ Alpha @ Gamma )
% 0.31/1.54 => ( ( ord_less_eq @ A @ C2 @ ( Gamma @ A4 ) )
% 0.31/1.54 = ( ord_less_eq @ B @ ( Alpha @ C2 ) @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_68_galois__connection_Ointro,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( comple187826305attice @ B )
% 0.31/1.54 & ( comple187826305attice @ A ) )
% 0.31/1.54 => ! [Gamma: B > A,Alpha: A > B] :
% 0.31/1.54 ( ! [C4: A,A6: B] :
% 0.31/1.54 ( ( ord_less_eq @ A @ C4 @ ( Gamma @ A6 ) )
% 0.31/1.54 = ( ord_less_eq @ B @ ( Alpha @ C4 ) @ A6 ) )
% 0.31/1.54 => ( refine1150083786ection @ A @ B @ Alpha @ Gamma ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_69_galois__connection__def,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( comple187826305attice @ A )
% 0.31/1.54 & ( comple187826305attice @ B ) )
% 0.31/1.54 => ( ( refine1150083786ection @ A @ B )
% 0.31/1.54 = ( ^ [Alpha2: A > B,Gamma2: B > A] :
% 0.31/1.54 ! [C5: A,A5: B] :
% 0.31/1.54 ( ( ord_less_eq @ A @ C5 @ ( Gamma2 @ A5 ) )
% 0.31/1.54 = ( ord_less_eq @ B @ ( Alpha2 @ C5 ) @ A5 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_70_mono__setup__loc__def,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( refine551993528up_loc @ A )
% 0.31/1.54 = ( ^ [Le: A > A > $o] :
% 0.31/1.54 ! [X4: A] : ( Le @ X4 @ X4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_71_mono__setup__loc_Orefl,axiom,
% 0.31/1.54 ! [A: $tType,Le2: A > A > $o,X3: A] :
% 0.31/1.54 ( ( refine551993528up_loc @ A @ Le2 )
% 0.31/1.54 => ( Le2 @ X3 @ X3 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_72_mono__setup__loc_Ointro,axiom,
% 0.31/1.54 ! [A: $tType,Le2: A > A > $o] :
% 0.31/1.54 ( ! [X2: A] : ( Le2 @ X2 @ X2 )
% 0.31/1.54 => ( refine551993528up_loc @ A @ Le2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_73_mono__setup__loc_Omono__if,axiom,
% 0.31/1.54 ! [A: $tType,Le2: A > A > $o,T2: A,T3: A,E: A,E2: A,B4: $o] :
% 0.31/1.54 ( ( refine551993528up_loc @ A @ Le2 )
% 0.31/1.54 => ( ( Le2 @ T2 @ T3 )
% 0.31/1.54 => ( ( Le2 @ E @ E2 )
% 0.31/1.54 => ( Le2 @ ( if @ A @ B4 @ T2 @ E ) @ ( if @ A @ B4 @ T3 @ E2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_74_mono__setup__loc_Omono__let,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType,Le2: A > A > $o,F: B > A,F2: B > A,X3: B] :
% 0.31/1.54 ( ( refine551993528up_loc @ A @ Le2 )
% 0.31/1.54 => ( ! [X2: B] : ( Le2 @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.31/1.54 => ( Le2 @ ( F @ X3 ) @ ( F2 @ X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_75_galois__connection_Oinf__dist___092_060alpha_062,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( comple187826305attice @ A )
% 0.31/1.54 & ( comple187826305attice @ B ) )
% 0.31/1.54 => ! [Alpha: A > B,Gamma: B > A] :
% 0.31/1.54 ( ( refine1150083786ection @ A @ B @ Alpha @ Gamma )
% 0.31/1.54 => ( refine_inf_distrib @ A @ B @ Alpha ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_76_strict__mono__less__eq,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( linorder @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ! [F: A > B,X3: A,Y2: A] :
% 0.31/1.54 ( ( order_strict_mono @ A @ B @ F )
% 0.31/1.54 => ( ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y2 ) )
% 0.31/1.54 = ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_77_greaterThan__subset__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_greaterThan @ A @ X3 ) @ ( set_ord_greaterThan @ A @ Y2 ) )
% 0.31/1.54 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_78_START__REFINEG__TRANSFER,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [D: A,C2: A,A4: A] :
% 0.31/1.54 ( ( refine111645177_ALIGN @ A @ A @ D @ C2 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.31/1.54 => ( ( refine574149253T_SIMP @ A @ C2 @ D )
% 0.31/1.54 => ( ord_less_eq @ A @ D @ A4 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_79_lessThan__subset__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_lessThan @ A @ X3 ) @ ( set_ord_lessThan @ A @ Y2 ) )
% 0.31/1.54 = ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_80_transfer_Otransfer__rec__list,axiom,
% 0.31/1.54 ! [C: $tType,D2: $tType,A: $tType,B: $tType] :
% 0.31/1.54 ( ( comple187826305attice @ A )
% 0.31/1.54 => ! [Alpha: C > A,Fn: B > C,Fn2: B > A,Fc: D2 > ( list @ D2 ) > ( B > C ) > B > C,Fc2: D2 > ( list @ D2 ) > ( B > A ) > B > A,L: list @ D2,S3: B] :
% 0.31/1.54 ( ! [S4: B] : ( ord_less_eq @ A @ ( Alpha @ ( Fn @ S4 ) ) @ ( Fn2 @ S4 ) )
% 0.31/1.54 => ( ! [X2: D2,L2: list @ D2,Rec: B > C,Rec2: B > A,S4: B] :
% 0.31/1.54 ( ! [Sa: B] : ( ord_less_eq @ A @ ( Alpha @ ( Rec @ Sa ) ) @ ( Rec2 @ Sa ) )
% 0.31/1.54 => ( ord_less_eq @ A @ ( Alpha @ ( Fc @ X2 @ L2 @ Rec @ S4 ) ) @ ( Fc2 @ X2 @ L2 @ Rec2 @ S4 ) ) )
% 0.31/1.54 => ( ord_less_eq @ A @ ( Alpha @ ( rec_list @ ( B > C ) @ D2 @ Fn @ Fc @ L @ S3 ) ) @ ( rec_list @ ( B > A ) @ D2 @ Fn2 @ Fc2 @ L @ S3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_81_atLeast__subset__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atLeast @ A @ X3 ) @ ( set_ord_atLeast @ A @ Y2 ) )
% 0.31/1.54 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_82_lessThan__eq__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ( set_ord_lessThan @ A @ X3 )
% 0.31/1.54 = ( set_ord_lessThan @ A @ Y2 ) )
% 0.31/1.54 = ( X3 = Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_83_atLeast__eq__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ( set_ord_atLeast @ A @ X3 )
% 0.31/1.54 = ( set_ord_atLeast @ A @ Y2 ) )
% 0.31/1.54 = ( X3 = Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_84_greaterThan__eq__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ( set_ord_greaterThan @ A @ X3 )
% 0.31/1.54 = ( set_ord_greaterThan @ A @ Y2 ) )
% 0.31/1.54 = ( X3 = Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_85_atLeast__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [I2: A,K: A] :
% 0.31/1.54 ( ( member @ A @ I2 @ ( set_ord_atLeast @ A @ K ) )
% 0.31/1.54 = ( ord_less_eq @ A @ K @ I2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_86_strict__mono__eq,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( linorder @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ! [F: A > B,X3: A,Y2: A] :
% 0.31/1.54 ( ( order_strict_mono @ A @ B @ F )
% 0.31/1.54 => ( ( ( F @ X3 )
% 0.31/1.54 = ( F @ Y2 ) )
% 0.31/1.54 = ( X3 = Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_87_Ioi__le__Ico,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [A4: A] : ( ord_less_eq @ ( set @ A ) @ ( set_ord_greaterThan @ A @ A4 ) @ ( set_ord_atLeast @ A @ A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_88_STOP__REFINEG__TRANSFER,axiom,
% 0.31/1.54 ! [A: $tType,C2: A] : ( refine574149253T_SIMP @ A @ C2 @ C2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_89_REFINEG__TRANSFER__ALIGNI,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType,X3: A,Y2: B] : ( refine111645177_ALIGN @ A @ B @ X3 @ Y2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_90_REFINEG__TRANSFER__ALIGN__def,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( refine111645177_ALIGN @ A @ B )
% 0.31/1.54 = ( ^ [X4: A,Y4: B] : $true ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_91_REFINEG__TRANSFER__POST__SIMP__def,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( refine574149253T_SIMP @ A )
% 0.31/1.54 = ( ^ [Y: A,Z: A] : ( Y = Z ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_92_Ici__subset__Ioi__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atLeast @ A @ A4 ) @ ( set_ord_greaterThan @ A @ B4 ) )
% 0.31/1.54 = ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_93_Icc__subset__Ici__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [L: A,H: A,L3: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_or331188842AtMost @ A @ L @ H ) @ ( set_ord_atLeast @ A @ L3 ) )
% 0.31/1.54 = ( ~ ( ord_less_eq @ A @ L @ H )
% 0.31/1.54 | ( ord_less_eq @ A @ L3 @ L ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_94_inf__distribD_I1_J,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( complete_Sup @ A )
% 0.31/1.54 & ( bot @ A )
% 0.31/1.54 & ( complete_Sup @ B )
% 0.31/1.54 & ( bot @ B ) )
% 0.31/1.54 => ! [F: A > B] :
% 0.31/1.54 ( ( refine_inf_distrib @ A @ B @ F )
% 0.31/1.54 => ( refine_strict @ A @ B @ F ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_95_Compl__atLeast,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [K: A] :
% 0.31/1.54 ( ( uminus_uminus @ ( set @ A ) @ ( set_ord_atLeast @ A @ K ) )
% 0.31/1.54 = ( set_ord_lessThan @ A @ K ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_96_Compl__lessThan,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [K: A] :
% 0.31/1.54 ( ( uminus_uminus @ ( set @ A ) @ ( set_ord_lessThan @ A @ K ) )
% 0.31/1.54 = ( set_ord_atLeast @ A @ K ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_97_atMost__subset__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ X3 ) @ ( set_ord_atMost @ A @ Y2 ) )
% 0.31/1.54 = ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_98_psubsetI,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ( A2 != B2 )
% 0.31/1.54 => ( ord_less @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_99_verit__minus__simplify_I4_J,axiom,
% 0.31/1.54 ! [B: $tType] :
% 0.31/1.54 ( ( group_add @ B )
% 0.31/1.54 => ! [B4: B] :
% 0.31/1.54 ( ( uminus_uminus @ B @ ( uminus_uminus @ B @ B4 ) )
% 0.31/1.54 = B4 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_100_atMost__eq__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ( set_ord_atMost @ A @ X3 )
% 0.31/1.54 = ( set_ord_atMost @ A @ Y2 ) )
% 0.31/1.54 = ( X3 = Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_101_ComplI,axiom,
% 0.31/1.54 ! [A: $tType,C2: A,A2: set @ A] :
% 0.31/1.54 ( ~ ( member @ A @ C2 @ A2 )
% 0.31/1.54 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_102_Compl__iff,axiom,
% 0.31/1.54 ! [A: $tType,C2: A,A2: set @ A] :
% 0.31/1.54 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.31/1.54 = ( ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_103_Compl__eq__Compl__iff,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( ( uminus_uminus @ ( set @ A ) @ A2 )
% 0.31/1.54 = ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.31/1.54 = ( A2 = B2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_104_atLeastAtMost__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [I2: A,L: A,U: A] :
% 0.31/1.54 ( ( member @ A @ I2 @ ( set_or331188842AtMost @ A @ L @ U ) )
% 0.31/1.54 = ( ( ord_less_eq @ A @ L @ I2 )
% 0.31/1.54 & ( ord_less_eq @ A @ I2 @ U ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_105_Icc__eq__Icc,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [L: A,H: A,L3: A,H2: A] :
% 0.31/1.54 ( ( ( set_or331188842AtMost @ A @ L @ H )
% 0.31/1.54 = ( set_or331188842AtMost @ A @ L3 @ H2 ) )
% 0.31/1.54 = ( ( ( L = L3 )
% 0.31/1.54 & ( H = H2 ) )
% 0.31/1.54 | ( ~ ( ord_less_eq @ A @ L @ H )
% 0.31/1.54 & ~ ( ord_less_eq @ A @ L3 @ H2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_106_atMost__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [I2: A,K: A] :
% 0.31/1.54 ( ( member @ A @ I2 @ ( set_ord_atMost @ A @ K ) )
% 0.31/1.54 = ( ord_less_eq @ A @ I2 @ K ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_107_lessThan__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [I2: A,K: A] :
% 0.31/1.54 ( ( member @ A @ I2 @ ( set_ord_lessThan @ A @ K ) )
% 0.31/1.54 = ( ord_less @ A @ I2 @ K ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_108_Compl__anti__mono,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_109_Compl__subset__Compl__iff,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ ( uminus_uminus @ ( set @ A ) @ B2 ) )
% 0.31/1.54 = ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_110_greaterThan__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [I2: A,K: A] :
% 0.31/1.54 ( ( member @ A @ I2 @ ( set_ord_greaterThan @ A @ K ) )
% 0.31/1.54 = ( ord_less @ A @ K @ I2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_111_atLeastatMost__subset__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A,D: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_or331188842AtMost @ A @ A4 @ B4 ) @ ( set_or331188842AtMost @ A @ C2 @ D ) )
% 0.31/1.54 = ( ~ ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 | ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.31/1.54 & ( ord_less_eq @ A @ B4 @ D ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_112_Compl__atMost,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [K: A] :
% 0.31/1.54 ( ( uminus_uminus @ ( set @ A ) @ ( set_ord_atMost @ A @ K ) )
% 0.31/1.54 = ( set_ord_greaterThan @ A @ K ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_113_Compl__greaterThan,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [K: A] :
% 0.31/1.54 ( ( uminus_uminus @ ( set @ A ) @ ( set_ord_greaterThan @ A @ K ) )
% 0.31/1.54 = ( set_ord_atMost @ A @ K ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_114_Icc__subset__Iic__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [L: A,H: A,H2: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_or331188842AtMost @ A @ L @ H ) @ ( set_ord_atMost @ A @ H2 ) )
% 0.31/1.54 = ( ~ ( ord_less_eq @ A @ L @ H )
% 0.31/1.54 | ( ord_less_eq @ A @ H @ H2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_115_lessThan__strict__subset__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [M: A,N: A] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) @ ( set_ord_lessThan @ A @ M ) @ ( set_ord_lessThan @ A @ N ) )
% 0.31/1.54 = ( ord_less @ A @ M @ N ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_116_not__Iic__eq__Icc,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( no_bot @ A )
% 0.31/1.54 => ! [H2: A,L: A,H: A] :
% 0.31/1.54 ( ( set_ord_atMost @ A @ H2 )
% 0.31/1.54 != ( set_or331188842AtMost @ A @ L @ H ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_117_not__Iic__le__Icc,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( no_bot @ A )
% 0.31/1.54 => ! [H: A,L3: A,H2: A] :
% 0.31/1.54 ~ ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ H ) @ ( set_or331188842AtMost @ A @ L3 @ H2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_118_atLeastatMost__psubset__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A,D: A] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) @ ( set_or331188842AtMost @ A @ A4 @ B4 ) @ ( set_or331188842AtMost @ A @ C2 @ D ) )
% 0.31/1.54 = ( ( ~ ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 | ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.31/1.54 & ( ord_less_eq @ A @ B4 @ D )
% 0.31/1.54 & ( ( ord_less @ A @ C2 @ A4 )
% 0.31/1.54 | ( ord_less @ A @ B4 @ D ) ) ) )
% 0.31/1.54 & ( ord_less_eq @ A @ C2 @ D ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_119_verit__comp__simplify1_I1_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A] :
% 0.31/1.54 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_120_verit__negate__coefficient_I3_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( A4 = B4 )
% 0.31/1.54 => ( ( uminus_uminus @ A @ A4 )
% 0.31/1.54 = ( uminus_uminus @ A @ B4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_121_verit__negate__coefficient_I2_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ord_less @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_122_all__nat__split__at,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [K: A,P: A > $o] :
% 0.31/1.54 ( ! [I3: A] :
% 0.31/1.54 ( ( ord_less @ A @ I3 @ K )
% 0.31/1.54 => ( P @ I3 ) )
% 0.31/1.54 => ( ( P @ K )
% 0.31/1.54 => ( ! [I3: A] :
% 0.31/1.54 ( ( ord_less @ A @ K @ I3 )
% 0.31/1.54 => ( P @ I3 ) )
% 0.31/1.54 => ! [X_1: A] : ( P @ X_1 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_123_ComplD,axiom,
% 0.31/1.54 ! [A: $tType,C2: A,A2: set @ A] :
% 0.31/1.54 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.31/1.54 => ~ ( member @ A @ C2 @ A2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_124_double__complement,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A] :
% 0.31/1.54 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.31/1.54 = A2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_125_ord__eq__less__subst,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( ord @ B )
% 0.31/1.54 & ( ord @ A ) )
% 0.31/1.54 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.31/1.54 ( ( A4
% 0.31/1.54 = ( F @ B4 ) )
% 0.31/1.54 => ( ( ord_less @ B @ B4 @ C2 )
% 0.31/1.54 => ( ! [X2: B,Y3: B] :
% 0.31/1.54 ( ( ord_less @ B @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_126_ord__less__eq__subst,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( ord @ B )
% 0.31/1.54 & ( ord @ A ) )
% 0.31/1.54 => ! [A4: A,B4: A,F: A > B,C2: B] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ( F @ B4 )
% 0.31/1.54 = C2 )
% 0.31/1.54 => ( ! [X2: A,Y3: A] :
% 0.31/1.54 ( ( ord_less @ A @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_127_order__less__subst1,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( order @ B )
% 0.31/1.54 & ( order @ A ) )
% 0.31/1.54 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ ( F @ B4 ) )
% 0.31/1.54 => ( ( ord_less @ B @ B4 @ C2 )
% 0.31/1.54 => ( ! [X2: B,Y3: B] :
% 0.31/1.54 ( ( ord_less @ B @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_128_order__less__subst2,axiom,
% 0.31/1.54 ! [A: $tType,C: $tType] :
% 0.31/1.54 ( ( ( order @ C )
% 0.31/1.54 & ( order @ A ) )
% 0.31/1.54 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less @ C @ ( F @ B4 ) @ C2 )
% 0.31/1.54 => ( ! [X2: A,Y3: A] :
% 0.31/1.54 ( ( ord_less @ A @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_129_lt__ex,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( no_bot @ A )
% 0.31/1.54 => ! [X3: A] :
% 0.31/1.54 ? [Y3: A] : ( ord_less @ A @ Y3 @ X3 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_130_gt__ex,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( no_top @ A )
% 0.31/1.54 => ! [X3: A] :
% 0.31/1.54 ? [X_12: A] : ( ord_less @ A @ X3 @ X_12 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_131_neqE,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( X3 != Y2 )
% 0.31/1.54 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_132_neq__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( X3 != Y2 )
% 0.31/1.54 = ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 | ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_133_order_Oasym,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ~ ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_134_dense,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( dense_order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ? [Z3: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Z3 )
% 0.31/1.54 & ( ord_less @ A @ Z3 @ Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_135_less__imp__neq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( X3 != Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_136_less__asym,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_137_less__asym_H,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ~ ( ord_less @ A @ B4 @ A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_138_less__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A,Z2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( ord_less @ A @ Y2 @ Z2 )
% 0.31/1.54 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_139_less__linear,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 | ( X3 = Y2 )
% 0.31/1.54 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_140_less__irrefl,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A] :
% 0.31/1.54 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_141_ord__eq__less__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.54 ( ( A4 = B4 )
% 0.31/1.54 => ( ( ord_less @ A @ B4 @ C2 )
% 0.31/1.54 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_142_ord__less__eq__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( B4 = C2 )
% 0.31/1.54 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_143_dual__order_Oasym,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [B4: A,A4: A] :
% 0.31/1.54 ( ( ord_less @ A @ B4 @ A4 )
% 0.31/1.54 => ~ ( ord_less @ A @ A4 @ B4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_144_less__imp__not__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( X3 != Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_145_less__not__sym,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_146_less__induct,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( wellorder @ A )
% 0.31/1.54 => ! [P: A > $o,A4: A] :
% 0.31/1.54 ( ! [X2: A] :
% 0.31/1.54 ( ! [Y5: A] :
% 0.31/1.54 ( ( ord_less @ A @ Y5 @ X2 )
% 0.31/1.54 => ( P @ Y5 ) )
% 0.31/1.54 => ( P @ X2 ) )
% 0.31/1.54 => ( P @ A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_147_antisym__conv3,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [Y2: A,X3: A] :
% 0.31/1.54 ( ~ ( ord_less @ A @ Y2 @ X3 )
% 0.31/1.54 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.31/1.54 = ( X3 = Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_148_less__imp__not__eq2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( Y2 != X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_149_less__imp__triv,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A,P: $o] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( ord_less @ A @ Y2 @ X3 )
% 0.31/1.54 => P ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_150_linorder__cases,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( X3 != Y2 )
% 0.31/1.54 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_151_dual__order_Oirrefl,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A] :
% 0.31/1.54 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_152_order_Ostrict__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less @ A @ B4 @ C2 )
% 0.31/1.54 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_153_less__imp__not__less,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_154_exists__least__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( wellorder @ A )
% 0.31/1.54 => ( ( ^ [P2: A > $o] :
% 0.31/1.54 ? [X6: A] : ( P2 @ X6 ) )
% 0.31/1.54 = ( ^ [P3: A > $o] :
% 0.31/1.54 ? [N2: A] :
% 0.31/1.54 ( ( P3 @ N2 )
% 0.31/1.54 & ! [M3: A] :
% 0.31/1.54 ( ( ord_less @ A @ M3 @ N2 )
% 0.31/1.54 => ~ ( P3 @ M3 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_155_linorder__less__wlog,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [P: A > A > $o,A4: A,B4: A] :
% 0.31/1.54 ( ! [A6: A,B6: A] :
% 0.31/1.54 ( ( ord_less @ A @ A6 @ B6 )
% 0.31/1.54 => ( P @ A6 @ B6 ) )
% 0.31/1.54 => ( ! [A6: A] : ( P @ A6 @ A6 )
% 0.31/1.54 => ( ! [A6: A,B6: A] :
% 0.31/1.54 ( ( P @ B6 @ A6 )
% 0.31/1.54 => ( P @ A6 @ B6 ) )
% 0.31/1.54 => ( P @ A4 @ B4 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_156_dual__order_Ostrict__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [B4: A,A4: A,C2: A] :
% 0.31/1.54 ( ( ord_less @ A @ B4 @ A4 )
% 0.31/1.54 => ( ( ord_less @ A @ C2 @ B4 )
% 0.31/1.54 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_157_not__less__iff__gr__or__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.31/1.54 = ( ( ord_less @ A @ Y2 @ X3 )
% 0.31/1.54 | ( X3 = Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_158_order_Ostrict__implies__not__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( A4 != B4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_159_dual__order_Ostrict__implies__not__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [B4: A,A4: A] :
% 0.31/1.54 ( ( ord_less @ A @ B4 @ A4 )
% 0.31/1.54 => ( A4 != B4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_160_Iic__subset__Iio__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ A4 ) @ ( set_ord_lessThan @ A @ B4 ) )
% 0.31/1.54 = ( ord_less @ A @ A4 @ B4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_161_leD,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [Y2: A,X3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.31/1.54 => ~ ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_162_leI,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_163_le__less,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ( ( ord_less_eq @ A )
% 0.31/1.54 = ( ^ [X4: A,Y4: A] :
% 0.31/1.54 ( ( ord_less @ A @ X4 @ Y4 )
% 0.31/1.54 | ( X4 = Y4 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_164_less__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ( ( ord_less @ A )
% 0.31/1.54 = ( ^ [X4: A,Y4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.31/1.54 & ( X4 != Y4 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_165_order__le__less__subst1,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( order @ B )
% 0.31/1.54 & ( order @ A ) )
% 0.31/1.54 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ ( F @ B4 ) )
% 0.31/1.54 => ( ( ord_less @ B @ B4 @ C2 )
% 0.31/1.54 => ( ! [X2: B,Y3: B] :
% 0.31/1.54 ( ( ord_less @ B @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_166_order__le__less__subst2,axiom,
% 0.31/1.54 ! [A: $tType,C: $tType] :
% 0.31/1.54 ( ( ( order @ C )
% 0.31/1.54 & ( order @ A ) )
% 0.31/1.54 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less @ C @ ( F @ B4 ) @ C2 )
% 0.31/1.54 => ( ! [X2: A,Y3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less_eq @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_167_order__less__le__subst1,axiom,
% 0.31/1.54 ! [A: $tType,B: $tType] :
% 0.31/1.54 ( ( ( order @ B )
% 0.31/1.54 & ( order @ A ) )
% 0.31/1.54 => ! [A4: A,F: B > A,B4: B,C2: B] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ ( F @ B4 ) )
% 0.31/1.54 => ( ( ord_less_eq @ B @ B4 @ C2 )
% 0.31/1.54 => ( ! [X2: B,Y3: B] :
% 0.31/1.54 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_168_order__less__le__subst2,axiom,
% 0.31/1.54 ! [A: $tType,C: $tType] :
% 0.31/1.54 ( ( ( order @ C )
% 0.31/1.54 & ( order @ A ) )
% 0.31/1.54 => ! [A4: A,B4: A,F: A > C,C2: C] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less_eq @ C @ ( F @ B4 ) @ C2 )
% 0.31/1.54 => ( ! [X2: A,Y3: A] :
% 0.31/1.54 ( ( ord_less @ A @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( ord_less @ C @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_169_not__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ~ ( ord_less_eq @ A @ X3 @ Y2 ) )
% 0.31/1.54 = ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_170_not__less,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.31/1.54 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_171_le__neq__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( A4 != B4 )
% 0.31/1.54 => ( ord_less @ A @ A4 @ B4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_172_antisym__conv1,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 = ( X3 = Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_173_antisym__conv2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.31/1.54 = ( X3 = Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_174_less__imp__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_175_le__less__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A,Z2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( ord_less @ A @ Y2 @ Z2 )
% 0.31/1.54 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_176_less__le__trans,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A,Z2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.31/1.54 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_177_dense__ge,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( dense_linorder @ A )
% 0.31/1.54 => ! [Z2: A,Y2: A] :
% 0.31/1.54 ( ! [X2: A] :
% 0.31/1.54 ( ( ord_less @ A @ Z2 @ X2 )
% 0.31/1.54 => ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.31/1.54 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_178_dense__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( dense_linorder @ A )
% 0.31/1.54 => ! [Y2: A,Z2: A] :
% 0.31/1.54 ( ! [X2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_eq @ A @ X2 @ Z2 ) )
% 0.31/1.54 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_179_le__less__linear,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_180_le__imp__less__or__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 | ( X3 = Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_181_less__le__not__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( preorder @ A )
% 0.31/1.54 => ( ( ord_less @ A )
% 0.31/1.54 = ( ^ [X4: A,Y4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.31/1.54 & ~ ( ord_less_eq @ A @ Y4 @ X4 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_182_not__le__imp__less,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [Y2: A,X3: A] :
% 0.31/1.54 ( ~ ( ord_less_eq @ A @ Y2 @ X3 )
% 0.31/1.54 => ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_183_order_Ostrict__trans1,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less @ A @ B4 @ C2 )
% 0.31/1.54 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_184_order_Ostrict__trans2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ B4 @ C2 )
% 0.31/1.54 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_185_order_Oorder__iff__strict,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ( ( ord_less_eq @ A )
% 0.31/1.54 = ( ^ [A5: A,B5: A] :
% 0.31/1.54 ( ( ord_less @ A @ A5 @ B5 )
% 0.31/1.54 | ( A5 = B5 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_186_order_Ostrict__iff__order,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ( ( ord_less @ A )
% 0.31/1.54 = ( ^ [A5: A,B5: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.31/1.54 & ( A5 != B5 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_187_dual__order_Ostrict__trans1,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [B4: A,A4: A,C2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.54 => ( ( ord_less @ A @ C2 @ B4 )
% 0.31/1.54 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_188_dual__order_Ostrict__trans2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [B4: A,A4: A,C2: A] :
% 0.31/1.54 ( ( ord_less @ A @ B4 @ A4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.31/1.54 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_189_dense__ge__bounded,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( dense_linorder @ A )
% 0.31/1.54 => ! [Z2: A,X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less @ A @ Z2 @ X3 )
% 0.31/1.54 => ( ! [W: A] :
% 0.31/1.54 ( ( ord_less @ A @ Z2 @ W )
% 0.31/1.54 => ( ( ord_less @ A @ W @ X3 )
% 0.31/1.54 => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 0.31/1.54 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_190_dense__le__bounded,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( dense_linorder @ A )
% 0.31/1.54 => ! [X3: A,Y2: A,Z2: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ! [W: A] :
% 0.31/1.54 ( ( ord_less @ A @ X3 @ W )
% 0.31/1.54 => ( ( ord_less @ A @ W @ Y2 )
% 0.31/1.54 => ( ord_less_eq @ A @ W @ Z2 ) ) )
% 0.31/1.54 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_191_order_Ostrict__implies__order,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ord_less_eq @ A @ A4 @ B4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_192_dual__order_Oorder__iff__strict,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ( ( ord_less_eq @ A )
% 0.31/1.54 = ( ^ [B5: A,A5: A] :
% 0.31/1.54 ( ( ord_less @ A @ B5 @ A5 )
% 0.31/1.54 | ( A5 = B5 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_193_dual__order_Ostrict__iff__order,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ( ( ord_less @ A )
% 0.31/1.54 = ( ^ [B5: A,A5: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.31/1.54 & ( A5 != B5 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_194_dual__order_Ostrict__implies__order,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [B4: A,A4: A] :
% 0.31/1.54 ( ( ord_less @ A @ B4 @ A4 )
% 0.31/1.54 => ( ord_less_eq @ A @ B4 @ A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_195_order_Onot__eq__order__implies__strict,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( A4 != B4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ord_less @ A @ A4 @ B4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_196_verit__comp__simplify1_I3_J,axiom,
% 0.31/1.54 ! [B: $tType] :
% 0.31/1.54 ( ( linorder @ B )
% 0.31/1.54 => ! [B7: B,A7: B] :
% 0.31/1.54 ( ( ~ ( ord_less_eq @ B @ B7 @ A7 ) )
% 0.31/1.54 = ( ord_less @ B @ A7 @ B7 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_197_psubsetE,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ord_less_eq @ ( set @ A ) @ B2 @ A2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_198_psubset__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) )
% 0.31/1.54 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.54 & ( A3 != B3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_199_psubset__imp__subset,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_200_psubset__subset__trans,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.31/1.54 => ( ord_less @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_201_subset__not__subset__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) )
% 0.31/1.54 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.54 & ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_202_subset__psubset__trans,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ( ord_less @ ( set @ A ) @ B2 @ C3 )
% 0.31/1.54 => ( ord_less @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_203_subset__iff__psubset__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.54 = ( ^ [A3: set @ A,B3: set @ A] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) @ A3 @ B3 )
% 0.31/1.54 | ( A3 = B3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_204_less__fun__def,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ord @ B )
% 0.31/1.54 => ( ( ord_less @ ( A > B ) )
% 0.31/1.54 = ( ^ [F4: A > B,G2: A > B] :
% 0.31/1.54 ( ( ord_less_eq @ ( A > B ) @ F4 @ G2 )
% 0.31/1.54 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F4 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_205_not__Ici__eq__Icc,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( no_top @ A )
% 0.31/1.54 => ! [L3: A,L: A,H: A] :
% 0.31/1.54 ( ( set_ord_atLeast @ A @ L3 )
% 0.31/1.54 != ( set_or331188842AtMost @ A @ L @ H ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_206_not__Iic__eq__Ici,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( no_top @ A )
% 0.31/1.54 => ! [H: A,L3: A] :
% 0.31/1.54 ( ( set_ord_atMost @ A @ H )
% 0.31/1.54 != ( set_ord_atLeast @ A @ L3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_207_strict__monoD,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( order @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ! [F: A > B,X3: A,Y2: A] :
% 0.31/1.54 ( ( order_strict_mono @ A @ B @ F )
% 0.31/1.54 => ( ( ord_less @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_208_strict__monoI,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( order @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ! [F: A > B] :
% 0.31/1.54 ( ! [X2: A,Y3: A] :
% 0.31/1.54 ( ( ord_less @ A @ X2 @ Y3 )
% 0.31/1.54 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.31/1.54 => ( order_strict_mono @ A @ B @ F ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_209_strict__mono__def,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( order @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ( ( order_strict_mono @ A @ B )
% 0.31/1.54 = ( ^ [F4: A > B] :
% 0.31/1.54 ! [X4: A,Y4: A] :
% 0.31/1.54 ( ( ord_less @ A @ X4 @ Y4 )
% 0.31/1.54 => ( ord_less @ B @ ( F4 @ X4 ) @ ( F4 @ Y4 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_210_strict__mono__less,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( linorder @ A )
% 0.31/1.54 & ( order @ B ) )
% 0.31/1.54 => ! [F: A > B,X3: A,Y2: A] :
% 0.31/1.54 ( ( order_strict_mono @ A @ B @ F )
% 0.31/1.54 => ( ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y2 ) )
% 0.31/1.54 = ( ord_less @ A @ X3 @ Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_211_not__Ici__le__Icc,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( no_top @ A )
% 0.31/1.54 => ! [L: A,L3: A,H2: A] :
% 0.31/1.54 ~ ( ord_less_eq @ ( set @ A ) @ ( set_ord_atLeast @ A @ L ) @ ( set_or331188842AtMost @ A @ L3 @ H2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_212_not__Ici__le__Iic,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( no_top @ A )
% 0.31/1.54 => ! [L: A,H2: A] :
% 0.31/1.54 ~ ( ord_less_eq @ ( set @ A ) @ ( set_ord_atLeast @ A @ L ) @ ( set_ord_atMost @ A @ H2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_213_not__Iic__le__Ici,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( no_bot @ A )
% 0.31/1.54 => ! [H: A,L3: A] :
% 0.31/1.54 ~ ( ord_less_eq @ ( set @ A ) @ ( set_ord_atMost @ A @ H ) @ ( set_ord_atLeast @ A @ L3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_214_compl__le__compl__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( boolean_algebra @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ ( uminus_uminus @ A @ Y2 ) )
% 0.31/1.54 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_215_neg__le__iff__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [B4: A,A4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A4 ) )
% 0.31/1.54 = ( ord_less_eq @ A @ A4 @ B4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_216_compl__mono,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( boolean_algebra @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y2 ) @ ( uminus_uminus @ A @ X3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_217_compl__le__swap1,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( boolean_algebra @ A )
% 0.31/1.54 => ! [Y2: A,X3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ Y2 @ ( uminus_uminus @ A @ X3 ) )
% 0.31/1.54 => ( ord_less_eq @ A @ X3 @ ( uminus_uminus @ A @ Y2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_218_compl__le__swap2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( boolean_algebra @ A )
% 0.31/1.54 => ! [Y2: A,X3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y2 ) @ X3 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_219_psubsetD,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A,C2: A] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ( member @ A @ C2 @ A2 )
% 0.31/1.54 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_220_psubset__trans,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.31/1.54 ( ( ord_less @ ( set @ A ) @ A2 @ B2 )
% 0.31/1.54 => ( ( ord_less @ ( set @ A ) @ B2 @ C3 )
% 0.31/1.54 => ( ord_less @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_221_le__imp__neg__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_222_minus__le__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A4 ) @ B4 )
% 0.31/1.54 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B4 ) @ A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_223_le__minus__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ ( uminus_uminus @ A @ B4 ) )
% 0.31/1.54 = ( ord_less_eq @ A @ B4 @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_224_complete__interval,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( condit1037483654norder @ A )
% 0.31/1.54 => ! [A4: A,B4: A,P: A > $o] :
% 0.31/1.54 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( P @ A4 )
% 0.31/1.54 => ( ~ ( P @ B4 )
% 0.31/1.54 => ? [C4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ C4 )
% 0.31/1.54 & ( ord_less_eq @ A @ C4 @ B4 )
% 0.31/1.54 & ! [X7: A] :
% 0.31/1.54 ( ( ( ord_less_eq @ A @ A4 @ X7 )
% 0.31/1.54 & ( ord_less @ A @ X7 @ C4 ) )
% 0.31/1.54 => ( P @ X7 ) )
% 0.31/1.54 & ! [D3: A] :
% 0.31/1.54 ( ! [X2: A] :
% 0.31/1.54 ( ( ( ord_less_eq @ A @ A4 @ X2 )
% 0.31/1.54 & ( ord_less @ A @ X2 @ D3 ) )
% 0.31/1.54 => ( P @ X2 ) )
% 0.31/1.54 => ( ord_less_eq @ A @ D3 @ C4 ) ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_225_pinf_I6_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [T2: A] :
% 0.31/1.54 ? [Z3: A] :
% 0.31/1.54 ! [X7: A] :
% 0.31/1.54 ( ( ord_less @ A @ Z3 @ X7 )
% 0.31/1.54 => ~ ( ord_less_eq @ A @ X7 @ T2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_226_minf_I8_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [T2: A] :
% 0.31/1.54 ? [Z3: A] :
% 0.31/1.54 ! [X7: A] :
% 0.31/1.54 ( ( ord_less @ A @ X7 @ Z3 )
% 0.31/1.54 => ~ ( ord_less_eq @ A @ T2 @ X7 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_227_minf_I6_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [T2: A] :
% 0.31/1.54 ? [Z3: A] :
% 0.31/1.54 ! [X7: A] :
% 0.31/1.54 ( ( ord_less @ A @ X7 @ Z3 )
% 0.31/1.54 => ( ord_less_eq @ A @ X7 @ T2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_228_pinf_I8_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [T2: A] :
% 0.31/1.54 ? [Z3: A] :
% 0.31/1.54 ! [X7: A] :
% 0.31/1.54 ( ( ord_less @ A @ Z3 @ X7 )
% 0.31/1.54 => ( ord_less_eq @ A @ T2 @ X7 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_229_inf__distribI,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( complete_Sup @ A )
% 0.31/1.54 & ( bot @ A )
% 0.31/1.54 & ( complete_Sup @ B )
% 0.31/1.54 & ( bot @ B ) )
% 0.31/1.54 => ! [F: A > B] :
% 0.31/1.54 ( ( refine_strict @ A @ B @ F )
% 0.31/1.54 => ( ( refine_cont @ A @ B @ F )
% 0.31/1.54 => ( refine_inf_distrib @ A @ B @ F ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_230_inf__distrib__def,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( complete_Sup @ A )
% 0.31/1.54 & ( bot @ A )
% 0.31/1.54 & ( complete_Sup @ B )
% 0.31/1.54 & ( bot @ B ) )
% 0.31/1.54 => ( ( refine_inf_distrib @ A @ B )
% 0.31/1.54 = ( ^ [F4: A > B] :
% 0.31/1.54 ( ( refine_strict @ A @ B @ F4 )
% 0.31/1.54 & ( refine_cont @ A @ B @ F4 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_231_inf__distribD_I2_J,axiom,
% 0.31/1.54 ! [B: $tType,A: $tType] :
% 0.31/1.54 ( ( ( complete_Sup @ A )
% 0.31/1.54 & ( bot @ A )
% 0.31/1.54 & ( complete_Sup @ B )
% 0.31/1.54 & ( bot @ B ) )
% 0.31/1.54 => ! [F: A > B] :
% 0.31/1.54 ( ( refine_inf_distrib @ A @ B @ F )
% 0.31/1.54 => ( refine_cont @ A @ B @ F ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_232_greaterThanLessThan__subseteq__atLeastAtMost__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( dense_linorder @ A )
% 0.31/1.54 => ! [A4: A,B4: A,C2: A,D: A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( set_or578182835ssThan @ A @ A4 @ B4 ) @ ( set_or331188842AtMost @ A @ C2 @ D ) )
% 0.31/1.54 = ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.31/1.54 & ( ord_less_eq @ A @ B4 @ D ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_233_ivl__disj__un__one_I7_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ! [L: A,U: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ L @ U )
% 0.31/1.54 => ( ( sup_sup @ ( set @ A ) @ ( set_or331188842AtMost @ A @ L @ U ) @ ( set_ord_greaterThan @ A @ U ) )
% 0.31/1.54 = ( set_ord_atLeast @ A @ L ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_234_UnCI,axiom,
% 0.31/1.54 ! [A: $tType,C2: A,B2: set @ A,A2: set @ A] :
% 0.31/1.54 ( ( ~ ( member @ A @ C2 @ B2 )
% 0.31/1.54 => ( member @ A @ C2 @ A2 ) )
% 0.31/1.54 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_235_Un__iff,axiom,
% 0.31/1.54 ! [A: $tType,C2: A,A2: set @ A,B2: set @ A] :
% 0.31/1.54 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/1.54 = ( ( member @ A @ C2 @ A2 )
% 0.31/1.54 | ( member @ A @ C2 @ B2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_236_le__sup__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [X3: A,Y2: A,Z2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X3 @ Y2 ) @ Z2 )
% 0.31/1.54 = ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.31/1.54 & ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_237_sup_Obounded__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [B4: A,C2: A,A4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A4 )
% 0.31/1.54 = ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.54 & ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_238_Un__subset__iff,axiom,
% 0.31/1.54 ! [A: $tType,A2: set @ A,B2: set @ A,C3: set @ A] :
% 0.31/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C3 )
% 0.31/1.54 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C3 )
% 0.31/1.54 & ( ord_less_eq @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_239_greaterThanLessThan__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ord @ A )
% 0.31/1.54 => ! [I2: A,L: A,U: A] :
% 0.31/1.54 ( ( member @ A @ I2 @ ( set_or578182835ssThan @ A @ L @ U ) )
% 0.31/1.54 = ( ( ord_less @ A @ L @ I2 )
% 0.31/1.54 & ( ord_less @ A @ I2 @ U ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_240_sup_OcoboundedI2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [C2: A,B4: A,A4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ C2 @ B4 )
% 0.31/1.54 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_241_sup_OcoboundedI1,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [C2: A,A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.31/1.54 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_242_sup_Oabsorb__iff2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ( ( ord_less_eq @ A )
% 0.31/1.54 = ( ^ [A5: A,B5: A] :
% 0.31/1.54 ( ( sup_sup @ A @ A5 @ B5 )
% 0.31/1.54 = B5 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_243_sup_Oabsorb__iff1,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ( ( ord_less_eq @ A )
% 0.31/1.54 = ( ^ [B5: A,A5: A] :
% 0.31/1.54 ( ( sup_sup @ A @ A5 @ B5 )
% 0.31/1.54 = A5 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_244_sup_Ocobounded2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [B4: A,A4: A] : ( ord_less_eq @ A @ B4 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_245_sup_Ocobounded1,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [A4: A,B4: A] : ( ord_less_eq @ A @ A4 @ ( sup_sup @ A @ A4 @ B4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_246_sup_Oorder__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ( ( ord_less_eq @ A )
% 0.31/1.54 = ( ^ [B5: A,A5: A] :
% 0.31/1.54 ( A5
% 0.31/1.54 = ( sup_sup @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_247_sup_OboundedI,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [B4: A,A4: A,C2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ C2 @ A4 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_248_sup_OboundedE,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [B4: A,C2: A,A4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A4 )
% 0.31/1.54 => ~ ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.54 => ~ ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_249_sup__absorb2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [X3: A,Y2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.31/1.54 => ( ( sup_sup @ A @ X3 @ Y2 )
% 0.31/1.54 = Y2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_250_sup__absorb1,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [Y2: A,X3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.31/1.54 => ( ( sup_sup @ A @ X3 @ Y2 )
% 0.31/1.54 = X3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_251_sup_Oabsorb2,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.54 => ( ( sup_sup @ A @ A4 @ B4 )
% 0.31/1.54 = B4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_252_sup_Oabsorb1,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [B4: A,A4: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/1.54 => ( ( sup_sup @ A @ A4 @ B4 )
% 0.31/1.54 = A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_253_sup__unique,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [F: A > A > A,X3: A,Y2: A] :
% 0.31/1.54 ( ! [X2: A,Y3: A] : ( ord_less_eq @ A @ X2 @ ( F @ X2 @ Y3 ) )
% 0.31/1.54 => ( ! [X2: A,Y3: A] : ( ord_less_eq @ A @ Y3 @ ( F @ X2 @ Y3 ) )
% 0.31/1.54 => ( ! [X2: A,Y3: A,Z3: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ Y3 @ X2 )
% 0.31/1.54 => ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( F @ Y3 @ Z3 ) @ X2 ) ) )
% 0.31/1.54 => ( ( sup_sup @ A @ X3 @ Y2 )
% 0.31/1.54 = ( F @ X3 @ Y2 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_254_sup_OorderI,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A )
% 0.31/1.54 => ! [A4: A,B4: A] :
% 0.31/1.54 ( ( A4
% 0.31/1.54 = ( sup_sup @ A @ A4 @ B4 ) )
% 0.31/1.54 => ( ord_less_eq @ A @ B4 @ A4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ( type @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ( ord @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ( order @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linorder @ A )
% 0.31/1.54 => ( preorder @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 0.31/1.54 ! [A8: $tType,A9: $tType] :
% 0.31/1.54 ( ( comple187826305attice @ A9 )
% 0.31/1.54 => ( comple187826305attice @ ( A8 > A9 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.31/1.54 ! [A8: $tType,A9: $tType] :
% 0.31/1.54 ( ( semilattice_sup @ A9 )
% 0.31/1.54 => ( semilattice_sup @ ( A8 > A9 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.31/1.54 ! [A8: $tType,A9: $tType] :
% 0.31/1.54 ( ( boolean_algebra @ A9 )
% 0.31/1.54 => ( boolean_algebra @ ( A8 > A9 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_fun___Complete__Lattices_OSup,axiom,
% 0.31/1.54 ! [A8: $tType,A9: $tType] :
% 0.31/1.54 ( ( complete_Sup @ A9 )
% 0.31/1.54 => ( complete_Sup @ ( A8 > A9 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/1.54 ! [A8: $tType,A9: $tType] :
% 0.31/1.54 ( ( preorder @ A9 )
% 0.31/1.54 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/1.54 ! [A8: $tType,A9: $tType] :
% 0.31/1.54 ( ( order @ A9 )
% 0.31/1.54 => ( order @ ( A8 > A9 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/1.54 ! [A8: $tType,A9: $tType] :
% 0.31/1.54 ( ( ord @ A9 )
% 0.31/1.54 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_fun___Orderings_Obot,axiom,
% 0.31/1.54 ! [A8: $tType,A9: $tType] :
% 0.31/1.54 ( ( bot @ A9 )
% 0.31/1.54 => ( bot @ ( A8 > A9 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1,axiom,
% 0.31/1.54 ! [A8: $tType] : ( comple187826305attice @ ( set @ A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_2,axiom,
% 0.31/1.54 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_3,axiom,
% 0.31/1.54 ! [A8: $tType] : ( boolean_algebra @ ( set @ A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Set_Oset___Complete__Lattices_OSup_4,axiom,
% 0.31/1.54 ! [A8: $tType] : ( complete_Sup @ ( set @ A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.31/1.54 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.31/1.54 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Set_Oset___Orderings_Oord_7,axiom,
% 0.31/1.54 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Set_Oset___Orderings_Obot_8,axiom,
% 0.31/1.54 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_9,axiom,
% 0.31/1.54 comple187826305attice @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_10,axiom,
% 0.31/1.54 semilattice_sup @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_11,axiom,
% 0.31/1.54 boolean_algebra @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Complete__Lattices_OSup_12,axiom,
% 0.31/1.54 complete_Sup @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 0.31/1.54 preorder @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.31/1.54 linorder @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Orderings_Oorder_14,axiom,
% 0.31/1.54 order @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Orderings_Oord_15,axiom,
% 0.31/1.54 ord @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Orderings_Obot_16,axiom,
% 0.31/1.54 bot @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(help_If_3_1_T,axiom,
% 0.31/1.54 ! [P: $o] :
% 0.31/1.54 ( ( P = $true )
% 0.31/1.54 | ( P = $false ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(help_If_2_1_T,axiom,
% 0.31/1.54 ! [A: $tType,X3: A,Y2: A] :
% 0.31/1.54 ( ( if @ A @ $false @ X3 @ Y2 )
% 0.31/1.54 = Y2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(help_If_1_1_T,axiom,
% 0.31/1.54 ! [A: $tType,X3: A,Y2: A] :
% 0.31/1.54 ( ( if @ A @ $true @ X3 @ Y2 )
% 0.31/1.54 = X3 ) ).
% 0.31/1.54
% 0.31/1.54 thf(tfree_0,hypothesis,
% 0.31/1.54 linorder @ val ).
% 0.31/1.54
% 0.31/1.54 thf(conj_0,conjecture,
% 0.31/1.54 ord_less_eq @ ( set @ val ) @ scc @ p ).
% 0.31/1.54 ------------------------
% 0.31/1.56 % (17816)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/183Mi)
% 0.31/1.56 % (17819)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/2Mi)
% 0.31/1.56 % (17819)Instruction limit reached!
% 0.31/1.56 % (17819)------------------------------
% 0.31/1.56 % (17819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.56 % (17819)Termination reason: Unknown
% 0.31/1.56 % (17819)Termination phase: shuffling
% 0.31/1.56
% 0.31/1.56 % (17819)Memory used [KB]: 1279
% 0.31/1.56 % (17819)Time elapsed: 0.002 s
% 0.31/1.56 % (17819)Instructions burned: 2 (million)
% 0.31/1.56 % (17819)------------------------------
% 0.31/1.56 % (17819)------------------------------
% 0.31/1.57 % (17821)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_17623 for (2999ds/275Mi)
% 0.31/1.57 % (17820)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_17623 for (2999ds/2Mi)
% 0.31/1.57 % (17817)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_17623 for (2999ds/4Mi)
% 0.31/1.57 % (17820)Instruction limit reached!
% 0.31/1.57 % (17820)------------------------------
% 0.31/1.57 % (17820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.57 % (17820)Termination reason: Unknown
% 0.31/1.57 % (17820)Termination phase: shuffling
% 0.31/1.57
% 0.31/1.57 % (17820)Memory used [KB]: 1407
% 0.31/1.57 % (17820)Time elapsed: 0.003 s
% 0.31/1.57 % (17820)Instructions burned: 3 (million)
% 0.31/1.57 % (17820)------------------------------
% 0.31/1.57 % (17820)------------------------------
% 0.31/1.57 % (17822)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/18Mi)
% 0.31/1.57 % (17818)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_17623 for (2999ds/27Mi)
% 0.31/1.57 % (17823)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/3Mi)
% 0.31/1.57 % (17817)Instruction limit reached!
% 0.31/1.57 % (17817)------------------------------
% 0.31/1.57 % (17817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.57 % (17817)Termination reason: Unknown
% 0.31/1.57 % (17817)Termination phase: shuffling
% 0.31/1.57
% 0.31/1.57 % (17817)Memory used [KB]: 1407
% 0.31/1.57 % (17817)Time elapsed: 0.005 s
% 0.31/1.57 % (17817)Instructions burned: 5 (million)
% 0.31/1.57 % (17817)------------------------------
% 0.31/1.57 % (17817)------------------------------
% 0.31/1.57 % (17823)Instruction limit reached!
% 0.31/1.57 % (17823)------------------------------
% 0.31/1.57 % (17823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.57 % (17823)Termination reason: Unknown
% 0.31/1.57 % (17823)Termination phase: shuffling
% 0.31/1.57
% 0.31/1.57 % (17823)Memory used [KB]: 1407
% 0.31/1.57 % (17823)Time elapsed: 0.003 s
% 0.31/1.57 % (17823)Instructions burned: 5 (million)
% 0.31/1.57 % (17823)------------------------------
% 0.31/1.57 % (17823)------------------------------
% 0.31/1.58 % (17822)Instruction limit reached!
% 0.31/1.58 % (17822)------------------------------
% 0.31/1.58 % (17822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.58 % (17822)Termination reason: Unknown
% 0.31/1.58 % (17822)Termination phase: Property scanning
% 0.31/1.58
% 0.31/1.58 % (17822)Memory used [KB]: 1791
% 0.31/1.58 % (17822)Time elapsed: 0.008 s
% 0.31/1.58 % (17822)Instructions burned: 20 (million)
% 0.31/1.58 % (17822)------------------------------
% 0.31/1.58 % (17822)------------------------------
% 0.31/1.58 % (17826)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_17623 for (2999ds/3Mi)
% 0.31/1.58 % (17826)Instruction limit reached!
% 0.31/1.58 % (17826)------------------------------
% 0.31/1.58 % (17826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.58 % (17826)Termination reason: Unknown
% 0.31/1.58 % (17826)Termination phase: shuffling
% 0.31/1.58
% 0.31/1.58 % (17826)Memory used [KB]: 1407
% 0.31/1.58 % (17826)Time elapsed: 0.003 s
% 0.31/1.58 % (17826)Instructions burned: 5 (million)
% 0.31/1.58 % (17826)------------------------------
% 0.31/1.58 % (17826)------------------------------
% 0.31/1.58 % (17818)Instruction limit reached!
% 0.31/1.58 % (17818)------------------------------
% 0.31/1.58 % (17818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.58 % (17818)Termination reason: Unknown
% 0.31/1.58 % (17818)Termination phase: Property scanning
% 0.31/1.58
% 0.31/1.58 % (17818)Memory used [KB]: 1791
% 0.31/1.58 % (17818)Time elapsed: 0.017 s
% 0.31/1.58 % (17818)Instructions burned: 28 (million)
% 0.31/1.58 % (17818)------------------------------
% 0.31/1.58 % (17818)------------------------------
% 0.31/1.59 % (17824)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_17623 for (2999ds/37Mi)
% 0.31/1.59 % (17827)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_17623 for (2999ds/1041Mi)
% 0.31/1.59 % (17825)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_17623 for (2999ds/15Mi)
% 0.31/1.59 % (17828)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/7Mi)
% 0.31/1.59 % (17825)Instruction limit reached!
% 0.31/1.59 % (17825)------------------------------
% 0.31/1.59 % (17825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (17825)Termination reason: Unknown
% 0.31/1.59 % (17825)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (17825)Memory used [KB]: 1791
% 0.31/1.59 % (17825)Time elapsed: 0.009 s
% 0.31/1.59 % (17825)Instructions burned: 16 (million)
% 0.31/1.59 % (17825)------------------------------
% 0.31/1.59 % (17825)------------------------------
% 0.31/1.60 % (17828)Instruction limit reached!
% 0.31/1.60 % (17828)------------------------------
% 0.31/1.60 % (17828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.60 % (17828)Termination reason: Unknown
% 0.31/1.60 % (17828)Termination phase: shuffling
% 0.31/1.60
% 0.31/1.60 % (17828)Memory used [KB]: 1535
% 0.31/1.60 % (17828)Time elapsed: 0.004 s
% 0.31/1.60 % (17828)Instructions burned: 8 (million)
% 0.31/1.60 % (17828)------------------------------
% 0.31/1.60 % (17828)------------------------------
% 2.82/1.60 % (17829)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/16Mi)
% 2.82/1.60 % (17824)Instruction limit reached!
% 2.82/1.60 % (17824)------------------------------
% 2.82/1.60 % (17824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.60 % (17824)Termination reason: Unknown
% 2.82/1.60 % (17824)Termination phase: Property scanning
% 2.82/1.60
% 2.82/1.60 % (17824)Memory used [KB]: 2174
% 2.82/1.60 % (17824)Time elapsed: 0.020 s
% 2.82/1.60 % (17824)Instructions burned: 37 (million)
% 2.82/1.60 % (17824)------------------------------
% 2.82/1.60 % (17824)------------------------------
% 2.82/1.60 % (17830)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_17623 for (2999ds/3Mi)
% 2.82/1.60 % (17829)Instruction limit reached!
% 2.82/1.60 % (17829)------------------------------
% 2.82/1.60 % (17829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.60 % (17829)Termination reason: Unknown
% 2.82/1.60 % (17829)Termination phase: shuffling
% 2.82/1.60
% 2.82/1.60 % (17829)Memory used [KB]: 1791
% 2.82/1.60 % (17829)Time elapsed: 0.007 s
% 2.82/1.60 % (17829)Instructions burned: 18 (million)
% 2.82/1.60 % (17829)------------------------------
% 2.82/1.60 % (17829)------------------------------
% 2.82/1.61 % (17831)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_17623 for (2999ds/3Mi)
% 2.82/1.61 % (17830)Instruction limit reached!
% 2.82/1.61 % (17830)------------------------------
% 2.82/1.61 % (17830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.61 % (17830)Termination reason: Unknown
% 2.82/1.61 % (17830)Termination phase: shuffling
% 2.82/1.61
% 2.82/1.61 % (17830)Memory used [KB]: 1407
% 2.82/1.61 % (17830)Time elapsed: 0.003 s
% 2.82/1.61 % (17830)Instructions burned: 4 (million)
% 2.82/1.61 % (17830)------------------------------
% 2.82/1.61 % (17830)------------------------------
% 2.82/1.61 % (17831)Instruction limit reached!
% 2.82/1.61 % (17831)------------------------------
% 2.82/1.61 % (17831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.61 % (17831)Termination reason: Unknown
% 2.82/1.61 % (17831)Termination phase: shuffling
% 2.82/1.61
% 2.82/1.61 % (17831)Memory used [KB]: 1407
% 2.82/1.61 % (17831)Time elapsed: 0.002 s
% 2.82/1.61 % (17831)Instructions burned: 3 (million)
% 2.82/1.61 % (17831)------------------------------
% 2.82/1.61 % (17831)------------------------------
% 2.82/1.61 % (17833)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/3Mi)
% 2.82/1.61 % (17832)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/7Mi)
% 2.82/1.62 % (17835)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/18Mi)
% 2.82/1.62 % (17833)Instruction limit reached!
% 2.82/1.62 % (17833)------------------------------
% 2.82/1.62 % (17833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (17833)Termination reason: Unknown
% 2.82/1.62 % (17833)Termination phase: shuffling
% 2.82/1.62
% 2.82/1.62 % (17833)Memory used [KB]: 1407
% 2.82/1.62 % (17833)Time elapsed: 0.003 s
% 2.82/1.62 % (17833)Instructions burned: 5 (million)
% 2.82/1.62 % (17833)------------------------------
% 2.82/1.62 % (17833)------------------------------
% 2.82/1.62 % (17834)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/4Mi)
% 2.82/1.62 % (17832)Instruction limit reached!
% 2.82/1.62 % (17832)------------------------------
% 2.82/1.62 % (17832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (17832)Termination reason: Unknown
% 2.82/1.62 % (17832)Termination phase: shuffling
% 2.82/1.62
% 2.82/1.62 % (17832)Memory used [KB]: 1535
% 2.82/1.62 % (17832)Time elapsed: 0.004 s
% 2.82/1.62 % (17832)Instructions burned: 8 (million)
% 2.82/1.62 % (17832)------------------------------
% 2.82/1.62 % (17832)------------------------------
% 2.82/1.62 % (17834)Instruction limit reached!
% 2.82/1.62 % (17834)------------------------------
% 2.82/1.62 % (17834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (17834)Termination reason: Unknown
% 2.82/1.62 % (17834)Termination phase: shuffling
% 2.82/1.62
% 2.82/1.62 % (17834)Memory used [KB]: 1407
% 2.82/1.62 % (17834)Time elapsed: 0.004 s
% 2.82/1.62 % (17834)Instructions burned: 6 (million)
% 2.82/1.62 % (17834)------------------------------
% 2.82/1.62 % (17834)------------------------------
% 2.82/1.62 % (17835)Instruction limit reached!
% 2.82/1.62 % (17835)------------------------------
% 2.82/1.62 % (17835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (17835)Termination reason: Unknown
% 2.82/1.62 % (17835)Termination phase: Property scanning
% 2.82/1.62
% 2.82/1.62 % (17835)Memory used [KB]: 1791
% 2.82/1.62 % (17835)Time elapsed: 0.008 s
% 2.82/1.62 % (17835)Instructions burned: 20 (million)
% 2.82/1.62 % (17835)------------------------------
% 2.82/1.62 % (17835)------------------------------
% 2.82/1.63 % (17836)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/710Mi)
% 2.82/1.63 % (17837)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/6Mi)
% 2.82/1.63 % (17838)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_17623 for (2999ds/902Mi)
% 2.82/1.63 % (17837)Instruction limit reached!
% 2.82/1.63 % (17837)------------------------------
% 2.82/1.63 % (17837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.63 % (17837)Termination reason: Unknown
% 2.82/1.63 % (17837)Termination phase: shuffling
% 2.82/1.63
% 2.82/1.63 % (17837)Memory used [KB]: 1407
% 2.82/1.63 % (17837)Time elapsed: 0.004 s
% 2.82/1.63 % (17837)Instructions burned: 6 (million)
% 2.82/1.63 % (17837)------------------------------
% 2.82/1.63 % (17837)------------------------------
% 2.82/1.64 % (17816)Instruction limit reached!
% 2.82/1.64 % (17816)------------------------------
% 2.82/1.64 % (17816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.64 % (17816)Termination reason: Unknown
% 2.82/1.64 % (17816)Termination phase: Saturation
% 2.82/1.64
% 2.82/1.64 % (17816)Memory used [KB]: 7164
% 2.82/1.64 % (17816)Time elapsed: 0.072 s
% 2.82/1.64 % (17816)Instructions burned: 185 (million)
% 2.82/1.64 % (17816)------------------------------
% 2.82/1.64 % (17816)------------------------------
% 2.82/1.64 % (17842)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_17623 for (2999ds/21Mi)
% 2.82/1.64 % (17845)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/5Mi)
% 2.82/1.64 % (17845)Instruction limit reached!
% 2.82/1.64 % (17845)------------------------------
% 2.82/1.64 % (17845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.64 % (17845)Termination reason: Unknown
% 2.82/1.64 % (17845)Termination phase: shuffling
% 2.82/1.64
% 2.82/1.64 % (17845)Memory used [KB]: 1407
% 2.82/1.64 % (17845)Time elapsed: 0.004 s
% 2.82/1.64 % (17845)Instructions burned: 7 (million)
% 2.82/1.64 % (17845)------------------------------
% 2.82/1.64 % (17845)------------------------------
% 2.82/1.65 % (17846)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_17623 for (2999ds/6Mi)
% 2.82/1.65 % (17846)Instruction limit reached!
% 2.82/1.65 % (17846)------------------------------
% 2.82/1.65 % (17846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.65 % (17846)Termination reason: Unknown
% 2.82/1.65 % (17846)Termination phase: shuffling
% 2.82/1.65
% 2.82/1.65 % (17846)Memory used [KB]: 1407
% 2.82/1.65 % (17846)Time elapsed: 0.003 s
% 2.82/1.65 % (17846)Instructions burned: 6 (million)
% 2.82/1.65 % (17846)------------------------------
% 2.82/1.65 % (17846)------------------------------
% 2.82/1.65 % (17842)Instruction limit reached!
% 2.82/1.65 % (17842)------------------------------
% 2.82/1.65 % (17842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.65 % (17842)Termination reason: Unknown
% 2.82/1.65 % (17842)Termination phase: Property scanning
% 2.82/1.65
% 2.82/1.65 % (17842)Memory used [KB]: 1791
% 2.82/1.65 % (17842)Time elapsed: 0.013 s
% 2.82/1.65 % (17842)Instructions burned: 22 (million)
% 2.82/1.65 % (17842)------------------------------
% 2.82/1.65 % (17842)------------------------------
% 2.82/1.65 % (17847)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17623 for (2999ds/377Mi)
% 2.82/1.66 % (17848)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_17623 for (2999ds/779Mi)
% 2.82/1.66 % (17821)Instruction limit reached!
% 2.82/1.66 % (17821)------------------------------
% 2.82/1.66 % (17821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.66 % (17821)Termination reason: Unknown
% 2.82/1.66 % (17821)Termination phase: Saturation
% 2.82/1.66
% 2.82/1.66 % (17821)Memory used [KB]: 6780
% 2.82/1.66 % (17821)Time elapsed: 0.094 s
% 2.82/1.66 % (17821)Instructions burned: 275 (million)
% 2.82/1.66 % (17821)------------------------------
% 2.82/1.66 % (17821)------------------------------
% 2.82/1.66 % (17849)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_17623 for (2999ds/19Mi)
% 2.82/1.67 % (17849)Instruction limit reached!
% 2.82/1.67 % (17849)------------------------------
% 2.82/1.67 % (17849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.67 % (17849)Termination reason: Unknown
% 2.82/1.67 % (17849)Termination phase: shuffling
% 2.82/1.67
% 2.82/1.67 % (17849)Memory used [KB]: 1791
% 2.82/1.67 % (17849)Time elapsed: 0.007 s
% 2.82/1.67 % (17849)Instructions burned: 20 (million)
% 2.82/1.67 % (17849)------------------------------
% 2.82/1.67 % (17849)------------------------------
% 2.82/1.67 % (17850)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_17623 for (2998ds/879Mi)
% 2.82/1.68 % (17852)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17623 for (2998ds/17Mi)
% 2.82/1.68 % (17852)Instruction limit reached!
% 2.82/1.68 % (17852)------------------------------
% 2.82/1.68 % (17852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.68 % (17852)Termination reason: Unknown
% 2.82/1.68 % (17852)Termination phase: shuffling
% 2.82/1.68
% 2.82/1.68 % (17852)Memory used [KB]: 1791
% 2.82/1.68 % (17852)Time elapsed: 0.008 s
% 2.82/1.68 % (17852)Instructions burned: 18 (million)
% 2.82/1.68 % (17852)------------------------------
% 2.82/1.68 % (17852)------------------------------
% 2.82/1.69 % (17854)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17623 for (2998ds/3Mi)
% 2.82/1.70 % (17854)Instruction limit reached!
% 2.82/1.70 % (17854)------------------------------
% 2.82/1.70 % (17854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.70 % (17854)Termination reason: Unknown
% 2.82/1.70 % (17854)Termination phase: shuffling
% 2.82/1.70
% 2.82/1.70 % (17854)Memory used [KB]: 1407
% 2.82/1.70 % (17854)Time elapsed: 0.003 s
% 2.82/1.70 % (17854)Instructions burned: 3 (million)
% 2.82/1.70 % (17854)------------------------------
% 2.82/1.70 % (17854)------------------------------
% 2.82/1.71 % (17862)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_17623 for (2998ds/30Mi)
% 2.82/1.72 % (17862)Instruction limit reached!
% 2.82/1.72 % (17862)------------------------------
% 2.82/1.72 % (17862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.72 % (17862)Termination reason: Unknown
% 2.82/1.72 % (17862)Termination phase: Preprocessing 1
% 2.82/1.72
% 2.82/1.72 % (17862)Memory used [KB]: 1791
% 2.82/1.72 % (17862)Time elapsed: 0.011 s
% 2.82/1.72 % (17862)Instructions burned: 31 (million)
% 2.82/1.72 % (17862)------------------------------
% 2.82/1.72 % (17862)------------------------------
% 2.82/1.73 % (17868)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_17623 for (2998ds/127Mi)
% 2.82/1.77 % (17868)Instruction limit reached!
% 2.82/1.77 % (17868)------------------------------
% 2.82/1.77 % (17868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.77 % (17868)Termination reason: Unknown
% 2.82/1.77 % (17868)Termination phase: Saturation
% 2.82/1.77
% 2.82/1.77 % (17868)Memory used [KB]: 7036
% 2.82/1.77 % (17868)Time elapsed: 0.041 s
% 2.82/1.77 % (17868)Instructions burned: 128 (million)
% 2.82/1.77 % (17868)------------------------------
% 2.82/1.77 % (17868)------------------------------
% 2.82/1.78 % (17883)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_17623 for (2997ds/100Mi)
% 2.82/1.82 % (17883)Instruction limit reached!
% 2.82/1.82 % (17883)------------------------------
% 2.82/1.82 % (17883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.82 % (17883)Termination reason: Unknown
% 2.82/1.82 % (17883)Termination phase: Saturation
% 2.82/1.82
% 2.82/1.82 % (17883)Memory used [KB]: 2302
% 2.82/1.82 % (17883)Time elapsed: 0.036 s
% 2.82/1.82 % (17883)Instructions burned: 100 (million)
% 2.82/1.82 % (17883)------------------------------
% 2.82/1.82 % (17883)------------------------------
% 2.82/1.82 % (17847)Instruction limit reached!
% 2.82/1.82 % (17847)------------------------------
% 2.82/1.82 % (17847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.82 % (17847)Termination reason: Unknown
% 2.82/1.82 % (17847)Termination phase: Saturation
% 2.82/1.82
% 2.82/1.82 % (17847)Memory used [KB]: 7803
% 2.82/1.82 % (17847)Time elapsed: 0.170 s
% 2.82/1.82 % (17847)Instructions burned: 378 (million)
% 2.82/1.82 % (17847)------------------------------
% 2.82/1.82 % (17847)------------------------------
% 2.82/1.84 % (17889)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_17623 for (2997ds/3Mi)
% 2.82/1.84 % (17890)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_17623 for (2997ds/20Mi)
% 2.82/1.84 % (17889)Instruction limit reached!
% 2.82/1.84 % (17889)------------------------------
% 2.82/1.84 % (17889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.84 % (17889)Termination reason: Unknown
% 2.82/1.84 % (17889)Termination phase: shuffling
% 2.82/1.84
% 2.82/1.84 % (17889)Memory used [KB]: 1407
% 2.82/1.84 % (17889)Time elapsed: 0.004 s
% 2.82/1.84 % (17889)Instructions burned: 4 (million)
% 2.82/1.84 % (17889)------------------------------
% 2.82/1.84 % (17889)------------------------------
% 2.82/1.85 % (17890)Instruction limit reached!
% 2.82/1.85 % (17890)------------------------------
% 2.82/1.85 % (17890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.85 % (17890)Termination reason: Unknown
% 2.82/1.85 % (17890)Termination phase: Property scanning
% 2.82/1.85
% 2.82/1.85 % (17890)Memory used [KB]: 1791
% 2.82/1.85 % (17890)Time elapsed: 0.012 s
% 2.82/1.85 % (17890)Instructions burned: 21 (million)
% 2.82/1.85 % (17890)------------------------------
% 2.82/1.85 % (17890)------------------------------
% 2.82/1.85 % (17891)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_17623 for (2997ds/86Mi)
% 2.82/1.87 % (17893)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_17623 for (2997ds/107Mi)
% 2.82/1.89 % (17891)Instruction limit reached!
% 2.82/1.89 % (17891)------------------------------
% 2.82/1.89 % (17891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.89 % (17891)Termination reason: Unknown
% 2.82/1.89 % (17891)Termination phase: Saturation
% 2.82/1.89
% 2.82/1.89 % (17891)Memory used [KB]: 6908
% 2.82/1.89 % (17891)Time elapsed: 0.043 s
% 2.82/1.89 % (17891)Instructions burned: 87 (million)
% 2.82/1.89 % (17891)------------------------------
% 2.82/1.89 % (17891)------------------------------
% 2.82/1.91 % (17893)Instruction limit reached!
% 2.82/1.91 % (17893)------------------------------
% 2.82/1.91 % (17893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.91 % (17893)Termination reason: Unknown
% 2.82/1.91 % (17893)Termination phase: Saturation
% 2.82/1.91
% 2.82/1.91 % (17893)Memory used [KB]: 6908
% 2.82/1.91 % (17893)Time elapsed: 0.043 s
% 2.82/1.91 % (17893)Instructions burned: 109 (million)
% 2.82/1.91 % (17893)------------------------------
% 2.82/1.91 % (17893)------------------------------
% 2.82/1.91 % (17836)Instruction limit reached!
% 2.82/1.91 % (17836)------------------------------
% 2.82/1.91 % (17836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.91 % (17836)Termination reason: Unknown
% 2.82/1.91 % (17836)Termination phase: Saturation
% 2.82/1.91
% 2.82/1.91 % (17836)Memory used [KB]: 7547
% 2.82/1.91 % (17836)Time elapsed: 0.284 s
% 2.82/1.91 % (17836)Instructions burned: 711 (million)
% 2.82/1.91 % (17836)------------------------------
% 2.82/1.91 % (17836)------------------------------
% 2.82/1.91 % (17897)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_17623 for (2996ds/39Mi)
% 2.82/1.92 % (17898)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_17623 for (2996ds/448Mi)
% 2.82/1.92 % (17899)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_17623 for (2996ds/46Mi)
% 2.82/1.93 % (17897)Instruction limit reached!
% 2.82/1.93 % (17897)------------------------------
% 2.82/1.93 % (17897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.93 % (17897)Termination reason: Unknown
% 2.82/1.93 % (17897)Termination phase: Property scanning
% 2.82/1.93
% 2.82/1.93 % (17897)Memory used [KB]: 2174
% 2.82/1.93 % (17897)Time elapsed: 0.015 s
% 2.82/1.93 % (17897)Instructions burned: 39 (million)
% 2.82/1.93 % (17897)------------------------------
% 2.82/1.93 % (17897)------------------------------
% 2.82/1.93 % (17902)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_17623 for (2996ds/98Mi)
% 2.82/1.94 % (17899)Instruction limit reached!
% 2.82/1.94 % (17899)------------------------------
% 2.82/1.94 % (17899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.94 % (17899)Termination reason: Unknown
% 2.82/1.94 % (17899)Termination phase: Preprocessing 3
% 2.82/1.94
% 2.82/1.94 % (17899)Memory used [KB]: 2174
% 2.82/1.94 % (17899)Time elapsed: 0.016 s
% 2.82/1.94 % (17899)Instructions burned: 46 (million)
% 2.82/1.94 % (17899)------------------------------
% 2.82/1.94 % (17899)------------------------------
% 2.82/1.95 % (17903)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_17623 for (2996ds/507Mi)
% 2.82/1.96 % (17902)Instruction limit reached!
% 2.82/1.96 % (17902)------------------------------
% 2.82/1.96 % (17902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.96 % (17902)Termination reason: Unknown
% 2.82/1.96 % (17902)Termination phase: Saturation
% 2.82/1.96
% 2.82/1.96 % (17902)Memory used [KB]: 2302
% 2.82/1.96 % (17902)Time elapsed: 0.028 s
% 2.82/1.96 % (17902)Instructions burned: 100 (million)
% 2.82/1.96 % (17902)------------------------------
% 2.82/1.96 % (17902)------------------------------
% 2.82/1.97 % (17904)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_17623 for (2995ds/149Mi)
% 2.82/1.98 % (17848)Instruction limit reached!
% 2.82/1.98 % (17848)------------------------------
% 2.82/1.98 % (17848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.98 % (17848)Termination reason: Unknown
% 2.82/1.98 % (17848)Termination phase: Saturation
% 2.82/1.98
% 2.82/1.98 % (17848)Memory used [KB]: 7803
% 2.82/1.98 % (17848)Time elapsed: 0.320 s
% 2.82/1.98 % (17848)Instructions burned: 779 (million)
% 2.82/1.98 % (17848)------------------------------
% 2.82/1.98 % (17848)------------------------------
% 2.82/1.98 % (17827)Instruction limit reached!
% 2.82/1.98 % (17827)------------------------------
% 2.82/1.98 % (17827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.98 % (17827)Termination reason: Unknown
% 2.82/1.98 % (17827)Termination phase: Saturation
% 2.82/1.98
% 2.82/1.98 % (17827)Memory used [KB]: 9466
% 2.82/1.98 % (17827)Time elapsed: 0.398 s
% 2.82/1.98 % (17827)Instructions burned: 1043 (million)
% 2.82/1.98 % (17827)------------------------------
% 2.82/1.98 % (17827)------------------------------
% 2.82/1.98 % (17838)Instruction limit reached!
% 2.82/1.98 % (17838)------------------------------
% 2.82/1.98 % (17838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.98 % (17838)Termination reason: Unknown
% 2.82/1.98 % (17838)Termination phase: Saturation
% 2.82/1.98
% 2.82/1.98 % (17838)Memory used [KB]: 9210
% 2.82/1.98 % (17838)Time elapsed: 0.357 s
% 2.82/1.98 % (17838)Instructions burned: 903 (million)
% 2.82/1.98 % (17838)------------------------------
% 2.82/1.98 % (17838)------------------------------
% 2.82/1.99 % (17905)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_17623 for (2995ds/39Mi)
% 2.82/1.99 % (17906)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_17623 for (2995ds/6Mi)
% 2.82/1.99 % (17907)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_17623 for (2995ds/1087Mi)
% 2.82/1.99 % (17906)Instruction limit reached!
% 2.82/1.99 % (17906)------------------------------
% 2.82/1.99 % (17906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.99 % (17906)Termination reason: Unknown
% 2.82/1.99 % (17906)Termination phase: shuffling
% 2.82/1.99
% 2.82/1.99 % (17906)Memory used [KB]: 1407
% 2.82/1.99 % (17906)Time elapsed: 0.003 s
% 2.82/1.99 % (17906)Instructions burned: 7 (million)
% 2.82/1.99 % (17906)------------------------------
% 2.82/1.99 % (17906)------------------------------
% 2.82/2.00 % (17905)Instruction limit reached!
% 2.82/2.00 % (17905)------------------------------
% 2.82/2.00 % (17905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/2.00 % (17905)Termination reason: Unknown
% 2.82/2.00 % (17905)Termination phase: Preprocessing 3
% 2.82/2.00
% 2.82/2.00 % (17905)Memory used [KB]: 2174
% 2.82/2.00 % (17905)Time elapsed: 0.013 s
% 2.82/2.00 % (17905)Instructions burned: 39 (million)
% 2.82/2.00 % (17905)------------------------------
% 2.82/2.00 % (17905)------------------------------
% 2.82/2.00 % (17908)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_17623 for (2995ds/47Mi)
% 2.82/2.01 % (17909)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_17623 for (2995ds/44Mi)
% 5.97/2.02 % (17904)Instruction limit reached!
% 5.97/2.02 % (17904)------------------------------
% 5.97/2.02 % (17904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.02 % (17904)Termination reason: Unknown
% 5.97/2.02 % (17904)Termination phase: Saturation
% 5.97/2.02
% 5.97/2.02 % (17904)Memory used [KB]: 7036
% 5.97/2.02 % (17904)Time elapsed: 0.067 s
% 5.97/2.02 % (17904)Instructions burned: 150 (million)
% 5.97/2.02 % (17904)------------------------------
% 5.97/2.02 % (17904)------------------------------
% 5.97/2.02 % (17908)Instruction limit reached!
% 5.97/2.02 % (17908)------------------------------
% 5.97/2.02 % (17908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.02 % (17908)Termination reason: Unknown
% 5.97/2.02 % (17908)Termination phase: Property scanning
% 5.97/2.02
% 5.97/2.02 % (17908)Memory used [KB]: 2302
% 5.97/2.02 % (17908)Time elapsed: 0.015 s
% 5.97/2.02 % (17908)Instructions burned: 47 (million)
% 5.97/2.02 % (17908)------------------------------
% 5.97/2.02 % (17908)------------------------------
% 5.97/2.02 % (17909)Instruction limit reached!
% 5.97/2.02 % (17909)------------------------------
% 5.97/2.02 % (17909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.02 % (17909)Termination reason: Unknown
% 5.97/2.02 % (17909)Termination phase: Property scanning
% 5.97/2.02
% 5.97/2.02 % (17909)Memory used [KB]: 2174
% 5.97/2.02 % (17909)Time elapsed: 0.013 s
% 5.97/2.02 % (17909)Instructions burned: 44 (million)
% 5.97/2.02 % (17909)------------------------------
% 5.97/2.02 % (17909)------------------------------
% 5.97/2.02 % (17850)Instruction limit reached!
% 5.97/2.02 % (17850)------------------------------
% 5.97/2.02 % (17850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.02 % (17850)Termination reason: Unknown
% 5.97/2.02 % (17850)Termination phase: Saturation
% 5.97/2.02
% 5.97/2.02 % (17850)Memory used [KB]: 7931
% 5.97/2.02 % (17850)Time elapsed: 0.357 s
% 5.97/2.02 % (17850)Instructions burned: 879 (million)
% 5.97/2.02 % (17850)------------------------------
% 5.97/2.02 % (17850)------------------------------
% 5.97/2.03 % (17910)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_17623 for (2995ds/432Mi)
% 5.97/2.03 % (17911)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_17623 for (2995ds/62Mi)
% 5.97/2.03 % (17912)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_17623 for (2995ds/31Mi)
% 5.97/2.03 % (17913)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_17623 for (2995ds/96Mi)
% 5.97/2.04 % (17912)Instruction limit reached!
% 5.97/2.04 % (17912)------------------------------
% 5.97/2.04 % (17912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.04 % (17912)Termination reason: Unknown
% 5.97/2.04 % (17912)Termination phase: Preprocessing 1
% 5.97/2.04
% 5.97/2.04 % (17912)Memory used [KB]: 1791
% 5.97/2.04 % (17912)Time elapsed: 0.011 s
% 5.97/2.04 % (17912)Instructions burned: 32 (million)
% 5.97/2.04 % (17912)------------------------------
% 5.97/2.04 % (17912)------------------------------
% 5.97/2.04 % (17911)Instruction limit reached!
% 5.97/2.04 % (17911)------------------------------
% 5.97/2.04 % (17911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.04 % (17911)Termination reason: Unknown
% 5.97/2.04 % (17911)Termination phase: Preprocessing 1
% 5.97/2.04
% 5.97/2.04 % (17911)Memory used [KB]: 2174
% 5.97/2.04 % (17911)Time elapsed: 0.018 s
% 5.97/2.04 % (17911)Instructions burned: 63 (million)
% 5.97/2.04 % (17911)------------------------------
% 5.97/2.04 % (17911)------------------------------
% 5.97/2.05 % (17920)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_17623 for (2995ds/453Mi)
% 5.97/2.05 % (17898)Instruction limit reached!
% 5.97/2.05 % (17898)------------------------------
% 5.97/2.05 % (17898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.05 % (17898)Termination reason: Unknown
% 5.97/2.05 % (17898)Termination phase: Saturation
% 5.97/2.05
% 5.97/2.05 % (17898)Memory used [KB]: 7675
% 5.97/2.05 % (17898)Time elapsed: 0.135 s
% 5.97/2.05 % (17898)Instructions burned: 450 (million)
% 5.97/2.05 % (17898)------------------------------
% 5.97/2.05 % (17898)------------------------------
% 5.97/2.05 % (17924)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_17623 for (2994ds/71Mi)
% 5.97/2.06 % (17929)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_17623 for (2994ds/83Mi)
% 5.97/2.06 % (17913)Instruction limit reached!
% 5.97/2.06 % (17913)------------------------------
% 5.97/2.06 % (17913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.06 % (17913)Termination reason: Unknown
% 5.97/2.06 % (17913)Termination phase: Saturation
% 5.97/2.06
% 5.97/2.06 % (17913)Memory used [KB]: 6908
% 5.97/2.06 % (17913)Time elapsed: 0.030 s
% 5.97/2.06 % (17913)Instructions burned: 97 (million)
% 5.97/2.06 % (17913)------------------------------
% 5.97/2.06 % (17913)------------------------------
% 5.97/2.07 % (17935)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_17623 for (2994ds/11Mi)
% 5.97/2.07 % (17924)Instruction limit reached!
% 5.97/2.07 % (17924)------------------------------
% 5.97/2.07 % (17924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.07 % (17924)Termination reason: Unknown
% 5.97/2.07 % (17924)Termination phase: Property scanning
% 5.97/2.07
% 5.97/2.07 % (17924)Memory used [KB]: 2302
% 5.97/2.07 % (17924)Time elapsed: 0.022 s
% 5.97/2.07 % (17924)Instructions burned: 71 (million)
% 5.97/2.07 % (17924)------------------------------
% 5.97/2.07 % (17924)------------------------------
% 5.97/2.08 % (17935)Instruction limit reached!
% 5.97/2.08 % (17935)------------------------------
% 5.97/2.08 % (17935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.08 % (17935)Termination reason: Unknown
% 5.97/2.08 % (17935)Termination phase: shuffling
% 5.97/2.08
% 5.97/2.08 % (17935)Memory used [KB]: 1663
% 5.97/2.08 % (17935)Time elapsed: 0.005 s
% 5.97/2.08 % (17935)Instructions burned: 14 (million)
% 5.97/2.08 % (17935)------------------------------
% 5.97/2.08 % (17935)------------------------------
% 5.97/2.08 % (17941)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_17623 for (2994ds/41Mi)
% 5.97/2.09 % (17943)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17623 for (2994ds/6Mi)
% 5.97/2.09 % (17943)Instruction limit reached!
% 5.97/2.09 % (17943)------------------------------
% 5.97/2.09 % (17943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.09 % (17943)Termination reason: Unknown
% 5.97/2.09 % (17943)Termination phase: shuffling
% 5.97/2.09 % (17929)Instruction limit reached!
% 5.97/2.09 % (17929)------------------------------
% 5.97/2.09 % (17929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.09
% 5.97/2.09 % (17929)Termination reason: Unknown
% 5.97/2.09 % (17943)Memory used [KB]: 1535
% 5.97/2.09 % (17929)Termination phase: Saturation
% 5.97/2.09 % (17943)Time elapsed: 0.003 s
% 5.97/2.09
% 5.97/2.09 % (17943)Instructions burned: 7 (million)
% 5.97/2.09 % (17943)------------------------------
% 5.97/2.09 % (17943)------------------------------
% 5.97/2.09 % (17929)Memory used [KB]: 6780
% 5.97/2.09 % (17929)Time elapsed: 0.027 s
% 5.97/2.09 % (17929)Instructions burned: 84 (million)
% 5.97/2.09 % (17929)------------------------------
% 5.97/2.09 % (17929)------------------------------
% 5.97/2.10 % (17941)Instruction limit reached!
% 5.97/2.10 % (17941)------------------------------
% 5.97/2.10 % (17941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.10 % (17941)Termination reason: Unknown
% 5.97/2.10 % (17941)Termination phase: Property scanning
% 5.97/2.10
% 5.97/2.10 % (17941)Memory used [KB]: 2174
% 5.97/2.10 % (17941)Time elapsed: 0.013 s
% 5.97/2.10 % (17941)Instructions burned: 44 (million)
% 5.97/2.10 % (17941)------------------------------
% 5.97/2.10 % (17941)------------------------------
% 5.97/2.10 % (17949)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_17623 for (2994ds/150Mi)
% 5.97/2.10 % (17950)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_17623 for (2994ds/343Mi)
% 5.97/2.11 % (17958)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_17623 for (2994ds/109Mi)
% 5.97/2.11 % (17903)Instruction limit reached!
% 5.97/2.11 % (17903)------------------------------
% 5.97/2.11 % (17903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.11 % (17903)Termination reason: Unknown
% 5.97/2.11 % (17903)Termination phase: Saturation
% 5.97/2.11
% 5.97/2.11 % (17903)Memory used [KB]: 7931
% 5.97/2.11 % (17903)Time elapsed: 0.182 s
% 5.97/2.11 % (17903)Instructions burned: 509 (million)
% 5.97/2.11 % (17903)------------------------------
% 5.97/2.11 % (17903)------------------------------
% 6.47/2.12 % (17964)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_17623 for (2994ds/253Mi)
% 6.47/2.14 % (17958)Instruction limit reached!
% 6.47/2.14 % (17958)------------------------------
% 6.47/2.14 % (17958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.14 % (17958)Termination reason: Unknown
% 6.47/2.14 % (17958)Termination phase: Saturation
% 6.47/2.14
% 6.47/2.14 % (17958)Memory used [KB]: 6908
% 6.47/2.14 % (17958)Time elapsed: 0.034 s
% 6.47/2.14 % (17958)Instructions burned: 111 (million)
% 6.47/2.14 % (17958)------------------------------
% 6.47/2.14 % (17958)------------------------------
% 6.47/2.14 % (17949)Instruction limit reached!
% 6.47/2.14 % (17949)------------------------------
% 6.47/2.14 % (17949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.14 % (17949)Termination reason: Unknown
% 6.47/2.14 % (17949)Termination phase: Saturation
% 6.47/2.14
% 6.47/2.14 % (17949)Memory used [KB]: 7164
% 6.47/2.14 % (17949)Time elapsed: 0.048 s
% 6.47/2.14 % (17949)Instructions burned: 151 (million)
% 6.47/2.14 % (17949)------------------------------
% 6.47/2.14 % (17949)------------------------------
% 6.47/2.15 % (17977)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_17623 for (2994ds/140Mi)
% 6.47/2.15 % (17979)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_17623 for (2994ds/614Mi)
% 6.47/2.16 % (17910)Instruction limit reached!
% 6.47/2.16 % (17910)------------------------------
% 6.47/2.16 % (17910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.16 % (17910)Termination reason: Unknown
% 6.47/2.16 % (17910)Termination phase: Saturation
% 6.47/2.16
% 6.47/2.16 % (17910)Memory used [KB]: 4477
% 6.47/2.16 % (17910)Time elapsed: 0.133 s
% 6.47/2.16 % (17910)Instructions burned: 434 (million)
% 6.47/2.16 % (17910)------------------------------
% 6.47/2.16 % (17910)------------------------------
% 6.47/2.17 % (17984)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_17623 for (2993ds/202Mi)
% 6.47/2.18 % (17920)Instruction limit reached!
% 6.47/2.18 % (17920)------------------------------
% 6.47/2.18 % (17920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.18 % (17920)Termination reason: Unknown
% 6.47/2.18 % (17920)Termination phase: Saturation
% 6.47/2.18
% 6.47/2.18 % (17920)Memory used [KB]: 7803
% 6.47/2.18 % (17920)Time elapsed: 0.134 s
% 6.47/2.18 % (17920)Instructions burned: 454 (million)
% 6.47/2.18 % (17920)------------------------------
% 6.47/2.18 % (17920)------------------------------
% 6.47/2.19 % (17994)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_17623 for (2993ds/339Mi)
% 6.47/2.19 % (17977)Instruction limit reached!
% 6.47/2.19 % (17977)------------------------------
% 6.47/2.19 % (17977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.19 % (17977)Termination reason: Unknown
% 6.47/2.19 % (17977)Termination phase: Saturation
% 6.47/2.19
% 6.47/2.19 % (17977)Memory used [KB]: 6780
% 6.47/2.19 % (17977)Time elapsed: 0.046 s
% 6.47/2.19 % (17977)Instructions burned: 141 (million)
% 6.47/2.19 % (17977)------------------------------
% 6.47/2.19 % (17977)------------------------------
% 6.47/2.20 % (17964)Instruction limit reached!
% 6.47/2.20 % (17964)------------------------------
% 6.47/2.20 % (17964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.20 % (17964)Termination reason: Unknown
% 6.47/2.20 % (17964)Termination phase: Saturation
% 6.47/2.20
% 6.47/2.20 % (17964)Memory used [KB]: 7291
% 6.47/2.20 % (17964)Time elapsed: 0.080 s
% 6.47/2.20 % (17964)Instructions burned: 254 (million)
% 6.47/2.20 % (17964)------------------------------
% 6.47/2.20 % (17964)------------------------------
% 7.09/2.20 % (17995)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_17623 for (2993ds/283Mi)
% 7.09/2.20 % (17999)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_17623 for (2993ds/134Mi)
% 7.09/2.21 % (17950)Instruction limit reached!
% 7.09/2.21 % (17950)------------------------------
% 7.09/2.21 % (17950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.21 % (17950)Termination reason: Unknown
% 7.09/2.21 % (17950)Termination phase: Saturation
% 7.09/2.21
% 7.09/2.21 % (17950)Memory used [KB]: 7547
% 7.09/2.21 % (17950)Time elapsed: 0.110 s
% 7.09/2.21 % (17950)Instructions burned: 344 (million)
% 7.09/2.21 % (17950)------------------------------
% 7.09/2.21 % (17950)------------------------------
% 7.09/2.22 % (18009)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_17623 for (2993ds/298Mi)
% 7.09/2.23 % (17984)Instruction limit reached!
% 7.09/2.23 % (17984)------------------------------
% 7.09/2.23 % (17984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.23 % (17984)Termination reason: Unknown
% 7.09/2.23 % (17984)Termination phase: Saturation
% 7.09/2.23
% 7.09/2.23 % (17984)Memory used [KB]: 6780
% 7.09/2.23 % (17984)Time elapsed: 0.061 s
% 7.09/2.23 % (17984)Instructions burned: 202 (million)
% 7.09/2.23 % (17984)------------------------------
% 7.09/2.23 % (17984)------------------------------
% 7.09/2.24 % (18018)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_17623 for (2993ds/192Mi)
% 7.09/2.25 % (17999)Instruction limit reached!
% 7.09/2.25 % (17999)------------------------------
% 7.09/2.25 % (17999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.25 % (17999)Termination reason: Unknown
% 7.09/2.25 % (17999)Termination phase: Saturation
% 7.09/2.25
% 7.09/2.25 % (17999)Memory used [KB]: 7164
% 7.09/2.25 % (17999)Time elapsed: 0.042 s
% 7.09/2.25 % (17999)Instructions burned: 134 (million)
% 7.09/2.25 % (17999)------------------------------
% 7.09/2.25 % (17999)------------------------------
% 7.09/2.26 % (18030)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_17623 for (2993ds/258Mi)
% 7.09/2.29 % (17995)Instruction limit reached!
% 7.09/2.29 % (17995)------------------------------
% 7.09/2.29 % (17995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.29 % (17995)Termination reason: Unknown
% 7.09/2.29 % (17995)Termination phase: Saturation
% 7.09/2.29
% 7.09/2.29 % (17995)Memory used [KB]: 7547
% 7.09/2.29 % (17995)Time elapsed: 0.087 s
% 7.09/2.29 % (17995)Instructions burned: 283 (million)
% 7.09/2.29 % (17995)------------------------------
% 7.09/2.29 % (17995)------------------------------
% 7.09/2.29 % (17994)Instruction limit reached!
% 7.09/2.29 % (17994)------------------------------
% 7.09/2.29 % (17994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.29 % (17994)Termination reason: Unknown
% 7.09/2.29 % (17994)Termination phase: Saturation
% 7.09/2.29
% 7.09/2.29 % (17994)Memory used [KB]: 7547
% 7.09/2.29 % (17994)Time elapsed: 0.101 s
% 7.09/2.29 % (17994)Instructions burned: 339 (million)
% 7.09/2.29 % (17994)------------------------------
% 7.09/2.29 % (17994)------------------------------
% 7.09/2.30 % (18018)Instruction limit reached!
% 7.09/2.30 % (18018)------------------------------
% 7.09/2.30 % (18018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.30 % (18018)Termination reason: Unknown
% 7.09/2.30 % (18018)Termination phase: Saturation
% 7.09/2.30
% 7.09/2.30 % (18018)Memory used [KB]: 7931
% 7.09/2.30 % (18018)Time elapsed: 0.060 s
% 7.09/2.30 % (18018)Instructions burned: 194 (million)
% 7.09/2.30 % (18018)------------------------------
% 7.09/2.30 % (18018)------------------------------
% 7.70/2.30 % (18052)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_17623 for (2992ds/90Mi)
% 7.70/2.30 % (18055)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_17623 for (2992ds/231Mi)
% 7.70/2.30 % (18009)Instruction limit reached!
% 7.70/2.30 % (18009)------------------------------
% 7.70/2.30 % (18009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.30 % (18009)Termination reason: Unknown
% 7.70/2.30 % (18009)Termination phase: Saturation
% 7.70/2.30
% 7.70/2.30 % (18009)Memory used [KB]: 7931
% 7.70/2.30 % (18009)Time elapsed: 0.087 s
% 7.70/2.30 % (18009)Instructions burned: 298 (million)
% 7.70/2.30 % (18009)------------------------------
% 7.70/2.30 % (18009)------------------------------
% 7.70/2.31 % (18060)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_17623 for (2992ds/458Mi)
% 7.70/2.31 % (18062)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_17623 for (2992ds/31Mi)
% 7.70/2.32 % (18062)Instruction limit reached!
% 7.70/2.32 % (18062)------------------------------
% 7.70/2.32 % (18062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.32 % (18062)Termination reason: Unknown
% 7.70/2.32 % (18062)Termination phase: Preprocessing 1
% 7.70/2.32
% 7.70/2.32 % (18062)Memory used [KB]: 1791
% 7.70/2.32 % (18062)Time elapsed: 0.011 s
% 7.70/2.32 % (18062)Instructions burned: 31 (million)
% 7.70/2.32 % (18062)------------------------------
% 7.70/2.32 % (18062)------------------------------
% 7.70/2.32 % (18052)Instruction limit reached!
% 7.70/2.32 % (18052)------------------------------
% 7.70/2.32 % (18052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.32 % (18052)Termination reason: Unknown
% 7.70/2.32 % (18052)Termination phase: Saturation
% 7.70/2.32
% 7.70/2.32 % (18052)Memory used [KB]: 6780
% 7.70/2.32 % (18052)Time elapsed: 0.028 s
% 7.70/2.32 % (18052)Instructions burned: 91 (million)
% 7.70/2.32 % (18052)------------------------------
% 7.70/2.32 % (18052)------------------------------
% 7.70/2.33 % (17907)Instruction limit reached!
% 7.70/2.33 % (17907)------------------------------
% 7.70/2.33 % (17907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.33 % (17907)Termination reason: Unknown
% 7.70/2.33 % (17907)Termination phase: Saturation
% 7.70/2.33
% 7.70/2.33 % (17907)Memory used [KB]: 7803
% 7.70/2.33 % (17907)Time elapsed: 0.337 s
% 7.70/2.33 % (17907)Instructions burned: 1090 (million)
% 7.70/2.33 % (17907)------------------------------
% 7.70/2.33 % (17907)------------------------------
% 7.70/2.33 % (18070)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_17623 for (2992ds/297Mi)
% 7.70/2.33 % (18073)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_17623 for (2992ds/987Mi)
% 7.70/2.34 % (18030)Instruction limit reached!
% 7.70/2.34 % (18030)------------------------------
% 7.70/2.34 % (18030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.34 % (18030)Termination reason: Unknown
% 7.70/2.34 % (18030)Termination phase: Saturation
% 7.70/2.34
% 7.70/2.34 % (18030)Memory used [KB]: 6908
% 7.70/2.34 % (18030)Time elapsed: 0.082 s
% 7.70/2.34 % (18030)Instructions burned: 260 (million)
% 7.70/2.34 % (18030)------------------------------
% 7.70/2.34 % (18030)------------------------------
% 7.70/2.34 % (18077)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_17623 for (2992ds/182Mi)
% 7.70/2.34 % (17979)Instruction limit reached!
% 7.70/2.34 % (17979)------------------------------
% 7.70/2.34 % (17979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.34 % (17979)Termination reason: Unknown
% 7.70/2.34 % (17979)Termination phase: Saturation
% 7.70/2.34
% 7.70/2.34 % (17979)Memory used [KB]: 8059
% 7.70/2.34 % (17979)Time elapsed: 0.192 s
% 7.70/2.34 % (17979)Instructions burned: 616 (million)
% 7.70/2.34 % (17979)------------------------------
% 7.70/2.34 % (17979)------------------------------
% 7.70/2.35 % (18081)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_17623 for (2992ds/182Mi)
% 7.70/2.35 % (18083)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_17623 for (2992ds/154Mi)
% 7.70/2.36 % (18055)Instruction limit reached!
% 7.70/2.36 % (18055)------------------------------
% 7.70/2.36 % (18055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.36 % (18055)Termination reason: Unknown
% 7.70/2.36 % (18055)Termination phase: Saturation
% 7.70/2.36
% 7.70/2.36 % (18055)Memory used [KB]: 7036
% 7.70/2.36 % (18055)Time elapsed: 0.064 s
% 7.70/2.36 % (18055)Instructions burned: 233 (million)
% 7.70/2.36 % (18055)------------------------------
% 7.70/2.36 % (18055)------------------------------
% 7.70/2.37 % (18092)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_17623 for (2991ds/79Mi)
% 7.70/2.39 % (18077)Instruction limit reached!
% 7.70/2.39 % (18077)------------------------------
% 7.70/2.39 % (18077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.39 % (18077)Termination reason: Unknown
% 7.70/2.39 % (18077)Termination phase: Saturation
% 7.70/2.39
% 7.70/2.39 % (18077)Memory used [KB]: 7036
% 7.70/2.39 % (18077)Time elapsed: 0.057 s
% 7.70/2.39 % (18077)Instructions burned: 183 (million)
% 7.70/2.39 % (18077)------------------------------
% 7.70/2.39 % (18077)------------------------------
% 7.70/2.40 % (18092)Instruction limit reached!
% 7.70/2.40 % (18092)------------------------------
% 7.70/2.40 % (18092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.40 % (18092)Termination reason: Unknown
% 7.70/2.40 % (18092)Termination phase: Saturation
% 7.70/2.40
% 7.70/2.40 % (18092)Memory used [KB]: 6780
% 7.70/2.40 % (18092)Time elapsed: 0.024 s
% 7.70/2.40 % (18092)Instructions burned: 79 (million)
% 7.70/2.40 % (18092)------------------------------
% 7.70/2.40 % (18092)------------------------------
% 8.32/2.40 % (18083)Instruction limit reached!
% 8.32/2.40 % (18083)------------------------------
% 8.32/2.40 % (18083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.40 % (18083)Termination reason: Unknown
% 8.32/2.40 % (18083)Termination phase: Saturation
% 8.32/2.40
% 8.32/2.40 % (18083)Memory used [KB]: 2942
% 8.32/2.40 % (18083)Time elapsed: 0.044 s
% 8.32/2.40 % (18083)Instructions burned: 156 (million)
% 8.32/2.40 % (18083)------------------------------
% 8.32/2.40 % (18083)------------------------------
% 8.32/2.40 % (18081)Instruction limit reached!
% 8.32/2.40 % (18081)------------------------------
% 8.32/2.40 % (18081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.40 % (18081)Termination reason: Unknown
% 8.32/2.40 % (18081)Termination phase: Saturation
% 8.32/2.40
% 8.32/2.40 % (18081)Memory used [KB]: 7164
% 8.32/2.40 % (18081)Time elapsed: 0.058 s
% 8.32/2.40 % (18081)Instructions burned: 182 (million)
% 8.32/2.40 % (18081)------------------------------
% 8.32/2.40 % (18081)------------------------------
% 8.32/2.40 % (18104)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_17623 for (2991ds/216Mi)
% 8.32/2.41 % (18105)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_17623 for (2991ds/114Mi)
% 8.32/2.41 % (18106)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_17623 for (2991ds/922Mi)
% 8.32/2.41 % (18111)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_17623 for (2991ds/182Mi)
% 8.32/2.42 % (18070)Instruction limit reached!
% 8.32/2.42 % (18070)------------------------------
% 8.32/2.42 % (18070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.42 % (18070)Termination reason: Unknown
% 8.32/2.42 % (18070)Termination phase: Saturation
% 8.32/2.42
% 8.32/2.42 % (18070)Memory used [KB]: 7419
% 8.32/2.42 % (18070)Time elapsed: 0.089 s
% 8.32/2.42 % (18070)Instructions burned: 297 (million)
% 8.32/2.42 % (18070)------------------------------
% 8.32/2.42 % (18070)------------------------------
% 8.32/2.43 % (18117)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_17623 for (2991ds/164Mi)
% 8.32/2.44 % (18105)Instruction limit reached!
% 8.32/2.44 % (18105)------------------------------
% 8.32/2.44 % (18105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.44 % (18105)Termination reason: Unknown
% 8.32/2.44 % (18105)Termination phase: Saturation
% 8.32/2.44
% 8.32/2.44 % (18105)Memory used [KB]: 6908
% 8.32/2.44 % (18105)Time elapsed: 0.036 s
% 8.32/2.44 % (18105)Instructions burned: 116 (million)
% 8.32/2.44 % (18105)------------------------------
% 8.32/2.44 % (18105)------------------------------
% 8.32/2.44 % (18060)Refutation not found, non-redundant clauses discarded% (18060)------------------------------
% 8.32/2.44 % (18060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.44 % (18060)Termination reason: Refutation not found, non-redundant clauses discarded
% 8.32/2.44
% 8.32/2.44 % (18060)Memory used [KB]: 7803
% 8.32/2.44 % (18060)Time elapsed: 0.140 s
% 8.32/2.44 % (18060)Instructions burned: 424 (million)
% 8.32/2.44 % (18060)------------------------------
% 8.32/2.44 % (18060)------------------------------
% 8.32/2.45 % (18123)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_17623 for (2991ds/50Mi)
% 8.32/2.45 % (18125)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_17623 for (2991ds/368Mi)
% 8.32/2.46 % (18111)Instruction limit reached!
% 8.32/2.46 % (18111)------------------------------
% 8.32/2.46 % (18111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.46 % (18111)Termination reason: Unknown
% 8.32/2.46 % (18111)Termination phase: Saturation
% 8.32/2.46
% 8.32/2.46 % (18111)Memory used [KB]: 7036
% 8.32/2.46 % (18111)Time elapsed: 0.052 s
% 8.32/2.46 % (18111)Instructions burned: 182 (million)
% 8.32/2.46 % (18111)------------------------------
% 8.32/2.46 % (18111)------------------------------
% 8.32/2.46 % (18123)Instruction limit reached!
% 8.32/2.46 % (18123)------------------------------
% 8.32/2.46 % (18123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.46 % (18123)Termination reason: Unknown
% 8.32/2.46 % (18123)Termination phase: Property scanning
% 8.32/2.46
% 8.32/2.46 % (18123)Memory used [KB]: 2174
% 8.32/2.46 % (18123)Time elapsed: 0.015 s
% 8.32/2.46 % (18123)Instructions burned: 52 (million)
% 8.32/2.46 % (18123)------------------------------
% 8.32/2.46 % (18123)------------------------------
% 8.32/2.47 % (18104)Instruction limit reached!
% 8.32/2.47 % (18104)------------------------------
% 8.32/2.47 % (18104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.47 % (18104)Termination reason: Unknown
% 8.32/2.47 % (18104)Termination phase: Saturation
% 8.32/2.47
% 8.32/2.47 % (18104)Memory used [KB]: 7291
% 8.32/2.47 % (18104)Time elapsed: 0.064 s
% 8.32/2.47 % (18104)Instructions burned: 218 (million)
% 8.32/2.47 % (18104)------------------------------
% 8.32/2.47 % (18104)------------------------------
% 8.32/2.47 % (18134)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_17623 for (2990ds/1021Mi)
% 8.32/2.47 % (18135)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_17623 for (2990ds/267Mi)
% 8.32/2.47 % (18117)Instruction limit reached!
% 8.32/2.47 % (18117)------------------------------
% 8.32/2.47 % (18117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.47 % (18117)Termination reason: Unknown
% 8.32/2.47 % (18117)Termination phase: Saturation
% 8.32/2.47
% 8.32/2.47 % (18117)Memory used [KB]: 2430
% 8.32/2.47 % (18117)Time elapsed: 0.048 s
% 8.32/2.47 % (18117)Instructions burned: 164 (million)
% 8.32/2.47 % (18117)------------------------------
% 8.32/2.47 % (18117)------------------------------
% 8.32/2.48 % (18139)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_17623 for (2990ds/204Mi)
% 8.32/2.48 % (18142)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17623 for (2990ds/26Mi)
% 8.32/2.49 % (18142)Instruction limit reached!
% 8.32/2.49 % (18142)------------------------------
% 8.32/2.49 % (18142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.49 % (18142)Termination reason: Unknown
% 8.32/2.49 % (18142)Termination phase: shuffling
% 8.32/2.49
% 8.32/2.49 % (18142)Memory used [KB]: 1791
% 8.32/2.49 % (18142)Time elapsed: 0.008 s
% 8.32/2.49 % (18142)Instructions burned: 26 (million)
% 8.32/2.49 % (18142)------------------------------
% 8.32/2.49 % (18142)------------------------------
% 8.99/2.50 % (18146)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_17623 for (2990ds/53Mi)
% 8.99/2.52 % (18146)Instruction limit reached!
% 8.99/2.52 % (18146)------------------------------
% 8.99/2.52 % (18146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.52 % (18146)Termination reason: Unknown
% 8.99/2.52 % (18146)Termination phase: Property scanning
% 8.99/2.52
% 8.99/2.52 % (18146)Memory used [KB]: 2174
% 8.99/2.52 % (18146)Time elapsed: 0.016 s
% 8.99/2.52 % (18146)Instructions burned: 54 (million)
% 8.99/2.52 % (18146)------------------------------
% 8.99/2.52 % (18146)------------------------------
% 8.99/2.52 % (18162)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_17623 for (2990ds/4436Mi)
% 8.99/2.54 % (18139)Instruction limit reached!
% 8.99/2.54 % (18139)------------------------------
% 8.99/2.54 % (18139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.54 % (18139)Termination reason: Unknown
% 8.99/2.54 % (18139)Termination phase: Saturation
% 8.99/2.54
% 8.99/2.54 % (18139)Memory used [KB]: 7036
% 8.99/2.54 % (18139)Time elapsed: 0.064 s
% 8.99/2.54 % (18139)Instructions burned: 204 (million)
% 8.99/2.54 % (18139)------------------------------
% 8.99/2.54 % (18139)------------------------------
% 8.99/2.55 % (18179)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_17623 for (2990ds/1539Mi)
% 8.99/2.56 % (18135)Instruction limit reached!
% 8.99/2.56 % (18135)------------------------------
% 8.99/2.56 % (18135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.56 % (18135)Termination reason: Unknown
% 8.99/2.56 % (18135)Termination phase: Saturation
% 8.99/2.56
% 8.99/2.56 % (18135)Memory used [KB]: 7547
% 8.99/2.56 % (18135)Time elapsed: 0.108 s
% 8.99/2.56 % (18135)Instructions burned: 268 (million)
% 8.99/2.56 % (18135)------------------------------
% 8.99/2.56 % (18135)------------------------------
% 8.99/2.57 % (18185)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_17623 for (2989ds/408Mi)
% 8.99/2.57 % (18125)Instruction limit reached!
% 8.99/2.57 % (18125)------------------------------
% 8.99/2.57 % (18125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.57 % (18125)Termination reason: Unknown
% 8.99/2.57 % (18125)Termination phase: Saturation
% 8.99/2.57
% 8.99/2.57 % (18125)Memory used [KB]: 7803
% 8.99/2.57 % (18125)Time elapsed: 0.143 s
% 8.99/2.57 % (18125)Instructions burned: 368 (million)
% 8.99/2.57 % (18125)------------------------------
% 8.99/2.57 % (18125)------------------------------
% 8.99/2.58 % (18191)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_17623 for (2989ds/5205Mi)
% 9.31/2.63 % (18073)Instruction limit reached!
% 9.31/2.63 % (18073)------------------------------
% 9.31/2.63 % (18073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.63 % (18073)Termination reason: Unknown
% 9.31/2.63 % (18073)Termination phase: Saturation
% 9.31/2.63
% 9.31/2.63 % (18073)Memory used [KB]: 9466
% 9.31/2.63 % (18073)Time elapsed: 0.300 s
% 9.31/2.63 % (18073)Instructions burned: 987 (million)
% 9.31/2.63 % (18073)------------------------------
% 9.31/2.63 % (18073)------------------------------
% 9.31/2.64 % (18192)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_17623 for (2989ds/1913Mi)
% 9.31/2.69 % (18185)Instruction limit reached!
% 9.31/2.69 % (18185)------------------------------
% 9.31/2.69 % (18185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.69 % (18185)Termination reason: Unknown
% 9.31/2.69 % (18185)Termination phase: Saturation
% 9.31/2.69
% 9.31/2.69 % (18185)Memory used [KB]: 7803
% 9.31/2.69 % (18185)Time elapsed: 0.126 s
% 9.31/2.69 % (18185)Instructions burned: 410 (million)
% 9.31/2.69 % (18185)------------------------------
% 9.31/2.69 % (18185)------------------------------
% 9.31/2.69 % (18106)Instruction limit reached!
% 9.31/2.69 % (18106)------------------------------
% 9.31/2.69 % (18106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.69 % (18106)Termination reason: Unknown
% 9.31/2.69 % (18106)Termination phase: Saturation
% 9.31/2.69
% 9.31/2.69 % (18106)Memory used [KB]: 7164
% 9.31/2.69 % (18106)Time elapsed: 0.307 s
% 9.31/2.69 % (18106)Instructions burned: 922 (million)
% 9.31/2.69 % (18106)------------------------------
% 9.31/2.69 % (18106)------------------------------
% 10.05/2.70 % (18194)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_17623 for (2988ds/4350Mi)
% 10.05/2.70 % (18195)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=68:si=on:rtra=on_0 on DTF2THF_17623 for (2988ds/68Mi)
% 10.05/2.72 % (18195)Instruction limit reached!
% 10.05/2.72 % (18195)------------------------------
% 10.05/2.72 % (18195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/2.72 % (18195)Termination reason: Unknown
% 10.05/2.72 % (18195)Termination phase: Property scanning
% 10.05/2.72
% 10.05/2.72 % (18195)Memory used [KB]: 2302
% 10.05/2.72 % (18195)Time elapsed: 0.022 s
% 10.05/2.72 % (18195)Instructions burned: 68 (million)
% 10.05/2.72 % (18195)------------------------------
% 10.05/2.72 % (18195)------------------------------
% 10.05/2.73 % (18196)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_17623 for (2988ds/358Mi)
% 10.05/2.78 % (18134)Instruction limit reached!
% 10.05/2.78 % (18134)------------------------------
% 10.05/2.78 % (18134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/2.78 % (18134)Termination reason: Unknown
% 10.05/2.78 % (18134)Termination phase: Saturation
% 10.05/2.78
% 10.05/2.78 % (18134)Memory used [KB]: 8571
% 10.05/2.78 % (18134)Time elapsed: 0.332 s
% 10.05/2.78 % (18134)Instructions burned: 1022 (million)
% 10.05/2.78 % (18134)------------------------------
% 10.05/2.78 % (18134)------------------------------
% 10.05/2.79 % (18197)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_17623 for (2987ds/31Mi)
% 10.40/2.80 % (18197)Instruction limit reached!
% 10.40/2.80 % (18197)------------------------------
% 10.40/2.80 % (18197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.80 % (18197)Termination reason: Unknown
% 10.40/2.80 % (18197)Termination phase: Preprocessing 1
% 10.40/2.80
% 10.40/2.80 % (18197)Memory used [KB]: 1791
% 10.40/2.80 % (18197)Time elapsed: 0.011 s
% 10.40/2.80 % (18197)Instructions burned: 31 (million)
% 10.40/2.80 % (18197)------------------------------
% 10.40/2.80 % (18197)------------------------------
% 10.40/2.81 % (18198)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_17623 for (2987ds/279Mi)
% 10.40/2.84 % (18196)Instruction limit reached!
% 10.40/2.84 % (18196)------------------------------
% 10.40/2.84 % (18196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.84 % (18196)Termination reason: Unknown
% 10.40/2.84 % (18196)Termination phase: Saturation
% 10.40/2.84
% 10.40/2.84 % (18196)Memory used [KB]: 7291
% 10.40/2.84 % (18196)Time elapsed: 0.112 s
% 10.40/2.84 % (18196)Instructions burned: 358 (million)
% 10.40/2.84 % (18196)------------------------------
% 10.40/2.84 % (18196)------------------------------
% 10.40/2.85 % (18199)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_17623 for (2987ds/258Mi)
% 10.40/2.89 % (18198)Instruction limit reached!
% 10.40/2.89 % (18198)------------------------------
% 10.40/2.89 % (18198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.89 % (18198)Termination reason: Unknown
% 10.40/2.89 % (18198)Termination phase: Saturation
% 10.40/2.89
% 10.40/2.89 % (18198)Memory used [KB]: 7419
% 10.40/2.89 % (18198)Time elapsed: 0.081 s
% 10.40/2.89 % (18198)Instructions burned: 280 (million)
% 10.40/2.89 % (18198)------------------------------
% 10.40/2.89 % (18198)------------------------------
% 10.63/2.90 % (18200)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17623 for (2986ds/26Mi)
% 10.63/2.91 % (18200)Instruction limit reached!
% 10.63/2.91 % (18200)------------------------------
% 10.63/2.91 % (18200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.63/2.91 % (18200)Termination reason: Unknown
% 10.63/2.91 % (18200)Termination phase: shuffling
% 10.63/2.91
% 10.63/2.91 % (18200)Memory used [KB]: 1791
% 10.63/2.91 % (18200)Time elapsed: 0.009 s
% 10.63/2.91 % (18200)Instructions burned: 28 (million)
% 10.63/2.91 % (18200)------------------------------
% 10.63/2.91 % (18200)------------------------------
% 10.63/2.92 % (18201)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_17623 for (2986ds/995Mi)
% 10.63/2.93 % (18199)Instruction limit reached!
% 10.63/2.93 % (18199)------------------------------
% 10.63/2.93 % (18199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.63/2.93 % (18199)Termination reason: Unknown
% 10.63/2.93 % (18199)Termination phase: Saturation
% 10.63/2.93
% 10.63/2.93 % (18199)Memory used [KB]: 7547
% 10.63/2.93 % (18199)Time elapsed: 0.083 s
% 10.63/2.93 % (18199)Instructions burned: 259 (million)
% 10.63/2.93 % (18199)------------------------------
% 10.63/2.93 % (18199)------------------------------
% 10.63/2.94 % (18202)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_17623 for (2986ds/373Mi)
% 10.63/3.00 % (18179)Instruction limit reached!
% 10.63/3.00 % (18179)------------------------------
% 10.63/3.00 % (18179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.63/3.00 % (18179)Termination reason: Unknown
% 10.63/3.00 % (18179)Termination phase: Saturation
% 10.63/3.00
% 10.63/3.00 % (18179)Memory used [KB]: 9850
% 10.63/3.00 % (18179)Time elapsed: 0.453 s
% 10.63/3.00 % (18179)Instructions burned: 1539 (million)
% 10.63/3.00 % (18179)------------------------------
% 10.63/3.00 % (18179)------------------------------
% 10.63/3.01 % (18203)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_17623 for (2985ds/253Mi)
% 13.03/3.06 % (18202)Instruction limit reached!
% 13.03/3.06 % (18202)------------------------------
% 13.03/3.06 % (18202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.06 % (18202)Termination reason: Unknown
% 13.03/3.06 % (18202)Termination phase: Saturation
% 13.03/3.06
% 13.03/3.06 % (18202)Memory used [KB]: 8315
% 13.03/3.06 % (18202)Time elapsed: 0.116 s
% 13.03/3.06 % (18202)Instructions burned: 373 (million)
% 13.03/3.06 % (18202)------------------------------
% 13.03/3.06 % (18202)------------------------------
% 13.03/3.07 % (18204)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_17623 for (2984ds/832Mi)
% 13.03/3.08 % (18203)Instruction limit reached!
% 13.03/3.08 % (18203)------------------------------
% 13.03/3.08 % (18203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.08 % (18203)Termination reason: Unknown
% 13.03/3.08 % (18203)Termination phase: Saturation
% 13.03/3.08
% 13.03/3.08 % (18203)Memory used [KB]: 7675
% 13.03/3.08 % (18203)Time elapsed: 0.074 s
% 13.03/3.08 % (18203)Instructions burned: 254 (million)
% 13.03/3.08 % (18203)------------------------------
% 13.03/3.08 % (18203)------------------------------
% 13.03/3.09 % (18205)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_17623 for (2984ds/668Mi)
% 14.04/3.21 % (18201)Instruction limit reached!
% 14.04/3.21 % (18201)------------------------------
% 14.04/3.21 % (18201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.04/3.21 % (18201)Termination reason: Unknown
% 14.04/3.21 % (18201)Termination phase: Saturation
% 14.04/3.21
% 14.04/3.21 % (18201)Memory used [KB]: 9210
% 14.04/3.21 % (18201)Time elapsed: 0.296 s
% 14.04/3.21 % (18201)Instructions burned: 995 (million)
% 14.04/3.21 % (18201)------------------------------
% 14.04/3.21 % (18201)------------------------------
% 14.04/3.22 % (18206)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=40:si=on:rtra=on_0 on DTF2THF_17623 for (2983ds/40Mi)
% 14.04/3.23 % (18206)Instruction limit reached!
% 14.04/3.23 % (18206)------------------------------
% 14.04/3.23 % (18206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.04/3.23 % (18206)Termination reason: Unknown
% 14.04/3.23 % (18206)Termination phase: Property scanning
% 14.04/3.23
% 14.04/3.23 % (18206)Memory used [KB]: 2174
% 14.04/3.23 % (18206)Time elapsed: 0.013 s
% 14.04/3.23 % (18206)Instructions burned: 41 (million)
% 14.04/3.23 % (18206)------------------------------
% 14.04/3.23 % (18206)------------------------------
% 14.04/3.23 % (18192)Instruction limit reached!
% 14.04/3.23 % (18192)------------------------------
% 14.04/3.23 % (18192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.04/3.23 % (18192)Termination reason: Unknown
% 14.04/3.23 % (18192)Termination phase: Saturation
% 14.04/3.23
% 14.04/3.23 % (18192)Memory used [KB]: 4605
% 14.04/3.23 % (18192)Time elapsed: 0.592 s
% 14.04/3.23 % (18192)Instructions burned: 1914 (million)
% 14.04/3.23 % (18192)------------------------------
% 14.04/3.23 % (18192)------------------------------
% 14.04/3.24 % (18207)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_17623 for (2983ds/294Mi)
% 14.04/3.24 % (18208)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_17623 for (2983ds/187Mi)
% 14.04/3.30 % (18205)Instruction limit reached!
% 14.04/3.30 % (18205)------------------------------
% 14.04/3.30 % (18205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.04/3.30 % (18205)Termination reason: Unknown
% 14.04/3.30 % (18205)Termination phase: Saturation
% 14.04/3.30
% 14.04/3.30 % (18205)Memory used [KB]: 14072
% 14.04/3.30 % (18205)Time elapsed: 0.203 s
% 14.04/3.30 % (18205)Instructions burned: 668 (million)
% 14.04/3.30 % (18205)------------------------------
% 14.04/3.30 % (18205)------------------------------
% 14.63/3.30 % (18208)Instruction limit reached!
% 14.63/3.30 % (18208)------------------------------
% 14.63/3.30 % (18208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.63/3.30 % (18208)Termination reason: Unknown
% 14.63/3.30 % (18208)Termination phase: Saturation
% 14.63/3.30
% 14.63/3.30 % (18208)Memory used [KB]: 7419
% 14.63/3.30 % (18208)Time elapsed: 0.061 s
% 14.63/3.30 % (18208)Instructions burned: 188 (million)
% 14.63/3.30 % (18208)------------------------------
% 14.63/3.30 % (18208)------------------------------
% 14.63/3.31 % (18209)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_17623 for (2982ds/371Mi)
% 14.63/3.31 % (18210)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_17623 for (2982ds/1827Mi)
% 14.63/3.33 % (18207)Instruction limit reached!
% 14.63/3.33 % (18207)------------------------------
% 14.63/3.33 % (18207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.63/3.33 % (18207)Termination reason: Unknown
% 14.63/3.33 % (18207)Termination phase: Saturation
% 14.63/3.33
% 14.63/3.33 % (18207)Memory used [KB]: 6908
% 14.63/3.33 % (18207)Time elapsed: 0.084 s
% 14.63/3.33 % (18207)Instructions burned: 295 (million)
% 14.63/3.33 % (18207)------------------------------
% 14.63/3.33 % (18207)------------------------------
% 14.63/3.33 % (18204)Instruction limit reached!
% 14.63/3.33 % (18204)------------------------------
% 14.63/3.33 % (18204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.63/3.33 % (18204)Termination reason: Unknown
% 14.63/3.33 % (18204)Termination phase: Saturation
% 14.63/3.33
% 14.63/3.33 % (18204)Memory used [KB]: 7931
% 14.63/3.33 % (18204)Time elapsed: 0.261 s
% 14.63/3.33 % (18204)Instructions burned: 834 (million)
% 14.63/3.33 % (18204)------------------------------
% 14.63/3.33 % (18204)------------------------------
% 14.63/3.33 % (18211)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_17623 for (2982ds/70Mi)
% 14.63/3.34 % (18212)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_17623 for (2982ds/316Mi)
% 14.63/3.35 % (18211)Instruction limit reached!
% 14.63/3.35 % (18211)------------------------------
% 14.63/3.35 % (18211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.63/3.35 % (18211)Termination reason: Unknown
% 14.63/3.35 % (18211)Termination phase: Preprocessing 3
% 14.63/3.35
% 14.63/3.35 % (18211)Memory used [KB]: 2174
% 14.63/3.35 % (18211)Time elapsed: 0.020 s
% 14.63/3.35 % (18211)Instructions burned: 70 (million)
% 14.63/3.35 % (18211)------------------------------
% 14.63/3.35 % (18211)------------------------------
% 14.63/3.36 % (18213)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_17623 for (2982ds/932Mi)
% 15.39/3.42 % (18209)Instruction limit reached!
% 15.39/3.42 % (18209)------------------------------
% 15.39/3.42 % (18209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.39/3.42 % (18209)Termination reason: Unknown
% 15.39/3.42 % (18209)Termination phase: Saturation
% 15.39/3.42
% 15.39/3.42 % (18209)Memory used [KB]: 7675
% 15.39/3.42 % (18209)Time elapsed: 0.118 s
% 15.39/3.42 % (18209)Instructions burned: 373 (million)
% 15.39/3.42 % (18209)------------------------------
% 15.39/3.42 % (18209)------------------------------
% 15.39/3.42 % (18212)Instruction limit reached!
% 15.39/3.42 % (18212)------------------------------
% 15.39/3.42 % (18212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.39/3.42 % (18212)Termination reason: Unknown
% 15.39/3.42 % (18212)Termination phase: Saturation
% 15.39/3.42
% 15.39/3.42 % (18212)Memory used [KB]: 7803
% 15.39/3.42 % (18212)Time elapsed: 0.088 s
% 15.39/3.42 % (18212)Instructions burned: 317 (million)
% 15.39/3.42 % (18212)------------------------------
% 15.39/3.42 % (18212)------------------------------
% 15.39/3.43 % (18214)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_17623 for (2981ds/4714Mi)
% 15.39/3.43 % (18215)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_17623 for (2981ds/8250Mi)
% 15.92/3.51 % (18210)First to succeed.
% 15.92/3.51 % (18210)Refutation found. Thanks to Tanya!
% 15.92/3.51 % SZS status Theorem for DTF2THF_17623
% 15.92/3.51 % SZS output start Proof for DTF2THF_17623
% 15.92/3.51 thf(type_def_6, type, list: ($tType) > $tType).
% 15.92/3.51 thf(type_def_7, type, set: ($tType) > $tType).
% 15.92/3.51 thf(type_def_8, type, val: $tType).
% 15.92/3.51 thf(func_def_0, type, list: ($tType) > $tType).
% 15.92/3.51 thf(func_def_1, type, set: ($tType) > $tType).
% 15.92/3.51 thf(func_def_2, type, val: $tType).
% 15.92/3.51 thf(func_def_3, type, type: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_4, type, bot: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_6, type, order: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_7, type, group_add: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_8, type, no_bot: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_9, type, no_top: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_11, type, preorder: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_12, type, wellorder: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_13, type, complete_Sup: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_14, type, dense_order: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_15, type, boolean_algebra: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_16, type, semilattice_sup: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_17, type, dense_linorder: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_18, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_19, type, comple187826305attice: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_20, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 15.92/3.51 thf(func_def_21, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 15.92/3.51 thf(func_def_22, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 15.92/3.51 thf(func_def_23, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 15.92/3.51 thf(func_def_24, type, rec_list: !>[X0: $tType, X1: $tType]:(X0 > (X1 > list @ X1 > X0 > X0) > list @ X1 > X0)).
% 15.92/3.51 thf(func_def_25, type, swap_args2: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 15.92/3.51 thf(func_def_26, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 15.92/3.51 thf(func_def_27, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 15.92/3.51 thf(func_def_28, type, order_Greatest: !>[X0: $tType]:((X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_29, type, order_antimono: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 15.92/3.51 thf(func_def_30, type, order_strict_mono: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 15.92/3.51 thf(func_def_31, type, refine111645177_ALIGN: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 15.92/3.51 thf(func_def_32, type, refine574149253T_SIMP: !>[X0: $tType]:(X0 > X0 > $o)).
% 15.92/3.51 thf(func_def_33, type, refine_cont: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 15.92/3.51 thf(func_def_34, type, refine1150083786ection: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > $o)).
% 15.92/3.51 thf(func_def_35, type, refine_inf_distrib: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 15.92/3.51 thf(func_def_36, type, refine_strict: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 15.92/3.51 thf(func_def_37, type, refine551993528up_loc: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 15.92/3.51 thf(func_def_38, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 15.92/3.51 thf(func_def_39, type, set_ord_atLeast: !>[X0: $tType]:(X0 > set @ X0)).
% 15.92/3.51 thf(func_def_40, type, set_or331188842AtMost: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 15.92/3.51 thf(func_def_41, type, set_ord_atMost: !>[X0: $tType]:(X0 > set @ X0)).
% 15.92/3.51 thf(func_def_42, type, set_ord_greaterThan: !>[X0: $tType]:(X0 > set @ X0)).
% 15.92/3.51 thf(func_def_43, type, set_or578182835ssThan: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 15.92/3.51 thf(func_def_44, type, set_ord_lessThan: !>[X0: $tType]:(X0 > set @ X0)).
% 15.92/3.51 thf(func_def_45, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 15.92/3.51 thf(func_def_46, type, p: set @ val).
% 15.92/3.51 thf(func_def_47, type, scc: set @ val).
% 15.92/3.51 thf(func_def_63, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 15.92/3.51 thf(func_def_64, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 15.92/3.51 thf(func_def_65, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 15.92/3.51 thf(func_def_66, type, sK3: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_67, type, sK4: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_68, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_69, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_70, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_71, type, sK8: !>[X0: $tType]:(X0 > X0)).
% 15.92/3.51 thf(func_def_72, type, sK9: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_73, type, sK10: !>[X0: $tType]:(X0 > X0 > X0 > X0)).
% 15.92/3.51 thf(func_def_74, type, sK11: !>[X0: $tType]:(X0 > X0 > X0)).
% 15.92/3.51 thf(func_def_75, type, sK12: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_76, type, sK13: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_77, type, sK14: !>[X0: $tType]:(X0 > X0 > X0 > X0)).
% 15.92/3.51 thf(func_def_78, type, sK15: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_79, type, sK16: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_80, type, sK17: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 15.92/3.51 thf(func_def_81, type, sK18: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_82, type, sK19: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_83, type, sK20: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_84, type, sK21: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_85, type, sK22: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_86, type, sK23: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_87, type, sK24: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_88, type, sK25: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_89, type, sK26: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_90, type, sK27: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_91, type, sK28: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_92, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1) > (X2 > X0) > (X0 > X1) > X2)).
% 15.92/3.51 thf(func_def_93, type, sK30: !>[X0: $tType]:(X0 > X0)).
% 15.92/3.51 thf(func_def_94, type, sK31: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_95, type, sK32: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > X0)).
% 15.92/3.51 thf(func_def_96, type, sK33: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_97, type, sK34: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_98, type, sK35: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_99, type, sK36: !>[X0: $tType]:((X0 > $o) > X0 > X0 > X0)).
% 15.92/3.51 thf(func_def_100, type, sK37: !>[X0: $tType]:(X0 > (X0 > $o) > X0 > X0)).
% 15.92/3.51 thf(func_def_101, type, sK38: !>[X0: $tType]:((X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_102, type, sK39: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_103, type, sK40: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_104, type, sK41: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_105, type, sK42: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_106, type, sK43: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_110, type, sK47: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_111, type, sK48: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_113, type, sK50: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_114, type, sK51: !>[X0: $tType]:((X0 > $o) > X0 > X0)).
% 15.92/3.51 thf(func_def_115, type, sK52: !>[X0: $tType]:((X0 > $o) > X0 > X0)).
% 15.92/3.51 thf(func_def_116, type, sK53: !>[X0: $tType]:(X0 > X0 > X0)).
% 15.92/3.51 thf(func_def_117, type, sK54: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_118, type, sK55: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_119, type, sK56: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_120, type, sK57: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_121, type, sK58: !>[X0: $tType]:(X0 > X0 > X0)).
% 15.92/3.51 thf(func_def_122, type, sK59: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_123, type, sK60: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_124, type, sK61: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_125, type, sK62: !>[X0: $tType]:(X0 > X0)).
% 15.92/3.51 thf(func_def_126, type, sK63: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > (X0 > X0 > $o) > X1)).
% 15.92/3.51 thf(func_def_127, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1) > (X2 > X0) > (X0 > X1) > X2)).
% 15.92/3.51 thf(func_def_128, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X1 > list @ X1 > (X3 > X2) > X3 > X2) > (X1 > list @ X1 > (X3 > X0) > X3 > X0) > (X0 > X2) > X1)).
% 15.92/3.51 thf(func_def_129, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X1 > list @ X1 > (X3 > X2) > X3 > X2) > (X1 > list @ X1 > (X3 > X0) > X3 > X0) > (X0 > X2) > list @ X1)).
% 15.92/3.51 thf(func_def_130, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X1 > list @ X1 > (X3 > X2) > X3 > X2) > (X1 > list @ X1 > (X3 > X0) > X3 > X0) > (X0 > X2) > X3 > X0)).
% 15.92/3.51 thf(func_def_131, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X1 > list @ X1 > (X3 > X2) > X3 > X2) > (X1 > list @ X1 > (X3 > X0) > X3 > X0) > (X0 > X2) > X3 > X2)).
% 15.92/3.51 thf(func_def_132, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X1 > list @ X1 > (X3 > X2) > X3 > X2) > (X1 > list @ X1 > (X3 > X0) > X3 > X0) > (X0 > X2) > X3)).
% 15.92/3.51 thf(func_def_133, type, sK70: !>[X0: $tType]:(X0 > X0)).
% 15.92/3.51 thf(func_def_134, type, sK71: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 15.92/3.51 thf(func_def_135, type, sK72: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_136, type, sK73: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 15.92/3.51 thf(func_def_137, type, sK74: !>[X0: $tType]:(X0 > X0)).
% 15.92/3.51 thf(func_def_138, type, sK75: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 15.92/3.51 thf(func_def_139, type, sK76: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 15.92/3.51 thf(func_def_140, type, sK77: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 15.92/3.51 thf(func_def_141, type, sK78: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 15.92/3.51 thf(func_def_142, type, sK79: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 15.92/3.51 thf(func_def_143, type, sK80: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 15.92/3.51 thf(func_def_144, type, sK81: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 15.92/3.51 thf(func_def_145, type, sK82: !>[X0: $tType]:(X0 > X0)).
% 15.92/3.51 thf(func_def_147, type, sK84: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_148, type, sK85: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 15.92/3.51 thf(func_def_149, type, ph86: !>[X0: $tType]:(X0)).
% 15.92/3.51 thf(f3972,plain,(
% 15.92/3.51 $false),
% 15.92/3.51 inference(trivial_inequality_removal,[status(thm)],[f3971])).
% 15.92/3.51 thf(f3971,plain,(
% 15.92/3.51 ($true = $false)),
% 15.92/3.51 inference(forward_demodulation,[status(thm)],[f3970,f2021])).
% 15.92/3.51 thf(f2021,plain,(
% 15.92/3.51 ((ord_less_eq @ set @ val @ scc @ p) = $false)),
% 15.92/3.51 inference(trivial_inequality_removal,[status(thm)],[f2015])).
% 15.92/3.51 thf(f2015,plain,(
% 15.92/3.51 ((ord_less_eq @ set @ val @ scc @ p) = $false) | ($true != $true)),
% 15.92/3.51 inference(superposition,[status(thm)],[f1513,f1453])).
% 15.92/3.51 thf(f1453,plain,(
% 15.92/3.51 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 15.92/3.51 inference(cnf_transformation,[status(thm)],[f751])).
% 15.92/3.51 thf(f751,plain,(
% 15.92/3.51 ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 15.92/3.51 inference(fool_elimination,[status(thm)],[f750])).
% 15.92/3.51 thf(f750,plain,(
% 15.92/3.51 ! [X0 : $o] : (($false = X0) | ($true = X0))),
% 15.92/3.51 inference(rectify,[status(thm)],[f285])).
% 15.92/3.51 thf(f285,axiom,(
% 15.92/3.51 ! [X23 : $o] : (($false = X23) | ($true = X23))),
% 15.92/3.51 file('/export/starexec/sandbox/tmp/tmp.Kpz0KHslZL/DTF2THF_17623.p',help_If_3_1_T)).
% 15.92/3.51 thf(f1513,plain,(
% 15.92/3.51 ((ord_less_eq @ set @ val @ scc @ p) != $true)),
% 15.92/3.51 inference(cnf_transformation,[status(thm)],[f890])).
% 15.92/3.51 thf(f890,plain,(
% 15.92/3.51 ((ord_less_eq @ set @ val @ scc @ p) != $true)),
% 15.92/3.51 inference(flattening,[status(thm)],[f707])).
% 15.92/3.51 thf(f707,plain,(
% 15.92/3.51 ~((ord_less_eq @ set @ val @ scc @ p) = $true)),
% 15.92/3.51 inference(fool_elimination,[status(thm)],[f706])).
% 15.92/3.51 thf(f706,plain,(
% 15.92/3.51 ~(ord_less_eq @ set @ val @ scc @ p)),
% 15.92/3.51 inference(rectify,[status(thm)],[f290])).
% 15.92/3.51 thf(f290,negated_conjecture,(
% 15.92/3.51 ~(ord_less_eq @ set @ val @ scc @ p)),
% 15.92/3.51 inference(negated_conjecture,[status(cth)],[f289])).
% 15.92/3.51 thf(f289,conjecture,(
% 15.92/3.51 (ord_less_eq @ set @ val @ scc @ p)),
% 15.92/3.51 file('/export/starexec/sandbox/tmp/tmp.Kpz0KHslZL/DTF2THF_17623.p',conj_0)).
% 15.92/3.51 thf(f3970,plain,(
% 15.92/3.51 ((ord_less_eq @ set @ val @ scc @ p) = $true)),
% 15.92/3.51 inference(trivial_inequality_removal,[status(thm)],[f3969])).
% 15.92/3.51 thf(f3969,plain,(
% 15.92/3.51 ($true != $true) | ((ord_less_eq @ set @ val @ scc @ p) = $true)),
% 15.92/3.51 inference(superposition,[status(thm)],[f1447,f3963])).
% 15.92/3.51 thf(f3963,plain,(
% 15.92/3.51 ($true = (member @ val @ (sK17 @ val @ p @ scc) @ p))),
% 15.92/3.51 inference(trivial_inequality_removal,[status(thm)],[f3962])).
% 15.92/3.51 thf(f3962,plain,(
% 15.92/3.51 ($true = (member @ val @ (sK17 @ val @ p @ scc) @ p)) | ($true != $true)),
% 15.92/3.51 inference(superposition,[status(thm)],[f1591,f3956])).
% 15.92/3.51 thf(f3956,plain,(
% 15.92/3.51 ((member @ val @ (sK17 @ val @ p @ scc) @ scc) = $true)),
% 15.92/3.51 inference(trivial_inequality_removal,[status(thm)],[f3950])).
% 15.92/3.51 thf(f3950,plain,(
% 15.92/3.51 ($true = $false) | ((member @ val @ (sK17 @ val @ p @ scc) @ scc) = $true)),
% 15.92/3.51 inference(superposition,[status(thm)],[f1446,f2021])).
% 15.92/3.51 thf(f1446,plain,(
% 15.92/3.51 ( ! [X0 : $tType,X2 : set @ X0,X1 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X2) = $true) | ((member @ X0 @ (sK17 @ X0 @ X2 @ X1) @ X1) = $true)) )),
% 15.92/3.51 inference(cnf_transformation,[status(thm)],[f1261])).
% 15.92/3.51 thf(f1261,plain,(
% 15.92/3.51 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X2) = $true) | (((member @ X0 @ (sK17 @ X0 @ X2 @ X1) @ X2) != $true) & ((member @ X0 @ (sK17 @ X0 @ X2 @ X1) @ X1) = $true)))),
% 15.92/3.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f914,f1260])).
% 15.92/3.51 thf(f1260,plain,(
% 15.92/3.51 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : (? [X3 : X0] : (((member @ X0 @ X3 @ X2) != $true) & ((member @ X0 @ X3 @ X1) = $true)) => (((member @ X0 @ (sK17 @ X0 @ X2 @ X1) @ X2) != $true) & ((member @ X0 @ (sK17 @ X0 @ X2 @ X1) @ X1) = $true)))),
% 15.92/3.51 introduced(definition,[],[choice_axiom])).
% 15.92/3.51 thf(f914,plain,(
% 15.92/3.51 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X2) = $true) | ? [X3 : X0] : (((member @ X0 @ X3 @ X2) != $true) & ((member @ X0 @ X3 @ X1) = $true)))),
% 15.92/3.51 inference(ennf_transformation,[status(thm)],[f615])).
% 15.92/3.51 thf(f615,plain,(
% 15.92/3.51 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : (! [X3 : X0] : (((member @ X0 @ X3 @ X1) = $true) => ((member @ X0 @ X3 @ X2) = $true)) => ((ord_less_eq @ set @ X0 @ X1 @ X2) = $true))),
% 15.92/3.51 inference(fool_elimination,[status(thm)],[f614])).
% 15.92/3.51 thf(f614,plain,(
% 15.92/3.51 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : (! [X3 : X0] : ((member @ X0 @ X3 @ X1) => (member @ X0 @ X3 @ X2)) => (ord_less_eq @ set @ X0 @ X1 @ X2))),
% 15.92/3.51 inference(rectify,[status(thm)],[f2])).
% 15.92/3.51 thf(f2,axiom,(
% 15.92/3.51 ! [X0 : $tType,X4 : set @ X0,X5 : set @ X0] : (! [X6 : X0] : ((member @ X0 @ X6 @ X4) => (member @ X0 @ X6 @ X5)) => (ord_less_eq @ set @ X0 @ X4 @ X5))),
% 15.92/3.51 file('/export/starexec/sandbox/tmp/tmp.Kpz0KHslZL/DTF2THF_17623.p',fact_1_subsetI)).
% 15.92/3.51 thf(f1591,plain,(
% 15.92/3.51 ( ! [X0 : val] : (($true != (member @ val @ X0 @ scc)) | ((member @ val @ X0 @ p) = $true)) )),
% 15.92/3.51 inference(cnf_transformation,[status(thm)],[f1112])).
% 15.92/3.51 thf(f1112,plain,(
% 15.92/3.51 ! [X0 : val] : (((member @ val @ X0 @ p) = $true) | ($true != (member @ val @ X0 @ scc)))),
% 15.92/3.51 inference(ennf_transformation,[status(thm)],[f527])).
% 15.92/3.51 thf(f527,plain,(
% 15.92/3.51 ! [X0 : val] : (($true = (member @ val @ X0 @ scc)) => ((member @ val @ X0 @ p) = $true))),
% 15.92/3.51 inference(fool_elimination,[status(thm)],[f526])).
% 15.92/3.51 thf(f526,plain,(
% 15.92/3.51 ! [X0 : val] : ((member @ val @ X0 @ scc) => (member @ val @ X0 @ p))),
% 15.92/3.51 inference(rectify,[status(thm)],[f1])).
% 15.92/3.51 thf(f1,axiom,(
% 15.92/3.51 ! [X3 : val] : ((member @ val @ X3 @ scc) => (member @ val @ X3 @ p))),
% 15.92/3.51 file('/export/starexec/sandbox/tmp/tmp.Kpz0KHslZL/DTF2THF_17623.p',fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062)).
% 15.92/3.51 thf(f1447,plain,(
% 15.92/3.51 ( ! [X0 : $tType,X2 : set @ X0,X1 : set @ X0] : (((member @ X0 @ (sK17 @ X0 @ X2 @ X1) @ X2) != $true) | ((ord_less_eq @ set @ X0 @ X1 @ X2) = $true)) )),
% 15.92/3.51 inference(cnf_transformation,[status(thm)],[f1261])).
% 15.92/3.51 % SZS output end Proof for DTF2THF_17623
% 15.92/3.51 % (18210)------------------------------
% 15.92/3.51 % (18210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.92/3.51 % (18210)Termination reason: Refutation
% 15.92/3.51
% 15.92/3.51 % (18210)Memory used [KB]: 7931
% 15.92/3.51 % (18210)Time elapsed: 0.194 s
% 15.92/3.51 % (18210)Instructions burned: 611 (million)
% 15.92/3.51 % (18210)------------------------------
% 15.92/3.51 % (18210)------------------------------
% 15.92/3.51 % (17815)Success in time 1.949 s
%------------------------------------------------------------------------------