%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP165^2 : 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 : n013.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 08:56:05 AM UTC 2026
% Result : Theorem 3.10s 1.72s
% Output : Refutation 3.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP165^2 : 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 : n013.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 08:28:23 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
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : ITP165^2 : TPTP v9.2.1. Released v7.5.0.
% 0.21/0.47 % Domain : Interactive Theorem Proving
% 0.21/0.47 % Problem : Sledgehammer Refine_Basic problem prob_892__3593680_1
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.21/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Des21]
% 0.21/0.47 % Names : Refine_Basic/prob_892__3593680_1 [Des21]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.21/0.47 % Syntax : Number of formulae : 355 ( 164 unt; 49 typ; 0 def)
% 0.21/0.47 % Number of atoms : 819 ( 279 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 13 ( 2 avg)
% 0.21/0.47 % Number of connectives : 3130 ( 81 ~; 11 |; 33 &;2696 @)
% 0.21/0.47 % ( 0 <=>; 309 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 19 ( 6 avg)
% 0.21/0.47 % Number of types : 3 ( 2 usr)
% 0.21/0.47 % Number of type conns : 157 ( 157 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 50 ( 47 usr; 5 con; 0-5 aty)
% 0.21/0.47 % Number of variables : 953 ( 53 ^; 849 !; 7 ?; 953 :)
% 0.21/0.47 % ( 44 !>; 0 ?*; 0 @-; 0 @+)
% 0.21/0.47 % SPC : TH1_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:19:47.460
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % Could-be-implicit typings (4)
% 0.21/0.47 thf(ty_t_Refine__Basic__Mirabelle__tqojlsrkwy_Onres,type,
% 0.21/0.47 refine1665802226e_nres: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Product__Type_Ounit,type,
% 0.21/0.47 product_unit: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Set_Oset,type,
% 0.21/0.47 set: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_a,type,
% 0.21/0.47 a: $tType ).
% 0.21/0.47
% 0.21/0.47 % Explicit typings (45)
% 0.21/0.47 thf(sy_cl_HOL_Otype,type,
% 0.21/0.47 type:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Obot,type,
% 0.21/0.47 bot:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.21/0.47 ord:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Otop,type,
% 0.21/0.47 top:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.21/0.47 order:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ogroup__add,type,
% 0.21/0.47 group_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.21/0.47 linorder:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.21/0.47 preorder:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.21/0.47 order_bot:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oorder__top,type,
% 0.21/0.47 order_top:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.21/0.47 boolean_algebra:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.21/0.47 ordered_ab_group_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 0.21/0.47 comple187826305attice:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.21/0.47 uminus_uminus:
% 0.21/0.47 !>[A: $tType] : ( A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_If,type,
% 0.21/0.47 if:
% 0.21/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.21/0.47 bot_bot:
% 0.21/0.47 !>[A: $tType] : A ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.21/0.47 ord_less_eq:
% 0.21/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.21/0.47 order_Greatest:
% 0.21/0.47 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.21/0.47 top_top:
% 0.21/0.47 !>[A: $tType] : A ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Partial__Function_Oflat__ord,type,
% 0.21/0.47 partial_flat_ord:
% 0.21/0.47 !>[A: $tType] : ( A > A > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_OASSUME,type,
% 0.21/0.47 refine1946708059ASSUME: $o > ( refine1665802226e_nres @ product_unit ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_ORETURN,type,
% 0.21/0.47 refine1687780735RETURN:
% 0.21/0.47 !>[A: $tType] : ( A > ( refine1665802226e_nres @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Obind,type,
% 0.21/0.47 refine463715084e_bind:
% 0.21/0.47 !>[B: $tType,A: $tType] : ( ( refine1665802226e_nres @ B ) > ( B > ( refine1665802226e_nres @ A ) ) > ( refine1665802226e_nres @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Oinres,type,
% 0.21/0.47 refine1315500908_inres:
% 0.21/0.47 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onf__inres,type,
% 0.21/0.47 refine406925620_inres:
% 0.21/0.47 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onofail,type,
% 0.21/0.47 refine1102455758nofail:
% 0.21/0.47 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_OFAILi,type,
% 0.21/0.47 refine1767639642_FAILi:
% 0.21/0.47 !>[A: $tType] : ( refine1665802226e_nres @ A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_ORES,type,
% 0.21/0.47 refine605929679le_RES:
% 0.21/0.47 !>[A: $tType] : ( ( set @ A ) > ( refine1665802226e_nres @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_Ocase__nres,type,
% 0.21/0.47 refine60818195e_nres:
% 0.21/0.47 !>[B: $tType,A: $tType] : ( B > ( ( set @ A ) > B ) > ( refine1665802226e_nres @ A ) > B ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_Orec__nres,type,
% 0.21/0.47 refine1442219249c_nres:
% 0.21/0.47 !>[C: $tType,A: $tType] : ( C > ( ( set @ A ) > C ) > ( refine1665802226e_nres @ A ) > C ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Othe__RES,type,
% 0.21/0.47 refine1672542526he_RES:
% 0.21/0.47 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Refine__Misc_Ostrict,type,
% 0.21/0.47 refine_strict:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_OCollect,type,
% 0.21/0.47 collect:
% 0.21/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_Oinsert,type,
% 0.21/0.47 insert:
% 0.21/0.47 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_Ois__empty,type,
% 0.21/0.47 is_empty:
% 0.21/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_Ois__singleton,type,
% 0.21/0.47 is_singleton:
% 0.21/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_Othe__elem,type,
% 0.21/0.47 the_elem:
% 0.21/0.47 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set__Interval_Oord_OatLeast,type,
% 0.21/0.47 set_atLeast:
% 0.21/0.47 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set__Interval_Oord_OatLeastAtMost,type,
% 0.21/0.47 set_atLeastAtMost:
% 0.21/0.47 !>[A: $tType] : ( ( A > A > $o ) > A > A > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set__Interval_Oord_OatMost,type,
% 0.21/0.47 set_atMost:
% 0.21/0.47 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member,type,
% 0.21/0.47 member:
% 0.21/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_S1,type,
% 0.21/0.47 s1: refine1665802226e_nres @ a ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_S2,type,
% 0.21/0.47 s2: refine1665802226e_nres @ a ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v__092_060Phi_062,type,
% 0.21/0.47 phi: a > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_b,type,
% 0.21/0.47 b: $o ).
% 0.21/0.47
% 0.21/0.47 % Relevant facts (254)
% 0.21/0.47 thf(fact_0_nres__more__simps_I4_J,axiom,
% 0.21/0.47 ! [A: $tType,X: set @ A,Y: set @ A] :
% 0.21/0.47 ( ( ( refine605929679le_RES @ A @ X )
% 0.21/0.47 = ( refine605929679le_RES @ A @ Y ) )
% 0.21/0.47 = ( X = Y ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_more_simps(4)
% 0.21/0.47 thf(fact_1_nres_Oinject,axiom,
% 0.21/0.47 ! [A: $tType,X2: set @ A,Y2: set @ A] :
% 0.21/0.47 ( ( ( refine605929679le_RES @ A @ X2 )
% 0.21/0.47 = ( refine605929679le_RES @ A @ Y2 ) )
% 0.21/0.47 = ( X2 = Y2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres.inject
% 0.21/0.47 thf(fact_2_RES__rule,axiom,
% 0.21/0.47 ! [A: $tType,S: set @ A,Phi: A > $o] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ S )
% 0.21/0.47 => ( Phi @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ S ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RES_rule
% 0.21/0.47 thf(fact_3_SPEC__rule,axiom,
% 0.21/0.47 ! [A: $tType,Phi: A > $o,Phi2: A > $o] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( Phi @ X3 )
% 0.21/0.47 => ( Phi2 @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % SPEC_rule
% 0.21/0.47 thf(fact_4_SPEC__trans,axiom,
% 0.21/0.47 ! [A: $tType,X4: refine1665802226e_nres @ A,Y3: refine1665802226e_nres @ A,Postcond: A > $o] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Y3 )
% 0.21/0.47 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ Y3 @ ( refine605929679le_RES @ A @ ( collect @ A @ Postcond ) ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ ( refine605929679le_RES @ A @ ( collect @ A @ Postcond ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % SPEC_trans
% 0.21/0.47 thf(fact_5_SPEC__cons__rule,axiom,
% 0.21/0.47 ! [A: $tType,M: refine1665802226e_nres @ A,Phi: A > $o,Psi: A > $o] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 0.21/0.47 => ( ! [X3: A] :
% 0.21/0.47 ( ( Phi @ X3 )
% 0.21/0.47 => ( Psi @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % SPEC_cons_rule
% 0.21/0.47 thf(fact_6_nf__inres__RES,axiom,
% 0.21/0.47 ! [A: $tType,X: set @ A,X4: A] :
% 0.21/0.47 ( ( refine406925620_inres @ A @ ( refine605929679le_RES @ A @ X ) @ X4 )
% 0.21/0.47 = ( member @ A @ X4 @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % nf_inres_RES
% 0.21/0.47 thf(fact_7_nf__inres__SPEC,axiom,
% 0.21/0.47 ! [A: $tType,Phi: A > $o,X4: A] :
% 0.21/0.47 ( ( refine406925620_inres @ A @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ X4 )
% 0.21/0.47 = ( Phi @ X4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nf_inres_SPEC
% 0.21/0.47 thf(fact_8_order__mono__setup_Orefl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X4: A] : ( ord_less_eq @ A @ X4 @ X4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_mono_setup.refl
% 0.21/0.47 thf(fact_9_the__RES_Osimps,axiom,
% 0.21/0.47 ! [A: $tType,X: set @ A] :
% 0.21/0.47 ( ( refine1672542526he_RES @ A @ ( refine605929679le_RES @ A @ X ) )
% 0.21/0.47 = X ) ).
% 0.21/0.47
% 0.21/0.47 % the_RES.simps
% 0.21/0.47 thf(fact_10_nres__order__simps_I21_J,axiom,
% 0.21/0.47 ! [X5: $tType,X4: X5,Y: set @ X5] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ X5 ) @ ( refine1687780735RETURN @ X5 @ X4 ) @ ( refine605929679le_RES @ X5 @ Y ) )
% 0.21/0.47 = ( member @ X5 @ X4 @ Y ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_order_simps(21)
% 0.21/0.47 thf(fact_11_nres_Osimps_I7_J,axiom,
% 0.21/0.47 ! [C: $tType,A: $tType,F1: C,F2: ( set @ A ) > C,X2: set @ A] :
% 0.21/0.47 ( ( refine1442219249c_nres @ C @ A @ F1 @ F2 @ ( refine605929679le_RES @ A @ X2 ) )
% 0.21/0.47 = ( F2 @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres.simps(7)
% 0.21/0.47 thf(fact_12_le__funD,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( ord @ B )
% 0.21/0.47 => ! [F: A > B,G: A > B,X4: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_funD
% 0.21/0.47 thf(fact_13_le__funE,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( ord @ B )
% 0.21/0.47 => ! [F: A > B,G: A > B,X4: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_funE
% 0.21/0.47 thf(fact_14_le__funI,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( ord @ B )
% 0.21/0.47 => ! [F: A > B,G: A > B] :
% 0.21/0.47 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_funI
% 0.21/0.47 thf(fact_15_Refine__Misc_Oif__mono,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [B2: $o,M1: A,M12: A,M2: A,M22: A] :
% 0.21/0.47 ( ( B2
% 0.21/0.47 => ( ord_less_eq @ A @ M1 @ M12 ) )
% 0.21/0.47 => ( ( ~ B2
% 0.21/0.47 => ( ord_less_eq @ A @ M2 @ M22 ) )
% 0.21/0.47 => ( ord_less_eq @ A @ ( if @ A @ B2 @ M1 @ M2 ) @ ( if @ A @ B2 @ M12 @ M22 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Refine_Misc.if_mono
% 0.21/0.47 thf(fact_16_le__fun__def,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( ord @ B )
% 0.21/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.21/0.47 = ( ^ [F3: A > B,G2: A > B] :
% 0.21/0.47 ! [X6: A] : ( ord_less_eq @ B @ ( F3 @ X6 ) @ ( G2 @ X6 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_fun_def
% 0.21/0.47 thf(fact_17_nres__more__simps_I6_J,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,Y3: A] :
% 0.21/0.47 ( ( ( refine1687780735RETURN @ A @ X4 )
% 0.21/0.47 = ( refine1687780735RETURN @ A @ Y3 ) )
% 0.21/0.47 = ( X4 = Y3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_more_simps(6)
% 0.21/0.47 thf(fact_18_nres__order__simps_I20_J,axiom,
% 0.21/0.47 ! [W: $tType,X4: W,Y3: W] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ W ) @ ( refine1687780735RETURN @ W @ X4 ) @ ( refine1687780735RETURN @ W @ Y3 ) )
% 0.21/0.47 = ( X4 = Y3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_order_simps(20)
% 0.21/0.47 thf(fact_19_less__eq__nres_Osimps_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ A2 ) @ ( refine605929679le_RES @ A @ B2 ) )
% 0.21/0.47 = ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_eq_nres.simps(2)
% 0.21/0.47 thf(fact_20_nres__order__simps_I5_J,axiom,
% 0.21/0.47 ! [E: $tType,X: set @ E,Y: set @ E] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ E ) @ ( refine605929679le_RES @ E @ X ) @ ( refine605929679le_RES @ E @ Y ) )
% 0.21/0.47 = ( ord_less_eq @ ( set @ E ) @ X @ Y ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_order_simps(5)
% 0.21/0.47 thf(fact_21_RETURN__to__SPEC__rule,axiom,
% 0.21/0.47 ! [A: $tType,M: refine1665802226e_nres @ A,V: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M
% 0.21/0.47 @ ( refine605929679le_RES @ A
% 0.21/0.47 @ ( collect @ A
% 0.21/0.47 @ ( ^ [Y4: A,Z: A] : ( Y4 = Z )
% 0.21/0.47 @ V ) ) ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine1687780735RETURN @ A @ V ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RETURN_to_SPEC_rule
% 0.21/0.47 thf(fact_22_RETURN__rule,axiom,
% 0.21/0.47 ! [A: $tType,Phi: A > $o,X4: A] :
% 0.21/0.47 ( ( Phi @ X4 )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RETURN_rule
% 0.21/0.47 thf(fact_23_order__mono__setup_Omono__let,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [F: B > A,F4: B > A,X4: B] :
% 0.21/0.47 ( ! [X3: B] : ( ord_less_eq @ A @ ( F @ X3 ) @ ( F4 @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F4 @ X4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_mono_setup.mono_let
% 0.21/0.47 thf(fact_24_order__mono__setup_Omono__if,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [T: A,T2: A,E2: A,E3: A,B2: $o] :
% 0.21/0.47 ( ( ord_less_eq @ A @ T @ T2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ E2 @ E3 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( if @ A @ B2 @ T @ E2 ) @ ( if @ A @ B2 @ T2 @ E3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_mono_setup.mono_if
% 0.21/0.47 thf(fact_25_dual__order_Oantisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [B2: A,A2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.21/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.antisym
% 0.21/0.47 thf(fact_26_dual__order_Oeq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.21/0.47 = ( ^ [A3: A,B3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.21/0.47 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.eq_iff
% 0.21/0.47 thf(fact_27_dual__order_Otrans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.21/0.47 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.trans
% 0.21/0.47 thf(fact_28_linorder__wlog,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.21/0.47 ( ! [A4: A,B4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.21/0.47 => ( P @ A4 @ B4 ) )
% 0.21/0.47 => ( ! [A4: A,B4: A] :
% 0.21/0.47 ( ( P @ B4 @ A4 )
% 0.21/0.47 => ( P @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_wlog
% 0.21/0.47 thf(fact_29_dual__order_Orefl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.refl
% 0.21/0.47 thf(fact_30_order__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X4: A,Y3: A,Z2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.21/0.47 => ( ord_less_eq @ A @ X4 @ Z2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_trans
% 0.21/0.47 thf(fact_31_order__class_Oorder_Oantisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A2: A,B2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.21/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_class.order.antisym
% 0.21/0.47 thf(fact_32_ord__le__eq__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.21/0.47 => ( ( B2 = C2 )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_le_eq_trans
% 0.21/0.47 thf(fact_33_ord__eq__le__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.21/0.47 ( ( A2 = B2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_trans
% 0.21/0.47 thf(fact_34_order__class_Oorder_Oeq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.21/0.47 = ( ^ [A3: A,B3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_class.order.eq_iff
% 0.21/0.47 thf(fact_35_antisym__conv,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [Y3: A,X4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ Y3 @ X4 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.21/0.47 = ( X4 = Y3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym_conv
% 0.21/0.47 thf(fact_36_le__cases3,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X4: A,Y3: A,Z2: A] :
% 0.21/0.47 ( ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Y3 @ X4 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ X4 @ Z2 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ X4 @ Z2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Y3 @ X4 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Z2 @ X4 ) )
% 0.21/0.47 => ~ ( ( ord_less_eq @ A @ Z2 @ X4 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases3
% 0.21/0.47 thf(fact_37_order_Otrans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.trans
% 0.21/0.47 thf(fact_38_le__cases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X4: A,Y3: A] :
% 0.21/0.47 ( ~ ( ord_less_eq @ A @ X4 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases
% 0.21/0.47 thf(fact_39_eq__refl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X4: A,Y3: A] :
% 0.21/0.47 ( ( X4 = Y3 )
% 0.21/0.47 => ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_refl
% 0.21/0.47 thf(fact_40_linear,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X4: A,Y3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.21/0.47 | ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linear
% 0.21/0.47 thf(fact_41_antisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [X4: A,Y3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ Y3 @ X4 )
% 0.21/0.47 => ( X4 = Y3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym
% 0.21/0.47 thf(fact_42_eq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.21/0.47 = ( ^ [X6: A,Y5: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X6 @ Y5 )
% 0.21/0.47 & ( ord_less_eq @ A @ Y5 @ X6 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_iff
% 0.21/0.47 thf(fact_43_ord__le__eq__subst,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( ord @ B )
% 0.21/0.47 & ( ord @ A ) )
% 0.21/0.47 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.21/0.47 => ( ( ( F @ B2 )
% 0.21/0.47 = C2 )
% 0.21/0.47 => ( ! [X3: A,Y6: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X3 @ Y6 )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_le_eq_subst
% 0.21/0.47 thf(fact_44_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.21/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.21/0.47 = ( P @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_45_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ( collect @ A
% 0.21/0.47 @ ^ [X6: A] : ( member @ A @ X6 @ A5 ) )
% 0.21/0.47 = A5 ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_46_Collect__cong,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( P @ X3 )
% 0.21/0.47 = ( Q @ X3 ) )
% 0.21/0.47 => ( ( collect @ A @ P )
% 0.21/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_cong
% 0.21/0.47 thf(fact_47_ext,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( F @ X3 )
% 0.21/0.47 = ( G @ X3 ) )
% 0.21/0.47 => ( F = G ) ) ).
% 0.21/0.47
% 0.21/0.47 % ext
% 0.21/0.47 thf(fact_48_ord__eq__le__subst,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( ord @ B )
% 0.21/0.47 & ( ord @ A ) )
% 0.21/0.47 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 = ( F @ B2 ) )
% 0.21/0.47 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.21/0.47 => ( ! [X3: B,Y6: B] :
% 0.21/0.47 ( ( ord_less_eq @ B @ X3 @ Y6 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_subst
% 0.21/0.47 thf(fact_49_order__subst2,axiom,
% 0.21/0.47 ! [A: $tType,C: $tType] :
% 0.21/0.47 ( ( ( order @ C )
% 0.21/0.47 & ( order @ A ) )
% 0.21/0.47 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.21/0.47 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 0.21/0.47 => ( ! [X3: A,Y6: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X3 @ Y6 )
% 0.21/0.47 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.21/0.47 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_subst2
% 0.21/0.47 thf(fact_50_order__subst1,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( order @ B )
% 0.21/0.47 & ( order @ A ) )
% 0.21/0.47 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.21/0.47 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.21/0.47 => ( ! [X3: B,Y6: B] :
% 0.21/0.47 ( ( ord_less_eq @ B @ X3 @ Y6 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_subst1
% 0.21/0.47 thf(fact_51_the__RES__inv,axiom,
% 0.21/0.47 ! [A: $tType,M: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( refine1102455758nofail @ A @ M )
% 0.21/0.47 => ( ( refine605929679le_RES @ A @ ( refine1672542526he_RES @ A @ M ) )
% 0.21/0.47 = M ) ) ).
% 0.21/0.47
% 0.21/0.47 % the_RES_inv
% 0.21/0.47 thf(fact_52_Greatest__equality,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [P: A > $o,X4: A] :
% 0.21/0.47 ( ( P @ X4 )
% 0.21/0.47 => ( ! [Y6: A] :
% 0.21/0.47 ( ( P @ Y6 )
% 0.21/0.47 => ( ord_less_eq @ A @ Y6 @ X4 ) )
% 0.21/0.47 => ( ( order_Greatest @ A @ P )
% 0.21/0.47 = X4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Greatest_equality
% 0.21/0.47 thf(fact_53_GreatestI2__order,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [P: A > $o,X4: A,Q: A > $o] :
% 0.21/0.47 ( ( P @ X4 )
% 0.21/0.47 => ( ! [Y6: A] :
% 0.21/0.47 ( ( P @ Y6 )
% 0.21/0.47 => ( ord_less_eq @ A @ Y6 @ X4 ) )
% 0.21/0.47 => ( ! [X3: A] :
% 0.21/0.47 ( ( P @ X3 )
% 0.21/0.47 => ( ! [Y7: A] :
% 0.21/0.47 ( ( P @ Y7 )
% 0.21/0.47 => ( ord_less_eq @ A @ Y7 @ X3 ) )
% 0.21/0.47 => ( Q @ X3 ) ) )
% 0.21/0.47 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % GreatestI2_order
% 0.21/0.47 thf(fact_54_transfer_Otransfer__Let,axiom,
% 0.21/0.47 ! [C: $tType,A: $tType,B: $tType] :
% 0.21/0.47 ( ( comple187826305attice @ A )
% 0.21/0.47 => ! [Alpha: C > A,F: B > C,F5: B > A,X4: B] :
% 0.21/0.47 ( ! [X3: B] : ( ord_less_eq @ A @ ( Alpha @ ( F @ X3 ) ) @ ( F5 @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ A @ ( Alpha @ ( F @ X4 ) ) @ ( F5 @ X4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % transfer.transfer_Let
% 0.21/0.47 thf(fact_55_transfer_Otransfer__if,axiom,
% 0.21/0.47 ! [C: $tType,A: $tType] :
% 0.21/0.47 ( ( comple187826305attice @ A )
% 0.21/0.47 => ! [B2: $o,Alpha: C > A,S1: C,S12: A,S2: C,S22: A] :
% 0.21/0.47 ( ( B2
% 0.21/0.47 => ( ord_less_eq @ A @ ( Alpha @ S1 ) @ S12 ) )
% 0.21/0.47 => ( ( ~ B2
% 0.21/0.47 => ( ord_less_eq @ A @ ( Alpha @ S2 ) @ S22 ) )
% 0.21/0.47 => ( ord_less_eq @ A @ ( Alpha @ ( if @ C @ B2 @ S1 @ S2 ) ) @ ( if @ A @ B2 @ S12 @ S22 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % transfer.transfer_if
% 0.21/0.47 thf(fact_56_le__rel__bool__arg__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ( ( ord_less_eq @ ( $o > A ) )
% 0.21/0.47 = ( ^ [X7: $o > A,Y8: $o > A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ ( X7 @ $false ) @ ( Y8 @ $false ) )
% 0.21/0.47 & ( ord_less_eq @ A @ ( X7 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_rel_bool_arg_iff
% 0.21/0.47 thf(fact_57_verit__la__disequality,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [A2: A,B2: A] :
% 0.21/0.47 ( ( A2 = B2 )
% 0.21/0.47 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 0.21/0.47 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % verit_la_disequality
% 0.21/0.47 thf(fact_58_ord__eq__le__eq__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [A2: A,B2: A,C2: A,D: A] :
% 0.21/0.47 ( ( A2 = B2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.21/0.47 => ( ( C2 = D )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ D ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_eq_trans
% 0.21/0.47 thf(fact_59_bind__cong,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,M: refine1665802226e_nres @ A,M3: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 0.21/0.47 ( ( M = M3 )
% 0.21/0.47 => ( ! [X3: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M3 )
% 0.21/0.47 => ( ( F @ X3 )
% 0.21/0.47 = ( F4 @ X3 ) ) )
% 0.21/0.47 => ( ( refine463715084e_bind @ A @ B @ M @ F )
% 0.21/0.47 = ( refine463715084e_bind @ A @ B @ M3 @ F4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bind_cong
% 0.21/0.47 thf(fact_60_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,M4: refine1665802226e_nres @ A,M5: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M5 )
% 0.21/0.47 => ( ! [X3: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M4 )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ ( F4 @ X3 ) ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M4 @ F ) @ ( refine463715084e_bind @ A @ B @ M5 @ F4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Refine_Basic_Mirabelle_tqojlsrkwy.bind_mono(1)
% 0.21/0.47 thf(fact_61_nofail__simps_I2_J,axiom,
% 0.21/0.47 ! [B: $tType,X: set @ B] : ( refine1102455758nofail @ B @ ( refine605929679le_RES @ B @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % nofail_simps(2)
% 0.21/0.47 thf(fact_62_nofail__simps_I3_J,axiom,
% 0.21/0.47 ! [C: $tType,X4: C] : ( refine1102455758nofail @ C @ ( refine1687780735RETURN @ C @ X4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nofail_simps(3)
% 0.21/0.47 thf(fact_63_nres__monad2,axiom,
% 0.21/0.47 ! [A: $tType,M4: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( refine463715084e_bind @ A @ A @ M4 @ ( refine1687780735RETURN @ A ) )
% 0.21/0.47 = M4 ) ).
% 0.21/0.47
% 0.21/0.47 % nres_monad2
% 0.21/0.47 thf(fact_64_nres__monad1,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,X4: B,F: B > ( refine1665802226e_nres @ A )] :
% 0.21/0.47 ( ( refine463715084e_bind @ B @ A @ ( refine1687780735RETURN @ B @ X4 ) @ F )
% 0.21/0.47 = ( F @ X4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_monad1
% 0.21/0.47 thf(fact_65_subset__Collect__conv,axiom,
% 0.21/0.47 ! [A: $tType,S: set @ A,P: A > $o] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 0.21/0.47 = ( ! [X6: A] :
% 0.21/0.47 ( ( member @ A @ X6 @ S )
% 0.21/0.47 => ( P @ X6 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_Collect_conv
% 0.21/0.47 thf(fact_66_nofail__antimono__fun,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,F: A > ( refine1665802226e_nres @ B ),G: A > ( refine1665802226e_nres @ B ),X4: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( A > ( refine1665802226e_nres @ B ) ) @ F @ G )
% 0.21/0.47 => ( ( refine1102455758nofail @ B @ ( G @ X4 ) )
% 0.21/0.47 => ( refine1102455758nofail @ B @ ( F @ X4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nofail_antimono_fun
% 0.21/0.47 thf(fact_67_nofail__RES__conv,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( refine1102455758nofail @ A )
% 0.21/0.47 = ( ^ [M6: refine1665802226e_nres @ A] :
% 0.21/0.47 ? [M7: set @ A] :
% 0.21/0.47 ( M6
% 0.21/0.47 = ( refine605929679le_RES @ A @ M7 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nofail_RES_conv
% 0.21/0.47 thf(fact_68_pwD1,axiom,
% 0.21/0.47 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S3 )
% 0.21/0.47 => ( ( refine1102455758nofail @ A @ S3 )
% 0.21/0.47 => ( refine1102455758nofail @ A @ S ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pwD1
% 0.21/0.47 thf(fact_69_le__nofailI,axiom,
% 0.21/0.47 ! [A: $tType,M5: refine1665802226e_nres @ A,M4: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ( refine1102455758nofail @ A @ M5 )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M5 ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_nofailI
% 0.21/0.47 thf(fact_70_subsetI,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ A5 )
% 0.21/0.47 => ( member @ A @ X3 @ B5 ) )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % subsetI
% 0.21/0.47 thf(fact_71_subset__antisym,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.21/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 0.21/0.47 => ( A5 = B5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_antisym
% 0.21/0.47 thf(fact_72_pw__bind__leI,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,S: refine1665802226e_nres @ A,M4: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A )] :
% 0.21/0.47 ( ( ( refine1102455758nofail @ A @ S )
% 0.21/0.47 => ( refine1102455758nofail @ B @ M4 ) )
% 0.21/0.47 => ( ! [X3: B] :
% 0.21/0.47 ( ( refine1102455758nofail @ B @ M4 )
% 0.21/0.47 => ( ( refine1315500908_inres @ B @ M4 @ X3 )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F @ X3 ) @ S ) ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M4 @ F ) @ S ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_bind_leI
% 0.21/0.47 thf(fact_73_pw__bind__le__iff,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,M4: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A ),S: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M4 @ F ) @ S )
% 0.21/0.47 = ( ( ( refine1102455758nofail @ A @ S )
% 0.21/0.47 => ( refine1102455758nofail @ B @ M4 ) )
% 0.21/0.47 & ! [X6: B] :
% 0.21/0.47 ( ( ( refine1102455758nofail @ B @ M4 )
% 0.21/0.47 & ( refine1315500908_inres @ B @ M4 @ X6 ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F @ X6 ) @ S ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_bind_le_iff
% 0.21/0.47 thf(fact_74_relprop__triggers_I6_J,axiom,
% 0.21/0.47 ! [I: $tType,R: set @ I,R2: set @ I] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ I ) @ R @ R2 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ I ) @ R @ R2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % relprop_triggers(6)
% 0.21/0.47 thf(fact_75_in__mono,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A,X4: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.21/0.47 => ( ( member @ A @ X4 @ A5 )
% 0.21/0.47 => ( member @ A @ X4 @ B5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % in_mono
% 0.21/0.47 thf(fact_76_subsetD,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A,C2: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.21/0.47 => ( ( member @ A @ C2 @ A5 )
% 0.21/0.47 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subsetD
% 0.21/0.47 thf(fact_77_inres__simps_I2_J,axiom,
% 0.21/0.47 ! [B: $tType,X: set @ B] :
% 0.21/0.47 ( ( refine1315500908_inres @ B @ ( refine605929679le_RES @ B @ X ) )
% 0.21/0.47 = ( ^ [X6: B] : ( member @ B @ X6 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % inres_simps(2)
% 0.21/0.47 thf(fact_78_inres__simps_I3_J,axiom,
% 0.21/0.47 ! [C: $tType,X4: C] :
% 0.21/0.47 ( ( refine1315500908_inres @ C @ ( refine1687780735RETURN @ C @ X4 ) )
% 0.21/0.47 = ( ^ [Y4: C,Z: C] : ( Y4 = Z )
% 0.21/0.47 @ X4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % inres_simps(3)
% 0.21/0.47 thf(fact_79_pwD2,axiom,
% 0.21/0.47 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A,X4: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S3 )
% 0.21/0.47 => ( ( refine1315500908_inres @ A @ S @ X4 )
% 0.21/0.47 => ( refine1315500908_inres @ A @ S3 @ X4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pwD2
% 0.21/0.47 thf(fact_80_pw__eqI,axiom,
% 0.21/0.47 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ( refine1102455758nofail @ A @ S )
% 0.21/0.47 = ( refine1102455758nofail @ A @ S3 ) )
% 0.21/0.47 => ( ! [X3: A] :
% 0.21/0.47 ( ( refine1315500908_inres @ A @ S @ X3 )
% 0.21/0.47 = ( refine1315500908_inres @ A @ S3 @ X3 ) )
% 0.21/0.47 => ( S = S3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_eqI
% 0.21/0.47 thf(fact_81_pw__eq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ^ [Y4: refine1665802226e_nres @ A,Z: refine1665802226e_nres @ A] : ( Y4 = Z ) )
% 0.21/0.47 = ( ^ [S4: refine1665802226e_nres @ A,S5: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ( refine1102455758nofail @ A @ S4 )
% 0.21/0.47 = ( refine1102455758nofail @ A @ S5 ) )
% 0.21/0.47 & ! [X6: A] :
% 0.21/0.47 ( ( refine1315500908_inres @ A @ S4 @ X6 )
% 0.21/0.47 = ( refine1315500908_inres @ A @ S5 @ X6 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_eq_iff
% 0.21/0.47 thf(fact_82_not__nofail__inres,axiom,
% 0.21/0.47 ! [A: $tType,S: refine1665802226e_nres @ A,X4: A] :
% 0.21/0.47 ( ~ ( refine1102455758nofail @ A @ S )
% 0.21/0.47 => ( refine1315500908_inres @ A @ S @ X4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_nofail_inres
% 0.21/0.47 thf(fact_83_pw__le__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) )
% 0.21/0.47 = ( ^ [S4: refine1665802226e_nres @ A,S5: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( refine1102455758nofail @ A @ S5 )
% 0.21/0.47 => ( ( refine1102455758nofail @ A @ S4 )
% 0.21/0.47 & ! [X6: A] :
% 0.21/0.47 ( ( refine1315500908_inres @ A @ S4 @ X6 )
% 0.21/0.47 => ( refine1315500908_inres @ A @ S5 @ X6 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_le_iff
% 0.21/0.47 thf(fact_84_pw__leI_H,axiom,
% 0.21/0.47 ! [A: $tType,S3: refine1665802226e_nres @ A,S: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ( refine1102455758nofail @ A @ S3 )
% 0.21/0.47 => ( refine1102455758nofail @ A @ S ) )
% 0.21/0.47 => ( ! [X3: A] :
% 0.21/0.47 ( ( refine1102455758nofail @ A @ S3 )
% 0.21/0.47 => ( ( refine1315500908_inres @ A @ S @ X3 )
% 0.21/0.47 => ( refine1315500908_inres @ A @ S3 @ X3 ) ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_leI'
% 0.21/0.47 thf(fact_85_pw__leI,axiom,
% 0.21/0.47 ! [A: $tType,S3: refine1665802226e_nres @ A,S: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ( refine1102455758nofail @ A @ S3 )
% 0.21/0.47 => ( ( refine1102455758nofail @ A @ S )
% 0.21/0.47 & ! [X3: A] :
% 0.21/0.47 ( ( refine1315500908_inres @ A @ S @ X3 )
% 0.21/0.47 => ( refine1315500908_inres @ A @ S3 @ X3 ) ) ) )
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_leI
% 0.21/0.47 thf(fact_86_pw__bind__nofail,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,M4: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A )] :
% 0.21/0.47 ( ( refine1102455758nofail @ A @ ( refine463715084e_bind @ B @ A @ M4 @ F ) )
% 0.21/0.47 = ( ( refine1102455758nofail @ B @ M4 )
% 0.21/0.47 & ! [X6: B] :
% 0.21/0.47 ( ( refine1315500908_inres @ B @ M4 @ X6 )
% 0.21/0.47 => ( refine1102455758nofail @ A @ ( F @ X6 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_bind_nofail
% 0.21/0.47 thf(fact_87_inres__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( refine1315500908_inres @ A )
% 0.21/0.47 = ( ^ [S4: refine1665802226e_nres @ A,X6: A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X6 ) @ S4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % inres_def
% 0.21/0.47 thf(fact_88_nf__inres__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( refine406925620_inres @ A )
% 0.21/0.47 = ( ^ [M6: refine1665802226e_nres @ A,X6: A] :
% 0.21/0.47 ( ( refine1102455758nofail @ A @ M6 )
% 0.21/0.47 & ( refine1315500908_inres @ A @ M6 @ X6 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nf_inres_def
% 0.21/0.47 thf(fact_89_Collect__mono__iff,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.21/0.47 = ( ! [X6: A] :
% 0.21/0.47 ( ( P @ X6 )
% 0.21/0.47 => ( Q @ X6 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mono_iff
% 0.21/0.47 thf(fact_90_set__eq__subset,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 0.21/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.21/0.47 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % set_eq_subset
% 0.21/0.47 thf(fact_91_subset__trans,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A,C3: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.21/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C3 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_trans
% 0.21/0.47 thf(fact_92_Collect__mono,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( P @ X3 )
% 0.21/0.47 => ( Q @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mono
% 0.21/0.47 thf(fact_93_subset__refl,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ A5 ) ).
% 0.21/0.47
% 0.21/0.47 % subset_refl
% 0.21/0.47 thf(fact_94_subset__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.21/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.21/0.47 ! [T3: A] :
% 0.21/0.47 ( ( member @ A @ T3 @ A6 )
% 0.21/0.47 => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_iff
% 0.21/0.47 thf(fact_95_equalityD2,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( A5 = B5 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % equalityD2
% 0.21/0.47 thf(fact_96_equalityD1,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( A5 = B5 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % equalityD1
% 0.21/0.47 thf(fact_97_subset__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.21/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.21/0.47 ! [X6: A] :
% 0.21/0.47 ( ( member @ A @ X6 @ A6 )
% 0.21/0.47 => ( member @ A @ X6 @ B6 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_eq
% 0.21/0.47 thf(fact_98_equalityE,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( A5 = B5 )
% 0.21/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.21/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % equalityE
% 0.21/0.47 thf(fact_99_less__eq__nres_Oelims_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A,Y3: $o] :
% 0.21/0.47 ( ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 0.21/0.47 = Y3 )
% 0.21/0.47 => ( ( ( Xa
% 0.21/0.47 = ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 => ~ Y3 )
% 0.21/0.47 => ( ! [A4: set @ A] :
% 0.21/0.47 ( ( X4
% 0.21/0.47 = ( refine605929679le_RES @ A @ A4 ) )
% 0.21/0.47 => ! [B4: set @ A] :
% 0.21/0.47 ( ( Xa
% 0.21/0.47 = ( refine605929679le_RES @ A @ B4 ) )
% 0.21/0.47 => ( Y3
% 0.21/0.47 = ( ~ ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ) )
% 0.21/0.47 => ~ ( ( X4
% 0.21/0.47 = ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 => ( ? [Uv: set @ A] :
% 0.21/0.47 ( Xa
% 0.21/0.47 = ( refine605929679le_RES @ A @ Uv ) )
% 0.21/0.47 => Y3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_eq_nres.elims(1)
% 0.21/0.47 thf(fact_100_less__eq__nres_Oelims_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 0.21/0.47 => ( ( Xa
% 0.21/0.47 != ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 => ~ ! [A4: set @ A] :
% 0.21/0.47 ( ( X4
% 0.21/0.47 = ( refine605929679le_RES @ A @ A4 ) )
% 0.21/0.47 => ! [B4: set @ A] :
% 0.21/0.47 ( ( Xa
% 0.21/0.47 = ( refine605929679le_RES @ A @ B4 ) )
% 0.21/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_eq_nres.elims(2)
% 0.21/0.47 thf(fact_101_less__eq__nres_Oelims_I3_J,axiom,
% 0.21/0.47 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ~ ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 0.21/0.47 => ( ! [A4: set @ A] :
% 0.21/0.47 ( ( X4
% 0.21/0.47 = ( refine605929679le_RES @ A @ A4 ) )
% 0.21/0.47 => ! [B4: set @ A] :
% 0.21/0.47 ( ( Xa
% 0.21/0.47 = ( refine605929679le_RES @ A @ B4 ) )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) )
% 0.21/0.47 => ~ ( ( X4
% 0.21/0.47 = ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 => ! [Uv: set @ A] :
% 0.21/0.47 ( Xa
% 0.21/0.47 != ( refine605929679le_RES @ A @ Uv ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_eq_nres.elims(3)
% 0.21/0.47 thf(fact_102_nres_Osimps_I5_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,F1: B,F2: ( set @ A ) > B,X2: set @ A] :
% 0.21/0.47 ( ( refine60818195e_nres @ B @ A @ F1 @ F2 @ ( refine605929679le_RES @ A @ X2 ) )
% 0.21/0.47 = ( F2 @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres.simps(5)
% 0.21/0.47 thf(fact_103_nres__order__simps_I22_J,axiom,
% 0.21/0.47 ! [Y9: $tType,X: set @ Y9,Y3: Y9] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ Y9 ) @ ( refine605929679le_RES @ Y9 @ X ) @ ( refine1687780735RETURN @ Y9 @ Y3 ) )
% 0.21/0.47 = ( ord_less_eq @ ( set @ Y9 ) @ X @ ( insert @ Y9 @ Y3 @ ( bot_bot @ ( set @ Y9 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_order_simps(22)
% 0.21/0.47 thf(fact_104_less__eq__nres_Osimps_I3_J,axiom,
% 0.21/0.47 ! [A: $tType,Uv2: set @ A] :
% 0.21/0.47 ~ ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ Uv2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_eq_nres.simps(3)
% 0.21/0.47 thf(fact_105_bot__apply,axiom,
% 0.21/0.47 ! [C: $tType,D2: $tType] :
% 0.21/0.47 ( ( bot @ C )
% 0.21/0.47 => ( ( bot_bot @ ( D2 > C ) )
% 0.21/0.47 = ( ^ [X6: D2] : ( bot_bot @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_apply
% 0.21/0.47 thf(fact_106_empty__iff,axiom,
% 0.21/0.47 ! [A: $tType,C2: A] :
% 0.21/0.47 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % empty_iff
% 0.21/0.47 thf(fact_107_all__not__in__conv,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ( ! [X6: A] :
% 0.21/0.47 ~ ( member @ A @ X6 @ A5 ) )
% 0.21/0.47 = ( A5
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % all_not_in_conv
% 0.21/0.47 thf(fact_108_Collect__empty__eq,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o] :
% 0.21/0.47 ( ( ( collect @ A @ P )
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( ! [X6: A] :
% 0.21/0.47 ~ ( P @ X6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_empty_eq
% 0.21/0.47 thf(fact_109_empty__Collect__eq,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o] :
% 0.21/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.21/0.47 = ( collect @ A @ P ) )
% 0.21/0.47 = ( ! [X6: A] :
% 0.21/0.47 ~ ( P @ X6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % empty_Collect_eq
% 0.21/0.47 thf(fact_110_insertCI,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,B5: set @ A,B2: A] :
% 0.21/0.47 ( ( ~ ( member @ A @ A2 @ B5 )
% 0.21/0.47 => ( A2 = B2 ) )
% 0.21/0.47 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insertCI
% 0.21/0.47 thf(fact_111_insert__iff,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,B2: A,A5: set @ A] :
% 0.21/0.47 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A5 ) )
% 0.21/0.47 = ( ( A2 = B2 )
% 0.21/0.47 | ( member @ A @ A2 @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_iff
% 0.21/0.47 thf(fact_112_insert__absorb2,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,A5: set @ A] :
% 0.21/0.47 ( ( insert @ A @ X4 @ ( insert @ A @ X4 @ A5 ) )
% 0.21/0.47 = ( insert @ A @ X4 @ A5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_absorb2
% 0.21/0.47 thf(fact_113_empty__subsetI,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A5 ) ).
% 0.21/0.47
% 0.21/0.47 % empty_subsetI
% 0.21/0.47 thf(fact_114_subset__empty,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( A5
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_empty
% 0.21/0.47 thf(fact_115_singletonI,axiom,
% 0.21/0.47 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % singletonI
% 0.21/0.47 thf(fact_116_insert__subset,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X4 @ A5 ) @ B5 )
% 0.21/0.47 = ( ( member @ A @ X4 @ B5 )
% 0.21/0.47 & ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_subset
% 0.21/0.47 thf(fact_117_singleton__insert__inj__eq,axiom,
% 0.21/0.47 ! [A: $tType,B2: A,A2: A,A5: set @ A] :
% 0.21/0.47 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( insert @ A @ A2 @ A5 ) )
% 0.21/0.47 = ( ( A2 = B2 )
% 0.21/0.47 & ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % singleton_insert_inj_eq
% 0.21/0.47 thf(fact_118_singleton__insert__inj__eq_H,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,A5: set @ A,B2: A] :
% 0.21/0.47 ( ( ( insert @ A @ A2 @ A5 )
% 0.21/0.47 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( ( A2 = B2 )
% 0.21/0.47 & ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % singleton_insert_inj_eq'
% 0.21/0.47 thf(fact_119_nres__more__simps_I5_J,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,X: set @ A] :
% 0.21/0.47 ( ( ( refine1687780735RETURN @ A @ X4 )
% 0.21/0.47 = ( refine605929679le_RES @ A @ X ) )
% 0.21/0.47 = ( ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = X ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_more_simps(5)
% 0.21/0.47 thf(fact_120_nres__more__simps_I3_J,axiom,
% 0.21/0.47 ! [A: $tType,X: set @ A,X4: A] :
% 0.21/0.47 ( ( ( refine605929679le_RES @ A @ X )
% 0.21/0.47 = ( refine1687780735RETURN @ A @ X4 ) )
% 0.21/0.47 = ( X
% 0.21/0.47 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_more_simps(3)
% 0.21/0.47 thf(fact_121_subset__singletonD,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,X4: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 => ( ( A5
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 | ( A5
% 0.21/0.47 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_singletonD
% 0.21/0.47 thf(fact_122_subset__singleton__iff,axiom,
% 0.21/0.47 ! [A: $tType,X: set @ A,A2: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ X @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( ( X
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 | ( X
% 0.21/0.47 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_singleton_iff
% 0.21/0.47 thf(fact_123_emptyE,axiom,
% 0.21/0.47 ! [A: $tType,A2: A] :
% 0.21/0.47 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % emptyE
% 0.21/0.47 thf(fact_124_insertE,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,B2: A,A5: set @ A] :
% 0.21/0.47 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A5 ) )
% 0.21/0.47 => ( ( A2 != B2 )
% 0.21/0.47 => ( member @ A @ A2 @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insertE
% 0.21/0.47 thf(fact_125_equals0D,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,A2: A] :
% 0.21/0.47 ( ( A5
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 => ~ ( member @ A @ A2 @ A5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % equals0D
% 0.21/0.47 thf(fact_126_equals0I,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ! [Y6: A] :
% 0.21/0.47 ~ ( member @ A @ Y6 @ A5 )
% 0.21/0.47 => ( A5
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % equals0I
% 0.21/0.47 thf(fact_127_insertI1,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,B5: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % insertI1
% 0.21/0.47 thf(fact_128_insertI2,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,B5: set @ A,B2: A] :
% 0.21/0.47 ( ( member @ A @ A2 @ B5 )
% 0.21/0.47 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insertI2
% 0.21/0.47 thf(fact_129_ex__in__conv,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ( ? [X6: A] : ( member @ A @ X6 @ A5 ) )
% 0.21/0.47 = ( A5
% 0.21/0.47 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ex_in_conv
% 0.21/0.47 thf(fact_130_Set_Oset__insert,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,A5: set @ A] :
% 0.21/0.47 ( ( member @ A @ X4 @ A5 )
% 0.21/0.47 => ~ ! [B7: set @ A] :
% 0.21/0.47 ( ( A5
% 0.21/0.47 = ( insert @ A @ X4 @ B7 ) )
% 0.21/0.47 => ( member @ A @ X4 @ B7 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Set.set_insert
% 0.21/0.47 thf(fact_131_singletonD,axiom,
% 0.21/0.47 ! [A: $tType,B2: A,A2: A] :
% 0.21/0.47 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 => ( B2 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % singletonD
% 0.21/0.47 thf(fact_132_insert__ident,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ~ ( member @ A @ X4 @ A5 )
% 0.21/0.47 => ( ~ ( member @ A @ X4 @ B5 )
% 0.21/0.47 => ( ( ( insert @ A @ X4 @ A5 )
% 0.21/0.47 = ( insert @ A @ X4 @ B5 ) )
% 0.21/0.47 = ( A5 = B5 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_ident
% 0.21/0.47 thf(fact_133_insert__absorb,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,A5: set @ A] :
% 0.21/0.47 ( ( member @ A @ A2 @ A5 )
% 0.21/0.47 => ( ( insert @ A @ A2 @ A5 )
% 0.21/0.47 = A5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_absorb
% 0.21/0.47 thf(fact_134_insert__eq__iff,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,A5: set @ A,B2: A,B5: set @ A] :
% 0.21/0.47 ( ~ ( member @ A @ A2 @ A5 )
% 0.21/0.47 => ( ~ ( member @ A @ B2 @ B5 )
% 0.21/0.47 => ( ( ( insert @ A @ A2 @ A5 )
% 0.21/0.47 = ( insert @ A @ B2 @ B5 ) )
% 0.21/0.47 = ( ( ( A2 = B2 )
% 0.21/0.47 => ( A5 = B5 ) )
% 0.21/0.47 & ( ( A2 != B2 )
% 0.21/0.47 => ? [C4: set @ A] :
% 0.21/0.47 ( ( A5
% 0.21/0.47 = ( insert @ A @ B2 @ C4 ) )
% 0.21/0.47 & ~ ( member @ A @ B2 @ C4 )
% 0.21/0.47 & ( B5
% 0.21/0.47 = ( insert @ A @ A2 @ C4 ) )
% 0.21/0.47 & ~ ( member @ A @ A2 @ C4 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_eq_iff
% 0.21/0.47 thf(fact_135_singleton__iff,axiom,
% 0.21/0.47 ! [A: $tType,B2: A,A2: A] :
% 0.21/0.47 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( B2 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % singleton_iff
% 0.21/0.47 thf(fact_136_insert__commute,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,Y3: A,A5: set @ A] :
% 0.21/0.47 ( ( insert @ A @ X4 @ ( insert @ A @ Y3 @ A5 ) )
% 0.21/0.47 = ( insert @ A @ Y3 @ ( insert @ A @ X4 @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_commute
% 0.21/0.47 thf(fact_137_doubleton__eq__iff,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,B2: A,C2: A,D: A] :
% 0.21/0.47 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( insert @ A @ C2 @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.21/0.47 = ( ( ( A2 = C2 )
% 0.21/0.47 & ( B2 = D ) )
% 0.21/0.47 | ( ( A2 = D )
% 0.21/0.47 & ( B2 = C2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % doubleton_eq_iff
% 0.21/0.47 thf(fact_138_insert__not__empty,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,A5: set @ A] :
% 0.21/0.47 ( ( insert @ A @ A2 @ A5 )
% 0.21/0.47 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_not_empty
% 0.21/0.47 thf(fact_139_singleton__inject,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,B2: A] :
% 0.21/0.47 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 => ( A2 = B2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % singleton_inject
% 0.21/0.47 thf(fact_140_mk__disjoint__insert,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,A5: set @ A] :
% 0.21/0.47 ( ( member @ A @ A2 @ A5 )
% 0.21/0.47 => ? [B7: set @ A] :
% 0.21/0.47 ( ( A5
% 0.21/0.47 = ( insert @ A @ A2 @ B7 ) )
% 0.21/0.47 & ~ ( member @ A @ A2 @ B7 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % mk_disjoint_insert
% 0.21/0.47 thf(fact_141_bot__fun__def,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( bot @ B )
% 0.21/0.47 => ( ( bot_bot @ ( A > B ) )
% 0.21/0.47 = ( ^ [X6: A] : ( bot_bot @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_fun_def
% 0.21/0.47 thf(fact_142_nres_Osimps_I4_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,F1: B,F2: ( set @ A ) > B] :
% 0.21/0.47 ( ( refine60818195e_nres @ B @ A @ F1 @ F2 @ ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 = F1 ) ).
% 0.21/0.47
% 0.21/0.47 % nres.simps(4)
% 0.21/0.47 thf(fact_143_set__notEmptyE,axiom,
% 0.21/0.47 ! [A: $tType,S: set @ A] :
% 0.21/0.47 ( ( S
% 0.21/0.47 != ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 => ~ ! [X3: A] :
% 0.21/0.47 ~ ( member @ A @ X3 @ S ) ) ).
% 0.21/0.47
% 0.21/0.47 % set_notEmptyE
% 0.21/0.47 thf(fact_144_memb__imp__not__empty,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,S: set @ A] :
% 0.21/0.47 ( ( member @ A @ X4 @ S )
% 0.21/0.47 => ( S
% 0.21/0.47 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % memb_imp_not_empty
% 0.21/0.47 thf(fact_145_bot_Oextremum,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order_bot @ A )
% 0.21/0.47 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot.extremum
% 0.21/0.47 thf(fact_146_bot_Oextremum__unique,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order_bot @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.21/0.47 = ( A2
% 0.21/0.47 = ( bot_bot @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot.extremum_unique
% 0.21/0.47 thf(fact_147_bot_Oextremum__uniqueI,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order_bot @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.21/0.47 => ( A2
% 0.21/0.47 = ( bot_bot @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot.extremum_uniqueI
% 0.21/0.47 thf(fact_148_subset__insertI2,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A,B2: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ B2 @ B5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_insertI2
% 0.21/0.47 thf(fact_149_subset__insertI,axiom,
% 0.21/0.47 ! [A: $tType,B5: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B5 @ ( insert @ A @ A2 @ B5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_insertI
% 0.21/0.47 thf(fact_150_subset__insert,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ~ ( member @ A @ X4 @ A5 )
% 0.21/0.47 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ X4 @ B5 ) )
% 0.21/0.47 = ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_insert
% 0.21/0.47 thf(fact_151_insert__mono,axiom,
% 0.21/0.47 ! [A: $tType,C3: set @ A,D3: set @ A,A2: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D3 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C3 ) @ ( insert @ A @ A2 @ D3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_mono
% 0.21/0.47 thf(fact_152_RETURN__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( refine1687780735RETURN @ A )
% 0.21/0.47 = ( ^ [X6: A] : ( refine605929679le_RES @ A @ ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RETURN_def
% 0.21/0.47 thf(fact_153_nres_Odistinct_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,X2: set @ A] :
% 0.21/0.47 ( ( refine1767639642_FAILi @ A )
% 0.21/0.47 != ( refine605929679le_RES @ A @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres.distinct(1)
% 0.21/0.47 thf(fact_154_nres_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > $o,Nres: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( P @ ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 => ( ! [X3: set @ A] : ( P @ ( refine605929679le_RES @ A @ X3 ) )
% 0.21/0.47 => ( P @ Nres ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres.induct
% 0.21/0.47 thf(fact_155_nres_Oexhaust,axiom,
% 0.21/0.47 ! [A: $tType,Y3: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( Y3
% 0.21/0.47 != ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 => ~ ! [X22: set @ A] :
% 0.21/0.47 ( Y3
% 0.21/0.47 != ( refine605929679le_RES @ A @ X22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres.exhaust
% 0.21/0.47 thf(fact_156_sup__nres_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ! [Uu: refine1665802226e_nres @ A] : ( P @ Uu @ ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 => ( ! [V2: set @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ V2 ) )
% 0.21/0.47 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % sup_nres.induct
% 0.21/0.47 thf(fact_157_less__nres_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ! [X_1: refine1665802226e_nres @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ X_1 )
% 0.21/0.47 => ( ! [Uv: set @ A] : ( P @ ( refine605929679le_RES @ A @ Uv ) @ ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_nres.induct
% 0.21/0.47 thf(fact_158_less__eq__nres_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ! [Uu: refine1665802226e_nres @ A] : ( P @ Uu @ ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 0.21/0.47 => ( ! [Uv: set @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ Uv ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_eq_nres.induct
% 0.21/0.47 thf(fact_159_less__eq__nres_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,Uu2: refine1665802226e_nres @ A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ Uu2 @ ( refine1767639642_FAILi @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_eq_nres.simps(1)
% 0.21/0.47 thf(fact_160_nres_Osimps_I6_J,axiom,
% 0.21/0.47 ! [A: $tType,C: $tType,F1: C,F2: ( set @ A ) > C] :
% 0.21/0.47 ( ( refine1442219249c_nres @ C @ A @ F1 @ F2 @ ( refine1767639642_FAILi @ A ) )
% 0.21/0.47 = F1 ) ).
% 0.21/0.47
% 0.21/0.47 % nres.simps(6)
% 0.21/0.47 thf(fact_161_the__elem__eq,axiom,
% 0.21/0.47 ! [A: $tType,X4: A] :
% 0.21/0.47 ( ( the_elem @ A @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = X4 ) ).
% 0.21/0.47
% 0.21/0.47 % the_elem_eq
% 0.21/0.47 thf(fact_162_is__singletonI,axiom,
% 0.21/0.47 ! [A: $tType,X4: A] : ( is_singleton @ A @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singletonI
% 0.21/0.47 thf(fact_163_insert__subsetI,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,A5: set @ A,X: set @ A] :
% 0.21/0.47 ( ( member @ A @ X4 @ A5 )
% 0.21/0.47 => ( ( ord_less_eq @ ( set @ A ) @ X @ A5 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X4 @ X ) @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_subsetI
% 0.21/0.47 thf(fact_164_subset__emptyI,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ~ ( member @ A @ X3 @ A5 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_emptyI
% 0.21/0.47 thf(fact_165_Set_Ois__empty__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( is_empty @ A )
% 0.21/0.47 = ( ^ [A6: set @ A] :
% 0.21/0.47 ( A6
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Set.is_empty_def
% 0.21/0.47 thf(fact_166_nres__order__simps_I2_J,axiom,
% 0.21/0.47 ! [B: $tType,M4: refine1665802226e_nres @ B] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M4 @ ( bot_bot @ ( refine1665802226e_nres @ B ) ) )
% 0.21/0.47 = ( M4
% 0.21/0.47 = ( bot_bot @ ( refine1665802226e_nres @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_order_simps(2)
% 0.21/0.47 thf(fact_167_nofail__simps_I4_J,axiom,
% 0.21/0.47 ! [D2: $tType] : ( refine1102455758nofail @ D2 @ ( bot_bot @ ( refine1665802226e_nres @ D2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nofail_simps(4)
% 0.21/0.47 thf(fact_168_inres__simps_I4_J,axiom,
% 0.21/0.47 ! [D2: $tType] :
% 0.21/0.47 ( ( refine1315500908_inres @ D2 @ ( bot_bot @ ( refine1665802226e_nres @ D2 ) ) )
% 0.21/0.47 = ( ^ [Uu3: D2] : $false ) ) ).
% 0.21/0.47
% 0.21/0.47 % inres_simps(4)
% 0.21/0.47 thf(fact_169_bind__SUCCEED,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,F: B > ( refine1665802226e_nres @ A )] :
% 0.21/0.47 ( ( refine463715084e_bind @ B @ A @ ( bot_bot @ ( refine1665802226e_nres @ B ) ) @ F )
% 0.21/0.47 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bind_SUCCEED
% 0.21/0.47 thf(fact_170_nres__more__simps_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,X: set @ A] :
% 0.21/0.47 ( ( ( refine605929679le_RES @ A @ X )
% 0.21/0.47 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) )
% 0.21/0.47 = ( X
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_more_simps(2)
% 0.21/0.47 thf(fact_171_nres__more__simps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,X: set @ A] :
% 0.21/0.47 ( ( ( bot_bot @ ( refine1665802226e_nres @ A ) )
% 0.21/0.47 = ( refine605929679le_RES @ A @ X ) )
% 0.21/0.47 = ( X
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_more_simps(1)
% 0.21/0.47 thf(fact_172_bot__set__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bot_bot @ ( set @ A ) )
% 0.21/0.47 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_set_def
% 0.21/0.47 thf(fact_173_nres__order__simps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,M4: refine1665802226e_nres @ A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ M4 ) ).
% 0.21/0.47
% 0.21/0.47 % nres_order_simps(1)
% 0.21/0.47 thf(fact_174_nres__inequalities_I5_J,axiom,
% 0.21/0.47 ! [C: $tType,X4: C] :
% 0.21/0.47 ( ( bot_bot @ ( refine1665802226e_nres @ C ) )
% 0.21/0.47 != ( refine1687780735RETURN @ C @ X4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_inequalities(5)
% 0.21/0.47 thf(fact_175_bot__nres__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bot_bot @ ( refine1665802226e_nres @ A ) )
% 0.21/0.47 = ( refine605929679le_RES @ A @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_nres_def
% 0.21/0.47 thf(fact_176_SUCCEED__rule,axiom,
% 0.21/0.47 ! [A: $tType,Phi: A > $o] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % SUCCEED_rule
% 0.21/0.47 thf(fact_177_is__singleton__the__elem,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( is_singleton @ A )
% 0.21/0.47 = ( ^ [A6: set @ A] :
% 0.21/0.47 ( A6
% 0.21/0.47 = ( insert @ A @ ( the_elem @ A @ A6 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singleton_the_elem
% 0.21/0.47 thf(fact_178_is__singletonI_H,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ( A5
% 0.21/0.47 != ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 => ( ! [X3: A,Y6: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ A5 )
% 0.21/0.47 => ( ( member @ A @ Y6 @ A5 )
% 0.21/0.47 => ( X3 = Y6 ) ) )
% 0.21/0.47 => ( is_singleton @ A @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singletonI'
% 0.21/0.47 thf(fact_179_is__singleton__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( is_singleton @ A )
% 0.21/0.47 = ( ^ [A6: set @ A] :
% 0.21/0.47 ? [X6: A] :
% 0.21/0.47 ( A6
% 0.21/0.47 = ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singleton_def
% 0.21/0.47 thf(fact_180_is__singletonE,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ( is_singleton @ A @ A5 )
% 0.21/0.47 => ~ ! [X3: A] :
% 0.21/0.47 ( A5
% 0.21/0.47 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singletonE
% 0.21/0.47 thf(fact_181_subset__Compl__singleton,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B2: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.21/0.47 = ( ~ ( member @ A @ B2 @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_Compl_singleton
% 0.21/0.47 thf(fact_182_strictD__simp,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bot @ A )
% 0.21/0.47 => ! [F: A > A] :
% 0.21/0.47 ( ( refine_strict @ A @ A @ F )
% 0.21/0.47 => ( ( F @ ( bot_bot @ A ) )
% 0.21/0.47 = ( bot_bot @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % strictD_simp
% 0.21/0.47 thf(fact_183_Collect__empty__eq__bot,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o] :
% 0.21/0.47 ( ( ( collect @ A @ P )
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( P
% 0.21/0.47 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_empty_eq_bot
% 0.21/0.47 thf(fact_184_verit__minus__simplify_I4_J,axiom,
% 0.21/0.47 ! [B: $tType] :
% 0.21/0.47 ( ( group_add @ B )
% 0.21/0.47 => ! [B2: B] :
% 0.21/0.47 ( ( uminus_uminus @ B @ ( uminus_uminus @ B @ B2 ) )
% 0.21/0.47 = B2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % verit_minus_simplify(4)
% 0.21/0.47 thf(fact_185_ComplI,axiom,
% 0.21/0.47 ! [A: $tType,C2: A,A5: set @ A] :
% 0.21/0.47 ( ~ ( member @ A @ C2 @ A5 )
% 0.21/0.47 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ComplI
% 0.21/0.47 thf(fact_186_Compl__iff,axiom,
% 0.21/0.47 ! [A: $tType,C2: A,A5: set @ A] :
% 0.21/0.47 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A5 ) )
% 0.21/0.47 = ( ~ ( member @ A @ C2 @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Compl_iff
% 0.21/0.47 thf(fact_187_Compl__eq__Compl__iff,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( ( uminus_uminus @ ( set @ A ) @ A5 )
% 0.21/0.47 = ( uminus_uminus @ ( set @ A ) @ B5 ) )
% 0.21/0.47 = ( A5 = B5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Compl_eq_Compl_iff
% 0.21/0.47 thf(fact_188_Compl__anti__mono,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B5 ) @ ( uminus_uminus @ ( set @ A ) @ A5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Compl_anti_mono
% 0.21/0.47 thf(fact_189_Compl__subset__Compl__iff,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A5 ) @ ( uminus_uminus @ ( set @ A ) @ B5 ) )
% 0.21/0.47 = ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Compl_subset_Compl_iff
% 0.21/0.47 thf(fact_190_ibind__strict_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,F: product_unit > ( refine1665802226e_nres @ A )] :
% 0.21/0.47 ( ( refine463715084e_bind @ product_unit @ A @ ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) @ F )
% 0.21/0.47 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ibind_strict(1)
% 0.21/0.47 thf(fact_191_ComplD,axiom,
% 0.21/0.47 ! [A: $tType,C2: A,A5: set @ A] :
% 0.21/0.47 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A5 ) )
% 0.21/0.47 => ~ ( member @ A @ C2 @ A5 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ComplD
% 0.21/0.47 thf(fact_192_double__complement,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A5 ) )
% 0.21/0.47 = A5 ) ).
% 0.21/0.47
% 0.21/0.47 % double_complement
% 0.21/0.47 thf(fact_193_verit__negate__coefficient_I3_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A] :
% 0.21/0.47 ( ( A2 = B2 )
% 0.21/0.47 => ( ( uminus_uminus @ A @ A2 )
% 0.21/0.47 = ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % verit_negate_coefficient(3)
% 0.21/0.47 thf(fact_194_subset__Compl__self__eq,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( uminus_uminus @ ( set @ A ) @ A5 ) )
% 0.21/0.47 = ( A5
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_Compl_self_eq
% 0.21/0.47 thf(fact_195_strictD,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( bot @ B )
% 0.21/0.47 & ( bot @ A ) )
% 0.21/0.47 => ! [F: A > B] :
% 0.21/0.47 ( ( refine_strict @ A @ B @ F )
% 0.21/0.47 => ( ( F @ ( bot_bot @ A ) )
% 0.21/0.47 = ( bot_bot @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % strictD
% 0.21/0.47 thf(fact_196_strictI,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( bot @ B )
% 0.21/0.47 & ( bot @ A ) )
% 0.21/0.47 => ! [F: B > A] :
% 0.21/0.47 ( ( ( F @ ( bot_bot @ B ) )
% 0.21/0.47 = ( bot_bot @ A ) )
% 0.21/0.47 => ( refine_strict @ B @ A @ F ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % strictI
% 0.21/0.47 thf(fact_197_strict__def,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( ( bot @ A )
% 0.21/0.47 & ( bot @ B ) )
% 0.21/0.47 => ( ( refine_strict @ A @ B )
% 0.21/0.47 = ( ^ [F3: A > B] :
% 0.21/0.47 ( ( F3 @ ( bot_bot @ A ) )
% 0.21/0.47 = ( bot_bot @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % strict_def
% 0.21/0.47 thf(fact_198_neg__le__iff__le,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [B2: A,A2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A2 ) )
% 0.21/0.47 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % neg_le_iff_le
% 0.21/0.47 thf(fact_199_compl__le__compl__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( boolean_algebra @ A )
% 0.21/0.47 => ! [X4: A,Y3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X4 ) @ ( uminus_uminus @ A @ Y3 ) )
% 0.21/0.47 = ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % compl_le_compl_iff
% 0.21/0.47 thf(fact_200_bot__empty__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bot_bot @ ( A > $o ) )
% 0.21/0.47 = ( ^ [X6: A] : ( member @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_empty_eq
% 0.21/0.47 thf(fact_201_le__imp__neg__le,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_imp_neg_le
% 0.21/0.47 thf(fact_202_minus__le__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A2 ) @ B2 )
% 0.21/0.47 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % minus_le_iff
% 0.21/0.47 thf(fact_203_le__minus__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ ( uminus_uminus @ A @ B2 ) )
% 0.21/0.47 = ( ord_less_eq @ A @ B2 @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_minus_iff
% 0.21/0.47 thf(fact_204_compl__le__swap2,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( boolean_algebra @ A )
% 0.21/0.47 => ! [Y3: A,X4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y3 ) @ X4 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X4 ) @ Y3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % compl_le_swap2
% 0.21/0.47 thf(fact_205_compl__le__swap1,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( boolean_algebra @ A )
% 0.21/0.47 => ! [Y3: A,X4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ Y3 @ ( uminus_uminus @ A @ X4 ) )
% 0.21/0.47 => ( ord_less_eq @ A @ X4 @ ( uminus_uminus @ A @ Y3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % compl_le_swap1
% 0.21/0.47 thf(fact_206_compl__mono,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( boolean_algebra @ A )
% 0.21/0.47 => ! [X4: A,Y3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y3 ) @ ( uminus_uminus @ A @ X4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % compl_mono
% 0.21/0.47 thf(fact_207_ASSUME__simps_I2_J,axiom,
% 0.21/0.47 ( ( refine1946708059ASSUME @ $false )
% 0.21/0.47 = ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ASSUME_simps(2)
% 0.21/0.47 thf(fact_208_pw__flat__le__iff,axiom,
% 0.21/0.47 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( partial_flat_ord @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ S @ S3 )
% 0.21/0.47 = ( ? [X8: A] : ( refine1315500908_inres @ A @ S @ X8 )
% 0.21/0.47 => ( ( ( refine1102455758nofail @ A @ S )
% 0.21/0.47 = ( refine1102455758nofail @ A @ S3 ) )
% 0.21/0.47 & ! [X6: A] :
% 0.21/0.47 ( ( refine1315500908_inres @ A @ S @ X6 )
% 0.21/0.47 = ( refine1315500908_inres @ A @ S3 @ X6 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_flat_le_iff
% 0.21/0.47 thf(fact_209_pw__ASSUME_I2_J,axiom,
% 0.21/0.47 ! [Phi: $o,X4: product_unit] :
% 0.21/0.47 ( ( refine1315500908_inres @ product_unit @ ( refine1946708059ASSUME @ Phi ) @ X4 )
% 0.21/0.47 = Phi ) ).
% 0.21/0.47
% 0.21/0.47 % pw_ASSUME(2)
% 0.21/0.47 thf(fact_210_pw__ASSUME_I1_J,axiom,
% 0.21/0.47 ! [Phi: $o] : ( refine1102455758nofail @ product_unit @ ( refine1946708059ASSUME @ Phi ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_ASSUME(1)
% 0.21/0.47 thf(fact_211_flat__ord__compat_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( comple187826305attice @ A )
% 0.21/0.47 => ! [X4: A,Y3: A] :
% 0.21/0.47 ( ( partial_flat_ord @ A @ ( bot_bot @ A ) @ X4 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord_compat(1)
% 0.21/0.47 thf(fact_212_pw__flat__ge__iff,axiom,
% 0.21/0.47 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( partial_flat_ord @ ( refine1665802226e_nres @ A ) @ ( top_top @ ( refine1665802226e_nres @ A ) ) @ S @ S3 )
% 0.21/0.47 = ( ( refine1102455758nofail @ A @ S )
% 0.21/0.47 => ( ( refine1102455758nofail @ A @ S3 )
% 0.21/0.47 & ! [X6: A] :
% 0.21/0.47 ( ( refine1315500908_inres @ A @ S @ X6 )
% 0.21/0.47 = ( refine1315500908_inres @ A @ S3 @ X6 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % pw_flat_ge_iff
% 0.21/0.47 thf(fact_213_top__apply,axiom,
% 0.21/0.47 ! [C: $tType,D2: $tType] :
% 0.21/0.47 ( ( top @ C )
% 0.21/0.47 => ( ( top_top @ ( D2 > C ) )
% 0.21/0.47 = ( ^ [X6: D2] : ( top_top @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % top_apply
% 0.21/0.47 thf(fact_214_nres__order__simps_I4_J,axiom,
% 0.21/0.47 ! [D2: $tType,M4: refine1665802226e_nres @ D2] :
% 0.21/0.47 ( ( ord_less_eq @ ( refine1665802226e_nres @ D2 ) @ ( top_top @ ( refine1665802226e_nres @ D2 ) ) @ M4 )
% 0.21/0.47 = ( M4
% 0.21/0.47 = ( top_top @ ( refine1665802226e_nres @ D2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_order_simps(4)
% 0.21/0.47 thf(fact_215_nofail__simps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ~ ( refine1102455758nofail @ A @ ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nofail_simps(1)
% 0.21/0.47 thf(fact_216_nres__simp__internals_I2_J,axiom,
% 0.21/0.47 ! [B: $tType] :
% 0.21/0.47 ( ( refine1767639642_FAILi @ B )
% 0.21/0.47 = ( top_top @ ( refine1665802226e_nres @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_simp_internals(2)
% 0.21/0.47 thf(fact_217_inres__simps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( refine1315500908_inres @ A @ ( top_top @ ( refine1665802226e_nres @ A ) ) )
% 0.21/0.47 = ( ^ [Uu3: A] : $true ) ) ).
% 0.21/0.47
% 0.21/0.47 % inres_simps(1)
% 0.21/0.47 thf(fact_218_bind__FAIL,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,F: B > ( refine1665802226e_nres @ A )] :
% 0.21/0.47 ( ( refine463715084e_bind @ B @ A @ ( top_top @ ( refine1665802226e_nres @ B ) ) @ F )
% 0.21/0.47 = ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bind_FAIL
% 0.21/0.47 thf(fact_219_compl__bot__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( boolean_algebra @ A )
% 0.21/0.47 => ( ( uminus_uminus @ A @ ( bot_bot @ A ) )
% 0.21/0.47 = ( top_top @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % compl_bot_eq
% 0.21/0.47 thf(fact_220_compl__top__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( boolean_algebra @ A )
% 0.21/0.47 => ( ( uminus_uminus @ A @ ( top_top @ A ) )
% 0.21/0.47 = ( bot_bot @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % compl_top_eq
% 0.21/0.47 thf(fact_221_flat__ord__compat_I2_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( comple187826305attice @ A )
% 0.21/0.47 => ! [X4: A,Y3: A] :
% 0.21/0.47 ( ( partial_flat_ord @ A @ ( top_top @ A ) @ X4 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord_compat(2)
% 0.21/0.47 thf(fact_222_top__greatest,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order_top @ A )
% 0.21/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( top_top @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % top_greatest
% 0.21/0.47 thf(fact_223_top_Oextremum__unique,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order_top @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 0.21/0.47 = ( A2
% 0.21/0.47 = ( top_top @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % top.extremum_unique
% 0.21/0.47 thf(fact_224_top_Oextremum__uniqueI,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order_top @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 0.21/0.47 => ( A2
% 0.21/0.47 = ( top_top @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % top.extremum_uniqueI
% 0.21/0.47 thf(fact_225_meta__le__everything__if__top,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order_top @ A )
% 0.21/0.47 => ! [M: A,X4: A] :
% 0.21/0.47 ( ( M
% 0.21/0.47 = ( top_top @ A ) )
% 0.21/0.47 => ( ord_less_eq @ A @ X4 @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % meta_le_everything_if_top
% 0.21/0.47 thf(fact_226_nres__inequalities_I3_J,axiom,
% 0.21/0.47 ! [C: $tType,X4: C] :
% 0.21/0.47 ( ( top_top @ ( refine1665802226e_nres @ C ) )
% 0.21/0.47 != ( refine1687780735RETURN @ C @ X4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_inequalities(3)
% 0.21/0.47 thf(fact_227_top__nres__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( top_top @ ( refine1665802226e_nres @ A ) )
% 0.21/0.47 = ( refine1767639642_FAILi @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % top_nres_def
% 0.21/0.47 thf(fact_228_not__nofail__iff,axiom,
% 0.21/0.47 ! [A: $tType,S: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ~ ( refine1102455758nofail @ A @ S ) )
% 0.21/0.47 = ( S
% 0.21/0.47 = ( top_top @ ( refine1665802226e_nres @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_nofail_iff
% 0.21/0.47 thf(fact_229_nofail__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( refine1102455758nofail @ A )
% 0.21/0.47 = ( ^ [S4: refine1665802226e_nres @ A] :
% 0.21/0.47 ( S4
% 0.21/0.47 != ( top_top @ ( refine1665802226e_nres @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nofail_def
% 0.21/0.47 thf(fact_230_intro__nofail_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,S: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( ( top_top @ ( refine1665802226e_nres @ A ) )
% 0.21/0.47 != S )
% 0.21/0.47 = ( refine1102455758nofail @ A @ S ) ) ).
% 0.21/0.47
% 0.21/0.47 % intro_nofail(2)
% 0.21/0.47 thf(fact_231_nres__order__simps_I3_J,axiom,
% 0.21/0.47 ! [C: $tType,M4: refine1665802226e_nres @ C] : ( ord_less_eq @ ( refine1665802226e_nres @ C ) @ M4 @ ( top_top @ ( refine1665802226e_nres @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_order_simps(3)
% 0.21/0.47 thf(fact_232_nres__inequalities_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,X: set @ A] :
% 0.21/0.47 ( ( top_top @ ( refine1665802226e_nres @ A ) )
% 0.21/0.47 != ( refine605929679le_RES @ A @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_inequalities(1)
% 0.21/0.47 thf(fact_233_nres__cases,axiom,
% 0.21/0.47 ! [A: $tType,M4: refine1665802226e_nres @ A] :
% 0.21/0.47 ( ( M4
% 0.21/0.47 != ( top_top @ ( refine1665802226e_nres @ A ) ) )
% 0.21/0.47 => ~ ! [X9: set @ A] :
% 0.21/0.47 ( M4
% 0.21/0.47 != ( refine605929679le_RES @ A @ X9 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_cases
% 0.21/0.47 thf(fact_234_ibind__strict_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,F: product_unit > ( refine1665802226e_nres @ A )] :
% 0.21/0.47 ( ( refine463715084e_bind @ product_unit @ A @ ( top_top @ ( refine1665802226e_nres @ product_unit ) ) @ F )
% 0.21/0.47 = ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ibind_strict(2)
% 0.21/0.47 thf(fact_235_nres__inequalities_I4_J,axiom,
% 0.21/0.47 ! [D2: $tType] :
% 0.21/0.47 ( ( bot_bot @ ( refine1665802226e_nres @ D2 ) )
% 0.21/0.47 != ( top_top @ ( refine1665802226e_nres @ D2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_inequalities(4)
% 0.21/0.47 thf(fact_236_nres__inequalities_I2_J,axiom,
% 0.21/0.47 ! [B: $tType] :
% 0.21/0.47 ( ( top_top @ ( refine1665802226e_nres @ B ) )
% 0.21/0.47 != ( bot_bot @ ( refine1665802226e_nres @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nres_inequalities(2)
% 0.21/0.47 thf(fact_237_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I2_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,M4: refine1665802226e_nres @ A,M5: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 0.21/0.47 ( ( partial_flat_ord @ ( refine1665802226e_nres @ A ) @ ( top_top @ ( refine1665802226e_nres @ A ) ) @ M4 @ M5 )
% 0.21/0.47 => ( ! [X3: A] : ( partial_flat_ord @ ( refine1665802226e_nres @ B ) @ ( top_top @ ( refine1665802226e_nres @ B ) ) @ ( F @ X3 ) @ ( F4 @ X3 ) )
% 0.21/0.47 => ( partial_flat_ord @ ( refine1665802226e_nres @ B ) @ ( top_top @ ( refine1665802226e_nres @ B ) ) @ ( refine463715084e_bind @ A @ B @ M4 @ F ) @ ( refine463715084e_bind @ A @ B @ M5 @ F4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Refine_Basic_Mirabelle_tqojlsrkwy.bind_mono(2)
% 0.21/0.47 thf(fact_238_flat__ord_OatLeastAtMost__singleton,axiom,
% 0.21/0.47 ! [A: $tType,B2: A,A2: A] :
% 0.21/0.47 ( ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ B2 ) @ A2 @ A2 )
% 0.21/0.47 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord.atLeastAtMost_singleton
% 0.21/0.47 thf(fact_239_flat__ord_OatLeastAtMost__singleton__iff,axiom,
% 0.21/0.47 ! [A: $tType,Ba: A,A2: A,B2: A,C2: A] :
% 0.21/0.47 ( ( ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 )
% 0.21/0.47 = ( insert @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( ( A2 = B2 )
% 0.21/0.47 & ( B2 = C2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord.atLeastAtMost_singleton_iff
% 0.21/0.47 thf(fact_240_flat__ord_OatLeastatMost__empty__iff,axiom,
% 0.21/0.47 ! [A: $tType,Ba: A,A2: A,B2: A] :
% 0.21/0.47 ( ( ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 )
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( ~ ( partial_flat_ord @ A @ Ba @ A2 @ B2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord.atLeastatMost_empty_iff
% 0.21/0.47 thf(fact_241_flat__ord_OatLeastatMost__empty__iff2,axiom,
% 0.21/0.47 ! [A: $tType,Ba: A,A2: A,B2: A] :
% 0.21/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.21/0.47 = ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 ) )
% 0.21/0.47 = ( ~ ( partial_flat_ord @ A @ Ba @ A2 @ B2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord.atLeastatMost_empty_iff2
% 0.21/0.47 thf(fact_242_flat__ord_OatLeastatMost__subset__iff,axiom,
% 0.21/0.47 ! [A: $tType,Ba: A,A2: A,B2: A,C2: A,D: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 ) @ ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ C2 @ D ) )
% 0.21/0.47 = ( ~ ( partial_flat_ord @ A @ Ba @ A2 @ B2 )
% 0.21/0.47 | ( ( partial_flat_ord @ A @ Ba @ C2 @ A2 )
% 0.21/0.47 & ( partial_flat_ord @ A @ Ba @ B2 @ D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord.atLeastatMost_subset_iff
% 0.21/0.47 thf(fact_243_insert__UNIV,axiom,
% 0.21/0.47 ! [A: $tType,X4: A] :
% 0.21/0.47 ( ( insert @ A @ X4 @ ( top_top @ ( set @ A ) ) )
% 0.21/0.47 = ( top_top @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_UNIV
% 0.21/0.47 thf(fact_244_subset__UNIV,axiom,
% 0.21/0.47 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ ( top_top @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_UNIV
% 0.21/0.47 thf(fact_245_Compl__UNIV__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) )
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Compl_UNIV_eq
% 0.21/0.47 thf(fact_246_Compl__empty__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( uminus_uminus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( top_top @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Compl_empty_eq
% 0.21/0.47 thf(fact_247_empty__not__UNIV,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bot_bot @ ( set @ A ) )
% 0.21/0.47 != ( top_top @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % empty_not_UNIV
% 0.21/0.47 thf(fact_248_flat__ord_OatLeastAtMost__singleton_H,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,B2: A,Ba: A] :
% 0.21/0.47 ( ( A2 = B2 )
% 0.21/0.47 => ( ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 )
% 0.21/0.47 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord.atLeastAtMost_singleton'
% 0.21/0.47 thf(fact_249_flat__ord_OIcc__subset__Iic__iff,axiom,
% 0.21/0.47 ! [A: $tType,B2: A,L: A,H: A,H2: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ B2 ) @ L @ H ) @ ( set_atMost @ A @ ( partial_flat_ord @ A @ B2 ) @ H2 ) )
% 0.21/0.47 = ( ~ ( partial_flat_ord @ A @ B2 @ L @ H )
% 0.21/0.47 | ( partial_flat_ord @ A @ B2 @ H @ H2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord.Icc_subset_Iic_iff
% 0.21/0.47 thf(fact_250_flat__ord_OIcc__subset__Ici__iff,axiom,
% 0.21/0.47 ! [A: $tType,B2: A,L: A,H: A,L2: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ B2 ) @ L @ H ) @ ( set_atLeast @ A @ ( partial_flat_ord @ A @ B2 ) @ L2 ) )
% 0.21/0.47 = ( ~ ( partial_flat_ord @ A @ B2 @ L @ H )
% 0.21/0.47 | ( partial_flat_ord @ A @ B2 @ L2 @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % flat_ord.Icc_subset_Ici_iff
% 0.21/0.47 thf(fact_251_UNIV__I,axiom,
% 0.21/0.47 ! [A: $tType,X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % UNIV_I
% 0.21/0.47 thf(fact_252_relprop__UNIV__orient,axiom,
% 0.21/0.47 ! [A: $tType,R: set @ A] :
% 0.21/0.47 ( ( R
% 0.21/0.47 = ( top_top @ ( set @ A ) ) )
% 0.21/0.47 => ( ( top_top @ ( set @ A ) )
% 0.21/0.47 = R ) ) ).
% 0.21/0.47
% 0.21/0.47 % relprop_UNIV_orient
% 0.21/0.47 thf(fact_253_eq__UNIV__iff,axiom,
% 0.21/0.47 ! [A: $tType,S: set @ A] :
% 0.21/0.47 ( ( S
% 0.21/0.47 = ( top_top @ ( set @ A ) ) )
% 0.21/0.47 = ( ! [X6: A] : ( member @ A @ X6 @ S ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_UNIV_iff
% 0.21/0.47
% 0.21/0.47 % Type constructors (46)
% 0.21/0.47 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 0.21/0.47 ! [A7: $tType,A8: $tType] :
% 0.21/0.47 ( ( comple187826305attice @ A8 )
% 0.21/0.47 => ( comple187826305attice @ ( A7 > A8 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.21/0.47 ! [A7: $tType,A8: $tType] :
% 0.21/0.47 ( ( boolean_algebra @ A8 )
% 0.21/0.47 => ( boolean_algebra @ ( A7 > A8 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.21/0.47 ! [A7: $tType,A8: $tType] :
% 0.21/0.47 ( ( order_top @ A8 )
% 0.21/0.47 => ( order_top @ ( A7 > A8 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.21/0.47 ! [A7: $tType,A8: $tType] :
% 0.21/0.47 ( ( order_bot @ A8 )
% 0.21/0.47 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.21/0.47 ! [A7: $tType,A8: $tType] :
% 0.21/0.47 ( ( preorder @ A8 )
% 0.21/0.47 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.21/0.47 ! [A7: $tType,A8: $tType] :
% 0.21/0.47 ( ( order @ A8 )
% 0.21/0.47 => ( order @ ( A7 > A8 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Otop,axiom,
% 0.21/0.47 ! [A7: $tType,A8: $tType] :
% 0.21/0.47 ( ( top @ A8 )
% 0.21/0.47 => ( top @ ( A7 > A8 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.21/0.47 ! [A7: $tType,A8: $tType] :
% 0.21/0.47 ( ( ord @ A8 )
% 0.21/0.47 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Obot,axiom,
% 0.21/0.47 ! [A7: $tType,A8: $tType] :
% 0.21/0.47 ( ( bot @ A8 )
% 0.21/0.47 => ( bot @ ( A7 > A8 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1,axiom,
% 0.21/0.47 ! [A7: $tType] : ( comple187826305attice @ ( set @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_2,axiom,
% 0.21/0.47 ! [A7: $tType] : ( boolean_algebra @ ( set @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Oorder__top_3,axiom,
% 0.21/0.47 ! [A7: $tType] : ( order_top @ ( set @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Oorder__bot_4,axiom,
% 0.21/0.47 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.21/0.47 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.21/0.47 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Otop_7,axiom,
% 0.21/0.47 ! [A7: $tType] : ( top @ ( set @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Oord_8,axiom,
% 0.21/0.47 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Obot_9,axiom,
% 0.21/0.47 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_10,axiom,
% 0.21/0.47 comple187826305attice @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_11,axiom,
% 0.21/0.47 boolean_algebra @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Oorder__top_12,axiom,
% 0.21/0.47 order_top @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Oorder__bot_13,axiom,
% 0.21/0.47 order_bot @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_14,axiom,
% 0.21/0.47 preorder @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.21/0.47 linorder @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 0.21/0.47 order @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Otop_16,axiom,
% 0.21/0.47 top @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Oord_17,axiom,
% 0.21/0.47 ord @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Obot_18,axiom,
% 0.21/0.47 bot @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Complete__Lattices_Ocomplete__lattice_19,axiom,
% 0.21/0.47 comple187826305attice @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Lattices_Oboolean__algebra_20,axiom,
% 0.21/0.47 boolean_algebra @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oorder__top_21,axiom,
% 0.21/0.47 order_top @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_22,axiom,
% 0.21/0.47 order_bot @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_23,axiom,
% 0.21/0.47 preorder @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_24,axiom,
% 0.21/0.47 linorder @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oorder_25,axiom,
% 0.21/0.47 order @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Otop_26,axiom,
% 0.21/0.47 top @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oord_27,axiom,
% 0.21/0.47 ord @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Obot_28,axiom,
% 0.21/0.47 bot @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Complete__Lattices_Ocomplete__lattice_29,axiom,
% 0.21/0.47 ! [A7: $tType] : ( comple187826305attice @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__top_30,axiom,
% 0.21/0.47 ! [A7: $tType] : ( order_top @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_31,axiom,
% 0.21/0.47 ! [A7: $tType] : ( order_bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_32,axiom,
% 0.21/0.47 ! [A7: $tType] : ( preorder @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_33,axiom,
% 0.21/0.47 ! [A7: $tType] : ( order @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_34,axiom,
% 0.21/0.47 ! [A7: $tType] : ( top @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_35,axiom,
% 0.21/0.47 ! [A7: $tType] : ( ord @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_36,axiom,
% 0.21/0.47 ! [A7: $tType] : ( bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Helper facts (3)
% 0.21/0.47 thf(help_If_3_1_T,axiom,
% 0.21/0.47 ! [P: $o] :
% 0.21/0.47 ( ( P = $true )
% 0.21/0.47 | ( P = $false ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(help_If_2_1_T,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,Y3: A] :
% 0.21/0.47 ( ( if @ A @ $false @ X4 @ Y3 )
% 0.21/0.47 = Y3 ) ).
% 0.21/0.47
% 0.21/0.47 thf(help_If_1_1_T,axiom,
% 0.21/0.47 ! [A: $tType,X4: A,Y3: A] :
% 0.21/0.47 ( ( if @ A @ $true @ X4 @ Y3 )
% 0.21/0.47 = X4 ) ).
% 0.21/0.47
% 0.21/0.47 % Conjectures (3)
% 0.21/0.47 thf(conj_0,hypothesis,
% 0.21/0.47 ( b
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ s1 @ ( refine605929679le_RES @ a @ ( collect @ a @ phi ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(conj_1,hypothesis,
% 0.21/0.47 ( ~ b
% 0.21/0.47 => ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ s2 @ ( refine605929679le_RES @ a @ ( collect @ a @ phi ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(conj_2,conjecture,
% 0.21/0.47 ord_less_eq @ ( refine1665802226e_nres @ a ) @ ( if @ ( refine1665802226e_nres @ a ) @ b @ s1 @ s2 ) @ ( refine605929679le_RES @ a @ ( collect @ a @ phi ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 2.89/1.55 ---- Embedded in THF ---
% 2.89/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.89/1.55 %%% Generated on Tue Feb 24 08:28:24 EST 2026
% 2.89/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.89/1.55 %%% Logic specification used:
% 2.89/1.55 %%% thf(spec, logic, $$dhol).
% 2.89/1.55
% 2.89/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.eee0ELY9Y3/DTF2DTF22115.p
% 2.89/1.55 thf(ty_t_Refine__Basic__Mirabelle__tqojlsrkwy_Onres, type, refine1665802226e_nres: ($tType > $tType)).
% 2.89/1.55 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.89/1.55 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.89/1.55 thf(ty_tf_a, type, a: $tType).
% 2.89/1.55 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_cl_Complete__Lattices_Ocomplete__lattice, type, comple187826305attice: (!> [A:$tType]: ($o))).
% 2.89/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 2.89/1.55 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.89/1.55 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.89/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.89/1.55 thf(sy_c_Orderings_Oorder__class_OGreatest, type, order_Greatest: (!> [A:$tType]: (((A > $o) > A)))).
% 2.89/1.55 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.89/1.55 thf(sy_c_Partial__Function_Oflat__ord, type, partial_flat_ord: (!> [A:$tType]: ((A > (A > (A > $o)))))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_OASSUME, type, refine1946708059ASSUME: ($o > (refine1665802226e_nres @ product_unit))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_ORETURN, type, refine1687780735RETURN: (!> [A:$tType]: ((A > (refine1665802226e_nres @ A))))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Obind, type, refine463715084e_bind: (!> [B:$tType,A:$tType]: (((refine1665802226e_nres @ B) > ((B > (refine1665802226e_nres @ A)) > (refine1665802226e_nres @ A)))))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Oinres, type, refine1315500908_inres: (!> [A:$tType]: (((refine1665802226e_nres @ A) > (A > $o))))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onf__inres, type, refine406925620_inres: (!> [A:$tType]: (((refine1665802226e_nres @ A) > (A > $o))))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onofail, type, refine1102455758nofail: (!> [A:$tType]: (((refine1665802226e_nres @ A) > $o)))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_OFAILi, type, refine1767639642_FAILi: (!> [A:$tType]: ((refine1665802226e_nres @ A)))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_ORES, type, refine605929679le_RES: (!> [A:$tType]: (((set @ A) > (refine1665802226e_nres @ A))))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_Ocase__nres, type, refine60818195e_nres: (!> [B:$tType,A:$tType]: ((B > (((set @ A) > B) > ((refine1665802226e_nres @ A) > B)))))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_Orec__nres, type, refine1442219249c_nres: (!> [C:$tType,A:$tType]: ((C > (((set @ A) > C) > ((refine1665802226e_nres @ A) > C)))))).
% 2.89/1.55 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Othe__RES, type, refine1672542526he_RES: (!> [A:$tType]: (((refine1665802226e_nres @ A) > (set @ A))))).
% 2.89/1.55 thf(sy_c_Refine__Misc_Ostrict, type, refine_strict: (!> [A:$tType,B:$tType]: (((A > B) > $o)))).
% 2.89/1.55 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.89/1.55 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.89/1.55 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.89/1.55 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.89/1.55 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.89/1.55 thf(sy_c_Set__Interval_Oord_OatLeast, type, set_atLeast: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.89/1.55 thf(sy_c_Set__Interval_Oord_OatLeastAtMost, type, set_atLeastAtMost: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > (set @ A))))))).
% 2.89/1.55 thf(sy_c_Set__Interval_Oord_OatMost, type, set_atMost: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.89/1.55 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.89/1.55 thf(sy_v_S1, type, s1: (refine1665802226e_nres @ a)).
% 2.89/1.55 thf(sy_v_S2, type, s2: (refine1665802226e_nres @ a)).
% 2.89/1.55 thf(sy_v__092_060Phi_062, type, phi: (a > $o)).
% 2.89/1.55 thf(sy_v_b, type, b: $o).
% 2.89/1.55 thf(fact_0_nres__more__simps_I4_J, axiom, (! [A:$tType,X:(set @ A),Y:(set @ A)]: (((((refine605929679le_RES @ A) @ X) = ((refine605929679le_RES @ A) @ Y)) = (X = Y))))).
% 2.89/1.55 thf(fact_1_nres_Oinject, axiom, (! [A:$tType,X2:(set @ A),Y2:(set @ A)]: (((((refine605929679le_RES @ A) @ X2) = ((refine605929679le_RES @ A) @ Y2)) = (X2 = Y2))))).
% 2.89/1.55 thf(fact_2_RES__rule, axiom, (! [A:$tType,S:(set @ A),Phi:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ S) => (Phi @ X3)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ S)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))))))).
% 2.89/1.55 thf(fact_3_SPEC__rule, axiom, (! [A:$tType,Phi:(A > $o),Phi2:(A > $o)]: (((! [X3:A]: (((Phi @ X3) => (Phi2 @ X3)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi2))))))).
% 2.89/1.55 thf(fact_4_SPEC__trans, axiom, (! [A:$tType,X4:(refine1665802226e_nres @ A),Y3:(refine1665802226e_nres @ A),Postcond:(A > $o)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ X4) @ Y3) => ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ Y3) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Postcond))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ X4) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Postcond)))))))).
% 2.89/1.55 thf(fact_5_SPEC__cons__rule, axiom, (! [A:$tType,M:(refine1665802226e_nres @ A),Phi:(A > $o),Psi:(A > $o)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) => ((! [X3:A]: (((Phi @ X3) => (Psi @ X3)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Psi)))))))).
% 2.89/1.55 thf(fact_6_nf__inres__RES, axiom, (! [A:$tType,X:(set @ A),X4:A]: (((((refine406925620_inres @ A) @ ((refine605929679le_RES @ A) @ X)) @ X4) = (((member @ A) @ X4) @ X))))).
% 2.89/1.55 thf(fact_7_nf__inres__SPEC, axiom, (! [A:$tType,Phi:(A > $o),X4:A]: (((((refine406925620_inres @ A) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) @ X4) = (Phi @ X4))))).
% 2.89/1.55 thf(fact_8_order__mono__setup_Orefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X4:A]: ((((ord_less_eq @ A) @ X4) @ X4))))))).
% 2.89/1.55 thf(fact_9_the__RES_Osimps, axiom, (! [A:$tType,X:(set @ A)]: ((((refine1672542526he_RES @ A) @ ((refine605929679le_RES @ A) @ X)) = X)))).
% 2.89/1.55 thf(fact_10_nres__order__simps_I21_J, axiom, (! [X5:$tType,X4:X5,Y:(set @ X5)]: (((((ord_less_eq @ (refine1665802226e_nres @ X5)) @ ((refine1687780735RETURN @ X5) @ X4)) @ ((refine605929679le_RES @ X5) @ Y)) = (((member @ X5) @ X4) @ Y))))).
% 2.89/1.55 thf(fact_11_nres_Osimps_I7_J, axiom, (! [C:$tType,A:$tType,F1:C,F2:((set @ A) > C),X2:(set @ A)]: (((((((refine1442219249c_nres @ C) @ A) @ F1) @ F2) @ ((refine605929679le_RES @ A) @ X2)) = (F2 @ X2))))).
% 2.89/1.55 thf(fact_12_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X4:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X4)) @ (G @ X4))))))))).
% 2.89/1.55 thf(fact_13_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X4:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X4)) @ (G @ X4))))))))).
% 2.89/1.55 thf(fact_14_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.89/1.55 thf(fact_15_Refine__Misc_Oif__mono, axiom, (! [A:$tType]: (((ord @ A) => (! [B2:$o,M1:A,M12:A,M2:A,M22:A]: (((B2 => (((ord_less_eq @ A) @ M1) @ M12)) => (((~ (B2)) => (((ord_less_eq @ A) @ M2) @ M22)) => (((ord_less_eq @ A) @ ((((if @ A) @ B2) @ M1) @ M2)) @ ((((if @ A) @ B2) @ M12) @ M22)))))))))).
% 2.89/1.55 thf(fact_16_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F3:(A > B),G2:(A > B)]: ((! [X6:A]: ((((ord_less_eq @ B) @ (F3 @ X6)) @ (G2 @ X6))))))))))).
% 2.89/1.55 thf(fact_17_nres__more__simps_I6_J, axiom, (! [A:$tType,X4:A,Y3:A]: (((((refine1687780735RETURN @ A) @ X4) = ((refine1687780735RETURN @ A) @ Y3)) = (X4 = Y3))))).
% 2.89/1.55 thf(fact_18_nres__order__simps_I20_J, axiom, (! [W:$tType,X4:W,Y3:W]: (((((ord_less_eq @ (refine1665802226e_nres @ W)) @ ((refine1687780735RETURN @ W) @ X4)) @ ((refine1687780735RETURN @ W) @ Y3)) = (X4 = Y3))))).
% 2.89/1.55 thf(fact_19_less__eq__nres_Osimps_I2_J, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ A2)) @ ((refine605929679le_RES @ A) @ B2)) = (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 2.89/1.55 thf(fact_20_nres__order__simps_I5_J, axiom, (! [E:$tType,X:(set @ E),Y:(set @ E)]: (((((ord_less_eq @ (refine1665802226e_nres @ E)) @ ((refine605929679le_RES @ E) @ X)) @ ((refine605929679le_RES @ E) @ Y)) = (((ord_less_eq @ (set @ E)) @ X) @ Y))))).
% 2.89/1.55 thf(fact_21_RETURN__to__SPEC__rule, axiom, (! [A:$tType,M:(refine1665802226e_nres @ A),V:A]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ ((^ [Y4:A,Z:A]: ((Y4 = Z))) @ V)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine1687780735RETURN @ A) @ V)))))).
% 2.89/1.55 thf(fact_22_RETURN__rule, axiom, (! [A:$tType,Phi:(A > $o),X4:A]: (((Phi @ X4) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X4)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))))))).
% 2.89/1.55 thf(fact_23_order__mono__setup_Omono__let, axiom, (! [A:$tType,B:$tType]: (((preorder @ A) => (! [F:(B > A),F4:(B > A),X4:B]: (((! [X3:B]: ((((ord_less_eq @ A) @ (F @ X3)) @ (F4 @ X3)))) => (((ord_less_eq @ A) @ (F @ X4)) @ (F4 @ X4))))))))).
% 2.89/1.55 thf(fact_24_order__mono__setup_Omono__if, axiom, (! [A:$tType]: (((preorder @ A) => (! [T:A,T2:A,E2:A,E3:A,B2:$o]: (((((ord_less_eq @ A) @ T) @ T2) => ((((ord_less_eq @ A) @ E2) @ E3) => (((ord_less_eq @ A) @ ((((if @ A) @ B2) @ T) @ E2)) @ ((((if @ A) @ B2) @ T2) @ E3)))))))))).
% 2.89/1.55 thf(fact_25_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.89/1.55 thf(fact_26_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ B3) @ A3) & (((ord_less_eq @ A) @ A3) @ B3))))))))).
% 2.89/1.55 thf(fact_27_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.89/1.55 thf(fact_28_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((P @ A4) @ B4)))) => ((! [A4:A,B4:A]: ((((P @ B4) @ A4) => ((P @ A4) @ B4)))) => ((P @ A2) @ B2))))))))).
% 2.89/1.55 thf(fact_29_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.89/1.55 thf(fact_30_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X4:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ Z2) => (((ord_less_eq @ A) @ X4) @ Z2))))))))).
% 2.89/1.55 thf(fact_31_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.89/1.55 thf(fact_32_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.89/1.55 thf(fact_33_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.89/1.55 thf(fact_34_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) & (((ord_less_eq @ A) @ B3) @ A3))))))))).
% 2.89/1.55 thf(fact_35_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y3:A,X4:A]: (((((ord_less_eq @ A) @ Y3) @ X4) => ((((ord_less_eq @ A) @ X4) @ Y3) = (X4 = Y3))))))))).
% 2.89/1.55 thf(fact_36_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X4:A,Y3:A,Z2:A]: ((((((ord_less_eq @ A) @ X4) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ Z2)))) => (((((ord_less_eq @ A) @ Y3) @ X4) => (~ ((((ord_less_eq @ A) @ X4) @ Z2)))) => (((((ord_less_eq @ A) @ X4) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y3)))) => (((((ord_less_eq @ A) @ Z2) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ X4)))) => (((((ord_less_eq @ A) @ Y3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X4)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X4) => (~ ((((ord_less_eq @ A) @ X4) @ Y3))))))))))))))))).
% 2.89/1.55 thf(fact_37_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.89/1.55 thf(fact_38_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X4:A,Y3:A]: (((~ ((((ord_less_eq @ A) @ X4) @ Y3))) => (((ord_less_eq @ A) @ Y3) @ X4)))))))).
% 2.89/1.55 thf(fact_39_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X4:A,Y3:A]: (((X4 = Y3) => (((ord_less_eq @ A) @ X4) @ Y3)))))))).
% 2.89/1.55 thf(fact_40_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) | (((ord_less_eq @ A) @ Y3) @ X4)))))))).
% 2.89/1.55 thf(fact_41_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ X4) => (X4 = Y3))))))))).
% 2.89/1.55 thf(fact_42_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [X6:A,Y5:A]: (((((ord_less_eq @ A) @ X6) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X6))))))))).
% 2.89/1.55 thf(fact_43_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C2) => ((! [X3:A,Y6:A]: (((((ord_less_eq @ A) @ X3) @ Y6) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y6))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C2)))))))))).
% 2.89/1.55 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.89/1.55 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X6:A]: ((((member @ A) @ X6) @ A5)))) = A5)))).
% 2.89/1.55 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.89/1.55 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.89/1.55 thf(fact_48_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B2:B,C2:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X3:B,Y6:B]: (((((ord_less_eq @ B) @ X3) @ Y6) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y6))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.89/1.55 thf(fact_49_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B2:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C) @ (F @ B2)) @ C2) => ((! [X3:A,Y6:A]: (((((ord_less_eq @ A) @ X3) @ Y6) => (((ord_less_eq @ C) @ (F @ X3)) @ (F @ Y6))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C2)))))))))).
% 2.89/1.55 thf(fact_50_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X3:B,Y6:B]: (((((ord_less_eq @ B) @ X3) @ Y6) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y6))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.89/1.55 thf(fact_51_the__RES__inv, axiom, (! [A:$tType,M:(refine1665802226e_nres @ A)]: ((((refine1102455758nofail @ A) @ M) => (((refine605929679le_RES @ A) @ ((refine1672542526he_RES @ A) @ M)) = M))))).
% 2.89/1.55 thf(fact_52_Greatest__equality, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X4:A]: (((P @ X4) => ((! [Y6:A]: (((P @ Y6) => (((ord_less_eq @ A) @ Y6) @ X4)))) => (((order_Greatest @ A) @ P) = X4))))))))).
% 2.89/1.55 thf(fact_53_GreatestI2__order, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X4:A,Q:(A > $o)]: (((P @ X4) => ((! [Y6:A]: (((P @ Y6) => (((ord_less_eq @ A) @ Y6) @ X4)))) => ((! [X3:A]: (((P @ X3) => ((! [Y7:A]: (((P @ Y7) => (((ord_less_eq @ A) @ Y7) @ X3)))) => (Q @ X3))))) => (Q @ ((order_Greatest @ A) @ P))))))))))).
% 2.89/1.55 thf(fact_54_transfer_Otransfer__Let, axiom, (! [C:$tType,A:$tType,B:$tType]: (((comple187826305attice @ A) => (! [Alpha:(C > A),F:(B > C),F5:(B > A),X4:B]: (((! [X3:B]: ((((ord_less_eq @ A) @ (Alpha @ (F @ X3))) @ (F5 @ X3)))) => (((ord_less_eq @ A) @ (Alpha @ (F @ X4))) @ (F5 @ X4))))))))).
% 2.89/1.55 thf(fact_55_transfer_Otransfer__if, axiom, (! [C:$tType,A:$tType]: (((comple187826305attice @ A) => (! [B2:$o,Alpha:(C > A),S1:C,S12:A,S2:C,S22:A]: (((B2 => (((ord_less_eq @ A) @ (Alpha @ S1)) @ S12)) => (((~ (B2)) => (((ord_less_eq @ A) @ (Alpha @ S2)) @ S22)) => (((ord_less_eq @ A) @ (Alpha @ ((((if @ C) @ B2) @ S1) @ S2))) @ ((((if @ A) @ B2) @ S12) @ S22)))))))))).
% 2.89/1.55 thf(fact_56_le__rel__bool__arg__iff, axiom, (! [A:$tType]: (((ord @ A) => ((ord_less_eq @ ($o > A)) = (^ [X7:($o > A),Y8:($o > A)]: (((((ord_less_eq @ A) @ (X7 @ $false)) @ (Y8 @ $false)) & (((ord_less_eq @ A) @ (X7 @ $true)) @ (Y8 @ $true)))))))))).
% 2.89/1.55 thf(fact_57_verit__la__disequality, axiom, (! [A:$tType]: (((linorder @ A) => (! [A2:A,B2:A]: (((A2 = B2) | ((~ ((((ord_less_eq @ A) @ A2) @ B2))) | (~ ((((ord_less_eq @ A) @ B2) @ A2))))))))))).
% 2.89/1.55 thf(fact_58_ord__eq__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A,D:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => ((C2 = D) => (((ord_less_eq @ A) @ A2) @ D)))))))))).
% 2.89/1.55 thf(fact_59_bind__cong, axiom, (! [B:$tType,A:$tType,M:(refine1665802226e_nres @ A),M3:(refine1665802226e_nres @ A),F:(A > (refine1665802226e_nres @ B)),F4:(A > (refine1665802226e_nres @ B))]: (((M = M3) => ((! [X3:A]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X3)) @ M3) => ((F @ X3) = (F4 @ X3))))) => (((((refine463715084e_bind @ A) @ B) @ M) @ F) = ((((refine463715084e_bind @ A) @ B) @ M3) @ F4))))))).
% 2.89/1.55 thf(fact_60_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J, axiom, (! [B:$tType,A:$tType,M4:(refine1665802226e_nres @ A),M5:(refine1665802226e_nres @ A),F:(A > (refine1665802226e_nres @ B)),F4:(A > (refine1665802226e_nres @ B))]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M4) @ M5) => ((! [X3:A]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X3)) @ M4) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ (F @ X3)) @ (F4 @ X3))))) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ ((((refine463715084e_bind @ A) @ B) @ M4) @ F)) @ ((((refine463715084e_bind @ A) @ B) @ M5) @ F4))))))).
% 2.89/1.55 thf(fact_61_nofail__simps_I2_J, axiom, (! [B:$tType,X:(set @ B)]: (((refine1102455758nofail @ B) @ ((refine605929679le_RES @ B) @ X))))).
% 2.89/1.55 thf(fact_62_nofail__simps_I3_J, axiom, (! [C:$tType,X4:C]: (((refine1102455758nofail @ C) @ ((refine1687780735RETURN @ C) @ X4))))).
% 2.89/1.55 thf(fact_63_nres__monad2, axiom, (! [A:$tType,M4:(refine1665802226e_nres @ A)]: ((((((refine463715084e_bind @ A) @ A) @ M4) @ (refine1687780735RETURN @ A)) = M4)))).
% 2.89/1.55 thf(fact_64_nres__monad1, axiom, (! [A:$tType,B:$tType,X4:B,F:(B > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ B) @ A) @ ((refine1687780735RETURN @ B) @ X4)) @ F) = (F @ X4))))).
% 2.89/1.55 thf(fact_65_subset__Collect__conv, axiom, (! [A:$tType,S:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ S) @ ((collect @ A) @ P)) = (! [X6:A]: (((((member @ A) @ X6) @ S) => (P @ X6)))))))).
% 2.89/1.55 thf(fact_66_nofail__antimono__fun, axiom, (! [B:$tType,A:$tType,F:(A > (refine1665802226e_nres @ B)),G:(A > (refine1665802226e_nres @ B)),X4:A]: (((((ord_less_eq @ (A > (refine1665802226e_nres @ B))) @ F) @ G) => (((refine1102455758nofail @ B) @ (G @ X4)) => ((refine1102455758nofail @ B) @ (F @ X4))))))).
% 2.89/1.55 thf(fact_67_nofail__RES__conv, axiom, (! [A:$tType]: (((refine1102455758nofail @ A) = (^ [M6:(refine1665802226e_nres @ A)]: ((? [M7:(set @ A)]: ((M6 = ((refine605929679le_RES @ A) @ M7)))))))))).
% 2.89/1.55 thf(fact_68_pwD1, axiom, (! [A:$tType,S:(refine1665802226e_nres @ A),S3:(refine1665802226e_nres @ A)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ S) @ S3) => (((refine1102455758nofail @ A) @ S3) => ((refine1102455758nofail @ A) @ S)))))).
% 2.89/1.55 thf(fact_69_le__nofailI, axiom, (! [A:$tType,M5:(refine1665802226e_nres @ A),M4:(refine1665802226e_nres @ A)]: (((((refine1102455758nofail @ A) @ M5) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ M4) @ M5)) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ M4) @ M5))))).
% 2.89/1.55 thf(fact_70_subsetI, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A5) => (((member @ A) @ X3) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A5) @ B5))))).
% 2.89/1.55 thf(fact_71_subset__antisym, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A5) => (A5 = B5)))))).
% 2.89/1.55 thf(fact_72_pw__bind__leI, axiom, (! [B:$tType,A:$tType,S:(refine1665802226e_nres @ A),M4:(refine1665802226e_nres @ B),F:(B > (refine1665802226e_nres @ A))]: (((((refine1102455758nofail @ A) @ S) => ((refine1102455758nofail @ B) @ M4)) => ((! [X3:B]: ((((refine1102455758nofail @ B) @ M4) => ((((refine1315500908_inres @ B) @ M4) @ X3) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ (F @ X3)) @ S))))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((((refine463715084e_bind @ B) @ A) @ M4) @ F)) @ S)))))).
% 2.89/1.55 thf(fact_73_pw__bind__le__iff, axiom, (! [A:$tType,B:$tType,M4:(refine1665802226e_nres @ B),F:(B > (refine1665802226e_nres @ A)),S:(refine1665802226e_nres @ A)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((((refine463715084e_bind @ B) @ A) @ M4) @ F)) @ S) = ((((refine1102455758nofail @ A) @ S) => ((refine1102455758nofail @ B) @ M4)) & (! [X6:B]: (((((refine1102455758nofail @ B) @ M4) & (((refine1315500908_inres @ B) @ M4) @ X6)) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ (F @ X6)) @ S))))))))).
% 2.89/1.55 thf(fact_74_relprop__triggers_I6_J, axiom, (! [I:$tType,R:(set @ I),R2:(set @ I)]: (((((ord_less_eq @ (set @ I)) @ R) @ R2) => (((ord_less_eq @ (set @ I)) @ R) @ R2))))).
% 2.89/1.55 thf(fact_75_in__mono, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),X4:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((member @ A) @ X4) @ A5) => (((member @ A) @ X4) @ B5)))))).
% 2.89/1.55 thf(fact_76_subsetD, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((member @ A) @ C2) @ A5) => (((member @ A) @ C2) @ B5)))))).
% 2.89/1.55 thf(fact_77_inres__simps_I2_J, axiom, (! [B:$tType,X:(set @ B)]: ((((refine1315500908_inres @ B) @ ((refine605929679le_RES @ B) @ X)) = (^ [X6:B]: ((((member @ B) @ X6) @ X))))))).
% 2.89/1.55 thf(fact_78_inres__simps_I3_J, axiom, (! [C:$tType,X4:C]: ((((refine1315500908_inres @ C) @ ((refine1687780735RETURN @ C) @ X4)) = ((^ [Y4:C,Z:C]: ((Y4 = Z))) @ X4))))).
% 2.89/1.55 thf(fact_79_pwD2, axiom, (! [A:$tType,S:(refine1665802226e_nres @ A),S3:(refine1665802226e_nres @ A),X4:A]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ S) @ S3) => ((((refine1315500908_inres @ A) @ S) @ X4) => (((refine1315500908_inres @ A) @ S3) @ X4)))))).
% 2.89/1.55 thf(fact_80_pw__eqI, axiom, (! [A:$tType,S:(refine1665802226e_nres @ A),S3:(refine1665802226e_nres @ A)]: (((((refine1102455758nofail @ A) @ S) = ((refine1102455758nofail @ A) @ S3)) => ((! [X3:A]: (((((refine1315500908_inres @ A) @ S) @ X3) = (((refine1315500908_inres @ A) @ S3) @ X3)))) => (S = S3)))))).
% 2.89/1.55 thf(fact_81_pw__eq__iff, axiom, (! [A:$tType]: (((^ [Y4:(refine1665802226e_nres @ A),Z:(refine1665802226e_nres @ A)]: ((Y4 = Z))) = (^ [S4:(refine1665802226e_nres @ A),S5:(refine1665802226e_nres @ A)]: (((((refine1102455758nofail @ A) @ S4) = ((refine1102455758nofail @ A) @ S5)) & (! [X6:A]: (((((refine1315500908_inres @ A) @ S4) @ X6) = (((refine1315500908_inres @ A) @ S5) @ X6))))))))))).
% 2.89/1.55 thf(fact_82_not__nofail__inres, axiom, (! [A:$tType,S:(refine1665802226e_nres @ A),X4:A]: (((~ (((refine1102455758nofail @ A) @ S))) => (((refine1315500908_inres @ A) @ S) @ X4))))).
% 2.89/1.55 thf(fact_83_pw__le__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (refine1665802226e_nres @ A)) = (^ [S4:(refine1665802226e_nres @ A),S5:(refine1665802226e_nres @ A)]: ((((refine1102455758nofail @ A) @ S5) => (((refine1102455758nofail @ A) @ S4) & (! [X6:A]: (((((refine1315500908_inres @ A) @ S4) @ X6) => (((refine1315500908_inres @ A) @ S5) @ X6)))))))))))).
% 2.89/1.55 thf(fact_84_pw__leI_H, axiom, (! [A:$tType,S3:(refine1665802226e_nres @ A),S:(refine1665802226e_nres @ A)]: (((((refine1102455758nofail @ A) @ S3) => ((refine1102455758nofail @ A) @ S)) => ((! [X3:A]: ((((refine1102455758nofail @ A) @ S3) => ((((refine1315500908_inres @ A) @ S) @ X3) => (((refine1315500908_inres @ A) @ S3) @ X3))))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ S) @ S3)))))).
% 2.89/1.55 thf(fact_85_pw__leI, axiom, (! [A:$tType,S3:(refine1665802226e_nres @ A),S:(refine1665802226e_nres @ A)]: (((((refine1102455758nofail @ A) @ S3) => (((refine1102455758nofail @ A) @ S) & (! [X3:A]: (((((refine1315500908_inres @ A) @ S) @ X3) => (((refine1315500908_inres @ A) @ S3) @ X3)))))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ S) @ S3))))).
% 2.89/1.55 thf(fact_86_pw__bind__nofail, axiom, (! [A:$tType,B:$tType,M4:(refine1665802226e_nres @ B),F:(B > (refine1665802226e_nres @ A))]: ((((refine1102455758nofail @ A) @ ((((refine463715084e_bind @ B) @ A) @ M4) @ F)) = (((refine1102455758nofail @ B) @ M4) & (! [X6:B]: (((((refine1315500908_inres @ B) @ M4) @ X6) => ((refine1102455758nofail @ A) @ (F @ X6)))))))))).
% 2.89/1.55 thf(fact_87_inres__def, axiom, (! [A:$tType]: (((refine1315500908_inres @ A) = (^ [S4:(refine1665802226e_nres @ A),X6:A]: ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X6)) @ S4))))))).
% 2.89/1.55 thf(fact_88_nf__inres__def, axiom, (! [A:$tType]: (((refine406925620_inres @ A) = (^ [M6:(refine1665802226e_nres @ A),X6:A]: ((((refine1102455758nofail @ A) @ M6) & (((refine1315500908_inres @ A) @ M6) @ X6)))))))).
% 2.89/1.55 thf(fact_89_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X6:A]: (((P @ X6) => (Q @ X6)))))))).
% 2.89/1.55 thf(fact_90_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z:(set @ A)]: ((Y4 = Z))) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))).
% 2.89/1.55 thf(fact_91_subset__trans, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C3) => (((ord_less_eq @ (set @ A)) @ A5) @ C3)))))).
% 2.89/1.55 thf(fact_92_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.89/1.55 thf(fact_93_subset__refl, axiom, (! [A:$tType,A5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A5) @ A5)))).
% 2.89/1.55 thf(fact_94_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A6) => (((member @ A) @ T3) @ B6)))))))))).
% 2.89/1.55 thf(fact_95_equalityD2, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A5))))).
% 2.89/1.55 thf(fact_96_equalityD1, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (((ord_less_eq @ (set @ A)) @ A5) @ B5))))).
% 2.89/1.55 thf(fact_97_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [X6:A]: (((((member @ A) @ X6) @ A6) => (((member @ A) @ X6) @ B6)))))))))).
% 2.89/1.55 thf(fact_98_equalityE, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A5)))))))))).
% 2.89/1.55 thf(fact_99_less__eq__nres_Oelims_I1_J, axiom, (! [A:$tType,X4:(refine1665802226e_nres @ A),Xa:(refine1665802226e_nres @ A),Y3:$o]: ((((((ord_less_eq @ (refine1665802226e_nres @ A)) @ X4) @ Xa) = Y3) => (((Xa = (refine1767639642_FAILi @ A)) => (~ (Y3))) => ((! [A4:(set @ A)]: (((X4 = ((refine605929679le_RES @ A) @ A4)) => (! [B4:(set @ A)]: (((Xa = ((refine605929679le_RES @ A) @ B4)) => (Y3 = (~ ((((ord_less_eq @ (set @ A)) @ A4) @ B4)))))))))) => (~ (((X4 = (refine1767639642_FAILi @ A)) => ((? [Uv:(set @ A)]: ((Xa = ((refine605929679le_RES @ A) @ Uv)))) => Y3)))))))))).
% 2.89/1.55 thf(fact_100_less__eq__nres_Oelims_I2_J, axiom, (! [A:$tType,X4:(refine1665802226e_nres @ A),Xa:(refine1665802226e_nres @ A)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ X4) @ Xa) => ((Xa != (refine1767639642_FAILi @ A)) => (~ ((! [A4:(set @ A)]: (((X4 = ((refine605929679le_RES @ A) @ A4)) => (! [B4:(set @ A)]: (((Xa = ((refine605929679le_RES @ A) @ B4)) => (~ ((((ord_less_eq @ (set @ A)) @ A4) @ B4)))))))))))))))).
% 2.89/1.55 thf(fact_101_less__eq__nres_Oelims_I3_J, axiom, (! [A:$tType,X4:(refine1665802226e_nres @ A),Xa:(refine1665802226e_nres @ A)]: (((~ ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ X4) @ Xa))) => ((! [A4:(set @ A)]: (((X4 = ((refine605929679le_RES @ A) @ A4)) => (! [B4:(set @ A)]: (((Xa = ((refine605929679le_RES @ A) @ B4)) => (((ord_less_eq @ (set @ A)) @ A4) @ B4))))))) => (~ (((X4 = (refine1767639642_FAILi @ A)) => (! [Uv:(set @ A)]: ((Xa != ((refine605929679le_RES @ A) @ Uv)))))))))))).
% 2.89/1.55 thf(fact_102_nres_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F2:((set @ A) > B),X2:(set @ A)]: (((((((refine60818195e_nres @ B) @ A) @ F1) @ F2) @ ((refine605929679le_RES @ A) @ X2)) = (F2 @ X2))))).
% 2.89/1.55 thf(fact_103_nres__order__simps_I22_J, axiom, (! [Y9:$tType,X:(set @ Y9),Y3:Y9]: (((((ord_less_eq @ (refine1665802226e_nres @ Y9)) @ ((refine605929679le_RES @ Y9) @ X)) @ ((refine1687780735RETURN @ Y9) @ Y3)) = (((ord_less_eq @ (set @ Y9)) @ X) @ (((insert @ Y9) @ Y3) @ (bot_bot @ (set @ Y9)))))))).
% 2.89/1.55 thf(fact_104_less__eq__nres_Osimps_I3_J, axiom, (! [A:$tType,Uv2:(set @ A)]: ((~ ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ (refine1767639642_FAILi @ A)) @ ((refine605929679le_RES @ A) @ Uv2))))))).
% 2.89/1.55 thf(fact_105_bot__apply, axiom, (! [C:$tType,D2:$tType]: (((bot @ C) => ((bot_bot @ (D2 > C)) = (^ [X6:D2]: ((bot_bot @ C)))))))).
% 2.89/1.55 thf(fact_106_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.89/1.55 thf(fact_107_all__not__in__conv, axiom, (! [A:$tType,A5:(set @ A)]: (((! [X6:A]: ((~ ((((member @ A) @ X6) @ A5))))) = (A5 = (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_108_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X6:A]: ((~ ((P @ X6))))))))).
% 2.89/1.55 thf(fact_109_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X6:A]: ((~ ((P @ X6))))))))).
% 2.89/1.55 thf(fact_110_insertCI, axiom, (! [A:$tType,A2:A,B5:(set @ A),B2:A]: ((((~ ((((member @ A) @ A2) @ B5))) => (A2 = B2)) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B5)))))).
% 2.89/1.55 thf(fact_111_insert__iff, axiom, (! [A:$tType,A2:A,B2:A,A5:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A5)) = ((A2 = B2) | (((member @ A) @ A2) @ A5)))))).
% 2.89/1.55 thf(fact_112_insert__absorb2, axiom, (! [A:$tType,X4:A,A5:(set @ A)]: (((((insert @ A) @ X4) @ (((insert @ A) @ X4) @ A5)) = (((insert @ A) @ X4) @ A5))))).
% 2.89/1.55 thf(fact_113_empty__subsetI, axiom, (! [A:$tType,A5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A5)))).
% 2.89/1.55 thf(fact_114_subset__empty, axiom, (! [A:$tType,A5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ (bot_bot @ (set @ A))) = (A5 = (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_115_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_116_insert__subset, axiom, (! [A:$tType,X4:A,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X4) @ A5)) @ B5) = ((((member @ A) @ X4) @ B5) & (((ord_less_eq @ (set @ A)) @ A5) @ B5)))))).
% 2.89/1.55 thf(fact_117_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A2:A,A5:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A2) @ A5)) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A5) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.89/1.55 thf(fact_118_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A2:A,A5:(set @ A),B2:A]: ((((((insert @ A) @ A2) @ A5) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A5) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.89/1.55 thf(fact_119_nres__more__simps_I5_J, axiom, (! [A:$tType,X4:A,X:(set @ A)]: (((((refine1687780735RETURN @ A) @ X4) = ((refine605929679le_RES @ A) @ X)) = ((((insert @ A) @ X4) @ (bot_bot @ (set @ A))) = X))))).
% 2.89/1.55 thf(fact_120_nres__more__simps_I3_J, axiom, (! [A:$tType,X:(set @ A),X4:A]: (((((refine605929679le_RES @ A) @ X) = ((refine1687780735RETURN @ A) @ X4)) = (X = (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))).
% 2.89/1.55 thf(fact_121_subset__singletonD, axiom, (! [A:$tType,A5:(set @ A),X4:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))) => ((A5 = (bot_bot @ (set @ A))) | (A5 = (((insert @ A) @ X4) @ (bot_bot @ (set @ A))))))))).
% 2.89/1.55 thf(fact_122_subset__singleton__iff, axiom, (! [A:$tType,X:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ X) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = ((X = (bot_bot @ (set @ A))) | (X = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))))).
% 2.89/1.55 thf(fact_123_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.89/1.55 thf(fact_124_insertE, axiom, (! [A:$tType,A2:A,B2:A,A5:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A5)) => ((A2 != B2) => (((member @ A) @ A2) @ A5)))))).
% 2.89/1.55 thf(fact_125_equals0D, axiom, (! [A:$tType,A5:(set @ A),A2:A]: (((A5 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A5))))))).
% 2.89/1.55 thf(fact_126_equals0I, axiom, (! [A:$tType,A5:(set @ A)]: (((! [Y6:A]: ((~ ((((member @ A) @ Y6) @ A5))))) => (A5 = (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_127_insertI1, axiom, (! [A:$tType,A2:A,B5:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B5))))).
% 2.89/1.55 thf(fact_128_insertI2, axiom, (! [A:$tType,A2:A,B5:(set @ A),B2:A]: (((((member @ A) @ A2) @ B5) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B5)))))).
% 2.89/1.55 thf(fact_129_ex__in__conv, axiom, (! [A:$tType,A5:(set @ A)]: (((? [X6:A]: ((((member @ A) @ X6) @ A5))) = (A5 != (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_130_Set_Oset__insert, axiom, (! [A:$tType,X4:A,A5:(set @ A)]: (((((member @ A) @ X4) @ A5) => (~ ((! [B7:(set @ A)]: (((A5 = (((insert @ A) @ X4) @ B7)) => (((member @ A) @ X4) @ B7)))))))))).
% 2.89/1.55 thf(fact_131_singletonD, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B2 = A2))))).
% 2.89/1.55 thf(fact_132_insert__ident, axiom, (! [A:$tType,X4:A,A5:(set @ A),B5:(set @ A)]: (((~ ((((member @ A) @ X4) @ A5))) => ((~ ((((member @ A) @ X4) @ B5))) => (((((insert @ A) @ X4) @ A5) = (((insert @ A) @ X4) @ B5)) = (A5 = B5))))))).
% 2.89/1.55 thf(fact_133_insert__absorb, axiom, (! [A:$tType,A2:A,A5:(set @ A)]: (((((member @ A) @ A2) @ A5) => ((((insert @ A) @ A2) @ A5) = A5))))).
% 2.89/1.55 thf(fact_134_insert__eq__iff, axiom, (! [A:$tType,A2:A,A5:(set @ A),B2:A,B5:(set @ A)]: (((~ ((((member @ A) @ A2) @ A5))) => ((~ ((((member @ A) @ B2) @ B5))) => (((((insert @ A) @ A2) @ A5) = (((insert @ A) @ B2) @ B5)) = (((A2 = B2) => (A5 = B5)) & ((A2 != B2) => (? [C4:(set @ A)]: (((A5 = (((insert @ A) @ B2) @ C4)) & ((~ ((((member @ A) @ B2) @ C4))) & ((B5 = (((insert @ A) @ A2) @ C4)) & (~ ((((member @ A) @ A2) @ C4)))))))))))))))).
% 2.89/1.55 thf(fact_135_singleton__iff, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B2 = A2))))).
% 2.89/1.55 thf(fact_136_insert__commute, axiom, (! [A:$tType,X4:A,Y3:A,A5:(set @ A)]: (((((insert @ A) @ X4) @ (((insert @ A) @ Y3) @ A5)) = (((insert @ A) @ Y3) @ (((insert @ A) @ X4) @ A5)))))).
% 2.89/1.55 thf(fact_137_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B2:A,C2:A,D:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C2) @ (((insert @ A) @ D) @ (bot_bot @ (set @ A))))) = (((A2 = C2) & (B2 = D)) | ((A2 = D) & (B2 = C2))))))).
% 2.89/1.55 thf(fact_138_insert__not__empty, axiom, (! [A:$tType,A2:A,A5:(set @ A)]: (((((insert @ A) @ A2) @ A5) != (bot_bot @ (set @ A)))))).
% 2.89/1.55 thf(fact_139_singleton__inject, axiom, (! [A:$tType,A2:A,B2:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A2 = B2))))).
% 2.89/1.55 thf(fact_140_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A5:(set @ A)]: (((((member @ A) @ A2) @ A5) => (? [B7:(set @ A)]: (((A5 = (((insert @ A) @ A2) @ B7)) & (~ ((((member @ A) @ A2) @ B7)))))))))).
% 2.89/1.55 thf(fact_141_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X6:A]: ((bot_bot @ B)))))))).
% 2.89/1.55 thf(fact_142_nres_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F2:((set @ A) > B)]: (((((((refine60818195e_nres @ B) @ A) @ F1) @ F2) @ (refine1767639642_FAILi @ A)) = F1)))).
% 2.89/1.55 thf(fact_143_set__notEmptyE, axiom, (! [A:$tType,S:(set @ A)]: (((S != (bot_bot @ (set @ A))) => (~ ((! [X3:A]: ((~ ((((member @ A) @ X3) @ S))))))))))).
% 2.89/1.55 thf(fact_144_memb__imp__not__empty, axiom, (! [A:$tType,X4:A,S:(set @ A)]: (((((member @ A) @ X4) @ S) => (S != (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_145_bot_Oextremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A2))))))).
% 2.89/1.55 thf(fact_146_bot_Oextremum__unique, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) = (A2 = (bot_bot @ A))))))))).
% 2.89/1.55 thf(fact_147_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) => (A2 = (bot_bot @ A))))))))).
% 2.89/1.55 thf(fact_148_subset__insertI2, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => (((ord_less_eq @ (set @ A)) @ A5) @ (((insert @ A) @ B2) @ B5)))))).
% 2.89/1.55 thf(fact_149_subset__insertI, axiom, (! [A:$tType,B5:(set @ A),A2:A]: ((((ord_less_eq @ (set @ A)) @ B5) @ (((insert @ A) @ A2) @ B5))))).
% 2.89/1.55 thf(fact_150_subset__insert, axiom, (! [A:$tType,X4:A,A5:(set @ A),B5:(set @ A)]: (((~ ((((member @ A) @ X4) @ A5))) => ((((ord_less_eq @ (set @ A)) @ A5) @ (((insert @ A) @ X4) @ B5)) = (((ord_less_eq @ (set @ A)) @ A5) @ B5)))))).
% 2.89/1.55 thf(fact_151_insert__mono, axiom, (! [A:$tType,C3:(set @ A),D3:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ C3) @ D3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A2) @ C3)) @ (((insert @ A) @ A2) @ D3)))))).
% 2.89/1.55 thf(fact_152_RETURN__def, axiom, (! [A:$tType]: (((refine1687780735RETURN @ A) = (^ [X6:A]: (((refine605929679le_RES @ A) @ (((insert @ A) @ X6) @ (bot_bot @ (set @ A)))))))))).
% 2.89/1.55 thf(fact_153_nres_Odistinct_I1_J, axiom, (! [A:$tType,X2:(set @ A)]: (((refine1767639642_FAILi @ A) != ((refine605929679le_RES @ A) @ X2))))).
% 2.89/1.55 thf(fact_154_nres_Oinduct, axiom, (! [A:$tType,P:((refine1665802226e_nres @ A) > $o),Nres:(refine1665802226e_nres @ A)]: (((P @ (refine1767639642_FAILi @ A)) => ((! [X3:(set @ A)]: ((P @ ((refine605929679le_RES @ A) @ X3)))) => (P @ Nres)))))).
% 2.89/1.55 thf(fact_155_nres_Oexhaust, axiom, (! [A:$tType,Y3:(refine1665802226e_nres @ A)]: (((Y3 != (refine1767639642_FAILi @ A)) => (~ ((! [X22:(set @ A)]: ((Y3 != ((refine605929679le_RES @ A) @ X22)))))))))).
% 2.89/1.55 thf(fact_156_sup__nres_Oinduct, axiom, (! [A:$tType,P:((refine1665802226e_nres @ A) > ((refine1665802226e_nres @ A) > $o)),A0:(refine1665802226e_nres @ A),A1:(refine1665802226e_nres @ A)]: (((! [Uu:(refine1665802226e_nres @ A)]: (((P @ Uu) @ (refine1767639642_FAILi @ A)))) => ((! [V2:(set @ A)]: (((P @ (refine1767639642_FAILi @ A)) @ ((refine605929679le_RES @ A) @ V2)))) => ((! [A4:(set @ A),B4:(set @ A)]: (((P @ ((refine605929679le_RES @ A) @ A4)) @ ((refine605929679le_RES @ A) @ B4)))) => ((P @ A0) @ A1))))))).
% 2.89/1.55 thf(fact_157_less__nres_Oinduct, axiom, (! [A:$tType,P:((refine1665802226e_nres @ A) > ((refine1665802226e_nres @ A) > $o)),A0:(refine1665802226e_nres @ A),A1:(refine1665802226e_nres @ A)]: (((! [X_1:(refine1665802226e_nres @ A)]: (((P @ (refine1767639642_FAILi @ A)) @ X_1))) => ((! [Uv:(set @ A)]: (((P @ ((refine605929679le_RES @ A) @ Uv)) @ (refine1767639642_FAILi @ A)))) => ((! [A4:(set @ A),B4:(set @ A)]: (((P @ ((refine605929679le_RES @ A) @ A4)) @ ((refine605929679le_RES @ A) @ B4)))) => ((P @ A0) @ A1))))))).
% 2.89/1.55 thf(fact_158_less__eq__nres_Oinduct, axiom, (! [A:$tType,P:((refine1665802226e_nres @ A) > ((refine1665802226e_nres @ A) > $o)),A0:(refine1665802226e_nres @ A),A1:(refine1665802226e_nres @ A)]: (((! [Uu:(refine1665802226e_nres @ A)]: (((P @ Uu) @ (refine1767639642_FAILi @ A)))) => ((! [A4:(set @ A),B4:(set @ A)]: (((P @ ((refine605929679le_RES @ A) @ A4)) @ ((refine605929679le_RES @ A) @ B4)))) => ((! [Uv:(set @ A)]: (((P @ (refine1767639642_FAILi @ A)) @ ((refine605929679le_RES @ A) @ Uv)))) => ((P @ A0) @ A1))))))).
% 2.89/1.55 thf(fact_159_less__eq__nres_Osimps_I1_J, axiom, (! [A:$tType,Uu2:(refine1665802226e_nres @ A)]: ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ Uu2) @ (refine1767639642_FAILi @ A))))).
% 2.89/1.55 thf(fact_160_nres_Osimps_I6_J, axiom, (! [A:$tType,C:$tType,F1:C,F2:((set @ A) > C)]: (((((((refine1442219249c_nres @ C) @ A) @ F1) @ F2) @ (refine1767639642_FAILi @ A)) = F1)))).
% 2.89/1.55 thf(fact_161_the__elem__eq, axiom, (! [A:$tType,X4:A]: ((((the_elem @ A) @ (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))) = X4)))).
% 2.89/1.55 thf(fact_162_is__singletonI, axiom, (! [A:$tType,X4:A]: (((is_singleton @ A) @ (((insert @ A) @ X4) @ (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_163_insert__subsetI, axiom, (! [A:$tType,X4:A,A5:(set @ A),X:(set @ A)]: (((((member @ A) @ X4) @ A5) => ((((ord_less_eq @ (set @ A)) @ X) @ A5) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X4) @ X)) @ A5)))))).
% 2.89/1.55 thf(fact_164_subset__emptyI, axiom, (! [A:$tType,A5:(set @ A)]: (((! [X3:A]: ((~ ((((member @ A) @ X3) @ A5))))) => (((ord_less_eq @ (set @ A)) @ A5) @ (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_165_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A6:(set @ A)]: ((A6 = (bot_bot @ (set @ A))))))))).
% 2.89/1.55 thf(fact_166_nres__order__simps_I2_J, axiom, (! [B:$tType,M4:(refine1665802226e_nres @ B)]: (((((ord_less_eq @ (refine1665802226e_nres @ B)) @ M4) @ (bot_bot @ (refine1665802226e_nres @ B))) = (M4 = (bot_bot @ (refine1665802226e_nres @ B))))))).
% 2.89/1.55 thf(fact_167_nofail__simps_I4_J, axiom, (! [D2:$tType]: (((refine1102455758nofail @ D2) @ (bot_bot @ (refine1665802226e_nres @ D2)))))).
% 2.89/1.55 thf(fact_168_inres__simps_I4_J, axiom, (! [D2:$tType]: ((((refine1315500908_inres @ D2) @ (bot_bot @ (refine1665802226e_nres @ D2))) = (^ [Uu3:D2]: ($false)))))).
% 2.89/1.55 thf(fact_169_bind__SUCCEED, axiom, (! [B:$tType,A:$tType,F:(B > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ B) @ A) @ (bot_bot @ (refine1665802226e_nres @ B))) @ F) = (bot_bot @ (refine1665802226e_nres @ A)))))).
% 2.89/1.55 thf(fact_170_nres__more__simps_I2_J, axiom, (! [A:$tType,X:(set @ A)]: (((((refine605929679le_RES @ A) @ X) = (bot_bot @ (refine1665802226e_nres @ A))) = (X = (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_171_nres__more__simps_I1_J, axiom, (! [A:$tType,X:(set @ A)]: ((((bot_bot @ (refine1665802226e_nres @ A)) = ((refine605929679le_RES @ A) @ X)) = (X = (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_172_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.89/1.55 thf(fact_173_nres__order__simps_I1_J, axiom, (! [A:$tType,M4:(refine1665802226e_nres @ A)]: ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ (bot_bot @ (refine1665802226e_nres @ A))) @ M4)))).
% 2.89/1.55 thf(fact_174_nres__inequalities_I5_J, axiom, (! [C:$tType,X4:C]: (((bot_bot @ (refine1665802226e_nres @ C)) != ((refine1687780735RETURN @ C) @ X4))))).
% 2.89/1.55 thf(fact_175_bot__nres__def, axiom, (! [A:$tType]: (((bot_bot @ (refine1665802226e_nres @ A)) = ((refine605929679le_RES @ A) @ (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_176_SUCCEED__rule, axiom, (! [A:$tType,Phi:(A > $o)]: ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ (bot_bot @ (refine1665802226e_nres @ A))) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi)))))).
% 2.89/1.55 thf(fact_177_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A6:(set @ A)]: ((A6 = (((insert @ A) @ ((the_elem @ A) @ A6)) @ (bot_bot @ (set @ A)))))))))).
% 2.89/1.55 thf(fact_178_is__singletonI_H, axiom, (! [A:$tType,A5:(set @ A)]: (((A5 != (bot_bot @ (set @ A))) => ((! [X3:A,Y6:A]: (((((member @ A) @ X3) @ A5) => ((((member @ A) @ Y6) @ A5) => (X3 = Y6))))) => ((is_singleton @ A) @ A5)))))).
% 2.89/1.55 thf(fact_179_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A6:(set @ A)]: ((? [X6:A]: ((A6 = (((insert @ A) @ X6) @ (bot_bot @ (set @ A)))))))))))).
% 2.89/1.55 thf(fact_180_is__singletonE, axiom, (! [A:$tType,A5:(set @ A)]: ((((is_singleton @ A) @ A5) => (~ ((! [X3:A]: ((A5 != (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))))))))).
% 2.89/1.55 thf(fact_181_subset__Compl__singleton, axiom, (! [A:$tType,A5:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ ((uminus_uminus @ (set @ A)) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))) = (~ ((((member @ A) @ B2) @ A5))))))).
% 2.89/1.55 thf(fact_182_strictD__simp, axiom, (! [A:$tType]: (((bot @ A) => (! [F:(A > A)]: (((((refine_strict @ A) @ A) @ F) => ((F @ (bot_bot @ A)) = (bot_bot @ A))))))))).
% 2.89/1.55 thf(fact_183_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.89/1.55 thf(fact_184_verit__minus__simplify_I4_J, axiom, (! [B:$tType]: (((group_add @ B) => (! [B2:B]: ((((uminus_uminus @ B) @ ((uminus_uminus @ B) @ B2)) = B2))))))).
% 2.89/1.55 thf(fact_185_ComplI, axiom, (! [A:$tType,C2:A,A5:(set @ A)]: (((~ ((((member @ A) @ C2) @ A5))) => (((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A5)))))).
% 2.89/1.55 thf(fact_186_Compl__iff, axiom, (! [A:$tType,C2:A,A5:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A5)) = (~ ((((member @ A) @ C2) @ A5))))))).
% 2.89/1.55 thf(fact_187_Compl__eq__Compl__iff, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A5) = ((uminus_uminus @ (set @ A)) @ B5)) = (A5 = B5))))).
% 2.89/1.55 thf(fact_188_Compl__anti__mono, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => (((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ B5)) @ ((uminus_uminus @ (set @ A)) @ A5)))))).
% 2.89/1.55 thf(fact_189_Compl__subset__Compl__iff, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A5)) @ ((uminus_uminus @ (set @ A)) @ B5)) = (((ord_less_eq @ (set @ A)) @ B5) @ A5))))).
% 2.89/1.55 thf(fact_190_ibind__strict_I1_J, axiom, (! [A:$tType,F:(product_unit > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ product_unit) @ A) @ (bot_bot @ (refine1665802226e_nres @ product_unit))) @ F) = (bot_bot @ (refine1665802226e_nres @ A)))))).
% 2.89/1.55 thf(fact_191_ComplD, axiom, (! [A:$tType,C2:A,A5:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A5)) => (~ ((((member @ A) @ C2) @ A5))))))).
% 2.89/1.55 thf(fact_192_double__complement, axiom, (! [A:$tType,A5:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A5)) = A5)))).
% 2.89/1.55 thf(fact_193_verit__negate__coefficient_I3_J, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A]: (((A2 = B2) => (((uminus_uminus @ A) @ A2) = ((uminus_uminus @ A) @ B2))))))))).
% 2.89/1.55 thf(fact_194_subset__Compl__self__eq, axiom, (! [A:$tType,A5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ ((uminus_uminus @ (set @ A)) @ A5)) = (A5 = (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_195_strictD, axiom, (! [A:$tType,B:$tType]: ((((bot @ B) & (bot @ A)) => (! [F:(A > B)]: (((((refine_strict @ A) @ B) @ F) => ((F @ (bot_bot @ A)) = (bot_bot @ B))))))))).
% 2.89/1.55 thf(fact_196_strictI, axiom, (! [A:$tType,B:$tType]: ((((bot @ B) & (bot @ A)) => (! [F:(B > A)]: ((((F @ (bot_bot @ B)) = (bot_bot @ A)) => (((refine_strict @ B) @ A) @ F)))))))).
% 2.89/1.55 thf(fact_197_strict__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ A) & (bot @ B)) => (((refine_strict @ A) @ B) = (^ [F3:(A > B)]: (((F3 @ (bot_bot @ A)) = (bot_bot @ B))))))))).
% 2.89/1.55 thf(fact_198_neg__le__iff__le, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.89/1.55 thf(fact_199_compl__le__compl__iff, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X4)) @ ((uminus_uminus @ A) @ Y3)) = (((ord_less_eq @ A) @ Y3) @ X4)))))))).
% 2.89/1.55 thf(fact_200_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X6:A]: ((((member @ A) @ X6) @ (bot_bot @ (set @ A))))))))).
% 2.89/1.55 thf(fact_201_le__imp__neg__le, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A2))))))))).
% 2.89/1.55 thf(fact_202_minus__le__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ A2)) @ B2) = (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B2)) @ A2)))))))).
% 2.89/1.55 thf(fact_203_le__minus__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ ((uminus_uminus @ A) @ B2)) = (((ord_less_eq @ A) @ B2) @ ((uminus_uminus @ A) @ A2))))))))).
% 2.89/1.55 thf(fact_204_compl__le__swap2, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y3:A,X4:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y3)) @ X4) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X4)) @ Y3)))))))).
% 2.89/1.55 thf(fact_205_compl__le__swap1, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y3:A,X4:A]: (((((ord_less_eq @ A) @ Y3) @ ((uminus_uminus @ A) @ X4)) => (((ord_less_eq @ A) @ X4) @ ((uminus_uminus @ A) @ Y3))))))))).
% 2.89/1.55 thf(fact_206_compl__mono, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y3)) @ ((uminus_uminus @ A) @ X4))))))))).
% 2.89/1.55 thf(fact_207_ASSUME__simps_I2_J, axiom, ((refine1946708059ASSUME @ $false) = (bot_bot @ (refine1665802226e_nres @ product_unit)))).
% 2.89/1.55 thf(fact_208_pw__flat__le__iff, axiom, (! [A:$tType,S:(refine1665802226e_nres @ A),S3:(refine1665802226e_nres @ A)]: ((((((partial_flat_ord @ (refine1665802226e_nres @ A)) @ (bot_bot @ (refine1665802226e_nres @ A))) @ S) @ S3) = ((? [X8:A]: ((((refine1315500908_inres @ A) @ S) @ X8))) => ((((refine1102455758nofail @ A) @ S) = ((refine1102455758nofail @ A) @ S3)) & (! [X6:A]: (((((refine1315500908_inres @ A) @ S) @ X6) = (((refine1315500908_inres @ A) @ S3) @ X6)))))))))).
% 2.89/1.55 thf(fact_209_pw__ASSUME_I2_J, axiom, (! [Phi:$o,X4:product_unit]: (((((refine1315500908_inres @ product_unit) @ (refine1946708059ASSUME @ Phi)) @ X4) = Phi)))).
% 2.89/1.55 thf(fact_210_pw__ASSUME_I1_J, axiom, (! [Phi:$o]: (((refine1102455758nofail @ product_unit) @ (refine1946708059ASSUME @ Phi))))).
% 2.89/1.55 thf(fact_211_flat__ord__compat_I1_J, axiom, (! [A:$tType]: (((comple187826305attice @ A) => (! [X4:A,Y3:A]: ((((((partial_flat_ord @ A) @ (bot_bot @ A)) @ X4) @ Y3) => (((ord_less_eq @ A) @ X4) @ Y3)))))))).
% 2.89/1.55 thf(fact_212_pw__flat__ge__iff, axiom, (! [A:$tType,S:(refine1665802226e_nres @ A),S3:(refine1665802226e_nres @ A)]: ((((((partial_flat_ord @ (refine1665802226e_nres @ A)) @ (top_top @ (refine1665802226e_nres @ A))) @ S) @ S3) = (((refine1102455758nofail @ A) @ S) => (((refine1102455758nofail @ A) @ S3) & (! [X6:A]: (((((refine1315500908_inres @ A) @ S) @ X6) = (((refine1315500908_inres @ A) @ S3) @ X6)))))))))).
% 2.89/1.55 thf(fact_213_top__apply, axiom, (! [C:$tType,D2:$tType]: (((top @ C) => ((top_top @ (D2 > C)) = (^ [X6:D2]: ((top_top @ C)))))))).
% 2.89/1.55 thf(fact_214_nres__order__simps_I4_J, axiom, (! [D2:$tType,M4:(refine1665802226e_nres @ D2)]: (((((ord_less_eq @ (refine1665802226e_nres @ D2)) @ (top_top @ (refine1665802226e_nres @ D2))) @ M4) = (M4 = (top_top @ (refine1665802226e_nres @ D2))))))).
% 2.89/1.55 thf(fact_215_nofail__simps_I1_J, axiom, (! [A:$tType]: ((~ (((refine1102455758nofail @ A) @ (top_top @ (refine1665802226e_nres @ A)))))))).
% 2.89/1.55 thf(fact_216_nres__simp__internals_I2_J, axiom, (! [B:$tType]: (((refine1767639642_FAILi @ B) = (top_top @ (refine1665802226e_nres @ B)))))).
% 2.89/1.55 thf(fact_217_inres__simps_I1_J, axiom, (! [A:$tType]: ((((refine1315500908_inres @ A) @ (top_top @ (refine1665802226e_nres @ A))) = (^ [Uu3:A]: ($true)))))).
% 2.89/1.55 thf(fact_218_bind__FAIL, axiom, (! [B:$tType,A:$tType,F:(B > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ B) @ A) @ (top_top @ (refine1665802226e_nres @ B))) @ F) = (top_top @ (refine1665802226e_nres @ A)))))).
% 2.89/1.55 thf(fact_219_compl__bot__eq, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (((uminus_uminus @ A) @ (bot_bot @ A)) = (top_top @ A)))))).
% 2.89/1.55 thf(fact_220_compl__top__eq, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (((uminus_uminus @ A) @ (top_top @ A)) = (bot_bot @ A)))))).
% 2.89/1.55 thf(fact_221_flat__ord__compat_I2_J, axiom, (! [A:$tType]: (((comple187826305attice @ A) => (! [X4:A,Y3:A]: ((((((partial_flat_ord @ A) @ (top_top @ A)) @ X4) @ Y3) => (((ord_less_eq @ A) @ Y3) @ X4)))))))).
% 2.89/1.55 thf(fact_222_top__greatest, axiom, (! [A:$tType]: (((order_top @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ (top_top @ A)))))))).
% 2.89/1.55 thf(fact_223_top_Oextremum__unique, axiom, (! [A:$tType]: (((order_top @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A2) = (A2 = (top_top @ A))))))))).
% 2.89/1.55 thf(fact_224_top_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_top @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A2) => (A2 = (top_top @ A))))))))).
% 2.89/1.55 thf(fact_225_meta__le__everything__if__top, axiom, (! [A:$tType]: (((order_top @ A) => (! [M:A,X4:A]: (((M = (top_top @ A)) => (((ord_less_eq @ A) @ X4) @ M)))))))).
% 2.89/1.55 thf(fact_226_nres__inequalities_I3_J, axiom, (! [C:$tType,X4:C]: (((top_top @ (refine1665802226e_nres @ C)) != ((refine1687780735RETURN @ C) @ X4))))).
% 2.89/1.55 thf(fact_227_top__nres__def, axiom, (! [A:$tType]: (((top_top @ (refine1665802226e_nres @ A)) = (refine1767639642_FAILi @ A))))).
% 2.89/1.55 thf(fact_228_not__nofail__iff, axiom, (! [A:$tType,S:(refine1665802226e_nres @ A)]: (((~ (((refine1102455758nofail @ A) @ S))) = (S = (top_top @ (refine1665802226e_nres @ A))))))).
% 2.89/1.55 thf(fact_229_nofail__def, axiom, (! [A:$tType]: (((refine1102455758nofail @ A) = (^ [S4:(refine1665802226e_nres @ A)]: ((S4 != (top_top @ (refine1665802226e_nres @ A))))))))).
% 2.89/1.55 thf(fact_230_intro__nofail_I2_J, axiom, (! [A:$tType,S:(refine1665802226e_nres @ A)]: ((((top_top @ (refine1665802226e_nres @ A)) != S) = ((refine1102455758nofail @ A) @ S))))).
% 2.89/1.55 thf(fact_231_nres__order__simps_I3_J, axiom, (! [C:$tType,M4:(refine1665802226e_nres @ C)]: ((((ord_less_eq @ (refine1665802226e_nres @ C)) @ M4) @ (top_top @ (refine1665802226e_nres @ C)))))).
% 2.89/1.55 thf(fact_232_nres__inequalities_I1_J, axiom, (! [A:$tType,X:(set @ A)]: (((top_top @ (refine1665802226e_nres @ A)) != ((refine605929679le_RES @ A) @ X))))).
% 2.89/1.55 thf(fact_233_nres__cases, axiom, (! [A:$tType,M4:(refine1665802226e_nres @ A)]: (((M4 != (top_top @ (refine1665802226e_nres @ A))) => (~ ((! [X9:(set @ A)]: ((M4 != ((refine605929679le_RES @ A) @ X9)))))))))).
% 2.89/1.55 thf(fact_234_ibind__strict_I2_J, axiom, (! [A:$tType,F:(product_unit > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ product_unit) @ A) @ (top_top @ (refine1665802226e_nres @ product_unit))) @ F) = (top_top @ (refine1665802226e_nres @ A)))))).
% 2.89/1.55 thf(fact_235_nres__inequalities_I4_J, axiom, (! [D2:$tType]: (((bot_bot @ (refine1665802226e_nres @ D2)) != (top_top @ (refine1665802226e_nres @ D2)))))).
% 2.89/1.55 thf(fact_236_nres__inequalities_I2_J, axiom, (! [B:$tType]: (((top_top @ (refine1665802226e_nres @ B)) != (bot_bot @ (refine1665802226e_nres @ B)))))).
% 2.89/1.55 thf(fact_237_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I2_J, axiom, (! [B:$tType,A:$tType,M4:(refine1665802226e_nres @ A),M5:(refine1665802226e_nres @ A),F:(A > (refine1665802226e_nres @ B)),F4:(A > (refine1665802226e_nres @ B))]: ((((((partial_flat_ord @ (refine1665802226e_nres @ A)) @ (top_top @ (refine1665802226e_nres @ A))) @ M4) @ M5) => ((! [X3:A]: (((((partial_flat_ord @ (refine1665802226e_nres @ B)) @ (top_top @ (refine1665802226e_nres @ B))) @ (F @ X3)) @ (F4 @ X3)))) => ((((partial_flat_ord @ (refine1665802226e_nres @ B)) @ (top_top @ (refine1665802226e_nres @ B))) @ ((((refine463715084e_bind @ A) @ B) @ M4) @ F)) @ ((((refine463715084e_bind @ A) @ B) @ M5) @ F4))))))).
% 2.89/1.55 thf(fact_238_flat__ord_OatLeastAtMost__singleton, axiom, (! [A:$tType,B2:A,A2:A]: ((((((set_atLeastAtMost @ A) @ ((partial_flat_ord @ A) @ B2)) @ A2) @ A2) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.89/1.55 thf(fact_239_flat__ord_OatLeastAtMost__singleton__iff, axiom, (! [A:$tType,Ba:A,A2:A,B2:A,C2:A]: (((((((set_atLeastAtMost @ A) @ ((partial_flat_ord @ A) @ Ba)) @ A2) @ B2) = (((insert @ A) @ C2) @ (bot_bot @ (set @ A)))) = ((A2 = B2) & (B2 = C2)))))).
% 2.89/1.55 thf(fact_240_flat__ord_OatLeastatMost__empty__iff, axiom, (! [A:$tType,Ba:A,A2:A,B2:A]: (((((((set_atLeastAtMost @ A) @ ((partial_flat_ord @ A) @ Ba)) @ A2) @ B2) = (bot_bot @ (set @ A))) = (~ (((((partial_flat_ord @ A) @ Ba) @ A2) @ B2))))))).
% 2.89/1.55 thf(fact_241_flat__ord_OatLeastatMost__empty__iff2, axiom, (! [A:$tType,Ba:A,A2:A,B2:A]: ((((bot_bot @ (set @ A)) = ((((set_atLeastAtMost @ A) @ ((partial_flat_ord @ A) @ Ba)) @ A2) @ B2)) = (~ (((((partial_flat_ord @ A) @ Ba) @ A2) @ B2))))))).
% 2.89/1.55 thf(fact_242_flat__ord_OatLeastatMost__subset__iff, axiom, (! [A:$tType,Ba:A,A2:A,B2:A,C2:A,D:A]: (((((ord_less_eq @ (set @ A)) @ ((((set_atLeastAtMost @ A) @ ((partial_flat_ord @ A) @ Ba)) @ A2) @ B2)) @ ((((set_atLeastAtMost @ A) @ ((partial_flat_ord @ A) @ Ba)) @ C2) @ D)) = ((~ (((((partial_flat_ord @ A) @ Ba) @ A2) @ B2))) | (((((partial_flat_ord @ A) @ Ba) @ C2) @ A2) & ((((partial_flat_ord @ A) @ Ba) @ B2) @ D))))))).
% 2.89/1.55 thf(fact_243_insert__UNIV, axiom, (! [A:$tType,X4:A]: (((((insert @ A) @ X4) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.89/1.55 thf(fact_244_subset__UNIV, axiom, (! [A:$tType,A5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A5) @ (top_top @ (set @ A)))))).
% 2.89/1.55 thf(fact_245_Compl__UNIV__eq, axiom, (! [A:$tType]: ((((uminus_uminus @ (set @ A)) @ (top_top @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.89/1.55 thf(fact_246_Compl__empty__eq, axiom, (! [A:$tType]: ((((uminus_uminus @ (set @ A)) @ (bot_bot @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.89/1.55 thf(fact_247_empty__not__UNIV, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) != (top_top @ (set @ A)))))).
% 2.89/1.55 thf(fact_248_flat__ord_OatLeastAtMost__singleton_H, axiom, (! [A:$tType,A2:A,B2:A,Ba:A]: (((A2 = B2) => (((((set_atLeastAtMost @ A) @ ((partial_flat_ord @ A) @ Ba)) @ A2) @ B2) = (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.89/1.55 thf(fact_249_flat__ord_OIcc__subset__Iic__iff, axiom, (! [A:$tType,B2:A,L:A,H:A,H2:A]: (((((ord_less_eq @ (set @ A)) @ ((((set_atLeastAtMost @ A) @ ((partial_flat_ord @ A) @ B2)) @ L) @ H)) @ (((set_atMost @ A) @ ((partial_flat_ord @ A) @ B2)) @ H2)) = ((~ (((((partial_flat_ord @ A) @ B2) @ L) @ H))) | ((((partial_flat_ord @ A) @ B2) @ H) @ H2)))))).
% 2.89/1.55 thf(fact_250_flat__ord_OIcc__subset__Ici__iff, axiom, (! [A:$tType,B2:A,L:A,H:A,L2:A]: (((((ord_less_eq @ (set @ A)) @ ((((set_atLeastAtMost @ A) @ ((partial_flat_ord @ A) @ B2)) @ L) @ H)) @ (((set_atLeast @ A) @ ((partial_flat_ord @ A) @ B2)) @ L2)) = ((~ (((((partial_flat_ord @ A) @ B2) @ L) @ H))) | ((((partial_flat_ord @ A) @ B2) @ L2) @ L)))))).
% 2.89/1.55 thf(fact_251_UNIV__I, axiom, (! [A:$tType,X4:A]: ((((member @ A) @ X4) @ (top_top @ (set @ A)))))).
% 2.89/1.55 thf(fact_252_relprop__UNIV__orient, axiom, (! [A:$tType,R:(set @ A)]: (((R = (top_top @ (set @ A))) => ((top_top @ (set @ A)) = R))))).
% 2.89/1.55 thf(fact_253_eq__UNIV__iff, axiom, (! [A:$tType,S:(set @ A)]: (((S = (top_top @ (set @ A))) = (! [X6:A]: ((((member @ A) @ X6) @ S))))))).
% 2.89/1.55 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice, axiom, (! [A7:$tType,A8:$tType]: (((comple187826305attice @ A8) => (comple187826305attice @ (A7 > A8)))))).
% 2.89/1.55 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A7:$tType,A8:$tType]: (((boolean_algebra @ A8) => (boolean_algebra @ (A7 > A8)))))).
% 2.89/1.55 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A7:$tType,A8:$tType]: (((order_top @ A8) => (order_top @ (A7 > A8)))))).
% 2.89/1.55 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A7:$tType,A8:$tType]: (((order_bot @ A8) => (order_bot @ (A7 > A8)))))).
% 2.89/1.55 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 2.89/1.55 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 2.89/1.55 thf(tcon_fun___Orderings_Otop, axiom, (! [A7:$tType,A8:$tType]: (((top @ A8) => (top @ (A7 > A8)))))).
% 2.89/1.55 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.89/1.55 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A8:$tType]: (((bot @ A8) => (bot @ (A7 > A8)))))).
% 2.89/1.55 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1, axiom, (! [A7:$tType]: ((comple187826305attice @ (set @ A7))))).
% 2.89/1.55 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_2, axiom, (! [A7:$tType]: ((boolean_algebra @ (set @ A7))))).
% 2.89/1.55 thf(tcon_Set_Oset___Orderings_Oorder__top_3, axiom, (! [A7:$tType]: ((order_top @ (set @ A7))))).
% 2.89/1.55 thf(tcon_Set_Oset___Orderings_Oorder__bot_4, axiom, (! [A7:$tType]: ((order_bot @ (set @ A7))))).
% 2.89/1.55 thf(tcon_Set_Oset___Orderings_Opreorder_5, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 2.89/1.55 thf(tcon_Set_Oset___Orderings_Oorder_6, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 2.89/1.55 thf(tcon_Set_Oset___Orderings_Otop_7, axiom, (! [A7:$tType]: ((top @ (set @ A7))))).
% 2.89/1.55 thf(tcon_Set_Oset___Orderings_Oord_8, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.89/1.55 thf(tcon_Set_Oset___Orderings_Obot_9, axiom, (! [A7:$tType]: ((bot @ (set @ A7))))).
% 2.89/1.55 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_10, axiom, (comple187826305attice @ $o)).
% 2.89/1.55 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_11, axiom, (boolean_algebra @ $o)).
% 2.89/1.55 thf(tcon_HOL_Obool___Orderings_Oorder__top_12, axiom, (order_top @ $o)).
% 2.89/1.55 thf(tcon_HOL_Obool___Orderings_Oorder__bot_13, axiom, (order_bot @ $o)).
% 2.89/1.55 thf(tcon_HOL_Obool___Orderings_Opreorder_14, axiom, (preorder @ $o)).
% 2.89/1.55 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.89/1.55 thf(tcon_HOL_Obool___Orderings_Oorder_15, axiom, (order @ $o)).
% 2.89/1.55 thf(tcon_HOL_Obool___Orderings_Otop_16, axiom, (top @ $o)).
% 2.89/1.55 thf(tcon_HOL_Obool___Orderings_Oord_17, axiom, (ord @ $o)).
% 2.89/1.55 thf(tcon_HOL_Obool___Orderings_Obot_18, axiom, (bot @ $o)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Complete__Lattices_Ocomplete__lattice_19, axiom, (comple187826305attice @ product_unit)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Lattices_Oboolean__algebra_20, axiom, (boolean_algebra @ product_unit)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Orderings_Oorder__top_21, axiom, (order_top @ product_unit)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_22, axiom, (order_bot @ product_unit)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_23, axiom, (preorder @ product_unit)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_24, axiom, (linorder @ product_unit)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Orderings_Oorder_25, axiom, (order @ product_unit)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Orderings_Otop_26, axiom, (top @ product_unit)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Orderings_Oord_27, axiom, (ord @ product_unit)).
% 2.89/1.55 thf(tcon_Product__Type_Ounit___Orderings_Obot_28, axiom, (bot @ product_unit)).
% 2.89/1.55 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Complete__Lattices_Ocomplete__lattice_29, axiom, (! [A7:$tType]: ((comple187826305attice @ (refine1665802226e_nres @ A7))))).
% 2.89/1.55 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__top_30, axiom, (! [A7:$tType]: ((order_top @ (refine1665802226e_nres @ A7))))).
% 2.89/1.55 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_31, axiom, (! [A7:$tType]: ((order_bot @ (refine1665802226e_nres @ A7))))).
% 2.89/1.55 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_32, axiom, (! [A7:$tType]: ((preorder @ (refine1665802226e_nres @ A7))))).
% 2.89/1.55 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_33, axiom, (! [A7:$tType]: ((order @ (refine1665802226e_nres @ A7))))).
% 2.89/1.55 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_34, axiom, (! [A7:$tType]: ((top @ (refine1665802226e_nres @ A7))))).
% 2.89/1.55 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_35, axiom, (! [A7:$tType]: ((ord @ (refine1665802226e_nres @ A7))))).
% 2.89/1.55 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_36, axiom, (! [A7:$tType]: ((bot @ (refine1665802226e_nres @ A7))))).
% 2.89/1.55 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.89/1.55 thf(help_If_2_1_T, axiom, (! [A:$tType,X4:A,Y3:A]: ((((((if @ A) @ $false) @ X4) @ Y3) = Y3)))).
% 2.89/1.55 thf(help_If_1_1_T, axiom, (! [A:$tType,X4:A,Y3:A]: ((((((if @ A) @ $true) @ X4) @ Y3) = X4)))).
% 2.89/1.55 thf(conj_0, hypothesis, (b => (((ord_less_eq @ (refine1665802226e_nres @ a)) @ s1) @ ((refine605929679le_RES @ a) @ ((collect @ a) @ phi))))).
% 2.89/1.55 thf(conj_1, hypothesis, ((~ (b)) => (((ord_less_eq @ (refine1665802226e_nres @ a)) @ s2) @ ((refine605929679le_RES @ a) @ ((collect @ a) @ phi))))).
% 2.89/1.55 thf(conj_2, conjecture, (((ord_less_eq @ (refine1665802226e_nres @ a)) @ ((((if @ (refine1665802226e_nres @ a)) @ b) @ s1) @ s2)) @ ((refine605929679le_RES @ a) @ ((collect @ a) @ phi)))).
% 2.89/1.55 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.eee0ELY9Y3/DTF2DTF22115.p
% 2.89/1.55 ------------------------
% 2.89/1.58 ---- Cleaned THF ---
% 2.89/1.58 thf(ty_t_Refine__Basic__Mirabelle__tqojlsrkwy_Onres,type,
% 2.89/1.58 refine1665802226e_nres: $tType > $tType ).
% 2.89/1.58
% 2.89/1.58 thf(ty_t_Product__Type_Ounit,type,
% 2.89/1.58 product_unit: $tType ).
% 2.89/1.58
% 2.89/1.58 thf(ty_t_Set_Oset,type,
% 2.89/1.58 set: $tType > $tType ).
% 2.89/1.58
% 2.89/1.58 thf(ty_tf_a,type,
% 2.89/1.58 a: $tType ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_HOL_Otype,type,
% 2.89/1.58 type:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Orderings_Obot,type,
% 2.89/1.58 bot:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Orderings_Oord,type,
% 2.89/1.58 ord:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Orderings_Otop,type,
% 2.89/1.58 top:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Orderings_Oorder,type,
% 2.89/1.58 order:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Groups_Ogroup__add,type,
% 2.89/1.58 group_add:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Orderings_Olinorder,type,
% 2.89/1.58 linorder:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Orderings_Opreorder,type,
% 2.89/1.58 preorder:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.89/1.58 order_bot:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Orderings_Oorder__top,type,
% 2.89/1.58 order_top:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 2.89/1.58 boolean_algebra:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.89/1.58 ordered_ab_group_add:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 2.89/1.58 comple187826305attice:
% 2.89/1.58 !>[A: $tType] : $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 2.89/1.58 uminus_uminus:
% 2.89/1.58 !>[A: $tType] : ( A > A ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_If,type,
% 2.89/1.58 if:
% 2.89/1.58 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.89/1.58 bot_bot:
% 2.89/1.58 !>[A: $tType] : A ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.89/1.58 ord_less_eq:
% 2.89/1.58 !>[A: $tType] : ( A > A > $o ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 2.89/1.58 order_Greatest:
% 2.89/1.58 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.89/1.58 top_top:
% 2.89/1.58 !>[A: $tType] : A ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Partial__Function_Oflat__ord,type,
% 2.89/1.58 partial_flat_ord:
% 2.89/1.58 !>[A: $tType] : ( A > A > A > $o ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_OASSUME,type,
% 2.89/1.58 refine1946708059ASSUME: $o > ( refine1665802226e_nres @ product_unit ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_ORETURN,type,
% 2.89/1.58 refine1687780735RETURN:
% 2.89/1.58 !>[A: $tType] : ( A > ( refine1665802226e_nres @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Obind,type,
% 2.89/1.58 refine463715084e_bind:
% 2.89/1.58 !>[B: $tType,A: $tType] : ( ( refine1665802226e_nres @ B ) > ( B > ( refine1665802226e_nres @ A ) ) > ( refine1665802226e_nres @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Oinres,type,
% 2.89/1.58 refine1315500908_inres:
% 2.89/1.58 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > A > $o ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onf__inres,type,
% 2.89/1.58 refine406925620_inres:
% 2.89/1.58 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > A > $o ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onofail,type,
% 2.89/1.58 refine1102455758nofail:
% 2.89/1.58 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > $o ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_OFAILi,type,
% 2.89/1.58 refine1767639642_FAILi:
% 2.89/1.58 !>[A: $tType] : ( refine1665802226e_nres @ A ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_ORES,type,
% 2.89/1.58 refine605929679le_RES:
% 2.89/1.58 !>[A: $tType] : ( ( set @ A ) > ( refine1665802226e_nres @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_Ocase__nres,type,
% 2.89/1.58 refine60818195e_nres:
% 2.89/1.58 !>[B: $tType,A: $tType] : ( B > ( ( set @ A ) > B ) > ( refine1665802226e_nres @ A ) > B ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_Orec__nres,type,
% 2.89/1.58 refine1442219249c_nres:
% 2.89/1.58 !>[C: $tType,A: $tType] : ( C > ( ( set @ A ) > C ) > ( refine1665802226e_nres @ A ) > C ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Othe__RES,type,
% 2.89/1.58 refine1672542526he_RES:
% 2.89/1.58 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > ( set @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Refine__Misc_Ostrict,type,
% 2.89/1.58 refine_strict:
% 2.89/1.58 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Set_OCollect,type,
% 2.89/1.58 collect:
% 2.89/1.58 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Set_Oinsert,type,
% 2.89/1.58 insert:
% 2.89/1.58 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Set_Ois__empty,type,
% 2.89/1.58 is_empty:
% 2.89/1.58 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Set_Ois__singleton,type,
% 2.89/1.58 is_singleton:
% 2.89/1.58 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Set_Othe__elem,type,
% 2.89/1.58 the_elem:
% 2.89/1.58 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Set__Interval_Oord_OatLeast,type,
% 2.89/1.58 set_atLeast:
% 2.89/1.58 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Set__Interval_Oord_OatLeastAtMost,type,
% 2.89/1.58 set_atLeastAtMost:
% 2.89/1.58 !>[A: $tType] : ( ( A > A > $o ) > A > A > ( set @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_Set__Interval_Oord_OatMost,type,
% 2.89/1.58 set_atMost:
% 2.89/1.58 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_c_member,type,
% 2.89/1.58 member:
% 2.89/1.58 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.89/1.58
% 2.89/1.58 thf(sy_v_S1,type,
% 2.89/1.58 s1: refine1665802226e_nres @ a ).
% 2.89/1.58
% 2.89/1.58 thf(sy_v_S2,type,
% 2.89/1.58 s2: refine1665802226e_nres @ a ).
% 2.89/1.58
% 2.89/1.58 thf(sy_v__092_060Phi_062,type,
% 2.89/1.58 phi: a > $o ).
% 2.89/1.58
% 2.89/1.58 thf(sy_v_b,type,
% 2.89/1.58 b: $o ).
% 2.89/1.58
% 2.89/1.58 thf(fact_0_nres__more__simps_I4_J,axiom,
% 2.89/1.58 ! [A: $tType,X: set @ A,Y: set @ A] :
% 2.89/1.58 ( ( ( refine605929679le_RES @ A @ X )
% 2.89/1.58 = ( refine605929679le_RES @ A @ Y ) )
% 2.89/1.58 = ( X = Y ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_1_nres_Oinject,axiom,
% 2.89/1.58 ! [A: $tType,X2: set @ A,Y2: set @ A] :
% 2.89/1.58 ( ( ( refine605929679le_RES @ A @ X2 )
% 2.89/1.58 = ( refine605929679le_RES @ A @ Y2 ) )
% 2.89/1.58 = ( X2 = Y2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_2_RES__rule,axiom,
% 2.89/1.58 ! [A: $tType,S: set @ A,Phi: A > $o] :
% 2.89/1.58 ( ! [X3: A] :
% 2.89/1.58 ( ( member @ A @ X3 @ S )
% 2.89/1.58 => ( Phi @ X3 ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ S ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_3_SPEC__rule,axiom,
% 2.89/1.58 ! [A: $tType,Phi: A > $o,Phi2: A > $o] :
% 2.89/1.58 ( ! [X3: A] :
% 2.89/1.58 ( ( Phi @ X3 )
% 2.89/1.58 => ( Phi2 @ X3 ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_4_SPEC__trans,axiom,
% 2.89/1.58 ! [A: $tType,X4: refine1665802226e_nres @ A,Y3: refine1665802226e_nres @ A,Postcond: A > $o] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Y3 )
% 2.89/1.58 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ Y3 @ ( refine605929679le_RES @ A @ ( collect @ A @ Postcond ) ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ ( refine605929679le_RES @ A @ ( collect @ A @ Postcond ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_5_SPEC__cons__rule,axiom,
% 2.89/1.58 ! [A: $tType,M: refine1665802226e_nres @ A,Phi: A > $o,Psi: A > $o] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 2.89/1.58 => ( ! [X3: A] :
% 2.89/1.58 ( ( Phi @ X3 )
% 2.89/1.58 => ( Psi @ X3 ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_6_nf__inres__RES,axiom,
% 2.89/1.58 ! [A: $tType,X: set @ A,X4: A] :
% 2.89/1.58 ( ( refine406925620_inres @ A @ ( refine605929679le_RES @ A @ X ) @ X4 )
% 2.89/1.58 = ( member @ A @ X4 @ X ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_7_nf__inres__SPEC,axiom,
% 2.89/1.58 ! [A: $tType,Phi: A > $o,X4: A] :
% 2.89/1.58 ( ( refine406925620_inres @ A @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ X4 )
% 2.89/1.58 = ( Phi @ X4 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_8_order__mono__setup_Orefl,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( preorder @ A )
% 2.89/1.58 => ! [X4: A] : ( ord_less_eq @ A @ X4 @ X4 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_9_the__RES_Osimps,axiom,
% 2.89/1.58 ! [A: $tType,X: set @ A] :
% 2.89/1.58 ( ( refine1672542526he_RES @ A @ ( refine605929679le_RES @ A @ X ) )
% 2.89/1.58 = X ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_10_nres__order__simps_I21_J,axiom,
% 2.89/1.58 ! [X5: $tType,X4: X5,Y: set @ X5] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ X5 ) @ ( refine1687780735RETURN @ X5 @ X4 ) @ ( refine605929679le_RES @ X5 @ Y ) )
% 2.89/1.58 = ( member @ X5 @ X4 @ Y ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_11_nres_Osimps_I7_J,axiom,
% 2.89/1.58 ! [C: $tType,A: $tType,F1: C,F2: ( set @ A ) > C,X2: set @ A] :
% 2.89/1.58 ( ( refine1442219249c_nres @ C @ A @ F1 @ F2 @ ( refine605929679le_RES @ A @ X2 ) )
% 2.89/1.58 = ( F2 @ X2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_12_le__funD,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType] :
% 2.89/1.58 ( ( ord @ B )
% 2.89/1.58 => ! [F: A > B,G: A > B,X4: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.89/1.58 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_13_le__funE,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType] :
% 2.89/1.58 ( ( ord @ B )
% 2.89/1.58 => ! [F: A > B,G: A > B,X4: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.89/1.58 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_14_le__funI,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType] :
% 2.89/1.58 ( ( ord @ B )
% 2.89/1.58 => ! [F: A > B,G: A > B] :
% 2.89/1.58 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 2.89/1.58 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_15_Refine__Misc_Oif__mono,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ord @ A )
% 2.89/1.58 => ! [B2: $o,M1: A,M12: A,M2: A,M22: A] :
% 2.89/1.58 ( ( B2
% 2.89/1.58 => ( ord_less_eq @ A @ M1 @ M12 ) )
% 2.89/1.58 => ( ( ~ B2
% 2.89/1.58 => ( ord_less_eq @ A @ M2 @ M22 ) )
% 2.89/1.58 => ( ord_less_eq @ A @ ( if @ A @ B2 @ M1 @ M2 ) @ ( if @ A @ B2 @ M12 @ M22 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_16_le__fun__def,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType] :
% 2.89/1.58 ( ( ord @ B )
% 2.89/1.58 => ( ( ord_less_eq @ ( A > B ) )
% 2.89/1.58 = ( ^ [F3: A > B,G2: A > B] :
% 2.89/1.58 ! [X6: A] : ( ord_less_eq @ B @ ( F3 @ X6 ) @ ( G2 @ X6 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_17_nres__more__simps_I6_J,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,Y3: A] :
% 2.89/1.58 ( ( ( refine1687780735RETURN @ A @ X4 )
% 2.89/1.58 = ( refine1687780735RETURN @ A @ Y3 ) )
% 2.89/1.58 = ( X4 = Y3 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_18_nres__order__simps_I20_J,axiom,
% 2.89/1.58 ! [W: $tType,X4: W,Y3: W] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ W ) @ ( refine1687780735RETURN @ W @ X4 ) @ ( refine1687780735RETURN @ W @ Y3 ) )
% 2.89/1.58 = ( X4 = Y3 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_19_less__eq__nres_Osimps_I2_J,axiom,
% 2.89/1.58 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ A2 ) @ ( refine605929679le_RES @ A @ B2 ) )
% 2.89/1.58 = ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_20_nres__order__simps_I5_J,axiom,
% 2.89/1.58 ! [E: $tType,X: set @ E,Y: set @ E] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ E ) @ ( refine605929679le_RES @ E @ X ) @ ( refine605929679le_RES @ E @ Y ) )
% 2.89/1.58 = ( ord_less_eq @ ( set @ E ) @ X @ Y ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_21_RETURN__to__SPEC__rule,axiom,
% 2.89/1.58 ! [A: $tType,M: refine1665802226e_nres @ A,V: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M
% 2.89/1.58 @ ( refine605929679le_RES @ A
% 2.89/1.58 @ ( collect @ A
% 2.89/1.58 @ ( ^ [Y4: A,Z: A] : ( Y4 = Z )
% 2.89/1.58 @ V ) ) ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine1687780735RETURN @ A @ V ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_22_RETURN__rule,axiom,
% 2.89/1.58 ! [A: $tType,Phi: A > $o,X4: A] :
% 2.89/1.58 ( ( Phi @ X4 )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_23_order__mono__setup_Omono__let,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType] :
% 2.89/1.58 ( ( preorder @ A )
% 2.89/1.58 => ! [F: B > A,F4: B > A,X4: B] :
% 2.89/1.58 ( ! [X3: B] : ( ord_less_eq @ A @ ( F @ X3 ) @ ( F4 @ X3 ) )
% 2.89/1.58 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F4 @ X4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_24_order__mono__setup_Omono__if,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( preorder @ A )
% 2.89/1.58 => ! [T: A,T2: A,E2: A,E3: A,B2: $o] :
% 2.89/1.58 ( ( ord_less_eq @ A @ T @ T2 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ E2 @ E3 )
% 2.89/1.58 => ( ord_less_eq @ A @ ( if @ A @ B2 @ T @ E2 ) @ ( if @ A @ B2 @ T2 @ E3 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_25_dual__order_Oantisym,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ! [B2: A,A2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.89/1.58 => ( A2 = B2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_26_dual__order_Oeq__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.89/1.58 = ( ^ [A3: A,B3: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ B3 @ A3 )
% 2.89/1.58 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_27_dual__order_Otrans,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ! [B2: A,A2: A,C2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 2.89/1.58 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_28_linorder__wlog,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( linorder @ A )
% 2.89/1.58 => ! [P: A > A > $o,A2: A,B2: A] :
% 2.89/1.58 ( ! [A4: A,B4: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A4 @ B4 )
% 2.89/1.58 => ( P @ A4 @ B4 ) )
% 2.89/1.58 => ( ! [A4: A,B4: A] :
% 2.89/1.58 ( ( P @ B4 @ A4 )
% 2.89/1.58 => ( P @ A4 @ B4 ) )
% 2.89/1.58 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_29_dual__order_Orefl,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_30_order__trans,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( preorder @ A )
% 2.89/1.58 => ! [X4: A,Y3: A,Z2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 2.89/1.58 => ( ord_less_eq @ A @ X4 @ Z2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_31_order__class_Oorder_Oantisym,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ! [A2: A,B2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.89/1.58 => ( A2 = B2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_32_ord__le__eq__trans,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ord @ A )
% 2.89/1.58 => ! [A2: A,B2: A,C2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.89/1.58 => ( ( B2 = C2 )
% 2.89/1.58 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_33_ord__eq__le__trans,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ord @ A )
% 2.89/1.58 => ! [A2: A,B2: A,C2: A] :
% 2.89/1.58 ( ( A2 = B2 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.89/1.58 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_34_order__class_Oorder_Oeq__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.89/1.58 = ( ^ [A3: A,B3: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.89/1.58 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_35_antisym__conv,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ! [Y3: A,X4: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ Y3 @ X4 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ X4 @ Y3 )
% 2.89/1.58 = ( X4 = Y3 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_36_le__cases3,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( linorder @ A )
% 2.89/1.58 => ! [X4: A,Y3: A,Z2: A] :
% 2.89/1.58 ( ( ( ord_less_eq @ A @ X4 @ Y3 )
% 2.89/1.58 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 2.89/1.58 => ( ( ( ord_less_eq @ A @ Y3 @ X4 )
% 2.89/1.58 => ~ ( ord_less_eq @ A @ X4 @ Z2 ) )
% 2.89/1.58 => ( ( ( ord_less_eq @ A @ X4 @ Z2 )
% 2.89/1.58 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 2.89/1.58 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 2.89/1.58 => ~ ( ord_less_eq @ A @ Y3 @ X4 ) )
% 2.89/1.58 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 2.89/1.58 => ~ ( ord_less_eq @ A @ Z2 @ X4 ) )
% 2.89/1.58 => ~ ( ( ord_less_eq @ A @ Z2 @ X4 )
% 2.89/1.58 => ~ ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_37_order_Otrans,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ! [A2: A,B2: A,C2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.89/1.58 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_38_le__cases,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( linorder @ A )
% 2.89/1.58 => ! [X4: A,Y3: A] :
% 2.89/1.58 ( ~ ( ord_less_eq @ A @ X4 @ Y3 )
% 2.89/1.58 => ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_39_eq__refl,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( preorder @ A )
% 2.89/1.58 => ! [X4: A,Y3: A] :
% 2.89/1.58 ( ( X4 = Y3 )
% 2.89/1.58 => ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_40_linear,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( linorder @ A )
% 2.89/1.58 => ! [X4: A,Y3: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 2.89/1.58 | ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_41_antisym,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ! [X4: A,Y3: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ Y3 @ X4 )
% 2.89/1.58 => ( X4 = Y3 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_42_eq__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.89/1.58 = ( ^ [X6: A,Y5: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ X6 @ Y5 )
% 2.89/1.58 & ( ord_less_eq @ A @ Y5 @ X6 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_43_ord__le__eq__subst,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType] :
% 2.89/1.58 ( ( ( ord @ B )
% 2.89/1.58 & ( ord @ A ) )
% 2.89/1.58 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.89/1.58 => ( ( ( F @ B2 )
% 2.89/1.58 = C2 )
% 2.89/1.58 => ( ! [X3: A,Y6: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ X3 @ Y6 )
% 2.89/1.58 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 2.89/1.58 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_44_mem__Collect__eq,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,P: A > $o] :
% 2.89/1.58 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.89/1.58 = ( P @ A2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_45_Collect__mem__eq,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ( collect @ A
% 2.89/1.58 @ ^ [X6: A] : ( member @ A @ X6 @ A5 ) )
% 2.89/1.58 = A5 ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_46_Collect__cong,axiom,
% 2.89/1.58 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.89/1.58 ( ! [X3: A] :
% 2.89/1.58 ( ( P @ X3 )
% 2.89/1.58 = ( Q @ X3 ) )
% 2.89/1.58 => ( ( collect @ A @ P )
% 2.89/1.58 = ( collect @ A @ Q ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_47_ext,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.89/1.58 ( ! [X3: A] :
% 2.89/1.58 ( ( F @ X3 )
% 2.89/1.58 = ( G @ X3 ) )
% 2.89/1.58 => ( F = G ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_48_ord__eq__le__subst,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType] :
% 2.89/1.58 ( ( ( ord @ B )
% 2.89/1.58 & ( ord @ A ) )
% 2.89/1.58 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 2.89/1.58 ( ( A2
% 2.89/1.58 = ( F @ B2 ) )
% 2.89/1.58 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.89/1.58 => ( ! [X3: B,Y6: B] :
% 2.89/1.58 ( ( ord_less_eq @ B @ X3 @ Y6 )
% 2.89/1.58 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 2.89/1.58 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_49_order__subst2,axiom,
% 2.89/1.58 ! [A: $tType,C: $tType] :
% 2.89/1.58 ( ( ( order @ C )
% 2.89/1.58 & ( order @ A ) )
% 2.89/1.58 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.89/1.58 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 2.89/1.58 => ( ! [X3: A,Y6: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ X3 @ Y6 )
% 2.89/1.58 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 2.89/1.58 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_50_order__subst1,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType] :
% 2.89/1.58 ( ( ( order @ B )
% 2.89/1.58 & ( order @ A ) )
% 2.89/1.58 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 2.89/1.58 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.89/1.58 => ( ! [X3: B,Y6: B] :
% 2.89/1.58 ( ( ord_less_eq @ B @ X3 @ Y6 )
% 2.89/1.58 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 2.89/1.58 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_51_the__RES__inv,axiom,
% 2.89/1.58 ! [A: $tType,M: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( refine1102455758nofail @ A @ M )
% 2.89/1.58 => ( ( refine605929679le_RES @ A @ ( refine1672542526he_RES @ A @ M ) )
% 2.89/1.58 = M ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_52_Greatest__equality,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ! [P: A > $o,X4: A] :
% 2.89/1.58 ( ( P @ X4 )
% 2.89/1.58 => ( ! [Y6: A] :
% 2.89/1.58 ( ( P @ Y6 )
% 2.89/1.58 => ( ord_less_eq @ A @ Y6 @ X4 ) )
% 2.89/1.58 => ( ( order_Greatest @ A @ P )
% 2.89/1.58 = X4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_53_GreatestI2__order,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order @ A )
% 2.89/1.58 => ! [P: A > $o,X4: A,Q: A > $o] :
% 2.89/1.58 ( ( P @ X4 )
% 2.89/1.58 => ( ! [Y6: A] :
% 2.89/1.58 ( ( P @ Y6 )
% 2.89/1.58 => ( ord_less_eq @ A @ Y6 @ X4 ) )
% 2.89/1.58 => ( ! [X3: A] :
% 2.89/1.58 ( ( P @ X3 )
% 2.89/1.58 => ( ! [Y7: A] :
% 2.89/1.58 ( ( P @ Y7 )
% 2.89/1.58 => ( ord_less_eq @ A @ Y7 @ X3 ) )
% 2.89/1.58 => ( Q @ X3 ) ) )
% 2.89/1.58 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_54_transfer_Otransfer__Let,axiom,
% 2.89/1.58 ! [C: $tType,A: $tType,B: $tType] :
% 2.89/1.58 ( ( comple187826305attice @ A )
% 2.89/1.58 => ! [Alpha: C > A,F: B > C,F5: B > A,X4: B] :
% 2.89/1.58 ( ! [X3: B] : ( ord_less_eq @ A @ ( Alpha @ ( F @ X3 ) ) @ ( F5 @ X3 ) )
% 2.89/1.58 => ( ord_less_eq @ A @ ( Alpha @ ( F @ X4 ) ) @ ( F5 @ X4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_55_transfer_Otransfer__if,axiom,
% 2.89/1.58 ! [C: $tType,A: $tType] :
% 2.89/1.58 ( ( comple187826305attice @ A )
% 2.89/1.58 => ! [B2: $o,Alpha: C > A,S1: C,S12: A,S2: C,S22: A] :
% 2.89/1.58 ( ( B2
% 2.89/1.58 => ( ord_less_eq @ A @ ( Alpha @ S1 ) @ S12 ) )
% 2.89/1.58 => ( ( ~ B2
% 2.89/1.58 => ( ord_less_eq @ A @ ( Alpha @ S2 ) @ S22 ) )
% 2.89/1.58 => ( ord_less_eq @ A @ ( Alpha @ ( if @ C @ B2 @ S1 @ S2 ) ) @ ( if @ A @ B2 @ S12 @ S22 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_56_le__rel__bool__arg__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ord @ A )
% 2.89/1.58 => ( ( ord_less_eq @ ( $o > A ) )
% 2.89/1.58 = ( ^ [X7: $o > A,Y8: $o > A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ ( X7 @ $false ) @ ( Y8 @ $false ) )
% 2.89/1.58 & ( ord_less_eq @ A @ ( X7 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_57_verit__la__disequality,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( linorder @ A )
% 2.89/1.58 => ! [A2: A,B2: A] :
% 2.89/1.58 ( ( A2 = B2 )
% 2.89/1.58 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 2.89/1.58 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_58_ord__eq__le__eq__trans,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ord @ A )
% 2.89/1.58 => ! [A2: A,B2: A,C2: A,D: A] :
% 2.89/1.58 ( ( A2 = B2 )
% 2.89/1.58 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.89/1.58 => ( ( C2 = D )
% 2.89/1.58 => ( ord_less_eq @ A @ A2 @ D ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_59_bind__cong,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType,M: refine1665802226e_nres @ A,M3: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 2.89/1.58 ( ( M = M3 )
% 2.89/1.58 => ( ! [X3: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M3 )
% 2.89/1.58 => ( ( F @ X3 )
% 2.89/1.58 = ( F4 @ X3 ) ) )
% 2.89/1.58 => ( ( refine463715084e_bind @ A @ B @ M @ F )
% 2.89/1.58 = ( refine463715084e_bind @ A @ B @ M3 @ F4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_60_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType,M4: refine1665802226e_nres @ A,M5: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M5 )
% 2.89/1.58 => ( ! [X3: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M4 )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ ( F4 @ X3 ) ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M4 @ F ) @ ( refine463715084e_bind @ A @ B @ M5 @ F4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_61_nofail__simps_I2_J,axiom,
% 2.89/1.58 ! [B: $tType,X: set @ B] : ( refine1102455758nofail @ B @ ( refine605929679le_RES @ B @ X ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_62_nofail__simps_I3_J,axiom,
% 2.89/1.58 ! [C: $tType,X4: C] : ( refine1102455758nofail @ C @ ( refine1687780735RETURN @ C @ X4 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_63_nres__monad2,axiom,
% 2.89/1.58 ! [A: $tType,M4: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( refine463715084e_bind @ A @ A @ M4 @ ( refine1687780735RETURN @ A ) )
% 2.89/1.58 = M4 ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_64_nres__monad1,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType,X4: B,F: B > ( refine1665802226e_nres @ A )] :
% 2.89/1.58 ( ( refine463715084e_bind @ B @ A @ ( refine1687780735RETURN @ B @ X4 ) @ F )
% 2.89/1.58 = ( F @ X4 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_65_subset__Collect__conv,axiom,
% 2.89/1.58 ! [A: $tType,S: set @ A,P: A > $o] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 2.89/1.58 = ( ! [X6: A] :
% 2.89/1.58 ( ( member @ A @ X6 @ S )
% 2.89/1.58 => ( P @ X6 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_66_nofail__antimono__fun,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType,F: A > ( refine1665802226e_nres @ B ),G: A > ( refine1665802226e_nres @ B ),X4: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( A > ( refine1665802226e_nres @ B ) ) @ F @ G )
% 2.89/1.58 => ( ( refine1102455758nofail @ B @ ( G @ X4 ) )
% 2.89/1.58 => ( refine1102455758nofail @ B @ ( F @ X4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_67_nofail__RES__conv,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( refine1102455758nofail @ A )
% 2.89/1.58 = ( ^ [M6: refine1665802226e_nres @ A] :
% 2.89/1.58 ? [M7: set @ A] :
% 2.89/1.58 ( M6
% 2.89/1.58 = ( refine605929679le_RES @ A @ M7 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_68_pwD1,axiom,
% 2.89/1.58 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S3 )
% 2.89/1.58 => ( ( refine1102455758nofail @ A @ S3 )
% 2.89/1.58 => ( refine1102455758nofail @ A @ S ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_69_le__nofailI,axiom,
% 2.89/1.58 ! [A: $tType,M5: refine1665802226e_nres @ A,M4: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ( refine1102455758nofail @ A @ M5 )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M5 ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_70_subsetI,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ! [X3: A] :
% 2.89/1.58 ( ( member @ A @ X3 @ A5 )
% 2.89/1.58 => ( member @ A @ X3 @ B5 ) )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_71_subset__antisym,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.89/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 2.89/1.58 => ( A5 = B5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_72_pw__bind__leI,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType,S: refine1665802226e_nres @ A,M4: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A )] :
% 2.89/1.58 ( ( ( refine1102455758nofail @ A @ S )
% 2.89/1.58 => ( refine1102455758nofail @ B @ M4 ) )
% 2.89/1.58 => ( ! [X3: B] :
% 2.89/1.58 ( ( refine1102455758nofail @ B @ M4 )
% 2.89/1.58 => ( ( refine1315500908_inres @ B @ M4 @ X3 )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F @ X3 ) @ S ) ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M4 @ F ) @ S ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_73_pw__bind__le__iff,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType,M4: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A ),S: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M4 @ F ) @ S )
% 2.89/1.58 = ( ( ( refine1102455758nofail @ A @ S )
% 2.89/1.58 => ( refine1102455758nofail @ B @ M4 ) )
% 2.89/1.58 & ! [X6: B] :
% 2.89/1.58 ( ( ( refine1102455758nofail @ B @ M4 )
% 2.89/1.58 & ( refine1315500908_inres @ B @ M4 @ X6 ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F @ X6 ) @ S ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_74_relprop__triggers_I6_J,axiom,
% 2.89/1.58 ! [I: $tType,R: set @ I,R2: set @ I] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ I ) @ R @ R2 )
% 2.89/1.58 => ( ord_less_eq @ ( set @ I ) @ R @ R2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_75_in__mono,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A,X4: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.89/1.58 => ( ( member @ A @ X4 @ A5 )
% 2.89/1.58 => ( member @ A @ X4 @ B5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_76_subsetD,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A,C2: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.89/1.58 => ( ( member @ A @ C2 @ A5 )
% 2.89/1.58 => ( member @ A @ C2 @ B5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_77_inres__simps_I2_J,axiom,
% 2.89/1.58 ! [B: $tType,X: set @ B] :
% 2.89/1.58 ( ( refine1315500908_inres @ B @ ( refine605929679le_RES @ B @ X ) )
% 2.89/1.58 = ( ^ [X6: B] : ( member @ B @ X6 @ X ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_78_inres__simps_I3_J,axiom,
% 2.89/1.58 ! [C: $tType,X4: C] :
% 2.89/1.58 ( ( refine1315500908_inres @ C @ ( refine1687780735RETURN @ C @ X4 ) )
% 2.89/1.58 = ( ^ [Y4: C,Z: C] : ( Y4 = Z )
% 2.89/1.58 @ X4 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_79_pwD2,axiom,
% 2.89/1.58 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A,X4: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S3 )
% 2.89/1.58 => ( ( refine1315500908_inres @ A @ S @ X4 )
% 2.89/1.58 => ( refine1315500908_inres @ A @ S3 @ X4 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_80_pw__eqI,axiom,
% 2.89/1.58 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ( refine1102455758nofail @ A @ S )
% 2.89/1.58 = ( refine1102455758nofail @ A @ S3 ) )
% 2.89/1.58 => ( ! [X3: A] :
% 2.89/1.58 ( ( refine1315500908_inres @ A @ S @ X3 )
% 2.89/1.58 = ( refine1315500908_inres @ A @ S3 @ X3 ) )
% 2.89/1.58 => ( S = S3 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_81_pw__eq__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ^ [Y4: refine1665802226e_nres @ A,Z: refine1665802226e_nres @ A] : ( Y4 = Z ) )
% 2.89/1.58 = ( ^ [S4: refine1665802226e_nres @ A,S5: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ( refine1102455758nofail @ A @ S4 )
% 2.89/1.58 = ( refine1102455758nofail @ A @ S5 ) )
% 2.89/1.58 & ! [X6: A] :
% 2.89/1.58 ( ( refine1315500908_inres @ A @ S4 @ X6 )
% 2.89/1.58 = ( refine1315500908_inres @ A @ S5 @ X6 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_82_not__nofail__inres,axiom,
% 2.89/1.58 ! [A: $tType,S: refine1665802226e_nres @ A,X4: A] :
% 2.89/1.58 ( ~ ( refine1102455758nofail @ A @ S )
% 2.89/1.58 => ( refine1315500908_inres @ A @ S @ X4 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_83_pw__le__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) )
% 2.89/1.58 = ( ^ [S4: refine1665802226e_nres @ A,S5: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( refine1102455758nofail @ A @ S5 )
% 2.89/1.58 => ( ( refine1102455758nofail @ A @ S4 )
% 2.89/1.58 & ! [X6: A] :
% 2.89/1.58 ( ( refine1315500908_inres @ A @ S4 @ X6 )
% 2.89/1.58 => ( refine1315500908_inres @ A @ S5 @ X6 ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_84_pw__leI_H,axiom,
% 2.89/1.58 ! [A: $tType,S3: refine1665802226e_nres @ A,S: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ( refine1102455758nofail @ A @ S3 )
% 2.89/1.58 => ( refine1102455758nofail @ A @ S ) )
% 2.89/1.58 => ( ! [X3: A] :
% 2.89/1.58 ( ( refine1102455758nofail @ A @ S3 )
% 2.89/1.58 => ( ( refine1315500908_inres @ A @ S @ X3 )
% 2.89/1.58 => ( refine1315500908_inres @ A @ S3 @ X3 ) ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S3 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_85_pw__leI,axiom,
% 2.89/1.58 ! [A: $tType,S3: refine1665802226e_nres @ A,S: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ( refine1102455758nofail @ A @ S3 )
% 2.89/1.58 => ( ( refine1102455758nofail @ A @ S )
% 2.89/1.58 & ! [X3: A] :
% 2.89/1.58 ( ( refine1315500908_inres @ A @ S @ X3 )
% 2.89/1.58 => ( refine1315500908_inres @ A @ S3 @ X3 ) ) ) )
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S3 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_86_pw__bind__nofail,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType,M4: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A )] :
% 2.89/1.58 ( ( refine1102455758nofail @ A @ ( refine463715084e_bind @ B @ A @ M4 @ F ) )
% 2.89/1.58 = ( ( refine1102455758nofail @ B @ M4 )
% 2.89/1.58 & ! [X6: B] :
% 2.89/1.58 ( ( refine1315500908_inres @ B @ M4 @ X6 )
% 2.89/1.58 => ( refine1102455758nofail @ A @ ( F @ X6 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_87_inres__def,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( refine1315500908_inres @ A )
% 2.89/1.58 = ( ^ [S4: refine1665802226e_nres @ A,X6: A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X6 ) @ S4 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_88_nf__inres__def,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( refine406925620_inres @ A )
% 2.89/1.58 = ( ^ [M6: refine1665802226e_nres @ A,X6: A] :
% 2.89/1.58 ( ( refine1102455758nofail @ A @ M6 )
% 2.89/1.58 & ( refine1315500908_inres @ A @ M6 @ X6 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_89_Collect__mono__iff,axiom,
% 2.89/1.58 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.89/1.58 = ( ! [X6: A] :
% 2.89/1.58 ( ( P @ X6 )
% 2.89/1.58 => ( Q @ X6 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_90_set__eq__subset,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ^ [Y4: set @ A,Z: set @ A] : ( Y4 = Z ) )
% 2.89/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.89/1.58 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_91_subset__trans,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A,C3: set @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.89/1.58 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C3 )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_92_Collect__mono,axiom,
% 2.89/1.58 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.89/1.58 ( ! [X3: A] :
% 2.89/1.58 ( ( P @ X3 )
% 2.89/1.58 => ( Q @ X3 ) )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_93_subset__refl,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ A5 ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_94_subset__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) )
% 2.89/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.89/1.58 ! [T3: A] :
% 2.89/1.58 ( ( member @ A @ T3 @ A6 )
% 2.89/1.58 => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_95_equalityD2,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ( A5 = B5 )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_96_equalityD1,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ( A5 = B5 )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_97_subset__eq,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) )
% 2.89/1.58 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.89/1.58 ! [X6: A] :
% 2.89/1.58 ( ( member @ A @ X6 @ A6 )
% 2.89/1.58 => ( member @ A @ X6 @ B6 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_98_equalityE,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ( A5 = B5 )
% 2.89/1.58 => ~ ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.89/1.58 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_99_less__eq__nres_Oelims_I1_J,axiom,
% 2.89/1.58 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A,Y3: $o] :
% 2.89/1.58 ( ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 2.89/1.58 = Y3 )
% 2.89/1.58 => ( ( ( Xa
% 2.89/1.58 = ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 => ~ Y3 )
% 2.89/1.58 => ( ! [A4: set @ A] :
% 2.89/1.58 ( ( X4
% 2.89/1.58 = ( refine605929679le_RES @ A @ A4 ) )
% 2.89/1.58 => ! [B4: set @ A] :
% 2.89/1.58 ( ( Xa
% 2.89/1.58 = ( refine605929679le_RES @ A @ B4 ) )
% 2.89/1.58 => ( Y3
% 2.89/1.58 = ( ~ ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ) )
% 2.89/1.58 => ~ ( ( X4
% 2.89/1.58 = ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 => ( ? [Uv: set @ A] :
% 2.89/1.58 ( Xa
% 2.89/1.58 = ( refine605929679le_RES @ A @ Uv ) )
% 2.89/1.58 => Y3 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_100_less__eq__nres_Oelims_I2_J,axiom,
% 2.89/1.58 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 2.89/1.58 => ( ( Xa
% 2.89/1.58 != ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 => ~ ! [A4: set @ A] :
% 2.89/1.58 ( ( X4
% 2.89/1.58 = ( refine605929679le_RES @ A @ A4 ) )
% 2.89/1.58 => ! [B4: set @ A] :
% 2.89/1.58 ( ( Xa
% 2.89/1.58 = ( refine605929679le_RES @ A @ B4 ) )
% 2.89/1.58 => ~ ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_101_less__eq__nres_Oelims_I3_J,axiom,
% 2.89/1.58 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ~ ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 2.89/1.58 => ( ! [A4: set @ A] :
% 2.89/1.58 ( ( X4
% 2.89/1.58 = ( refine605929679le_RES @ A @ A4 ) )
% 2.89/1.58 => ! [B4: set @ A] :
% 2.89/1.58 ( ( Xa
% 2.89/1.58 = ( refine605929679le_RES @ A @ B4 ) )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) )
% 2.89/1.58 => ~ ( ( X4
% 2.89/1.58 = ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 => ! [Uv: set @ A] :
% 2.89/1.58 ( Xa
% 2.89/1.58 != ( refine605929679le_RES @ A @ Uv ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_102_nres_Osimps_I5_J,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType,F1: B,F2: ( set @ A ) > B,X2: set @ A] :
% 2.89/1.58 ( ( refine60818195e_nres @ B @ A @ F1 @ F2 @ ( refine605929679le_RES @ A @ X2 ) )
% 2.89/1.58 = ( F2 @ X2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_103_nres__order__simps_I22_J,axiom,
% 2.89/1.58 ! [Y9: $tType,X: set @ Y9,Y3: Y9] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ Y9 ) @ ( refine605929679le_RES @ Y9 @ X ) @ ( refine1687780735RETURN @ Y9 @ Y3 ) )
% 2.89/1.58 = ( ord_less_eq @ ( set @ Y9 ) @ X @ ( insert @ Y9 @ Y3 @ ( bot_bot @ ( set @ Y9 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_104_less__eq__nres_Osimps_I3_J,axiom,
% 2.89/1.58 ! [A: $tType,Uv2: set @ A] :
% 2.89/1.58 ~ ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ Uv2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_105_bot__apply,axiom,
% 2.89/1.58 ! [C: $tType,D2: $tType] :
% 2.89/1.58 ( ( bot @ C )
% 2.89/1.58 => ( ( bot_bot @ ( D2 > C ) )
% 2.89/1.58 = ( ^ [X6: D2] : ( bot_bot @ C ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_106_empty__iff,axiom,
% 2.89/1.58 ! [A: $tType,C2: A] :
% 2.89/1.58 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_107_all__not__in__conv,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ( ! [X6: A] :
% 2.89/1.58 ~ ( member @ A @ X6 @ A5 ) )
% 2.89/1.58 = ( A5
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_108_Collect__empty__eq,axiom,
% 2.89/1.58 ! [A: $tType,P: A > $o] :
% 2.89/1.58 ( ( ( collect @ A @ P )
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 = ( ! [X6: A] :
% 2.89/1.58 ~ ( P @ X6 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_109_empty__Collect__eq,axiom,
% 2.89/1.58 ! [A: $tType,P: A > $o] :
% 2.89/1.58 ( ( ( bot_bot @ ( set @ A ) )
% 2.89/1.58 = ( collect @ A @ P ) )
% 2.89/1.58 = ( ! [X6: A] :
% 2.89/1.58 ~ ( P @ X6 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_110_insertCI,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,B5: set @ A,B2: A] :
% 2.89/1.58 ( ( ~ ( member @ A @ A2 @ B5 )
% 2.89/1.58 => ( A2 = B2 ) )
% 2.89/1.58 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_111_insert__iff,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,B2: A,A5: set @ A] :
% 2.89/1.58 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A5 ) )
% 2.89/1.58 = ( ( A2 = B2 )
% 2.89/1.58 | ( member @ A @ A2 @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_112_insert__absorb2,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,A5: set @ A] :
% 2.89/1.58 ( ( insert @ A @ X4 @ ( insert @ A @ X4 @ A5 ) )
% 2.89/1.58 = ( insert @ A @ X4 @ A5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_113_empty__subsetI,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A5 ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_114_subset__empty,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 = ( A5
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_115_singletonI,axiom,
% 2.89/1.58 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_116_insert__subset,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X4 @ A5 ) @ B5 )
% 2.89/1.58 = ( ( member @ A @ X4 @ B5 )
% 2.89/1.58 & ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_117_singleton__insert__inj__eq,axiom,
% 2.89/1.58 ! [A: $tType,B2: A,A2: A,A5: set @ A] :
% 2.89/1.58 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 = ( insert @ A @ A2 @ A5 ) )
% 2.89/1.58 = ( ( A2 = B2 )
% 2.89/1.58 & ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_118_singleton__insert__inj__eq_H,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,A5: set @ A,B2: A] :
% 2.89/1.58 ( ( ( insert @ A @ A2 @ A5 )
% 2.89/1.58 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.89/1.58 = ( ( A2 = B2 )
% 2.89/1.58 & ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_119_nres__more__simps_I5_J,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,X: set @ A] :
% 2.89/1.58 ( ( ( refine1687780735RETURN @ A @ X4 )
% 2.89/1.58 = ( refine605929679le_RES @ A @ X ) )
% 2.89/1.58 = ( ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 = X ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_120_nres__more__simps_I3_J,axiom,
% 2.89/1.58 ! [A: $tType,X: set @ A,X4: A] :
% 2.89/1.58 ( ( ( refine605929679le_RES @ A @ X )
% 2.89/1.58 = ( refine1687780735RETURN @ A @ X4 ) )
% 2.89/1.58 = ( X
% 2.89/1.58 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_121_subset__singletonD,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,X4: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.89/1.58 => ( ( A5
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 | ( A5
% 2.89/1.58 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_122_subset__singleton__iff,axiom,
% 2.89/1.58 ! [A: $tType,X: set @ A,A2: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ X @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.89/1.58 = ( ( X
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 | ( X
% 2.89/1.58 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_123_emptyE,axiom,
% 2.89/1.58 ! [A: $tType,A2: A] :
% 2.89/1.58 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_124_insertE,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,B2: A,A5: set @ A] :
% 2.89/1.58 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A5 ) )
% 2.89/1.58 => ( ( A2 != B2 )
% 2.89/1.58 => ( member @ A @ A2 @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_125_equals0D,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,A2: A] :
% 2.89/1.58 ( ( A5
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 => ~ ( member @ A @ A2 @ A5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_126_equals0I,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ! [Y6: A] :
% 2.89/1.58 ~ ( member @ A @ Y6 @ A5 )
% 2.89/1.58 => ( A5
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_127_insertI1,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,B5: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_128_insertI2,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,B5: set @ A,B2: A] :
% 2.89/1.58 ( ( member @ A @ A2 @ B5 )
% 2.89/1.58 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_129_ex__in__conv,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ( ? [X6: A] : ( member @ A @ X6 @ A5 ) )
% 2.89/1.58 = ( A5
% 2.89/1.58 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_130_Set_Oset__insert,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,A5: set @ A] :
% 2.89/1.58 ( ( member @ A @ X4 @ A5 )
% 2.89/1.58 => ~ ! [B7: set @ A] :
% 2.89/1.58 ( ( A5
% 2.89/1.58 = ( insert @ A @ X4 @ B7 ) )
% 2.89/1.58 => ( member @ A @ X4 @ B7 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_131_singletonD,axiom,
% 2.89/1.58 ! [A: $tType,B2: A,A2: A] :
% 2.89/1.58 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.89/1.58 => ( B2 = A2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_132_insert__ident,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ~ ( member @ A @ X4 @ A5 )
% 2.89/1.58 => ( ~ ( member @ A @ X4 @ B5 )
% 2.89/1.58 => ( ( ( insert @ A @ X4 @ A5 )
% 2.89/1.58 = ( insert @ A @ X4 @ B5 ) )
% 2.89/1.58 = ( A5 = B5 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_133_insert__absorb,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,A5: set @ A] :
% 2.89/1.58 ( ( member @ A @ A2 @ A5 )
% 2.89/1.58 => ( ( insert @ A @ A2 @ A5 )
% 2.89/1.58 = A5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_134_insert__eq__iff,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,A5: set @ A,B2: A,B5: set @ A] :
% 2.89/1.58 ( ~ ( member @ A @ A2 @ A5 )
% 2.89/1.58 => ( ~ ( member @ A @ B2 @ B5 )
% 2.89/1.58 => ( ( ( insert @ A @ A2 @ A5 )
% 2.89/1.58 = ( insert @ A @ B2 @ B5 ) )
% 2.89/1.58 = ( ( ( A2 = B2 )
% 2.89/1.58 => ( A5 = B5 ) )
% 2.89/1.58 & ( ( A2 != B2 )
% 2.89/1.58 => ? [C4: set @ A] :
% 2.89/1.58 ( ( A5
% 2.89/1.58 = ( insert @ A @ B2 @ C4 ) )
% 2.89/1.58 & ~ ( member @ A @ B2 @ C4 )
% 2.89/1.58 & ( B5
% 2.89/1.58 = ( insert @ A @ A2 @ C4 ) )
% 2.89/1.58 & ~ ( member @ A @ A2 @ C4 ) ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_135_singleton__iff,axiom,
% 2.89/1.58 ! [A: $tType,B2: A,A2: A] :
% 2.89/1.58 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.89/1.58 = ( B2 = A2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_136_insert__commute,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,Y3: A,A5: set @ A] :
% 2.89/1.58 ( ( insert @ A @ X4 @ ( insert @ A @ Y3 @ A5 ) )
% 2.89/1.58 = ( insert @ A @ Y3 @ ( insert @ A @ X4 @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_137_doubleton__eq__iff,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,B2: A,C2: A,D: A] :
% 2.89/1.58 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.89/1.58 = ( insert @ A @ C2 @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.89/1.58 = ( ( ( A2 = C2 )
% 2.89/1.58 & ( B2 = D ) )
% 2.89/1.58 | ( ( A2 = D )
% 2.89/1.58 & ( B2 = C2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_138_insert__not__empty,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,A5: set @ A] :
% 2.89/1.58 ( ( insert @ A @ A2 @ A5 )
% 2.89/1.58 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_139_singleton__inject,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,B2: A] :
% 2.89/1.58 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.89/1.58 => ( A2 = B2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_140_mk__disjoint__insert,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,A5: set @ A] :
% 2.89/1.58 ( ( member @ A @ A2 @ A5 )
% 2.89/1.58 => ? [B7: set @ A] :
% 2.89/1.58 ( ( A5
% 2.89/1.58 = ( insert @ A @ A2 @ B7 ) )
% 2.89/1.58 & ~ ( member @ A @ A2 @ B7 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_141_bot__fun__def,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType] :
% 2.89/1.58 ( ( bot @ B )
% 2.89/1.58 => ( ( bot_bot @ ( A > B ) )
% 2.89/1.58 = ( ^ [X6: A] : ( bot_bot @ B ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_142_nres_Osimps_I4_J,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType,F1: B,F2: ( set @ A ) > B] :
% 2.89/1.58 ( ( refine60818195e_nres @ B @ A @ F1 @ F2 @ ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 = F1 ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_143_set__notEmptyE,axiom,
% 2.89/1.58 ! [A: $tType,S: set @ A] :
% 2.89/1.58 ( ( S
% 2.89/1.58 != ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 => ~ ! [X3: A] :
% 2.89/1.58 ~ ( member @ A @ X3 @ S ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_144_memb__imp__not__empty,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,S: set @ A] :
% 2.89/1.58 ( ( member @ A @ X4 @ S )
% 2.89/1.58 => ( S
% 2.89/1.58 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_145_bot_Oextremum,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order_bot @ A )
% 2.89/1.58 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_146_bot_Oextremum__unique,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order_bot @ A )
% 2.89/1.58 => ! [A2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.89/1.58 = ( A2
% 2.89/1.58 = ( bot_bot @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_147_bot_Oextremum__uniqueI,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order_bot @ A )
% 2.89/1.58 => ! [A2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.89/1.58 => ( A2
% 2.89/1.58 = ( bot_bot @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_148_subset__insertI2,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A,B2: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ B2 @ B5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_149_subset__insertI,axiom,
% 2.89/1.58 ! [A: $tType,B5: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B5 @ ( insert @ A @ A2 @ B5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_150_subset__insert,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ~ ( member @ A @ X4 @ A5 )
% 2.89/1.58 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( insert @ A @ X4 @ B5 ) )
% 2.89/1.58 = ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_151_insert__mono,axiom,
% 2.89/1.58 ! [A: $tType,C3: set @ A,D3: set @ A,A2: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D3 )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C3 ) @ ( insert @ A @ A2 @ D3 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_152_RETURN__def,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( refine1687780735RETURN @ A )
% 2.89/1.58 = ( ^ [X6: A] : ( refine605929679le_RES @ A @ ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_153_nres_Odistinct_I1_J,axiom,
% 2.89/1.58 ! [A: $tType,X2: set @ A] :
% 2.89/1.58 ( ( refine1767639642_FAILi @ A )
% 2.89/1.58 != ( refine605929679le_RES @ A @ X2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_154_nres_Oinduct,axiom,
% 2.89/1.58 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > $o,Nres: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( P @ ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 => ( ! [X3: set @ A] : ( P @ ( refine605929679le_RES @ A @ X3 ) )
% 2.89/1.58 => ( P @ Nres ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_155_nres_Oexhaust,axiom,
% 2.89/1.58 ! [A: $tType,Y3: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( Y3
% 2.89/1.58 != ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 => ~ ! [X22: set @ A] :
% 2.89/1.58 ( Y3
% 2.89/1.58 != ( refine605929679le_RES @ A @ X22 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_156_sup__nres_Oinduct,axiom,
% 2.89/1.58 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ! [Uu: refine1665802226e_nres @ A] : ( P @ Uu @ ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 => ( ! [V2: set @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ V2 ) )
% 2.89/1.58 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 2.89/1.58 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_157_less__nres_Oinduct,axiom,
% 2.89/1.58 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ! [X_1: refine1665802226e_nres @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ X_1 )
% 2.89/1.58 => ( ! [Uv: set @ A] : ( P @ ( refine605929679le_RES @ A @ Uv ) @ ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 2.89/1.58 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_158_less__eq__nres_Oinduct,axiom,
% 2.89/1.58 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ! [Uu: refine1665802226e_nres @ A] : ( P @ Uu @ ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 2.89/1.58 => ( ! [Uv: set @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ Uv ) )
% 2.89/1.58 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_159_less__eq__nres_Osimps_I1_J,axiom,
% 2.89/1.58 ! [A: $tType,Uu2: refine1665802226e_nres @ A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ Uu2 @ ( refine1767639642_FAILi @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_160_nres_Osimps_I6_J,axiom,
% 2.89/1.58 ! [A: $tType,C: $tType,F1: C,F2: ( set @ A ) > C] :
% 2.89/1.58 ( ( refine1442219249c_nres @ C @ A @ F1 @ F2 @ ( refine1767639642_FAILi @ A ) )
% 2.89/1.58 = F1 ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_161_the__elem__eq,axiom,
% 2.89/1.58 ! [A: $tType,X4: A] :
% 2.89/1.58 ( ( the_elem @ A @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.89/1.58 = X4 ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_162_is__singletonI,axiom,
% 2.89/1.58 ! [A: $tType,X4: A] : ( is_singleton @ A @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_163_insert__subsetI,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,A5: set @ A,X: set @ A] :
% 2.89/1.58 ( ( member @ A @ X4 @ A5 )
% 2.89/1.58 => ( ( ord_less_eq @ ( set @ A ) @ X @ A5 )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X4 @ X ) @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_164_subset__emptyI,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ! [X3: A] :
% 2.89/1.58 ~ ( member @ A @ X3 @ A5 )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_165_Set_Ois__empty__def,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( is_empty @ A )
% 2.89/1.58 = ( ^ [A6: set @ A] :
% 2.89/1.58 ( A6
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_166_nres__order__simps_I2_J,axiom,
% 2.89/1.58 ! [B: $tType,M4: refine1665802226e_nres @ B] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M4 @ ( bot_bot @ ( refine1665802226e_nres @ B ) ) )
% 2.89/1.58 = ( M4
% 2.89/1.58 = ( bot_bot @ ( refine1665802226e_nres @ B ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_167_nofail__simps_I4_J,axiom,
% 2.89/1.58 ! [D2: $tType] : ( refine1102455758nofail @ D2 @ ( bot_bot @ ( refine1665802226e_nres @ D2 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_168_inres__simps_I4_J,axiom,
% 2.89/1.58 ! [D2: $tType] :
% 2.89/1.58 ( ( refine1315500908_inres @ D2 @ ( bot_bot @ ( refine1665802226e_nres @ D2 ) ) )
% 2.89/1.58 = ( ^ [Uu3: D2] : $false ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_169_bind__SUCCEED,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType,F: B > ( refine1665802226e_nres @ A )] :
% 2.89/1.58 ( ( refine463715084e_bind @ B @ A @ ( bot_bot @ ( refine1665802226e_nres @ B ) ) @ F )
% 2.89/1.58 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_170_nres__more__simps_I2_J,axiom,
% 2.89/1.58 ! [A: $tType,X: set @ A] :
% 2.89/1.58 ( ( ( refine605929679le_RES @ A @ X )
% 2.89/1.58 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) )
% 2.89/1.58 = ( X
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_171_nres__more__simps_I1_J,axiom,
% 2.89/1.58 ! [A: $tType,X: set @ A] :
% 2.89/1.58 ( ( ( bot_bot @ ( refine1665802226e_nres @ A ) )
% 2.89/1.58 = ( refine605929679le_RES @ A @ X ) )
% 2.89/1.58 = ( X
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_172_bot__set__def,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( bot_bot @ ( set @ A ) )
% 2.89/1.58 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_173_nres__order__simps_I1_J,axiom,
% 2.89/1.58 ! [A: $tType,M4: refine1665802226e_nres @ A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ M4 ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_174_nres__inequalities_I5_J,axiom,
% 2.89/1.58 ! [C: $tType,X4: C] :
% 2.89/1.58 ( ( bot_bot @ ( refine1665802226e_nres @ C ) )
% 2.89/1.58 != ( refine1687780735RETURN @ C @ X4 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_175_bot__nres__def,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( bot_bot @ ( refine1665802226e_nres @ A ) )
% 2.89/1.58 = ( refine605929679le_RES @ A @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_176_SUCCEED__rule,axiom,
% 2.89/1.58 ! [A: $tType,Phi: A > $o] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_177_is__singleton__the__elem,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( is_singleton @ A )
% 2.89/1.58 = ( ^ [A6: set @ A] :
% 2.89/1.58 ( A6
% 2.89/1.58 = ( insert @ A @ ( the_elem @ A @ A6 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_178_is__singletonI_H,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ( A5
% 2.89/1.58 != ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 => ( ! [X3: A,Y6: A] :
% 2.89/1.58 ( ( member @ A @ X3 @ A5 )
% 2.89/1.58 => ( ( member @ A @ Y6 @ A5 )
% 2.89/1.58 => ( X3 = Y6 ) ) )
% 2.89/1.58 => ( is_singleton @ A @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_179_is__singleton__def,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( is_singleton @ A )
% 2.89/1.58 = ( ^ [A6: set @ A] :
% 2.89/1.58 ? [X6: A] :
% 2.89/1.58 ( A6
% 2.89/1.58 = ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_180_is__singletonE,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ( is_singleton @ A @ A5 )
% 2.89/1.58 => ~ ! [X3: A] :
% 2.89/1.58 ( A5
% 2.89/1.58 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_181_subset__Compl__singleton,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B2: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.89/1.58 = ( ~ ( member @ A @ B2 @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_182_strictD__simp,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( bot @ A )
% 2.89/1.58 => ! [F: A > A] :
% 2.89/1.58 ( ( refine_strict @ A @ A @ F )
% 2.89/1.58 => ( ( F @ ( bot_bot @ A ) )
% 2.89/1.58 = ( bot_bot @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_183_Collect__empty__eq__bot,axiom,
% 2.89/1.58 ! [A: $tType,P: A > $o] :
% 2.89/1.58 ( ( ( collect @ A @ P )
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 = ( P
% 2.89/1.58 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_184_verit__minus__simplify_I4_J,axiom,
% 2.89/1.58 ! [B: $tType] :
% 2.89/1.58 ( ( group_add @ B )
% 2.89/1.58 => ! [B2: B] :
% 2.89/1.58 ( ( uminus_uminus @ B @ ( uminus_uminus @ B @ B2 ) )
% 2.89/1.58 = B2 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_185_ComplI,axiom,
% 2.89/1.58 ! [A: $tType,C2: A,A5: set @ A] :
% 2.89/1.58 ( ~ ( member @ A @ C2 @ A5 )
% 2.89/1.58 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_186_Compl__iff,axiom,
% 2.89/1.58 ! [A: $tType,C2: A,A5: set @ A] :
% 2.89/1.58 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A5 ) )
% 2.89/1.58 = ( ~ ( member @ A @ C2 @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_187_Compl__eq__Compl__iff,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ( ( uminus_uminus @ ( set @ A ) @ A5 )
% 2.89/1.58 = ( uminus_uminus @ ( set @ A ) @ B5 ) )
% 2.89/1.58 = ( A5 = B5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_188_Compl__anti__mono,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.89/1.58 => ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ B5 ) @ ( uminus_uminus @ ( set @ A ) @ A5 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_189_Compl__subset__Compl__iff,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A5 ) @ ( uminus_uminus @ ( set @ A ) @ B5 ) )
% 2.89/1.58 = ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_190_ibind__strict_I1_J,axiom,
% 2.89/1.58 ! [A: $tType,F: product_unit > ( refine1665802226e_nres @ A )] :
% 2.89/1.58 ( ( refine463715084e_bind @ product_unit @ A @ ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) @ F )
% 2.89/1.58 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_191_ComplD,axiom,
% 2.89/1.58 ! [A: $tType,C2: A,A5: set @ A] :
% 2.89/1.58 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A5 ) )
% 2.89/1.58 => ~ ( member @ A @ C2 @ A5 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_192_double__complement,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A5 ) )
% 2.89/1.58 = A5 ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_193_verit__negate__coefficient_I3_J,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ordered_ab_group_add @ A )
% 2.89/1.58 => ! [A2: A,B2: A] :
% 2.89/1.58 ( ( A2 = B2 )
% 2.89/1.58 => ( ( uminus_uminus @ A @ A2 )
% 2.89/1.58 = ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_194_subset__Compl__self__eq,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( uminus_uminus @ ( set @ A ) @ A5 ) )
% 2.89/1.58 = ( A5
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_195_strictD,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType] :
% 2.89/1.58 ( ( ( bot @ B )
% 2.89/1.58 & ( bot @ A ) )
% 2.89/1.58 => ! [F: A > B] :
% 2.89/1.58 ( ( refine_strict @ A @ B @ F )
% 2.89/1.58 => ( ( F @ ( bot_bot @ A ) )
% 2.89/1.58 = ( bot_bot @ B ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_196_strictI,axiom,
% 2.89/1.58 ! [A: $tType,B: $tType] :
% 2.89/1.58 ( ( ( bot @ B )
% 2.89/1.58 & ( bot @ A ) )
% 2.89/1.58 => ! [F: B > A] :
% 2.89/1.58 ( ( ( F @ ( bot_bot @ B ) )
% 2.89/1.58 = ( bot_bot @ A ) )
% 2.89/1.58 => ( refine_strict @ B @ A @ F ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_197_strict__def,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType] :
% 2.89/1.58 ( ( ( bot @ A )
% 2.89/1.58 & ( bot @ B ) )
% 2.89/1.58 => ( ( refine_strict @ A @ B )
% 2.89/1.58 = ( ^ [F3: A > B] :
% 2.89/1.58 ( ( F3 @ ( bot_bot @ A ) )
% 2.89/1.58 = ( bot_bot @ B ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_198_neg__le__iff__le,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ordered_ab_group_add @ A )
% 2.89/1.58 => ! [B2: A,A2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A2 ) )
% 2.89/1.58 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_199_compl__le__compl__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( boolean_algebra @ A )
% 2.89/1.58 => ! [X4: A,Y3: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X4 ) @ ( uminus_uminus @ A @ Y3 ) )
% 2.89/1.58 = ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_200_bot__empty__eq,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( bot_bot @ ( A > $o ) )
% 2.89/1.58 = ( ^ [X6: A] : ( member @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_201_le__imp__neg__le,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ordered_ab_group_add @ A )
% 2.89/1.58 => ! [A2: A,B2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.89/1.58 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_202_minus__le__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ordered_ab_group_add @ A )
% 2.89/1.58 => ! [A2: A,B2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A2 ) @ B2 )
% 2.89/1.58 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ A2 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_203_le__minus__iff,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( ordered_ab_group_add @ A )
% 2.89/1.58 => ! [A2: A,B2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ A2 @ ( uminus_uminus @ A @ B2 ) )
% 2.89/1.58 = ( ord_less_eq @ A @ B2 @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_204_compl__le__swap2,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( boolean_algebra @ A )
% 2.89/1.58 => ! [Y3: A,X4: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y3 ) @ X4 )
% 2.89/1.58 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X4 ) @ Y3 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_205_compl__le__swap1,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( boolean_algebra @ A )
% 2.89/1.58 => ! [Y3: A,X4: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ Y3 @ ( uminus_uminus @ A @ X4 ) )
% 2.89/1.58 => ( ord_less_eq @ A @ X4 @ ( uminus_uminus @ A @ Y3 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_206_compl__mono,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( boolean_algebra @ A )
% 2.89/1.58 => ! [X4: A,Y3: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 2.89/1.58 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y3 ) @ ( uminus_uminus @ A @ X4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_207_ASSUME__simps_I2_J,axiom,
% 2.89/1.58 ( ( refine1946708059ASSUME @ $false )
% 2.89/1.58 = ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_208_pw__flat__le__iff,axiom,
% 2.89/1.58 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( partial_flat_ord @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ S @ S3 )
% 2.89/1.58 = ( ? [X8: A] : ( refine1315500908_inres @ A @ S @ X8 )
% 2.89/1.58 => ( ( ( refine1102455758nofail @ A @ S )
% 2.89/1.58 = ( refine1102455758nofail @ A @ S3 ) )
% 2.89/1.58 & ! [X6: A] :
% 2.89/1.58 ( ( refine1315500908_inres @ A @ S @ X6 )
% 2.89/1.58 = ( refine1315500908_inres @ A @ S3 @ X6 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_209_pw__ASSUME_I2_J,axiom,
% 2.89/1.58 ! [Phi: $o,X4: product_unit] :
% 2.89/1.58 ( ( refine1315500908_inres @ product_unit @ ( refine1946708059ASSUME @ Phi ) @ X4 )
% 2.89/1.58 = Phi ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_210_pw__ASSUME_I1_J,axiom,
% 2.89/1.58 ! [Phi: $o] : ( refine1102455758nofail @ product_unit @ ( refine1946708059ASSUME @ Phi ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_211_flat__ord__compat_I1_J,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( comple187826305attice @ A )
% 2.89/1.58 => ! [X4: A,Y3: A] :
% 2.89/1.58 ( ( partial_flat_ord @ A @ ( bot_bot @ A ) @ X4 @ Y3 )
% 2.89/1.58 => ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_212_pw__flat__ge__iff,axiom,
% 2.89/1.58 ! [A: $tType,S: refine1665802226e_nres @ A,S3: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( partial_flat_ord @ ( refine1665802226e_nres @ A ) @ ( top_top @ ( refine1665802226e_nres @ A ) ) @ S @ S3 )
% 2.89/1.58 = ( ( refine1102455758nofail @ A @ S )
% 2.89/1.58 => ( ( refine1102455758nofail @ A @ S3 )
% 2.89/1.58 & ! [X6: A] :
% 2.89/1.58 ( ( refine1315500908_inres @ A @ S @ X6 )
% 2.89/1.58 = ( refine1315500908_inres @ A @ S3 @ X6 ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_213_top__apply,axiom,
% 2.89/1.58 ! [C: $tType,D2: $tType] :
% 2.89/1.58 ( ( top @ C )
% 2.89/1.58 => ( ( top_top @ ( D2 > C ) )
% 2.89/1.58 = ( ^ [X6: D2] : ( top_top @ C ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_214_nres__order__simps_I4_J,axiom,
% 2.89/1.58 ! [D2: $tType,M4: refine1665802226e_nres @ D2] :
% 2.89/1.58 ( ( ord_less_eq @ ( refine1665802226e_nres @ D2 ) @ ( top_top @ ( refine1665802226e_nres @ D2 ) ) @ M4 )
% 2.89/1.58 = ( M4
% 2.89/1.58 = ( top_top @ ( refine1665802226e_nres @ D2 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_215_nofail__simps_I1_J,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ~ ( refine1102455758nofail @ A @ ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_216_nres__simp__internals_I2_J,axiom,
% 2.89/1.58 ! [B: $tType] :
% 2.89/1.58 ( ( refine1767639642_FAILi @ B )
% 2.89/1.58 = ( top_top @ ( refine1665802226e_nres @ B ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_217_inres__simps_I1_J,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( refine1315500908_inres @ A @ ( top_top @ ( refine1665802226e_nres @ A ) ) )
% 2.89/1.58 = ( ^ [Uu3: A] : $true ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_218_bind__FAIL,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType,F: B > ( refine1665802226e_nres @ A )] :
% 2.89/1.58 ( ( refine463715084e_bind @ B @ A @ ( top_top @ ( refine1665802226e_nres @ B ) ) @ F )
% 2.89/1.58 = ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_219_compl__bot__eq,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( boolean_algebra @ A )
% 2.89/1.58 => ( ( uminus_uminus @ A @ ( bot_bot @ A ) )
% 2.89/1.58 = ( top_top @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_220_compl__top__eq,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( boolean_algebra @ A )
% 2.89/1.58 => ( ( uminus_uminus @ A @ ( top_top @ A ) )
% 2.89/1.58 = ( bot_bot @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_221_flat__ord__compat_I2_J,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( comple187826305attice @ A )
% 2.89/1.58 => ! [X4: A,Y3: A] :
% 2.89/1.58 ( ( partial_flat_ord @ A @ ( top_top @ A ) @ X4 @ Y3 )
% 2.89/1.58 => ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_222_top__greatest,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order_top @ A )
% 2.89/1.58 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( top_top @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_223_top_Oextremum__unique,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order_top @ A )
% 2.89/1.58 => ! [A2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 2.89/1.58 = ( A2
% 2.89/1.58 = ( top_top @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_224_top_Oextremum__uniqueI,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order_top @ A )
% 2.89/1.58 => ! [A2: A] :
% 2.89/1.58 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A2 )
% 2.89/1.58 => ( A2
% 2.89/1.58 = ( top_top @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_225_meta__le__everything__if__top,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( order_top @ A )
% 2.89/1.58 => ! [M: A,X4: A] :
% 2.89/1.58 ( ( M
% 2.89/1.58 = ( top_top @ A ) )
% 2.89/1.58 => ( ord_less_eq @ A @ X4 @ M ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_226_nres__inequalities_I3_J,axiom,
% 2.89/1.58 ! [C: $tType,X4: C] :
% 2.89/1.58 ( ( top_top @ ( refine1665802226e_nres @ C ) )
% 2.89/1.58 != ( refine1687780735RETURN @ C @ X4 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_227_top__nres__def,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( top_top @ ( refine1665802226e_nres @ A ) )
% 2.89/1.58 = ( refine1767639642_FAILi @ A ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_228_not__nofail__iff,axiom,
% 2.89/1.58 ! [A: $tType,S: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ~ ( refine1102455758nofail @ A @ S ) )
% 2.89/1.58 = ( S
% 2.89/1.58 = ( top_top @ ( refine1665802226e_nres @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_229_nofail__def,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( refine1102455758nofail @ A )
% 2.89/1.58 = ( ^ [S4: refine1665802226e_nres @ A] :
% 2.89/1.58 ( S4
% 2.89/1.58 != ( top_top @ ( refine1665802226e_nres @ A ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_230_intro__nofail_I2_J,axiom,
% 2.89/1.58 ! [A: $tType,S: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( ( top_top @ ( refine1665802226e_nres @ A ) )
% 2.89/1.58 != S )
% 2.89/1.58 = ( refine1102455758nofail @ A @ S ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_231_nres__order__simps_I3_J,axiom,
% 2.89/1.58 ! [C: $tType,M4: refine1665802226e_nres @ C] : ( ord_less_eq @ ( refine1665802226e_nres @ C ) @ M4 @ ( top_top @ ( refine1665802226e_nres @ C ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_232_nres__inequalities_I1_J,axiom,
% 2.89/1.58 ! [A: $tType,X: set @ A] :
% 2.89/1.58 ( ( top_top @ ( refine1665802226e_nres @ A ) )
% 2.89/1.58 != ( refine605929679le_RES @ A @ X ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_233_nres__cases,axiom,
% 2.89/1.58 ! [A: $tType,M4: refine1665802226e_nres @ A] :
% 2.89/1.58 ( ( M4
% 2.89/1.58 != ( top_top @ ( refine1665802226e_nres @ A ) ) )
% 2.89/1.58 => ~ ! [X9: set @ A] :
% 2.89/1.58 ( M4
% 2.89/1.58 != ( refine605929679le_RES @ A @ X9 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_234_ibind__strict_I2_J,axiom,
% 2.89/1.58 ! [A: $tType,F: product_unit > ( refine1665802226e_nres @ A )] :
% 2.89/1.58 ( ( refine463715084e_bind @ product_unit @ A @ ( top_top @ ( refine1665802226e_nres @ product_unit ) ) @ F )
% 2.89/1.58 = ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_235_nres__inequalities_I4_J,axiom,
% 2.89/1.58 ! [D2: $tType] :
% 2.89/1.58 ( ( bot_bot @ ( refine1665802226e_nres @ D2 ) )
% 2.89/1.58 != ( top_top @ ( refine1665802226e_nres @ D2 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_236_nres__inequalities_I2_J,axiom,
% 2.89/1.58 ! [B: $tType] :
% 2.89/1.58 ( ( top_top @ ( refine1665802226e_nres @ B ) )
% 2.89/1.58 != ( bot_bot @ ( refine1665802226e_nres @ B ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_237_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I2_J,axiom,
% 2.89/1.58 ! [B: $tType,A: $tType,M4: refine1665802226e_nres @ A,M5: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 2.89/1.58 ( ( partial_flat_ord @ ( refine1665802226e_nres @ A ) @ ( top_top @ ( refine1665802226e_nres @ A ) ) @ M4 @ M5 )
% 2.89/1.58 => ( ! [X3: A] : ( partial_flat_ord @ ( refine1665802226e_nres @ B ) @ ( top_top @ ( refine1665802226e_nres @ B ) ) @ ( F @ X3 ) @ ( F4 @ X3 ) )
% 2.89/1.58 => ( partial_flat_ord @ ( refine1665802226e_nres @ B ) @ ( top_top @ ( refine1665802226e_nres @ B ) ) @ ( refine463715084e_bind @ A @ B @ M4 @ F ) @ ( refine463715084e_bind @ A @ B @ M5 @ F4 ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_238_flat__ord_OatLeastAtMost__singleton,axiom,
% 2.89/1.58 ! [A: $tType,B2: A,A2: A] :
% 2.89/1.58 ( ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ B2 ) @ A2 @ A2 )
% 2.89/1.58 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_239_flat__ord_OatLeastAtMost__singleton__iff,axiom,
% 2.89/1.58 ! [A: $tType,Ba: A,A2: A,B2: A,C2: A] :
% 2.89/1.58 ( ( ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 )
% 2.89/1.58 = ( insert @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.89/1.58 = ( ( A2 = B2 )
% 2.89/1.58 & ( B2 = C2 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_240_flat__ord_OatLeastatMost__empty__iff,axiom,
% 2.89/1.58 ! [A: $tType,Ba: A,A2: A,B2: A] :
% 2.89/1.58 ( ( ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 )
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 = ( ~ ( partial_flat_ord @ A @ Ba @ A2 @ B2 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_241_flat__ord_OatLeastatMost__empty__iff2,axiom,
% 2.89/1.58 ! [A: $tType,Ba: A,A2: A,B2: A] :
% 2.89/1.58 ( ( ( bot_bot @ ( set @ A ) )
% 2.89/1.58 = ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 ) )
% 2.89/1.58 = ( ~ ( partial_flat_ord @ A @ Ba @ A2 @ B2 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_242_flat__ord_OatLeastatMost__subset__iff,axiom,
% 2.89/1.58 ! [A: $tType,Ba: A,A2: A,B2: A,C2: A,D: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 ) @ ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ C2 @ D ) )
% 2.89/1.58 = ( ~ ( partial_flat_ord @ A @ Ba @ A2 @ B2 )
% 2.89/1.58 | ( ( partial_flat_ord @ A @ Ba @ C2 @ A2 )
% 2.89/1.58 & ( partial_flat_ord @ A @ Ba @ B2 @ D ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_243_insert__UNIV,axiom,
% 2.89/1.58 ! [A: $tType,X4: A] :
% 2.89/1.58 ( ( insert @ A @ X4 @ ( top_top @ ( set @ A ) ) )
% 2.89/1.58 = ( top_top @ ( set @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_244_subset__UNIV,axiom,
% 2.89/1.58 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ ( top_top @ ( set @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_245_Compl__UNIV__eq,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( uminus_uminus @ ( set @ A ) @ ( top_top @ ( set @ A ) ) )
% 2.89/1.58 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_246_Compl__empty__eq,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( uminus_uminus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) )
% 2.89/1.58 = ( top_top @ ( set @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_247_empty__not__UNIV,axiom,
% 2.89/1.58 ! [A: $tType] :
% 2.89/1.58 ( ( bot_bot @ ( set @ A ) )
% 2.89/1.58 != ( top_top @ ( set @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_248_flat__ord_OatLeastAtMost__singleton_H,axiom,
% 2.89/1.58 ! [A: $tType,A2: A,B2: A,Ba: A] :
% 2.89/1.58 ( ( A2 = B2 )
% 2.89/1.58 => ( ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ Ba ) @ A2 @ B2 )
% 2.89/1.58 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_249_flat__ord_OIcc__subset__Iic__iff,axiom,
% 2.89/1.58 ! [A: $tType,B2: A,L: A,H: A,H2: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ B2 ) @ L @ H ) @ ( set_atMost @ A @ ( partial_flat_ord @ A @ B2 ) @ H2 ) )
% 2.89/1.58 = ( ~ ( partial_flat_ord @ A @ B2 @ L @ H )
% 2.89/1.58 | ( partial_flat_ord @ A @ B2 @ H @ H2 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_250_flat__ord_OIcc__subset__Ici__iff,axiom,
% 2.89/1.58 ! [A: $tType,B2: A,L: A,H: A,L2: A] :
% 2.89/1.58 ( ( ord_less_eq @ ( set @ A ) @ ( set_atLeastAtMost @ A @ ( partial_flat_ord @ A @ B2 ) @ L @ H ) @ ( set_atLeast @ A @ ( partial_flat_ord @ A @ B2 ) @ L2 ) )
% 2.89/1.58 = ( ~ ( partial_flat_ord @ A @ B2 @ L @ H )
% 2.89/1.58 | ( partial_flat_ord @ A @ B2 @ L2 @ L ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_251_UNIV__I,axiom,
% 2.89/1.58 ! [A: $tType,X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_252_relprop__UNIV__orient,axiom,
% 2.89/1.58 ! [A: $tType,R: set @ A] :
% 2.89/1.58 ( ( R
% 2.89/1.58 = ( top_top @ ( set @ A ) ) )
% 2.89/1.58 => ( ( top_top @ ( set @ A ) )
% 2.89/1.58 = R ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(fact_253_eq__UNIV__iff,axiom,
% 2.89/1.58 ! [A: $tType,S: set @ A] :
% 2.89/1.58 ( ( S
% 2.89/1.58 = ( top_top @ ( set @ A ) ) )
% 2.89/1.58 = ( ! [X6: A] : ( member @ A @ X6 @ S ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 2.89/1.58 ! [A7: $tType,A8: $tType] :
% 2.89/1.58 ( ( comple187826305attice @ A8 )
% 2.89/1.58 => ( comple187826305attice @ ( A7 > A8 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 2.89/1.58 ! [A7: $tType,A8: $tType] :
% 2.89/1.58 ( ( boolean_algebra @ A8 )
% 2.89/1.58 => ( boolean_algebra @ ( A7 > A8 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 2.89/1.58 ! [A7: $tType,A8: $tType] :
% 2.89/1.58 ( ( order_top @ A8 )
% 2.89/1.58 => ( order_top @ ( A7 > A8 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.89/1.58 ! [A7: $tType,A8: $tType] :
% 2.89/1.58 ( ( order_bot @ A8 )
% 2.89/1.58 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.89/1.58 ! [A7: $tType,A8: $tType] :
% 2.89/1.58 ( ( preorder @ A8 )
% 2.89/1.58 => ( preorder @ ( A7 > A8 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.89/1.58 ! [A7: $tType,A8: $tType] :
% 2.89/1.58 ( ( order @ A8 )
% 2.89/1.58 => ( order @ ( A7 > A8 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_fun___Orderings_Otop,axiom,
% 2.89/1.58 ! [A7: $tType,A8: $tType] :
% 2.89/1.58 ( ( top @ A8 )
% 2.89/1.58 => ( top @ ( A7 > A8 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_fun___Orderings_Oord,axiom,
% 2.89/1.58 ! [A7: $tType,A8: $tType] :
% 2.89/1.58 ( ( ord @ A8 )
% 2.89/1.58 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_fun___Orderings_Obot,axiom,
% 2.89/1.58 ! [A7: $tType,A8: $tType] :
% 2.89/1.58 ( ( bot @ A8 )
% 2.89/1.58 => ( bot @ ( A7 > A8 ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1,axiom,
% 2.89/1.58 ! [A7: $tType] : ( comple187826305attice @ ( set @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_2,axiom,
% 2.89/1.58 ! [A7: $tType] : ( boolean_algebra @ ( set @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Set_Oset___Orderings_Oorder__top_3,axiom,
% 2.89/1.58 ! [A7: $tType] : ( order_top @ ( set @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Set_Oset___Orderings_Oorder__bot_4,axiom,
% 2.89/1.58 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 2.89/1.58 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 2.89/1.58 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Set_Oset___Orderings_Otop_7,axiom,
% 2.89/1.58 ! [A7: $tType] : ( top @ ( set @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Set_Oset___Orderings_Oord_8,axiom,
% 2.89/1.58 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Set_Oset___Orderings_Obot_9,axiom,
% 2.89/1.58 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_10,axiom,
% 2.89/1.58 comple187826305attice @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_11,axiom,
% 2.89/1.58 boolean_algebra @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Orderings_Oorder__top_12,axiom,
% 2.89/1.58 order_top @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Orderings_Oorder__bot_13,axiom,
% 2.89/1.58 order_bot @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Orderings_Opreorder_14,axiom,
% 2.89/1.58 preorder @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.89/1.58 linorder @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 2.89/1.58 order @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Orderings_Otop_16,axiom,
% 2.89/1.58 top @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Orderings_Oord_17,axiom,
% 2.89/1.58 ord @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_HOL_Obool___Orderings_Obot_18,axiom,
% 2.89/1.58 bot @ $o ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Complete__Lattices_Ocomplete__lattice_19,axiom,
% 2.89/1.58 comple187826305attice @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Lattices_Oboolean__algebra_20,axiom,
% 2.89/1.58 boolean_algebra @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Orderings_Oorder__top_21,axiom,
% 2.89/1.58 order_top @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_22,axiom,
% 2.89/1.58 order_bot @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_23,axiom,
% 2.89/1.58 preorder @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_24,axiom,
% 2.89/1.58 linorder @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Orderings_Oorder_25,axiom,
% 2.89/1.58 order @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Orderings_Otop_26,axiom,
% 2.89/1.58 top @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Orderings_Oord_27,axiom,
% 2.89/1.58 ord @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Product__Type_Ounit___Orderings_Obot_28,axiom,
% 2.89/1.58 bot @ product_unit ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Complete__Lattices_Ocomplete__lattice_29,axiom,
% 2.89/1.58 ! [A7: $tType] : ( comple187826305attice @ ( refine1665802226e_nres @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__top_30,axiom,
% 2.89/1.58 ! [A7: $tType] : ( order_top @ ( refine1665802226e_nres @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_31,axiom,
% 2.89/1.58 ! [A7: $tType] : ( order_bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_32,axiom,
% 2.89/1.58 ! [A7: $tType] : ( preorder @ ( refine1665802226e_nres @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_33,axiom,
% 2.89/1.58 ! [A7: $tType] : ( order @ ( refine1665802226e_nres @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_34,axiom,
% 2.89/1.58 ! [A7: $tType] : ( top @ ( refine1665802226e_nres @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_35,axiom,
% 2.89/1.58 ! [A7: $tType] : ( ord @ ( refine1665802226e_nres @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_36,axiom,
% 2.89/1.58 ! [A7: $tType] : ( bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(help_If_3_1_T,axiom,
% 2.89/1.58 ! [P: $o] :
% 2.89/1.58 ( ( P = $true )
% 2.89/1.58 | ( P = $false ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(help_If_2_1_T,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,Y3: A] :
% 2.89/1.58 ( ( if @ A @ $false @ X4 @ Y3 )
% 2.89/1.58 = Y3 ) ).
% 2.89/1.58
% 2.89/1.58 thf(help_If_1_1_T,axiom,
% 2.89/1.58 ! [A: $tType,X4: A,Y3: A] :
% 2.89/1.58 ( ( if @ A @ $true @ X4 @ Y3 )
% 2.89/1.58 = X4 ) ).
% 2.89/1.58
% 2.89/1.58 thf(conj_0,hypothesis,
% 2.89/1.58 ( b
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ s1 @ ( refine605929679le_RES @ a @ ( collect @ a @ phi ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(conj_1,hypothesis,
% 2.89/1.58 ( ~ b
% 2.89/1.58 => ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ s2 @ ( refine605929679le_RES @ a @ ( collect @ a @ phi ) ) ) ) ).
% 2.89/1.58
% 2.89/1.58 thf(conj_2,conjecture,
% 2.89/1.58 ord_less_eq @ ( refine1665802226e_nres @ a ) @ ( if @ ( refine1665802226e_nres @ a ) @ b @ s1 @ s2 ) @ ( refine605929679le_RES @ a @ ( collect @ a @ phi ) ) ).
% 2.89/1.58 ------------------------
% 3.10/1.60 % (22307)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/183Mi)
% 3.10/1.60 % (22313)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/18Mi)
% 3.10/1.60 % (22309)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_22115 for (2999ds/27Mi)
% 3.10/1.60 % (22312)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_22115 for (2999ds/275Mi)
% 3.10/1.61 % (22313)Instruction limit reached!
% 3.10/1.61 % (22313)------------------------------
% 3.10/1.61 % (22313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.61 % (22313)Termination reason: Unknown
% 3.10/1.61 % (22313)Termination phase: Property scanning
% 3.10/1.61
% 3.10/1.61 % (22313)Memory used [KB]: 1791
% 3.10/1.61 % (22313)Time elapsed: 0.008 s
% 3.10/1.61 % (22313)Instructions burned: 20 (million)
% 3.10/1.61 % (22313)------------------------------
% 3.10/1.61 % (22313)------------------------------
% 3.10/1.61 % (22310)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/2Mi)
% 3.10/1.61 % (22310)Instruction limit reached!
% 3.10/1.61 % (22310)------------------------------
% 3.10/1.61 % (22310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.61 % (22310)Termination reason: Unknown
% 3.10/1.61 % (22310)Termination phase: shuffling
% 3.10/1.61
% 3.10/1.61 % (22310)Memory used [KB]: 1407
% 3.10/1.61 % (22310)Time elapsed: 0.002 s
% 3.10/1.61 % (22310)Instructions burned: 3 (million)
% 3.10/1.61 % (22310)------------------------------
% 3.10/1.61 % (22310)------------------------------
% 3.10/1.61 % (22311)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_22115 for (2999ds/2Mi)
% 3.10/1.61 % (22311)Instruction limit reached!
% 3.10/1.61 % (22311)------------------------------
% 3.10/1.61 % (22311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.61 % (22311)Termination reason: Unknown
% 3.10/1.61 % (22311)Termination phase: shuffling
% 3.10/1.61
% 3.10/1.61 % (22311)Memory used [KB]: 1407
% 3.10/1.61 % (22311)Time elapsed: 0.003 s
% 3.10/1.61 % (22311)Instructions burned: 3 (million)
% 3.10/1.61 % (22311)------------------------------
% 3.10/1.61 % (22311)------------------------------
% 3.10/1.61 % (22308)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_22115 for (2999ds/4Mi)
% 3.10/1.61 % (22308)Instruction limit reached!
% 3.10/1.61 % (22308)------------------------------
% 3.10/1.61 % (22308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.61 % (22308)Termination reason: Unknown
% 3.10/1.61 % (22308)Termination phase: shuffling
% 3.10/1.61
% 3.10/1.61 % (22308)Memory used [KB]: 1407
% 3.10/1.61 % (22308)Time elapsed: 0.003 s
% 3.10/1.61 % (22308)Instructions burned: 6 (million)
% 3.10/1.61 % (22308)------------------------------
% 3.10/1.61 % (22308)------------------------------
% 3.10/1.61 % (22314)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/3Mi)
% 3.10/1.62 % (22314)Instruction limit reached!
% 3.10/1.62 % (22314)------------------------------
% 3.10/1.62 % (22314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.62 % (22314)Termination reason: Unknown
% 3.10/1.62 % (22314)Termination phase: shuffling
% 3.10/1.62
% 3.10/1.62 % (22314)Memory used [KB]: 1407
% 3.10/1.62 % (22314)Time elapsed: 0.002 s
% 3.10/1.62 % (22314)Instructions burned: 3 (million)
% 3.10/1.62 % (22314)------------------------------
% 3.10/1.62 % (22314)------------------------------
% 3.10/1.62 % (22309)Instruction limit reached!
% 3.10/1.62 % (22309)------------------------------
% 3.10/1.62 % (22309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.62 % (22309)Termination reason: Unknown
% 3.10/1.62 % (22309)Termination phase: Preprocessing 1
% 3.10/1.62
% 3.10/1.62 % (22309)Memory used [KB]: 1791
% 3.10/1.62 % (22309)Time elapsed: 0.016 s
% 3.10/1.62 % (22309)Instructions burned: 28 (million)
% 3.10/1.62 % (22309)------------------------------
% 3.10/1.62 % (22309)------------------------------
% 3.10/1.62 % (22316)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_22115 for (2999ds/15Mi)
% 3.10/1.62 % (22317)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_22115 for (2999ds/3Mi)
% 3.10/1.62 % (22317)Instruction limit reached!
% 3.10/1.62 % (22317)------------------------------
% 3.10/1.62 % (22317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.62 % (22317)Termination reason: Unknown
% 3.10/1.62 % (22317)Termination phase: shuffling
% 3.10/1.62
% 3.10/1.62 % (22317)Memory used [KB]: 1407
% 3.10/1.62 % (22317)Time elapsed: 0.003 s
% 3.10/1.62 % (22317)Instructions burned: 3 (million)
% 3.10/1.62 % (22317)------------------------------
% 3.10/1.62 % (22317)------------------------------
% 3.10/1.62 % (22315)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_22115 for (2999ds/37Mi)
% 3.10/1.63 % (22318)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_22115 for (2999ds/1041Mi)
% 3.10/1.63 % (22316)Instruction limit reached!
% 3.10/1.63 % (22316)------------------------------
% 3.10/1.63 % (22316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.63 % (22316)Termination reason: Unknown
% 3.10/1.63 % (22316)Termination phase: shuffling
% 3.10/1.63
% 3.10/1.63 % (22316)Memory used [KB]: 1791
% 3.10/1.63 % (22316)Time elapsed: 0.007 s
% 3.10/1.63 % (22316)Instructions burned: 17 (million)
% 3.10/1.63 % (22316)------------------------------
% 3.10/1.63 % (22316)------------------------------
% 3.10/1.63 % (22319)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/7Mi)
% 3.10/1.63 % (22320)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/16Mi)
% 3.10/1.64 % (22321)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_22115 for (2999ds/3Mi)
% 3.10/1.64 % (22319)Instruction limit reached!
% 3.10/1.64 % (22319)------------------------------
% 3.10/1.64 % (22319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.64 % (22319)Termination reason: Unknown
% 3.10/1.64 % (22319)Termination phase: shuffling
% 3.10/1.64
% 3.10/1.64 % (22319)Memory used [KB]: 1535
% 3.10/1.64 % (22319)Time elapsed: 0.006 s
% 3.10/1.64 % (22319)Instructions burned: 7 (million)
% 3.10/1.64 % (22319)------------------------------
% 3.10/1.64 % (22319)------------------------------
% 3.10/1.64 % (22321)Instruction limit reached!
% 3.10/1.64 % (22321)------------------------------
% 3.10/1.64 % (22321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.64 % (22321)Termination reason: Unknown
% 3.10/1.64 % (22321)Termination phase: shuffling
% 3.10/1.64
% 3.10/1.64 % (22321)Memory used [KB]: 1407
% 3.10/1.64 % (22321)Time elapsed: 0.003 s
% 3.10/1.64 % (22321)Instructions burned: 4 (million)
% 3.10/1.64 % (22321)------------------------------
% 3.10/1.64 % (22321)------------------------------
% 3.10/1.64 % (22320)Instruction limit reached!
% 3.10/1.64 % (22320)------------------------------
% 3.10/1.64 % (22320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.64 % (22320)Termination reason: Unknown
% 3.10/1.64 % (22320)Termination phase: shuffling
% 3.10/1.64
% 3.10/1.64 % (22320)Memory used [KB]: 1791
% 3.10/1.64 % (22320)Time elapsed: 0.008 s
% 3.10/1.64 % (22320)Instructions burned: 17 (million)
% 3.10/1.64 % (22320)------------------------------
% 3.10/1.64 % (22320)------------------------------
% 3.10/1.64 % (22315)Instruction limit reached!
% 3.10/1.64 % (22315)------------------------------
% 3.10/1.64 % (22315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.64 % (22315)Termination reason: Unknown
% 3.10/1.64 % (22315)Termination phase: Property scanning
% 3.10/1.64
% 3.10/1.64 % (22315)Memory used [KB]: 2174
% 3.10/1.64 % (22315)Time elapsed: 0.019 s
% 3.10/1.64 % (22315)Instructions burned: 37 (million)
% 3.10/1.64 % (22315)------------------------------
% 3.10/1.64 % (22315)------------------------------
% 3.10/1.65 % (22322)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_22115 for (2999ds/3Mi)
% 3.10/1.65 % (22322)Instruction limit reached!
% 3.10/1.65 % (22322)------------------------------
% 3.10/1.65 % (22322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.65 % (22322)Termination reason: Unknown
% 3.10/1.65 % (22322)Termination phase: shuffling
% 3.10/1.65
% 3.10/1.65 % (22322)Memory used [KB]: 1407
% 3.10/1.65 % (22322)Time elapsed: 0.002 s
% 3.10/1.65 % (22322)Instructions burned: 3 (million)
% 3.10/1.65 % (22322)------------------------------
% 3.10/1.65 % (22322)------------------------------
% 3.10/1.65 % (22323)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/7Mi)
% 3.10/1.65 % (22323)Instruction limit reached!
% 3.10/1.65 % (22323)------------------------------
% 3.10/1.65 % (22323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.65 % (22323)Termination reason: Unknown
% 3.10/1.65 % (22323)Termination phase: shuffling
% 3.10/1.65
% 3.10/1.65 % (22323)Memory used [KB]: 1535
% 3.10/1.65 % (22323)Time elapsed: 0.004 s
% 3.10/1.65 % (22323)Instructions burned: 8 (million)
% 3.10/1.65 % (22323)------------------------------
% 3.10/1.65 % (22323)------------------------------
% 3.10/1.65 % (22324)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/3Mi)
% 3.10/1.65 % (22324)Instruction limit reached!
% 3.10/1.65 % (22324)------------------------------
% 3.10/1.65 % (22324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.65 % (22324)Termination reason: Unknown
% 3.10/1.65 % (22324)Termination phase: shuffling
% 3.10/1.65
% 3.10/1.65 % (22324)Memory used [KB]: 1407
% 3.10/1.65 % (22324)Time elapsed: 0.003 s
% 3.10/1.65 % (22324)Instructions burned: 4 (million)
% 3.10/1.65 % (22324)------------------------------
% 3.10/1.65 % (22324)------------------------------
% 3.10/1.66 % (22326)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/18Mi)
% 3.10/1.66 % (22325)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/4Mi)
% 3.10/1.66 % (22325)Instruction limit reached!
% 3.10/1.66 % (22325)------------------------------
% 3.10/1.66 % (22325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.66 % (22325)Termination reason: Unknown
% 3.10/1.66 % (22325)Termination phase: shuffling
% 3.10/1.66
% 3.10/1.66 % (22325)Memory used [KB]: 1407
% 3.10/1.66 % (22325)Time elapsed: 0.004 s
% 3.10/1.66 % (22325)Instructions burned: 5 (million)
% 3.10/1.66 % (22325)------------------------------
% 3.10/1.66 % (22325)------------------------------
% 3.10/1.66 % (22327)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/710Mi)
% 3.10/1.66 % (22328)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/6Mi)
% 3.10/1.66 % (22326)Instruction limit reached!
% 3.10/1.66 % (22326)------------------------------
% 3.10/1.66 % (22326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.66 % (22326)Termination reason: Unknown
% 3.10/1.66 % (22326)Termination phase: shuffling
% 3.10/1.66
% 3.10/1.66 % (22326)Memory used [KB]: 1791
% 3.10/1.66 % (22326)Time elapsed: 0.007 s
% 3.10/1.66 % (22326)Instructions burned: 18 (million)
% 3.10/1.66 % (22326)------------------------------
% 3.10/1.66 % (22326)------------------------------
% 3.10/1.66 % (22328)Instruction limit reached!
% 3.10/1.66 % (22328)------------------------------
% 3.10/1.66 % (22328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.66 % (22328)Termination reason: Unknown
% 3.10/1.66 % (22328)Termination phase: shuffling
% 3.10/1.66
% 3.10/1.66 % (22328)Memory used [KB]: 1535
% 3.10/1.66 % (22328)Time elapsed: 0.004 s
% 3.10/1.66 % (22328)Instructions burned: 6 (million)
% 3.10/1.66 % (22328)------------------------------
% 3.10/1.66 % (22328)------------------------------
% 3.10/1.67 % (22329)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_22115 for (2999ds/902Mi)
% 3.10/1.67 % (22307)Instruction limit reached!
% 3.10/1.67 % (22307)------------------------------
% 3.10/1.67 % (22307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.67 % (22307)Termination reason: Unknown
% 3.10/1.67 % (22307)Termination phase: Saturation
% 3.10/1.67
% 3.10/1.67 % (22307)Memory used [KB]: 7164
% 3.10/1.67 % (22307)Time elapsed: 0.075 s
% 3.10/1.67 % (22307)Instructions burned: 183 (million)
% 3.10/1.67 % (22307)------------------------------
% 3.10/1.67 % (22307)------------------------------
% 3.10/1.67 % (22330)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_22115 for (2999ds/21Mi)
% 3.10/1.67 % (22331)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/5Mi)
% 3.10/1.68 % (22331)Instruction limit reached!
% 3.10/1.68 % (22331)------------------------------
% 3.10/1.68 % (22331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.68 % (22331)Termination reason: Unknown
% 3.10/1.68 % (22331)Termination phase: shuffling
% 3.10/1.68
% 3.10/1.68 % (22331)Memory used [KB]: 1535
% 3.10/1.68 % (22331)Time elapsed: 0.003 s
% 3.10/1.68 % (22331)Instructions burned: 7 (million)
% 3.10/1.68 % (22331)------------------------------
% 3.10/1.68 % (22331)------------------------------
% 3.10/1.68 % (22330)Instruction limit reached!
% 3.10/1.68 % (22330)------------------------------
% 3.10/1.68 % (22330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.68 % (22330)Termination reason: Unknown
% 3.10/1.68 % (22330)Termination phase: Property scanning
% 3.10/1.68
% 3.10/1.68 % (22330)Memory used [KB]: 1791
% 3.10/1.68 % (22330)Time elapsed: 0.009 s
% 3.10/1.68 % (22330)Instructions burned: 24 (million)
% 3.10/1.68 % (22330)------------------------------
% 3.10/1.68 % (22330)------------------------------
% 3.10/1.69 % (22333)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22115 for (2999ds/377Mi)
% 3.10/1.69 % (22332)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_22115 for (2999ds/6Mi)
% 3.10/1.69 % (22334)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_22115 for (2999ds/779Mi)
% 3.10/1.69 % (22332)Instruction limit reached!
% 3.10/1.69 % (22332)------------------------------
% 3.10/1.69 % (22332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.69 % (22332)Termination reason: Unknown
% 3.10/1.69 % (22332)Termination phase: shuffling
% 3.10/1.69
% 3.10/1.69 % (22332)Memory used [KB]: 1535
% 3.10/1.69 % (22332)Time elapsed: 0.003 s
% 3.10/1.69 % (22332)Instructions burned: 6 (million)
% 3.10/1.69 % (22332)------------------------------
% 3.10/1.69 % (22332)------------------------------
% 3.10/1.70 % (22340)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_22115 for (2999ds/19Mi)
% 3.10/1.70 % (22312)Instruction limit reached!
% 3.10/1.70 % (22312)------------------------------
% 3.10/1.70 % (22312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.70 % (22312)Termination reason: Unknown
% 3.10/1.70 % (22312)Termination phase: Saturation
% 3.10/1.70
% 3.10/1.70 % (22312)Memory used [KB]: 6908
% 3.10/1.70 % (22312)Time elapsed: 0.099 s
% 3.10/1.70 % (22312)Instructions burned: 276 (million)
% 3.10/1.70 % (22312)------------------------------
% 3.10/1.70 % (22312)------------------------------
% 3.10/1.71 % (22340)Instruction limit reached!
% 3.10/1.71 % (22340)------------------------------
% 3.10/1.71 % (22340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.71 % (22340)Termination reason: Unknown
% 3.10/1.71 % (22340)Termination phase: shuffling
% 3.10/1.71
% 3.10/1.71 % (22340)Memory used [KB]: 1791
% 3.10/1.71 % (22340)Time elapsed: 0.007 s
% 3.10/1.71 % (22340)Instructions burned: 20 (million)
% 3.10/1.71 % (22340)------------------------------
% 3.10/1.71 % (22340)------------------------------
% 3.10/1.71 % (22341)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22115 for (2998ds/879Mi)
% 3.10/1.71 % (22327)First to succeed.
% 3.10/1.72 % (22327)Refutation found. Thanks to Tanya!
% 3.10/1.72 % SZS status Theorem for DTF2THF_22115
% 3.10/1.72 % SZS output start Proof for DTF2THF_22115
% 3.10/1.72 thf(type_def_6, type, product_unit: $tType).
% 3.10/1.72 thf(type_def_7, type, refine1665802226e_nres: ($tType) > $tType).
% 3.10/1.72 thf(type_def_8, type, set: ($tType) > $tType).
% 3.10/1.72 thf(type_def_9, type, a: $tType).
% 3.10/1.72 thf(func_def_0, type, refine1665802226e_nres: ($tType) > $tType).
% 3.10/1.72 thf(func_def_1, type, product_unit: $tType).
% 3.10/1.72 thf(func_def_2, type, set: ($tType) > $tType).
% 3.10/1.72 thf(func_def_3, type, a: $tType).
% 3.10/1.72 thf(func_def_4, type, type: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_5, type, bot: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_6, type, ord: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_7, type, top: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_8, type, order: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_9, type, group_add: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_11, type, preorder: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_12, type, order_bot: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_13, type, order_top: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_14, type, boolean_algebra: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_16, type, comple187826305attice: !>[X0: $tType]:($o)).
% 3.10/1.72 thf(func_def_17, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 3.10/1.72 thf(func_def_18, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.10/1.72 thf(func_def_19, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.10/1.72 thf(func_def_20, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.10/1.72 thf(func_def_21, type, order_Greatest: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.10/1.72 thf(func_def_22, type, top_top: !>[X0: $tType]:(X0)).
% 3.10/1.72 thf(func_def_23, type, partial_flat_ord: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 3.10/1.72 thf(func_def_24, type, refine1946708059ASSUME: $o > refine1665802226e_nres @ product_unit).
% 3.10/1.72 thf(func_def_25, type, refine1687780735RETURN: !>[X0: $tType]:(X0 > refine1665802226e_nres @ X0)).
% 3.10/1.72 thf(func_def_26, type, refine463715084e_bind: !>[X0: $tType, X1: $tType]:(refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1)).
% 3.10/1.72 thf(func_def_27, type, refine1315500908_inres: !>[X0: $tType]:(refine1665802226e_nres @ X0 > X0 > $o)).
% 3.10/1.72 thf(func_def_28, type, refine406925620_inres: !>[X0: $tType]:(refine1665802226e_nres @ X0 > X0 > $o)).
% 3.10/1.72 thf(func_def_29, type, refine1102455758nofail: !>[X0: $tType]:(refine1665802226e_nres @ X0 > $o)).
% 3.10/1.72 thf(func_def_30, type, refine1767639642_FAILi: !>[X0: $tType]:(refine1665802226e_nres @ X0)).
% 3.10/1.72 thf(func_def_31, type, refine605929679le_RES: !>[X0: $tType]:(set @ X0 > refine1665802226e_nres @ X0)).
% 3.10/1.72 thf(func_def_32, type, refine60818195e_nres: !>[X0: $tType, X1: $tType]:(X0 > (set @ X1 > X0) > refine1665802226e_nres @ X1 > X0)).
% 3.10/1.72 thf(func_def_33, type, refine1442219249c_nres: !>[X0: $tType, X1: $tType]:(X0 > (set @ X1 > X0) > refine1665802226e_nres @ X1 > X0)).
% 3.10/1.72 thf(func_def_34, type, refine1672542526he_RES: !>[X0: $tType]:(refine1665802226e_nres @ X0 > set @ X0)).
% 3.10/1.72 thf(func_def_35, type, refine_strict: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 3.10/1.72 thf(func_def_36, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.10/1.72 thf(func_def_37, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 3.10/1.72 thf(func_def_38, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 3.10/1.72 thf(func_def_39, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 3.10/1.72 thf(func_def_40, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 3.10/1.72 thf(func_def_41, type, set_atLeast: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 3.10/1.72 thf(func_def_42, type, set_atLeastAtMost: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > set @ X0)).
% 3.10/1.72 thf(func_def_43, type, set_atMost: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 3.10/1.72 thf(func_def_44, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.10/1.72 thf(func_def_45, type, s1: refine1665802226e_nres @ a).
% 3.10/1.72 thf(func_def_46, type, s2: refine1665802226e_nres @ a).
% 3.10/1.72 thf(func_def_47, type, phi: a > $o).
% 3.10/1.72 thf(func_def_62, type, sK0: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.10/1.72 thf(func_def_63, type, sK1: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.10/1.72 thf(func_def_64, type, sK2: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 3.10/1.72 thf(func_def_65, type, sK3: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 3.10/1.72 thf(func_def_66, type, sK4: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.10/1.72 thf(func_def_67, type, sK5: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.10/1.72 thf(func_def_68, type, sK6: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.10/1.72 thf(func_def_69, type, sK7: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.10/1.72 thf(func_def_70, type, sK8: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.10/1.72 thf(func_def_71, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.10/1.72 thf(func_def_73, type, ph11: !>[X0: $tType]:(X0)).
% 3.10/1.72 thf(f1319,plain,(
% 3.10/1.72 $false),
% 3.10/1.72 inference(avatar_sat_refutation,[status(thm)],[f989,f994,f1002,f1315])).
% 3.10/1.72 thf(f1315,plain,(
% 3.10/1.72 ~spl10_1 | spl10_2),
% 3.10/1.72 inference(avatar_contradiction_clause,[status(thm)],[f1314])).
% 3.10/1.72 thf(f1314,plain,(
% 3.10/1.72 $false | (~spl10_1 | spl10_2)),
% 3.10/1.72 inference(subsumption_resolution,[status(thm)],[f1313,f984])).
% 3.10/1.72 thf(f984,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true) | ~spl10_1),
% 3.10/1.72 inference(avatar_component_clause,[status(thm)],[f982])).
% 3.10/1.72 thf(f982,definition,(
% 3.10/1.72 spl10_1 <=> ((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true)),
% 3.10/1.72 introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition])).
% 3.10/1.72 thf(f1313,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) != $true) | spl10_2),
% 3.10/1.72 inference(forward_demodulation,[status(thm)],[f1311,f925])).
% 3.10/1.72 thf(f925,plain,(
% 3.10/1.72 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((if @ X0 @ $false @ X1 @ X2) = X2)) )),
% 3.10/1.72 inference(cnf_transformation,[status(thm)],[f360])).
% 3.10/1.72 thf(f360,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0,X2 : X0] : ((if @ X0 @ $false @ X1 @ X2) = X2)),
% 3.10/1.72 inference(fool_elimination,[status(thm)],[f359])).
% 3.10/1.72 thf(f359,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0,X2 : X0] : (X2 = (if @ X0 @ $false @ X1 @ X2))),
% 3.10/1.72 inference(rectify,[status(thm)],[f302])).
% 3.10/1.72 thf(f302,axiom,(
% 3.10/1.72 ! [X0 : $tType,X11 : X0,X12 : X0] : (X12 = (if @ X0 @ $false @ X11 @ X12))),
% 3.10/1.72 file('/export/starexec/sandbox/tmp/tmp.eee0ELY9Y3/DTF2THF_22115.p',help_If_2_1_T)).
% 3.10/1.72 thf(f1311,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ $false @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi))) != $true) | spl10_2),
% 3.10/1.72 inference(backward_demodulation,[status(thm)],[f899,f1310])).
% 3.10/1.72 thf(f1310,plain,(
% 3.10/1.72 (b = $false) | spl10_2),
% 3.10/1.72 inference(trivial_inequality_removal,[status(thm)],[f1309])).
% 3.10/1.72 thf(f1309,plain,(
% 3.10/1.72 ($false = $true) | (b = $false) | spl10_2),
% 3.10/1.72 inference(forward_demodulation,[status(thm)],[f1305,f1307])).
% 3.10/1.72 thf(f1307,plain,(
% 3.10/1.72 ( ! [X0 : $tType,X1 : X0] : (($false = (bot_bot @ (X0 > $o) @ X1))) ) | spl10_2),
% 3.10/1.72 inference(subsumption_resolution,[status(thm)],[f1304,f987])).
% 3.10/1.72 thf(f987,plain,(
% 3.10/1.72 (b != $true) | spl10_2),
% 3.10/1.72 inference(avatar_component_clause,[status(thm)],[f986])).
% 3.10/1.72 thf(f986,definition,(
% 3.10/1.72 spl10_2 <=> (b = $true)),
% 3.10/1.72 introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition])).
% 3.10/1.72 thf(f1304,plain,(
% 3.10/1.72 ( ! [X0 : $tType,X1 : X0] : (($false = (bot_bot @ (X0 > $o) @ X1)) | (b = $true)) ) | spl10_2),
% 3.10/1.72 inference(binary_proxy_clausification,[status(thm)],[f1303])).
% 3.10/1.72 thf(f1303,plain,(
% 3.10/1.72 ( ! [X0 : $tType,X1 : X0] : ((b = (bot_bot @ (X0 > $o) @ X1))) ) | spl10_2),
% 3.10/1.72 inference(beta_eta_normalization,[status(thm)],[f1298])).
% 3.10/1.72 thf(f1298,plain,(
% 3.10/1.72 ( ! [X0 : $tType,X1 : X0] : ((((^[Y0 : X0]: (b)) @ X1) = (bot_bot @ (X0 > $o) @ X1))) ) | spl10_2),
% 3.10/1.72 inference(argument_congruence,[status(thm)],[f1292])).
% 3.10/1.72 thf(f1292,plain,(
% 3.10/1.72 ( ! [X0 : $tType] : ((bot_bot @ (X0 > $o) = (^[Y0 : X0]: (b)))) ) | spl10_2),
% 3.10/1.72 inference(trivial_inequality_removal,[status(thm)],[f1291])).
% 3.10/1.72 thf(f1291,plain,(
% 3.10/1.72 ( ! [X0 : $tType] : ((bot_bot @ set @ X0 != bot_bot @ set @ X0) | (bot_bot @ (X0 > $o) = (^[Y0 : X0]: (b)))) ) | spl10_2),
% 3.10/1.72 inference(superposition,[status(thm)],[f938,f1039])).
% 3.10/1.72 thf(f1039,plain,(
% 3.10/1.72 ( ! [X0 : $tType] : ((bot_bot @ set @ X0 = (collect @ X0 @ (^[Y0 : X0]: (b))))) ) | spl10_2),
% 3.10/1.72 inference(trivial_inequality_removal,[status(thm)],[f1028])).
% 3.10/1.72 thf(f1028,plain,(
% 3.10/1.72 ( ! [X0 : $tType] : ((bot_bot @ set @ X0 = (collect @ X0 @ (^[Y0 : X0]: (b)))) | ($true != $true)) ) | spl10_2),
% 3.10/1.72 inference(superposition,[status(thm)],[f987,f941])).
% 3.10/1.72 thf(f941,plain,(
% 3.10/1.72 ( ! [X0 : $tType,X1 : X0 > $o] : (((X1 @ (sK6 @ X0 @ X1)) = $true) | (bot_bot @ set @ X0 = (collect @ X0 @ X1))) )),
% 3.10/1.72 inference(cnf_transformation,[status(thm)],[f887])).
% 3.10/1.72 thf(f887,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : (((bot_bot @ set @ X0 = (collect @ X0 @ X1)) | ((X1 @ (sK6 @ X0 @ X1)) = $true)) & (! [X3 : X0] : ((X1 @ X3) != $true) | (bot_bot @ set @ X0 != (collect @ X0 @ X1))))),
% 3.10/1.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f885,f886])).
% 3.10/1.72 thf(f886,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0] : ((X1 @ X2) = $true) => ((X1 @ (sK6 @ X0 @ X1)) = $true))),
% 3.10/1.72 introduced(definition,[],[choice_axiom])).
% 3.10/1.72 thf(f885,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : (((bot_bot @ set @ X0 = (collect @ X0 @ X1)) | ? [X2 : X0] : ((X1 @ X2) = $true)) & (! [X3 : X0] : ((X1 @ X3) != $true) | (bot_bot @ set @ X0 != (collect @ X0 @ X1))))),
% 3.10/1.72 inference(rectify,[status(thm)],[f884])).
% 3.10/1.72 thf(f884,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : (((bot_bot @ set @ X0 = (collect @ X0 @ X1)) | ? [X2 : X0] : ((X1 @ X2) = $true)) & (! [X2 : X0] : ((X1 @ X2) != $true) | (bot_bot @ set @ X0 != (collect @ X0 @ X1))))),
% 3.10/1.72 inference(nnf_transformation,[status(thm)],[f831])).
% 3.10/1.72 thf(f831,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : ((bot_bot @ set @ X0 = (collect @ X0 @ X1)) <=> ! [X2 : X0] : ((X1 @ X2) != $true))),
% 3.10/1.72 inference(flattening,[status(thm)],[f725])).
% 3.10/1.72 thf(f725,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : (! [X2 : X0] : ~((X1 @ X2) = $true) <=> (bot_bot @ set @ X0 = (collect @ X0 @ X1)))),
% 3.10/1.72 inference(fool_elimination,[status(thm)],[f724])).
% 3.10/1.72 thf(f724,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : (! [X2 : X0] : ~(X1 @ X2) = (bot_bot @ set @ X0 = (collect @ X0 @ X1)))),
% 3.10/1.72 inference(rectify,[status(thm)],[f109])).
% 3.10/1.72 thf(f109,axiom,(
% 3.10/1.72 ! [X0 : $tType,X43 : X0 > $o] : (! [X28 : X0] : ~(X43 @ X28) = ((collect @ X0 @ X43) = bot_bot @ set @ X0))),
% 3.10/1.72 file('/export/starexec/sandbox/tmp/tmp.eee0ELY9Y3/DTF2THF_22115.p',fact_108_Collect__empty__eq)).
% 3.10/1.72 thf(f938,plain,(
% 3.10/1.72 ( ! [X0 : $tType,X1 : X0 > $o] : ((bot_bot @ set @ X0 != (collect @ X0 @ X1)) | (bot_bot @ (X0 > $o) = X1)) )),
% 3.10/1.72 inference(cnf_transformation,[status(thm)],[f883])).
% 3.10/1.72 thf(f883,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : (((bot_bot @ (X0 > $o) = X1) | (bot_bot @ set @ X0 != (collect @ X0 @ X1))) & ((bot_bot @ set @ X0 = (collect @ X0 @ X1)) | (bot_bot @ (X0 > $o) != X1)))),
% 3.10/1.72 inference(nnf_transformation,[status(thm)],[f701])).
% 3.10/1.72 thf(f701,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : ((bot_bot @ (X0 > $o) = X1) <=> (bot_bot @ set @ X0 = (collect @ X0 @ X1)))),
% 3.10/1.72 inference(fool_elimination,[status(thm)],[f700])).
% 3.10/1.72 thf(f700,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0 > $o] : ((bot_bot @ set @ X0 = (collect @ X0 @ X1)) = (bot_bot @ (X0 > $o) = X1))),
% 3.10/1.72 inference(rectify,[status(thm)],[f184])).
% 3.10/1.72 thf(f184,axiom,(
% 3.10/1.72 ! [X0 : $tType,X43 : X0 > $o] : (((collect @ X0 @ X43) = bot_bot @ set @ X0) = (bot_bot @ (X0 > $o) = X43))),
% 3.10/1.72 file('/export/starexec/sandbox/tmp/tmp.eee0ELY9Y3/DTF2THF_22115.p',fact_183_Collect__empty__eq__bot)).
% 3.10/1.72 thf(f1305,plain,(
% 3.10/1.72 ( ! [X0 : $tType,X1 : X0] : ((b = $false) | ((bot_bot @ (X0 > $o) @ X1) = $true)) ) | spl10_2),
% 3.10/1.72 inference(binary_proxy_clausification,[status(thm)],[f1303])).
% 3.10/1.72 thf(f899,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi))) != $true)),
% 3.10/1.72 inference(cnf_transformation,[status(thm)],[f824])).
% 3.10/1.72 thf(f824,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi))) != $true)),
% 3.10/1.72 inference(flattening,[status(thm)],[f344])).
% 3.10/1.72 thf(f344,plain,(
% 3.10/1.72 ~((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true)),
% 3.10/1.72 inference(fool_elimination,[status(thm)],[f343])).
% 3.10/1.72 thf(f343,plain,(
% 3.10/1.72 ~(ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 3.10/1.72 inference(rectify,[status(thm)],[f307])).
% 3.10/1.72 thf(f307,negated_conjecture,(
% 3.10/1.72 ~(ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 3.10/1.72 inference(negated_conjecture,[status(cth)],[f306])).
% 3.10/1.72 thf(f306,conjecture,(
% 3.10/1.72 (ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 3.10/1.72 file('/export/starexec/sandbox/tmp/tmp.eee0ELY9Y3/DTF2THF_22115.p',conj_2)).
% 3.10/1.72 thf(f1002,plain,(
% 3.10/1.72 ~spl10_2 | ~spl10_3),
% 3.10/1.72 inference(avatar_contradiction_clause,[status(thm)],[f1001])).
% 3.10/1.72 thf(f1001,plain,(
% 3.10/1.72 $false | (~spl10_2 | ~spl10_3)),
% 3.10/1.72 inference(subsumption_resolution,[status(thm)],[f1000,f993])).
% 3.10/1.72 thf(f993,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true) | ~spl10_3),
% 3.10/1.72 inference(avatar_component_clause,[status(thm)],[f991])).
% 3.10/1.72 thf(f991,definition,(
% 3.10/1.72 spl10_3 <=> ((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true)),
% 3.10/1.72 introduced(definition,[new_symbols(naming,[spl10_3])],[avatar_definition])).
% 3.10/1.72 thf(f1000,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) != $true) | ~spl10_2),
% 3.10/1.72 inference(forward_demodulation,[status(thm)],[f999,f939])).
% 3.10/1.72 thf(f939,plain,(
% 3.10/1.72 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((if @ X0 @ $true @ X1 @ X2) = X1)) )),
% 3.10/1.72 inference(cnf_transformation,[status(thm)],[f440])).
% 3.10/1.72 thf(f440,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0,X2 : X0] : ((if @ X0 @ $true @ X1 @ X2) = X1)),
% 3.10/1.72 inference(fool_elimination,[status(thm)],[f439])).
% 3.10/1.72 thf(f439,plain,(
% 3.10/1.72 ! [X0 : $tType,X1 : X0,X2 : X0] : ((if @ X0 @ $true @ X1 @ X2) = X1)),
% 3.10/1.72 inference(rectify,[status(thm)],[f303])).
% 3.10/1.72 thf(f303,axiom,(
% 3.10/1.72 ! [X0 : $tType,X11 : X0,X12 : X0] : ((if @ X0 @ $true @ X11 @ X12) = X11)),
% 3.10/1.72 file('/export/starexec/sandbox/tmp/tmp.eee0ELY9Y3/DTF2THF_22115.p',help_If_1_1_T)).
% 3.10/1.72 thf(f999,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ $true @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi))) != $true) | ~spl10_2),
% 3.10/1.72 inference(backward_demodulation,[status(thm)],[f899,f988])).
% 3.10/1.72 thf(f988,plain,(
% 3.10/1.72 (b = $true) | ~spl10_2),
% 3.10/1.72 inference(avatar_component_clause,[status(thm)],[f986])).
% 3.10/1.72 thf(f994,plain,(
% 3.10/1.72 ~spl10_2 | spl10_3),
% 3.10/1.72 inference(avatar_split_clause,[status(thm)],[f936,f991,f986])).
% 3.10/1.72 thf(f936,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true) | (b != $true)),
% 3.10/1.72 inference(cnf_transformation,[status(thm)],[f840])).
% 3.10/1.72 thf(f840,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true) | (b != $true)),
% 3.10/1.72 inference(ennf_transformation,[status(thm)],[f603])).
% 3.10/1.72 thf(f603,plain,(
% 3.10/1.72 (b = $true) => ((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true)),
% 3.10/1.72 inference(fool_elimination,[status(thm)],[f602])).
% 3.10/1.72 thf(f602,plain,(
% 3.10/1.72 b => (ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 3.10/1.72 inference(rectify,[status(thm)],[f304])).
% 3.10/1.72 thf(f304,axiom,(
% 3.10/1.72 b => (ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 3.10/1.72 file('/export/starexec/sandbox/tmp/tmp.eee0ELY9Y3/DTF2THF_22115.p',conj_0)).
% 3.10/1.72 thf(f989,plain,(
% 3.10/1.72 spl10_1 | spl10_2),
% 3.10/1.72 inference(avatar_split_clause,[status(thm)],[f917,f986,f982])).
% 3.10/1.72 thf(f917,plain,(
% 3.10/1.72 ((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true) | (b = $true)),
% 3.10/1.72 inference(cnf_transformation,[status(thm)],[f856])).
% 3.10/1.72 thf(f856,plain,(
% 3.10/1.72 (b = $true) | ((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true)),
% 3.10/1.72 inference(ennf_transformation,[status(thm)],[f825])).
% 3.10/1.72 thf(f825,plain,(
% 3.10/1.72 (b != $true) => ((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true)),
% 3.10/1.72 inference(flattening,[status(thm)],[f412])).
% 3.10/1.72 thf(f412,plain,(
% 3.10/1.72 ~(b = $true) => ((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi))) = $true)),
% 3.10/1.72 inference(fool_elimination,[status(thm)],[f411])).
% 3.10/1.72 thf(f411,plain,(
% 3.10/1.72 ~b => (ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 3.10/1.72 inference(rectify,[status(thm)],[f305])).
% 3.10/1.72 thf(f305,axiom,(
% 3.10/1.72 ~b => (ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 3.10/1.72 file('/export/starexec/sandbox/tmp/tmp.eee0ELY9Y3/DTF2THF_22115.p',conj_1)).
% 3.10/1.72 % SZS output end Proof for DTF2THF_22115
% 3.10/1.72 % (22327)------------------------------
% 3.10/1.72 % (22327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.72 % (22327)Termination reason: Refutation
% 3.10/1.72
% 3.10/1.72 % (22327)Memory used [KB]: 6652
% 3.10/1.72 % (22327)Time elapsed: 0.055 s
% 3.10/1.72 % (22327)Instructions burned: 147 (million)
% 3.10/1.72 % (22327)------------------------------
% 3.10/1.72 % (22327)------------------------------
% 3.10/1.72 % (22306)Success in time 0.122 s
%------------------------------------------------------------------------------