%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP162^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 08:56:03 AM UTC 2026
% Result : Theorem 3.06s 1.77s
% Output : Refutation 3.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP162^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n015.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 08:28:31 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP162^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer Refine_Basic problem prob_1909__3604894_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : Refine_Basic/prob_1909__3604894_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 350 ( 128 unt; 38 typ; 0 def)
% 0.30/0.46 % Number of atoms : 789 ( 223 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.30/0.46 % Number of connectives : 3541 ( 46 ~; 3 |; 33 &;3068 @)
% 0.30/0.46 % ( 0 <=>; 391 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 19 ( 7 avg)
% 0.30/0.46 % Number of types : 3 ( 2 usr)
% 0.30/0.46 % Number of type conns : 190 ( 190 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 39 ( 36 usr; 3 con; 0-5 aty)
% 0.30/0.46 % Number of variables : 1063 ( 97 ^; 931 !; 2 ?;1063 :)
% 0.30/0.46 % ( 33 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:21:30.432
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (4)
% 0.30/0.46 thf(ty_t_Refine__Basic__Mirabelle__tqojlsrkwy_Onres,type,
% 0.30/0.46 refine1665802226e_nres: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Product__Type_Ounit,type,
% 0.30/0.46 product_unit: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (34)
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/0.46 bounded_lattice:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_HOL_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Obot,type,
% 0.30/0.46 bot:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.46 ord:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Otop,type,
% 0.30/0.46 top:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.46 order:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Olattice,type,
% 0.30/0.46 lattice:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.46 linorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.46 preorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.30/0.46 order_bot:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.30/0.46 semilattice_inf:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.30/0.46 bounded_lattice_bot:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__semilattice__inf__top,type,
% 0.30/0.46 bounde1561333602nf_top:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_If,type,
% 0.30/0.46 if:
% 0.30/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.30/0.46 inf_inf:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/0.46 bot_bot:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.46 ord_less_eq:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.30/0.46 order_Greatest:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.30/0.46 top_top:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_ORETURN,type,
% 0.30/0.46 refine1687780735RETURN:
% 0.30/0.46 !>[A: $tType] : ( A > ( refine1665802226e_nres @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Obind,type,
% 0.30/0.46 refine463715084e_bind:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( ( refine1665802226e_nres @ B ) > ( B > ( refine1665802226e_nres @ A ) ) > ( refine1665802226e_nres @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Oinres,type,
% 0.30/0.46 refine1315500908_inres:
% 0.30/0.46 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onf__inres,type,
% 0.30/0.46 refine406925620_inres:
% 0.30/0.46 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onofail,type,
% 0.30/0.46 refine1102455758nofail:
% 0.30/0.46 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_OFAILi,type,
% 0.30/0.46 refine1767639642_FAILi:
% 0.30/0.46 !>[A: $tType] : ( refine1665802226e_nres @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_ORES,type,
% 0.30/0.46 refine605929679le_RES:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > ( refine1665802226e_nres @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_Orec__nres,type,
% 0.30/0.46 refine1442219249c_nres:
% 0.30/0.46 !>[C: $tType,A: $tType] : ( C > ( ( set @ A ) > C ) > ( refine1665802226e_nres @ A ) > C ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Othe__RES,type,
% 0.30/0.46 refine1672542526he_RES:
% 0.30/0.46 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_OPowp,type,
% 0.30/0.46 powp:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_A,type,
% 0.30/0.46 a2: refine1665802226e_nres @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_P,type,
% 0.30/0.46 p: a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_Q,type,
% 0.30/0.46 q: a > $o ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (251)
% 0.30/0.46 thf(fact_0_nres__more__simps_I4_J,axiom,
% 0.30/0.46 ! [A: $tType,X: set @ A,Y: set @ A] :
% 0.30/0.46 ( ( ( refine605929679le_RES @ A @ X )
% 0.30/0.46 = ( refine605929679le_RES @ A @ Y ) )
% 0.30/0.46 = ( X = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_more_simps(4)
% 0.30/0.46 thf(fact_1_nres_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,X2: set @ A,Y2: set @ A] :
% 0.30/0.46 ( ( ( refine605929679le_RES @ A @ X2 )
% 0.30/0.46 = ( refine605929679le_RES @ A @ Y2 ) )
% 0.30/0.46 = ( X2 = Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres.inject
% 0.30/0.46 thf(fact_2_assms_I2_J,axiom,
% 0.30/0.46 ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( refine605929679le_RES @ a @ ( collect @ a @ q ) ) ).
% 0.30/0.46
% 0.30/0.46 % assms(2)
% 0.30/0.46 thf(fact_3_assms_I1_J,axiom,
% 0.30/0.46 ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( refine605929679le_RES @ a @ ( collect @ a @ p ) ) ).
% 0.30/0.46
% 0.30/0.46 % assms(1)
% 0.30/0.46 thf(fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062,axiom,
% 0.30/0.46 ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( inf_inf @ ( refine1665802226e_nres @ a ) @ ( refine605929679le_RES @ a @ ( collect @ a @ p ) ) @ ( refine605929679le_RES @ a @ ( collect @ a @ q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>A \<le> inf (SPEC P) (SPEC Q)\<close>
% 0.30/0.46 thf(fact_5_if__rule,axiom,
% 0.30/0.46 ! [A: $tType,B2: $o,S1: refine1665802226e_nres @ A,Phi: A > $o,S2: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S1 @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) )
% 0.30/0.46 => ( ( ~ B2
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S2 @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( if @ ( refine1665802226e_nres @ A ) @ B2 @ S1 @ S2 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % if_rule
% 0.30/0.46 thf(fact_6_RES__rule,axiom,
% 0.30/0.46 ! [A: $tType,S: set @ A,Phi: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ S )
% 0.30/0.46 => ( Phi @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ S ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % RES_rule
% 0.30/0.46 thf(fact_7_SPEC__iff,axiom,
% 0.30/0.46 ! [A: $tType,P: refine1665802226e_nres @ A,Q: A > $o,R: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ P
% 0.30/0.46 @ ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [S3: A] :
% 0.30/0.46 ( ( Q @ S3 )
% 0.30/0.46 => ( R @ S3 ) ) ) ) )
% 0.30/0.46 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ P
% 0.30/0.46 @ ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [S3: A] :
% 0.30/0.46 ( ~ ( Q @ S3 )
% 0.30/0.46 => ~ ( R @ S3 ) ) ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ P
% 0.30/0.46 @ ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [S3: A] :
% 0.30/0.46 ( ( Q @ S3 )
% 0.30/0.46 = ( R @ S3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % SPEC_iff
% 0.30/0.46 thf(fact_8_SPEC__rule,axiom,
% 0.30/0.46 ! [A: $tType,Phi: A > $o,Phi2: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( Phi @ X3 )
% 0.30/0.46 => ( Phi2 @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % SPEC_rule
% 0.30/0.46 thf(fact_9_SPEC__trans,axiom,
% 0.30/0.46 ! [A: $tType,X4: refine1665802226e_nres @ A,Y3: refine1665802226e_nres @ A,Postcond: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Y3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ Y3 @ ( refine605929679le_RES @ A @ ( collect @ A @ Postcond ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ ( refine605929679le_RES @ A @ ( collect @ A @ Postcond ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % SPEC_trans
% 0.30/0.46 thf(fact_10_lhs__step__If,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [B2: $o,T: A,M: A,E: A] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 => ( ord_less_eq @ A @ T @ M ) )
% 0.30/0.46 => ( ( ~ B2
% 0.30/0.46 => ( ord_less_eq @ A @ E @ M ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( if @ A @ B2 @ T @ E ) @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lhs_step_If
% 0.30/0.46 thf(fact_11_use__spec__rule,axiom,
% 0.30/0.46 ! [A: $tType,M: refine1665802226e_nres @ A,Psi: A > $o,Phi: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) )
% 0.30/0.46 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M
% 0.30/0.46 @ ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [S3: A] :
% 0.30/0.46 ( ( Psi @ S3 )
% 0.30/0.46 => ( Phi @ S3 ) ) ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % use_spec_rule
% 0.30/0.46 thf(fact_12_SPEC__cons__rule,axiom,
% 0.30/0.46 ! [A: $tType,M: refine1665802226e_nres @ A,Phi: A > $o,Psi: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( Phi @ X3 )
% 0.30/0.46 => ( Psi @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % SPEC_cons_rule
% 0.30/0.46 thf(fact_13_order__mono__setup_Orefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X4: A] : ( ord_less_eq @ A @ X4 @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_mono_setup.refl
% 0.30/0.46 thf(fact_14_the__RES_Osimps,axiom,
% 0.30/0.46 ! [A: $tType,X: set @ A] :
% 0.30/0.46 ( ( refine1672542526he_RES @ A @ ( refine605929679le_RES @ A @ X ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % the_RES.simps
% 0.30/0.46 thf(fact_15_nf__inres__RES,axiom,
% 0.30/0.46 ! [A: $tType,X: set @ A,X4: A] :
% 0.30/0.46 ( ( refine406925620_inres @ A @ ( refine605929679le_RES @ A @ X ) @ X4 )
% 0.30/0.46 = ( member @ A @ X4 @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % nf_inres_RES
% 0.30/0.46 thf(fact_16_nf__inres__SPEC,axiom,
% 0.30/0.46 ! [A: $tType,Phi: A > $o,X4: A] :
% 0.30/0.46 ( ( refine406925620_inres @ A @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ X4 )
% 0.30/0.46 = ( Phi @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nf_inres_SPEC
% 0.30/0.46 thf(fact_17_nres_Osimps_I7_J,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,F1: C,F2: ( set @ A ) > C,X2: set @ A] :
% 0.30/0.46 ( ( refine1442219249c_nres @ C @ A @ F1 @ F2 @ ( refine605929679le_RES @ A @ X2 ) )
% 0.30/0.46 = ( F2 @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres.simps(7)
% 0.30/0.46 thf(fact_18_le__funD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G: A > B,X4: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funD
% 0.30/0.46 thf(fact_19_le__funE,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G: A > B,X4: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funE
% 0.30/0.46 thf(fact_20_le__funI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funI
% 0.30/0.46 thf(fact_21_Refine__Misc_Oif__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [B2: $o,M1: A,M12: A,M2: A,M22: A] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 => ( ord_less_eq @ A @ M1 @ M12 ) )
% 0.30/0.46 => ( ( ~ B2
% 0.30/0.46 => ( ord_less_eq @ A @ M2 @ M22 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( if @ A @ B2 @ M1 @ M2 ) @ ( if @ A @ B2 @ M12 @ M22 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Refine_Misc.if_mono
% 0.30/0.46 thf(fact_22_le__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.30/0.46 = ( ^ [F3: A > B,G2: A > B] :
% 0.30/0.46 ! [X5: A] : ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_fun_def
% 0.30/0.46 thf(fact_23_order__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.30/0.46 => ( ! [X3: B,Y4: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_24_le__infD2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infD2
% 0.30/0.46 thf(fact_25_le__infD1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infD1
% 0.30/0.46 thf(fact_26_inf__leI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X3 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X3 @ C2 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_leI
% 0.30/0.46 thf(fact_27_less__eq__nres_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ A2 ) @ ( refine605929679le_RES @ A @ B2 ) )
% 0.30/0.46 = ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_nres.simps(2)
% 0.30/0.46 thf(fact_28_nres__order__simps_I5_J,axiom,
% 0.30/0.46 ! [E2: $tType,X: set @ E2,Y: set @ E2] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ E2 ) @ ( refine605929679le_RES @ E2 @ X ) @ ( refine605929679le_RES @ E2 @ Y ) )
% 0.30/0.46 = ( ord_less_eq @ ( set @ E2 ) @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_order_simps(5)
% 0.30/0.46 thf(fact_29_order__mono__setup_Omono__let,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [F: B > A,F4: B > A,X4: B] :
% 0.30/0.46 ( ! [X3: B] : ( ord_less_eq @ A @ ( F @ X3 ) @ ( F4 @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F4 @ X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_mono_setup.mono_let
% 0.30/0.46 thf(fact_30_order__mono__setup_Omono__if,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [T: A,T2: A,E: A,E3: A,B2: $o] :
% 0.30/0.46 ( ( ord_less_eq @ A @ T @ T2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ E @ E3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( if @ A @ B2 @ T @ E ) @ ( if @ A @ B2 @ T2 @ E3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_mono_setup.mono_if
% 0.30/0.46 thf(fact_31_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_32_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.30/0.46 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_33_dual__order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_34_linorder__wlog,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.30/0.46 ( ! [A4: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.30/0.46 => ( P @ A4 @ B4 ) )
% 0.30/0.46 => ( ! [A4: A,B4: A] :
% 0.30/0.46 ( ( P @ B4 @ A4 )
% 0.30/0.46 => ( P @ A4 @ B4 ) )
% 0.30/0.46 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_wlog
% 0.30/0.46 thf(fact_35_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_36_order__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X4: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X4 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_37_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_38_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( B2 = C2 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_39_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_40_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.30/0.46 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_41_antisym__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [Y3: A,X4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y3 @ X4 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 = ( X4 = Y3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_42_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_43_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ A5 ) )
% 0.30/0.46 = A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_44_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 = ( Q @ X3 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_45_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( F @ X3 )
% 0.30/0.46 = ( G @ X3 ) )
% 0.30/0.46 => ( F = G ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_46_le__cases3,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X4: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y3 @ X4 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X4 @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ X4 @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y3 @ X4 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X4 ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X4 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases3
% 0.30/0.46 thf(fact_47_order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_48_le__cases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ~ ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases
% 0.30/0.46 thf(fact_49_eq__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( X4 = Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_50_linear,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 | ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linear
% 0.30/0.46 thf(fact_51_antisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y3 @ X4 )
% 0.30/0.46 => ( X4 = Y3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_52_eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 0.30/0.46 = ( ^ [X5: A,Y6: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X5 @ Y6 )
% 0.30/0.46 & ( ord_less_eq @ A @ Y6 @ X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_53_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ( F @ B2 )
% 0.30/0.46 = C2 )
% 0.30/0.46 => ( ! [X3: A,Y4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_54_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.30/0.46 => ( ! [X3: B,Y4: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_55_order__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( order @ C )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 0.30/0.46 => ( ! [X3: A,Y4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_56_inf_Obounded__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 0.30/0.46 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 & ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.bounded_iff
% 0.30/0.46 thf(fact_57_le__inf__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 0.30/0.46 = ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 & ( ord_less_eq @ A @ X4 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_inf_iff
% 0.30/0.46 thf(fact_58_inf__apply,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ B )
% 0.30/0.46 => ( ( inf_inf @ ( A > B ) )
% 0.30/0.46 = ( ^ [F3: A > B,G2: A > B,X5: A] : ( inf_inf @ B @ ( F3 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_apply
% 0.30/0.46 thf(fact_59_inf_Oidem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A2 @ A2 )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.idem
% 0.30/0.46 thf(fact_60_inf__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ X4 )
% 0.30/0.46 = X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_idem
% 0.30/0.46 thf(fact_61_inf_Oleft__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.30/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.left_idem
% 0.30/0.46 thf(fact_62_inf__left__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ X4 @ Y3 ) )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_left_idem
% 0.30/0.46 thf(fact_63_inf_Oright__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.30/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.right_idem
% 0.30/0.46 thf(fact_64_inf__right__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Y3 )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_right_idem
% 0.30/0.46 thf(fact_65_inf__nres_Osimps_I3_J,axiom,
% 0.30/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ A2 ) @ ( refine605929679le_RES @ A @ B2 ) )
% 0.30/0.46 = ( refine605929679le_RES @ A @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_nres.simps(3)
% 0.30/0.46 thf(fact_66_inf__left__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 0.30/0.46 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X4 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_left_commute
% 0.30/0.46 thf(fact_67_inf_Oleft__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C2 ) )
% 0.30/0.46 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.left_commute
% 0.30/0.46 thf(fact_68_inf__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( inf_inf @ A )
% 0.30/0.46 = ( ^ [X5: A,Y6: A] : ( inf_inf @ A @ Y6 @ X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_commute
% 0.30/0.46 thf(fact_69_inf_Ocommute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( inf_inf @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] : ( inf_inf @ A @ B3 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.commute
% 0.30/0.46 thf(fact_70_inf__assoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Z2 )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_assoc
% 0.30/0.46 thf(fact_71_inf_Oassoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 )
% 0.30/0.46 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.assoc
% 0.30/0.46 thf(fact_72_boolean__algebra__cancel_Oinf2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B5: A,K: A,B2: A,A2: A] :
% 0.30/0.46 ( ( B5
% 0.30/0.46 = ( inf_inf @ A @ K @ B2 ) )
% 0.30/0.46 => ( ( inf_inf @ A @ A2 @ B5 )
% 0.30/0.46 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % boolean_algebra_cancel.inf2
% 0.30/0.46 thf(fact_73_boolean__algebra__cancel_Oinf1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A5: A,K: A,A2: A,B2: A] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( inf_inf @ A @ K @ A2 ) )
% 0.30/0.46 => ( ( inf_inf @ A @ A5 @ B2 )
% 0.30/0.46 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % boolean_algebra_cancel.inf1
% 0.30/0.46 thf(fact_74_inf__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ B )
% 0.30/0.46 => ( ( inf_inf @ ( A > B ) )
% 0.30/0.46 = ( ^ [F3: A > B,G2: A > B,X5: A] : ( inf_inf @ B @ ( F3 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_fun_def
% 0.30/0.46 thf(fact_75_inf__sup__aci_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ( ( inf_inf @ A )
% 0.30/0.46 = ( ^ [X5: A,Y6: A] : ( inf_inf @ A @ Y6 @ X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(1)
% 0.30/0.46 thf(fact_76_inf__sup__aci_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X4: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Z2 )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(2)
% 0.30/0.46 thf(fact_77_inf__sup__aci_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X4: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 0.30/0.46 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X4 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(3)
% 0.30/0.46 thf(fact_78_inf__sup__aci_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ X4 @ Y3 ) )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(4)
% 0.30/0.46 thf(fact_79_inf__sup__ord_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(2)
% 0.30/0.46 thf(fact_80_inf__sup__ord_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(1)
% 0.30/0.46 thf(fact_81_inf__le1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_le1
% 0.30/0.46 thf(fact_82_inf__le2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_le2
% 0.30/0.46 thf(fact_83_le__infE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ X4 @ A2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X4 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infE
% 0.30/0.46 thf(fact_84_le__infI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X4 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X4 @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infI
% 0.30/0.46 thf(fact_85_inf__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,C2: A,B2: A,D: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ D )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ ( inf_inf @ A @ C2 @ D ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_mono
% 0.30/0.46 thf(fact_86_le__infI1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,X4: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ X4 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infI1
% 0.30/0.46 thf(fact_87_le__infI2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B2: A,X4: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ X4 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_infI2
% 0.30/0.46 thf(fact_88_inf_OorderE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( A2
% 0.30/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.orderE
% 0.30/0.46 thf(fact_89_inf_OorderI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( inf_inf @ A @ A2 @ B2 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.orderI
% 0.30/0.46 thf(fact_90_inf__unique,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [F: A > A > A,X4: A,Y3: A] :
% 0.30/0.46 ( ! [X3: A,Y4: A] : ( ord_less_eq @ A @ ( F @ X3 @ Y4 ) @ X3 )
% 0.30/0.46 => ( ! [X3: A,Y4: A] : ( ord_less_eq @ A @ ( F @ X3 @ Y4 ) @ Y4 )
% 0.30/0.46 => ( ! [X3: A,Y4: A,Z3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X3 @ Z3 )
% 0.30/0.46 => ( ord_less_eq @ A @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 0.30/0.46 => ( ( inf_inf @ A @ X4 @ Y3 )
% 0.30/0.46 = ( F @ X4 @ Y3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_unique
% 0.30/0.46 thf(fact_91_le__iff__inf,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [X5: A,Y6: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X5 @ Y6 )
% 0.30/0.46 = X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_iff_inf
% 0.30/0.46 thf(fact_92_inf_Oabsorb1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( inf_inf @ A @ A2 @ B2 )
% 0.30/0.46 = A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.absorb1
% 0.30/0.46 thf(fact_93_inf_Oabsorb2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( inf_inf @ A @ A2 @ B2 )
% 0.30/0.46 = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.absorb2
% 0.30/0.46 thf(fact_94_inf__absorb1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 => ( ( inf_inf @ A @ X4 @ Y3 )
% 0.30/0.46 = X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_absorb1
% 0.30/0.46 thf(fact_95_inf__absorb2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [Y3: A,X4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y3 @ X4 )
% 0.30/0.46 => ( ( inf_inf @ A @ X4 @ Y3 )
% 0.30/0.46 = Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_absorb2
% 0.30/0.46 thf(fact_96_inf_OboundedE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.boundedE
% 0.30/0.46 thf(fact_97_inf_OboundedI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.boundedI
% 0.30/0.46 thf(fact_98_inf__greatest,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [X4: A,Y3: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X4 @ Z2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_greatest
% 0.30/0.46 thf(fact_99_inf_Oorder__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ( A3
% 0.30/0.46 = ( inf_inf @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.order_iff
% 0.30/0.46 thf(fact_100_inf_Ocobounded1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.cobounded1
% 0.30/0.46 thf(fact_101_inf_Ocobounded2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.cobounded2
% 0.30/0.46 thf(fact_102_inf_Oabsorb__iff1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A3 @ B3 )
% 0.30/0.46 = A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.absorb_iff1
% 0.30/0.46 thf(fact_103_inf_Oabsorb__iff2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [B3: A,A3: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A3 @ B3 )
% 0.30/0.46 = B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.absorb_iff2
% 0.30/0.46 thf(fact_104_inf_OcoboundedI1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.coboundedI1
% 0.30/0.46 thf(fact_105_inf_OcoboundedI2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_inf @ A )
% 0.30/0.46 => ! [B2: A,C2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf.coboundedI2
% 0.30/0.46 thf(fact_106_subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A5 )
% 0.30/0.46 => ( member @ A @ X3 @ B5 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_107_Int__subset__iff,axiom,
% 0.30/0.46 ! [A: $tType,C3: set @ A,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ C3 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 0.30/0.46 = ( ( ord_less_eq @ ( set @ A ) @ C3 @ A5 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ C3 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_subset_iff
% 0.30/0.46 thf(fact_108_subset__antisym,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 0.30/0.46 => ( A5 = B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_109_Collect__subset,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,P: A > $o] :
% 0.30/0.46 ( ord_less_eq @ ( set @ A )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A5 )
% 0.30/0.46 & ( P @ X5 ) ) )
% 0.30/0.46 @ A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_subset
% 0.30/0.46 thf(fact_110_less__eq__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ( ord_less_eq @ ( A > $o )
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ A6 )
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_set_def
% 0.30/0.46 thf(fact_111_pred__subset__eq,axiom,
% 0.30/0.46 ! [A: $tType,R: set @ A,S: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > $o )
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ R )
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ S ) )
% 0.30/0.46 = ( ord_less_eq @ ( set @ A ) @ R @ S ) ) ).
% 0.30/0.46
% 0.30/0.46 % pred_subset_eq
% 0.30/0.46 thf(fact_112_conj__subset__def,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X5: A] :
% 0.30/0.46 ( ( P @ X5 )
% 0.30/0.46 & ( Q @ X5 ) ) ) )
% 0.30/0.46 = ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( collect @ A @ P ) )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ A5 @ ( collect @ A @ Q ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % conj_subset_def
% 0.30/0.46 thf(fact_113_IntI,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ A5 )
% 0.30/0.46 => ( ( member @ A @ C2 @ B5 )
% 0.30/0.46 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntI
% 0.30/0.46 thf(fact_114_Int__iff,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 0.30/0.46 = ( ( member @ A @ C2 @ A5 )
% 0.30/0.46 & ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_iff
% 0.30/0.46 thf(fact_115_predicate1I,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( Q @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 0.30/0.46
% 0.30/0.46 % predicate1I
% 0.30/0.46 thf(fact_116_IntE,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 0.30/0.46 => ~ ( ( member @ A @ C2 @ A5 )
% 0.30/0.46 => ~ ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntE
% 0.30/0.46 thf(fact_117_IntD1,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 0.30/0.46 => ( member @ A @ C2 @ A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntD1
% 0.30/0.46 thf(fact_118_IntD2,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 0.30/0.46 => ( member @ A @ C2 @ B5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % IntD2
% 0.30/0.46 thf(fact_119_Int__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ( collect @ A
% 0.30/0.46 @ ^ [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A6 )
% 0.30/0.46 & ( member @ A @ X5 @ B6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_def
% 0.30/0.46 thf(fact_120_Int__assoc,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) @ C3 )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ A5 @ ( inf_inf @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_assoc
% 0.30/0.46 thf(fact_121_Int__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A5 @ A5 )
% 0.30/0.46 = A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Int_absorb
% 0.30/0.46 thf(fact_122_Int__Collect,axiom,
% 0.30/0.46 ! [A: $tType,X4: A,A5: set @ A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ X4 @ ( inf_inf @ ( set @ A ) @ A5 @ ( collect @ A @ P ) ) )
% 0.30/0.46 = ( ( member @ A @ X4 @ A5 )
% 0.30/0.46 & ( P @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_Collect
% 0.30/0.46 thf(fact_123_Int__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] : ( inf_inf @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_commute
% 0.30/0.46 thf(fact_124_inf__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ( collect @ A
% 0.30/0.46 @ ( inf_inf @ ( A > $o )
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ A6 )
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ B6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_set_def
% 0.30/0.46 thf(fact_125_inf__Int__eq,axiom,
% 0.30/0.46 ! [A: $tType,R: set @ A,S: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o )
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ R )
% 0.30/0.46 @ ^ [X5: A] : ( member @ A @ X5 @ S ) )
% 0.30/0.46 = ( ^ [X5: A] : ( member @ A @ X5 @ ( inf_inf @ ( set @ A ) @ R @ S ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_Int_eq
% 0.30/0.46 thf(fact_126_Collect__conj__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X5: A] :
% 0.30/0.46 ( ( P @ X5 )
% 0.30/0.46 & ( Q @ X5 ) ) )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_conj_eq
% 0.30/0.46 thf(fact_127_Int__left__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A5 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ A5 @ B5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_left_absorb
% 0.30/0.46 thf(fact_128_Int__left__commute,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( set @ A ) @ A5 @ ( inf_inf @ ( set @ A ) @ B5 @ C3 ) )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ B5 @ ( inf_inf @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_left_commute
% 0.30/0.46 thf(fact_129_predicate1D,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o,X4: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.30/0.46 => ( ( P @ X4 )
% 0.30/0.46 => ( Q @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % predicate1D
% 0.30/0.46 thf(fact_130_rev__predicate1D,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,X4: A,Q: A > $o] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.30/0.46 => ( Q @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_predicate1D
% 0.30/0.46 thf(fact_131_Int__Collect__mono,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A5 )
% 0.30/0.46 => ( ( P @ X3 )
% 0.30/0.46 => ( Q @ X3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ ( collect @ A @ P ) ) @ ( inf_inf @ ( set @ A ) @ B5 @ ( collect @ A @ Q ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_Collect_mono
% 0.30/0.46 thf(fact_132_Collect__mono__iff,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.30/0.46 = ( ! [X5: A] :
% 0.30/0.46 ( ( P @ X5 )
% 0.30/0.46 => ( Q @ X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono_iff
% 0.30/0.46 thf(fact_133_set__eq__subset,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [Y5: set @ A,Z: set @ A] : ( Y5 = Z ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_eq_subset
% 0.30/0.46 thf(fact_134_subset__trans,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_trans
% 0.30/0.46 thf(fact_135_Int__greatest,axiom,
% 0.30/0.46 ! [A: $tType,C3: set @ A,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ C3 @ A5 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ C3 @ B5 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ C3 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_greatest
% 0.30/0.46 thf(fact_136_Collect__mono,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( Q @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono
% 0.30/0.46 thf(fact_137_subset__refl,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ A5 ) ).
% 0.30/0.46
% 0.30/0.46 % subset_refl
% 0.30/0.46 thf(fact_138_Int__absorb2,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 => ( ( inf_inf @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 = A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_absorb2
% 0.30/0.46 thf(fact_139_Int__absorb1,axiom,
% 0.30/0.46 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 0.30/0.46 => ( ( inf_inf @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 = B5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_absorb1
% 0.30/0.46 thf(fact_140_subset__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ! [T3: A] :
% 0.30/0.46 ( ( member @ A @ T3 @ A6 )
% 0.30/0.46 => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_iff
% 0.30/0.46 thf(fact_141_equalityD2,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( A5 = B5 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD2
% 0.30/0.46 thf(fact_142_equalityD1,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( A5 = B5 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD1
% 0.30/0.46 thf(fact_143_Int__lower2,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) @ B5 ) ).
% 0.30/0.46
% 0.30/0.46 % Int_lower2
% 0.30/0.46 thf(fact_144_Int__lower1,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) @ A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Int_lower1
% 0.30/0.46 thf(fact_145_subset__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.30/0.46 ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A6 )
% 0.30/0.46 => ( member @ A @ X5 @ B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_eq
% 0.30/0.46 thf(fact_146_equalityE,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( A5 = B5 )
% 0.30/0.46 => ~ ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityE
% 0.30/0.46 thf(fact_147_Int__mono,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,C3: set @ A,B5: set @ A,D2: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ C3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ D2 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) @ ( inf_inf @ ( set @ A ) @ C3 @ D2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Int_mono
% 0.30/0.46 thf(fact_148_subsetD,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 => ( ( member @ A @ C2 @ A5 )
% 0.30/0.46 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetD
% 0.30/0.46 thf(fact_149_in__mono,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B5: set @ A,X4: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 => ( ( member @ A @ X4 @ A5 )
% 0.30/0.46 => ( member @ A @ X4 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mono
% 0.30/0.46 thf(fact_150_inter__eq__subsetI,axiom,
% 0.30/0.46 ! [A: $tType,S: set @ A,S4: set @ A,A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ S @ S4 )
% 0.30/0.46 => ( ( ( inf_inf @ ( set @ A ) @ A5 @ S4 )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ B5 @ S4 ) )
% 0.30/0.46 => ( ( inf_inf @ ( set @ A ) @ A5 @ S )
% 0.30/0.46 = ( inf_inf @ ( set @ A ) @ B5 @ S ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inter_eq_subsetI
% 0.30/0.46 thf(fact_151_subset__Collect__iff,axiom,
% 0.30/0.46 ! [A: $tType,B5: set @ A,A5: set @ A,P: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B5
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A5 )
% 0.30/0.46 & ( P @ X5 ) ) ) )
% 0.30/0.46 = ( ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ B5 )
% 0.30/0.46 => ( P @ X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Collect_iff
% 0.30/0.46 thf(fact_152_subset__CollectI,axiom,
% 0.30/0.46 ! [A: $tType,B5: set @ A,A5: set @ A,Q: A > $o,P: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ B5 )
% 0.30/0.46 => ( ( Q @ X3 )
% 0.30/0.46 => ( P @ X3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ B5 )
% 0.30/0.46 & ( Q @ X5 ) ) )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A5 )
% 0.30/0.46 & ( P @ X5 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_CollectI
% 0.30/0.46 thf(fact_153_Collect__restrict,axiom,
% 0.30/0.46 ! [A: $tType,X: set @ A,P: A > $o] :
% 0.30/0.46 ( ord_less_eq @ ( set @ A )
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ X )
% 0.30/0.46 & ( P @ X5 ) ) )
% 0.30/0.46 @ X ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_restrict
% 0.30/0.46 thf(fact_154_inf1I,axiom,
% 0.30/0.46 ! [A: $tType,A5: A > $o,X4: A,B5: A > $o] :
% 0.30/0.46 ( ( A5 @ X4 )
% 0.30/0.46 => ( ( B5 @ X4 )
% 0.30/0.46 => ( inf_inf @ ( A > $o ) @ A5 @ B5 @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1I
% 0.30/0.46 thf(fact_155_inf1E,axiom,
% 0.30/0.46 ! [A: $tType,A5: A > $o,B5: A > $o,X4: A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o ) @ A5 @ B5 @ X4 )
% 0.30/0.46 => ~ ( ( A5 @ X4 )
% 0.30/0.46 => ~ ( B5 @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1E
% 0.30/0.46 thf(fact_156_inf1D1,axiom,
% 0.30/0.46 ! [A: $tType,A5: A > $o,B5: A > $o,X4: A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o ) @ A5 @ B5 @ X4 )
% 0.30/0.46 => ( A5 @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1D1
% 0.30/0.46 thf(fact_157_inf1D2,axiom,
% 0.30/0.46 ! [A: $tType,A5: A > $o,B5: A > $o,X4: A] :
% 0.30/0.46 ( ( inf_inf @ ( A > $o ) @ A5 @ B5 @ X4 )
% 0.30/0.46 => ( B5 @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf1D2
% 0.30/0.46 thf(fact_158_ord__eq__le__eq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A,D: A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.30/0.46 => ( ( C2 = D )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ D ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_eq_trans
% 0.30/0.46 thf(fact_159_subset__Collect__conv,axiom,
% 0.30/0.46 ! [A: $tType,S: set @ A,P: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 0.30/0.46 = ( ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ S )
% 0.30/0.46 => ( P @ X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Collect_conv
% 0.30/0.46 thf(fact_160_prop__restrict,axiom,
% 0.30/0.46 ! [A: $tType,X4: A,Z4: set @ A,X: set @ A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ X4 @ Z4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ Z4
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ X )
% 0.30/0.46 & ( P @ X5 ) ) ) )
% 0.30/0.46 => ( P @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prop_restrict
% 0.30/0.46 thf(fact_161_Powp__mono,axiom,
% 0.30/0.46 ! [A: $tType,A5: A > $o,B5: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > $o ) @ A5 @ B5 )
% 0.30/0.46 => ( ord_less_eq @ ( ( set @ A ) > $o ) @ ( powp @ A @ A5 ) @ ( powp @ A @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Powp_mono
% 0.30/0.46 thf(fact_162_inf__nres_Oelims,axiom,
% 0.30/0.46 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A,Y3: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 0.30/0.46 = Y3 )
% 0.30/0.46 => ( ( ( Xa
% 0.30/0.46 = ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ( Y3 != X4 ) )
% 0.30/0.46 => ( ( ( X4
% 0.30/0.46 = ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ! [V: set @ A] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( refine605929679le_RES @ A @ V ) )
% 0.30/0.46 => ( Y3
% 0.30/0.46 != ( refine605929679le_RES @ A @ V ) ) ) )
% 0.30/0.46 => ~ ! [A4: set @ A] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( refine605929679le_RES @ A @ A4 ) )
% 0.30/0.46 => ! [B4: set @ A] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( refine605929679le_RES @ A @ B4 ) )
% 0.30/0.46 => ( Y3
% 0.30/0.46 != ( refine605929679le_RES @ A @ ( inf_inf @ ( set @ A ) @ A4 @ B4 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_nres.elims
% 0.30/0.46 thf(fact_163_GreatestI2__order,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [P: A > $o,X4: A,Q: A > $o] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 => ( ! [Y4: A] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y4 @ X4 ) )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( ! [Y7: A] :
% 0.30/0.46 ( ( P @ Y7 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y7 @ X3 ) )
% 0.30/0.46 => ( Q @ X3 ) ) )
% 0.30/0.46 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % GreatestI2_order
% 0.30/0.46 thf(fact_164_inf__nres_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X4: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ X4 @ ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 = X4 ) ).
% 0.30/0.46
% 0.30/0.46 % inf_nres.simps(1)
% 0.30/0.46 thf(fact_165_nres_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X2: set @ A] :
% 0.30/0.46 ( ( refine1767639642_FAILi @ A )
% 0.30/0.46 != ( refine605929679le_RES @ A @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres.distinct(1)
% 0.30/0.46 thf(fact_166_nres_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > $o,Nres: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( P @ ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ( ! [X3: set @ A] : ( P @ ( refine605929679le_RES @ A @ X3 ) )
% 0.30/0.46 => ( P @ Nres ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres.induct
% 0.30/0.46 thf(fact_167_nres_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Y3: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( Y3
% 0.30/0.46 != ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ~ ! [X22: set @ A] :
% 0.30/0.46 ( Y3
% 0.30/0.46 != ( refine605929679le_RES @ A @ X22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres.exhaust
% 0.30/0.46 thf(fact_168_sup__nres_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ! [Uu: refine1665802226e_nres @ A] : ( P @ Uu @ ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ( ! [V: set @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ V ) )
% 0.30/0.46 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_nres.induct
% 0.30/0.46 thf(fact_169_less__nres_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ! [X_1: refine1665802226e_nres @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ X_1 )
% 0.30/0.46 => ( ! [Uv: set @ A] : ( P @ ( refine605929679le_RES @ A @ Uv ) @ ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_nres.induct
% 0.30/0.46 thf(fact_170_less__eq__nres_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ! [Uu: refine1665802226e_nres @ A] : ( P @ Uu @ ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 0.30/0.46 => ( ! [Uv: set @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ Uv ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_nres.induct
% 0.30/0.46 thf(fact_171_less__eq__nres_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Uu2: refine1665802226e_nres @ A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ Uu2 @ ( refine1767639642_FAILi @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_nres.simps(1)
% 0.30/0.46 thf(fact_172_nres_Osimps_I6_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,F1: C,F2: ( set @ A ) > C] :
% 0.30/0.46 ( ( refine1442219249c_nres @ C @ A @ F1 @ F2 @ ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 = F1 ) ).
% 0.30/0.46
% 0.30/0.46 % nres.simps(6)
% 0.30/0.46 thf(fact_173_less__eq__nres_Osimps_I3_J,axiom,
% 0.30/0.46 ! [A: $tType,Uv2: set @ A] :
% 0.30/0.46 ~ ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ Uv2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_nres.simps(3)
% 0.30/0.46 thf(fact_174_inf__nres_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,V2: set @ A] :
% 0.30/0.46 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ V2 ) )
% 0.30/0.46 = ( refine605929679le_RES @ A @ V2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_nres.simps(2)
% 0.30/0.46 thf(fact_175_less__eq__nres_Oelims_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A,Y3: $o] :
% 0.30/0.46 ( ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 0.30/0.46 = Y3 )
% 0.30/0.46 => ( ( ( Xa
% 0.30/0.46 = ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ~ Y3 )
% 0.30/0.46 => ( ! [A4: set @ A] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( refine605929679le_RES @ A @ A4 ) )
% 0.30/0.46 => ! [B4: set @ A] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( refine605929679le_RES @ A @ B4 ) )
% 0.30/0.46 => ( Y3
% 0.30/0.46 = ( ~ ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ) )
% 0.30/0.46 => ~ ( ( X4
% 0.30/0.46 = ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ( ? [Uv: set @ A] :
% 0.30/0.46 ( Xa
% 0.30/0.46 = ( refine605929679le_RES @ A @ Uv ) )
% 0.30/0.46 => Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_nres.elims(1)
% 0.30/0.46 thf(fact_176_less__eq__nres_Oelims_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 0.30/0.46 => ( ( Xa
% 0.30/0.46 != ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ~ ! [A4: set @ A] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( refine605929679le_RES @ A @ A4 ) )
% 0.30/0.46 => ! [B4: set @ A] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( refine605929679le_RES @ A @ B4 ) )
% 0.30/0.46 => ~ ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_nres.elims(2)
% 0.30/0.46 thf(fact_177_less__eq__nres_Oelims_I3_J,axiom,
% 0.30/0.46 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ~ ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 0.30/0.46 => ( ! [A4: set @ A] :
% 0.30/0.46 ( ( X4
% 0.30/0.46 = ( refine605929679le_RES @ A @ A4 ) )
% 0.30/0.46 => ! [B4: set @ A] :
% 0.30/0.46 ( ( Xa
% 0.30/0.46 = ( refine605929679le_RES @ A @ B4 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) )
% 0.30/0.46 => ~ ( ( X4
% 0.30/0.46 = ( refine1767639642_FAILi @ A ) )
% 0.30/0.46 => ! [Uv: set @ A] :
% 0.30/0.46 ( Xa
% 0.30/0.46 != ( refine605929679le_RES @ A @ Uv ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_nres.elims(3)
% 0.30/0.46 thf(fact_178_Greatest__equality,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [P: A > $o,X4: A] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 => ( ! [Y4: A] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y4 @ X4 ) )
% 0.30/0.46 => ( ( order_Greatest @ A @ P )
% 0.30/0.46 = X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Greatest_equality
% 0.30/0.46 thf(fact_179_the__RES__inv,axiom,
% 0.30/0.46 ! [A: $tType,M: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( refine1102455758nofail @ A @ M )
% 0.30/0.46 => ( ( refine605929679le_RES @ A @ ( refine1672542526he_RES @ A @ M ) )
% 0.30/0.46 = M ) ) ).
% 0.30/0.46
% 0.30/0.46 % the_RES_inv
% 0.30/0.46 thf(fact_180_relprop__triggers_I6_J,axiom,
% 0.30/0.46 ! [I: $tType,R: set @ I,R2: set @ I] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ I ) @ R @ R2 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ I ) @ R @ R2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % relprop_triggers(6)
% 0.30/0.46 thf(fact_181_inf__RETURN__SPEC_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X4: A,Phi: A > $o] :
% 0.30/0.46 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 0.30/0.46 = ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [Y6: A] :
% 0.30/0.46 ( ( Y6 = X4 )
% 0.30/0.46 & ( Phi @ X4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_RETURN_SPEC(1)
% 0.30/0.46 thf(fact_182_nres__more__simps_I6_J,axiom,
% 0.30/0.46 ! [A: $tType,X4: A,Y3: A] :
% 0.30/0.46 ( ( ( refine1687780735RETURN @ A @ X4 )
% 0.30/0.46 = ( refine1687780735RETURN @ A @ Y3 ) )
% 0.30/0.46 = ( X4 = Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_more_simps(6)
% 0.30/0.46 thf(fact_183_nofail__simps_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,X: set @ B] : ( refine1102455758nofail @ B @ ( refine605929679le_RES @ B @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % nofail_simps(2)
% 0.30/0.46 thf(fact_184_nres__order__simps_I20_J,axiom,
% 0.30/0.46 ! [W: $tType,X4: W,Y3: W] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ W ) @ ( refine1687780735RETURN @ W @ X4 ) @ ( refine1687780735RETURN @ W @ Y3 ) )
% 0.30/0.46 = ( X4 = Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_order_simps(20)
% 0.30/0.46 thf(fact_185_nofail__simps_I3_J,axiom,
% 0.30/0.46 ! [C: $tType,X4: C] : ( refine1102455758nofail @ C @ ( refine1687780735RETURN @ C @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nofail_simps(3)
% 0.30/0.46 thf(fact_186_nres__order__simps_I21_J,axiom,
% 0.30/0.46 ! [X6: $tType,X4: X6,Y: set @ X6] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ X6 ) @ ( refine1687780735RETURN @ X6 @ X4 ) @ ( refine605929679le_RES @ X6 @ Y ) )
% 0.30/0.46 = ( member @ X6 @ X4 @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_order_simps(21)
% 0.30/0.46 thf(fact_187_inf__RETURN__SPEC_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Phi: A > $o,X4: A] :
% 0.30/0.46 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ ( refine1687780735RETURN @ A @ X4 ) )
% 0.30/0.46 = ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [Y6: A] :
% 0.30/0.46 ( ( Y6 = X4 )
% 0.30/0.46 & ( Phi @ X4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_RETURN_SPEC(2)
% 0.30/0.46 thf(fact_188_pwD1,axiom,
% 0.30/0.46 ! [A: $tType,S: refine1665802226e_nres @ A,S4: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S4 )
% 0.30/0.46 => ( ( refine1102455758nofail @ A @ S4 )
% 0.30/0.46 => ( refine1102455758nofail @ A @ S ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pwD1
% 0.30/0.46 thf(fact_189_le__nofailI,axiom,
% 0.30/0.46 ! [A: $tType,M3: refine1665802226e_nres @ A,M4: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( ( refine1102455758nofail @ A @ M3 )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_nofailI
% 0.30/0.46 thf(fact_190_nofail__antimono__fun,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > ( refine1665802226e_nres @ B ),G: A > ( refine1665802226e_nres @ B ),X4: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > ( refine1665802226e_nres @ B ) ) @ F @ G )
% 0.30/0.46 => ( ( refine1102455758nofail @ B @ ( G @ X4 ) )
% 0.30/0.46 => ( refine1102455758nofail @ B @ ( F @ X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nofail_antimono_fun
% 0.30/0.46 thf(fact_191_nofail__RES__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( refine1102455758nofail @ A )
% 0.30/0.46 = ( ^ [M5: refine1665802226e_nres @ A] :
% 0.30/0.46 ? [M6: set @ A] :
% 0.30/0.46 ( M5
% 0.30/0.46 = ( refine605929679le_RES @ A @ M6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nofail_RES_conv
% 0.30/0.46 thf(fact_192_SPEC__eq__is__RETURN_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X4: A] :
% 0.30/0.46 ( ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ( ^ [Y5: A,Z: A] : ( Y5 = Z )
% 0.30/0.46 @ X4 ) ) )
% 0.30/0.46 = ( refine1687780735RETURN @ A @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % SPEC_eq_is_RETURN(1)
% 0.30/0.46 thf(fact_193_RETURN__SPEC__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( refine1687780735RETURN @ A )
% 0.30/0.46 = ( ^ [R3: A] :
% 0.30/0.46 ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X5: A] : ( X5 = R3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % RETURN_SPEC_conv
% 0.30/0.46 thf(fact_194_SPEC__eq__is__RETURN_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,Y3: B] :
% 0.30/0.46 ( ( refine605929679le_RES @ B
% 0.30/0.46 @ ( collect @ B
% 0.30/0.46 @ ^ [X5: B] : ( X5 = Y3 ) ) )
% 0.30/0.46 = ( refine1687780735RETURN @ B @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % SPEC_eq_is_RETURN(2)
% 0.30/0.46 thf(fact_195_pw__inf__nofail,axiom,
% 0.30/0.46 ! [A: $tType,A2: refine1665802226e_nres @ A,B2: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( refine1102455758nofail @ A @ ( inf_inf @ ( refine1665802226e_nres @ A ) @ A2 @ B2 ) )
% 0.30/0.46 = ( ( refine1102455758nofail @ A @ A2 )
% 0.30/0.46 | ( refine1102455758nofail @ A @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pw_inf_nofail
% 0.30/0.46 thf(fact_196_le__RES__nofailI,axiom,
% 0.30/0.46 ! [A: $tType,A2: refine1665802226e_nres @ A,X4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ A2 @ ( refine605929679le_RES @ A @ X4 ) )
% 0.30/0.46 => ( refine1102455758nofail @ A @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_RES_nofailI
% 0.30/0.46 thf(fact_197_RETURN__rule,axiom,
% 0.30/0.46 ! [A: $tType,Phi: A > $o,X4: A] :
% 0.30/0.46 ( ( Phi @ X4 )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % RETURN_rule
% 0.30/0.46 thf(fact_198_lhs__step__RES,axiom,
% 0.30/0.46 ! [A: $tType,X: set @ A,M: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ X )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ X ) @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % lhs_step_RES
% 0.30/0.46 thf(fact_199_RETURN__to__SPEC__rule,axiom,
% 0.30/0.46 ! [A: $tType,M: refine1665802226e_nres @ A,V2: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M
% 0.30/0.46 @ ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ( ^ [Y5: A,Z: A] : ( Y5 = Z )
% 0.30/0.46 @ V2 ) ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine1687780735RETURN @ A @ V2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % RETURN_to_SPEC_rule
% 0.30/0.46 thf(fact_200_lhs__step__SPEC,axiom,
% 0.30/0.46 ! [A: $tType,Phi: A > $o,M: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( Phi @ X3 )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % lhs_step_SPEC
% 0.30/0.46 thf(fact_201_lhs__step__bind,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,M7: refine1665802226e_nres @ B,M: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B )] :
% 0.30/0.46 ( ( ( refine1102455758nofail @ B @ M7 )
% 0.30/0.46 => ( refine1102455758nofail @ A @ M ) )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( refine406925620_inres @ A @ M @ X3 )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ M7 ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M @ F ) @ M7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lhs_step_bind
% 0.30/0.46 thf(fact_202_inf__RETURN__RES_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X4: A,X: set @ A] :
% 0.30/0.46 ( ( ( member @ A @ X4 @ X )
% 0.30/0.46 => ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ X ) @ ( refine1687780735RETURN @ A @ X4 ) )
% 0.30/0.46 = ( refine1687780735RETURN @ A @ X4 ) ) )
% 0.30/0.46 & ( ~ ( member @ A @ X4 @ X )
% 0.30/0.46 => ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ X ) @ ( refine1687780735RETURN @ A @ X4 ) )
% 0.30/0.46 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_RETURN_RES(2)
% 0.30/0.46 thf(fact_203_inf__RETURN__RES_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X4: A,X: set @ A] :
% 0.30/0.46 ( ( ( member @ A @ X4 @ X )
% 0.30/0.46 => ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ X ) )
% 0.30/0.46 = ( refine1687780735RETURN @ A @ X4 ) ) )
% 0.30/0.46 & ( ~ ( member @ A @ X4 @ X )
% 0.30/0.46 => ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ X ) )
% 0.30/0.46 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_RETURN_RES(1)
% 0.30/0.46 thf(fact_204_bot__apply,axiom,
% 0.30/0.46 ! [C: $tType,D3: $tType] :
% 0.30/0.46 ( ( bot @ C )
% 0.30/0.46 => ( ( bot_bot @ ( D3 > C ) )
% 0.30/0.46 = ( ^ [X5: D3] : ( bot_bot @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_apply
% 0.30/0.46 thf(fact_205_nres__monad3,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,C: $tType,M4: refine1665802226e_nres @ C,F: C > ( refine1665802226e_nres @ B ),G: B > ( refine1665802226e_nres @ A )] :
% 0.30/0.46 ( ( refine463715084e_bind @ B @ A @ ( refine463715084e_bind @ C @ B @ M4 @ F ) @ G )
% 0.30/0.46 = ( refine463715084e_bind @ C @ A @ M4
% 0.30/0.46 @ ^ [X5: C] : ( refine463715084e_bind @ B @ A @ ( F @ X5 ) @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_monad3
% 0.30/0.46 thf(fact_206_If__bind__distrib,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,B2: $o,T: refine1665802226e_nres @ A,E: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B )] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 => ( ( refine463715084e_bind @ A @ B @ ( if @ ( refine1665802226e_nres @ A ) @ B2 @ T @ E ) @ F )
% 0.30/0.46 = ( refine463715084e_bind @ A @ B @ T @ F ) ) )
% 0.30/0.46 & ( ~ B2
% 0.30/0.46 => ( ( refine463715084e_bind @ A @ B @ ( if @ ( refine1665802226e_nres @ A ) @ B2 @ T @ E ) @ F )
% 0.30/0.46 = ( refine463715084e_bind @ A @ B @ E @ F ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % If_bind_distrib
% 0.30/0.46 thf(fact_207_inf__bot__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( bot_bot @ A ) )
% 0.30/0.46 = ( bot_bot @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_bot_right
% 0.30/0.46 thf(fact_208_inf__bot__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X4 )
% 0.30/0.46 = ( bot_bot @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_bot_left
% 0.30/0.46 thf(fact_209_nres__monad2,axiom,
% 0.30/0.46 ! [A: $tType,M4: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( refine463715084e_bind @ A @ A @ M4 @ ( refine1687780735RETURN @ A ) )
% 0.30/0.46 = M4 ) ).
% 0.30/0.46
% 0.30/0.46 % nres_monad2
% 0.30/0.46 thf(fact_210_nres__monad1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X4: B,F: B > ( refine1665802226e_nres @ A )] :
% 0.30/0.46 ( ( refine463715084e_bind @ B @ A @ ( refine1687780735RETURN @ B @ X4 ) @ F )
% 0.30/0.46 = ( F @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_monad1
% 0.30/0.46 thf(fact_211_nres__order__simps_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,M4: refine1665802226e_nres @ B] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M4 @ ( bot_bot @ ( refine1665802226e_nres @ B ) ) )
% 0.30/0.46 = ( M4
% 0.30/0.46 = ( bot_bot @ ( refine1665802226e_nres @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_order_simps(2)
% 0.30/0.46 thf(fact_212_bind__SUCCEED,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: B > ( refine1665802226e_nres @ A )] :
% 0.30/0.46 ( ( refine463715084e_bind @ B @ A @ ( bot_bot @ ( refine1665802226e_nres @ B ) ) @ F )
% 0.30/0.46 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_SUCCEED
% 0.30/0.46 thf(fact_213_nofail__simps_I4_J,axiom,
% 0.30/0.46 ! [D3: $tType] : ( refine1102455758nofail @ D3 @ ( bot_bot @ ( refine1665802226e_nres @ D3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nofail_simps(4)
% 0.30/0.46 thf(fact_214_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,M4: refine1665802226e_nres @ A,M3: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M3 )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M4 )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ ( F4 @ X3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M4 @ F ) @ ( refine463715084e_bind @ A @ B @ M3 @ F4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Refine_Basic_Mirabelle_tqojlsrkwy.bind_mono(1)
% 0.30/0.46 thf(fact_215_bind__cong,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,M: refine1665802226e_nres @ A,M7: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 0.30/0.46 ( ( M = M7 )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M7 )
% 0.30/0.46 => ( ( F @ X3 )
% 0.30/0.46 = ( F4 @ X3 ) ) )
% 0.30/0.46 => ( ( refine463715084e_bind @ A @ B @ M @ F )
% 0.30/0.46 = ( refine463715084e_bind @ A @ B @ M7 @ F4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_cong
% 0.30/0.46 thf(fact_216_pw__RES__bind__choose_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X: set @ B,F: B > ( refine1665802226e_nres @ A )] :
% 0.30/0.46 ( ( refine1102455758nofail @ A @ ( refine463715084e_bind @ B @ A @ ( refine605929679le_RES @ B @ X ) @ F ) )
% 0.30/0.46 = ( ! [X5: B] :
% 0.30/0.46 ( ( member @ B @ X5 @ X )
% 0.30/0.46 => ( refine1102455758nofail @ A @ ( F @ X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pw_RES_bind_choose(1)
% 0.30/0.46 thf(fact_217_let__to__bind__conv,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ^ [S3: B,F3: B > ( refine1665802226e_nres @ A )] : ( F3 @ S3 ) )
% 0.30/0.46 = ( ^ [X5: B] : ( refine463715084e_bind @ B @ A @ ( refine1687780735RETURN @ B @ X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % let_to_bind_conv
% 0.30/0.46 thf(fact_218_nres__inequalities_I5_J,axiom,
% 0.30/0.46 ! [C: $tType,X4: C] :
% 0.30/0.46 ( ( bot_bot @ ( refine1665802226e_nres @ C ) )
% 0.30/0.46 != ( refine1687780735RETURN @ C @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_inequalities(5)
% 0.30/0.46 thf(fact_219_le__SPEC__bindI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Phi: A > $o,X4: A,M: refine1665802226e_nres @ B,F: A > ( refine1665802226e_nres @ B )] :
% 0.30/0.46 ( ( Phi @ X4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M @ ( F @ X4 ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M @ ( refine463715084e_bind @ A @ B @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ F ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_SPEC_bindI
% 0.30/0.46 thf(fact_220_RES__bind__choose,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X4: A,X: set @ A,M: refine1665802226e_nres @ B,F: A > ( refine1665802226e_nres @ B )] :
% 0.30/0.46 ( ( member @ A @ X4 @ X )
% 0.30/0.46 => ( ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M @ ( F @ X4 ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M @ ( refine463715084e_bind @ A @ B @ ( refine605929679le_RES @ A @ X ) @ F ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % RES_bind_choose
% 0.30/0.46 thf(fact_221_SUCCEED__rule,axiom,
% 0.30/0.46 ! [A: $tType,Phi: A > $o] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % SUCCEED_rule
% 0.30/0.46 thf(fact_222_ibind__strict_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,F: product_unit > ( refine1665802226e_nres @ A )] :
% 0.30/0.46 ( ( refine463715084e_bind @ product_unit @ A @ ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) @ F )
% 0.30/0.46 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ibind_strict(1)
% 0.30/0.46 thf(fact_223_bot__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( bot @ B )
% 0.30/0.46 => ( ( bot_bot @ ( A > B ) )
% 0.30/0.46 = ( ^ [X5: A] : ( bot_bot @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_fun_def
% 0.30/0.46 thf(fact_224_bot_Oextremum__uniqueI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/0.46 => ( A2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_uniqueI
% 0.30/0.46 thf(fact_225_bot_Oextremum__unique,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/0.46 = ( A2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_unique
% 0.30/0.46 thf(fact_226_bot_Oextremum,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum
% 0.30/0.46 thf(fact_227_nres__order__simps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,M4: refine1665802226e_nres @ A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ M4 ) ).
% 0.30/0.46
% 0.30/0.46 % nres_order_simps(1)
% 0.30/0.46 thf(fact_228_bind__rule__complete,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,M4: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A ),Phi: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M4 @ F ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 0.30/0.46 = ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M4
% 0.30/0.46 @ ( refine605929679le_RES @ B
% 0.30/0.46 @ ( collect @ B
% 0.30/0.46 @ ^ [X5: B] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F @ X5 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_rule_complete
% 0.30/0.46 thf(fact_229_specify__left,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,M: refine1665802226e_nres @ A,Phi: A > $o,F: A > ( refine1665802226e_nres @ B ),M4: refine1665802226e_nres @ B] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( Phi @ X3 )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ M4 ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M @ F ) @ M4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % specify_left
% 0.30/0.46 thf(fact_230_bind__rule,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,M4: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),Phi: B > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4
% 0.30/0.46 @ ( refine605929679le_RES @ A
% 0.30/0.46 @ ( collect @ A
% 0.30/0.46 @ ^ [X5: A] : ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X5 ) @ ( refine605929679le_RES @ B @ ( collect @ B @ Phi ) ) ) ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M4 @ F ) @ ( refine605929679le_RES @ B @ ( collect @ B @ Phi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_rule
% 0.30/0.46 thf(fact_231_bind__le__nofailI,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,M: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),M7: refine1665802226e_nres @ B] :
% 0.30/0.46 ( ( refine1102455758nofail @ A @ M )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ M7 ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M @ F ) @ M7 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_le_nofailI
% 0.30/0.46 thf(fact_232_bind__le__shift,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,M: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A ),M7: refine1665802226e_nres @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M @ F ) @ M7 )
% 0.30/0.46 = ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M
% 0.30/0.46 @ ( if @ ( refine1665802226e_nres @ B ) @ ( refine1102455758nofail @ A @ M7 )
% 0.30/0.46 @ ( refine605929679le_RES @ B
% 0.30/0.46 @ ( collect @ B
% 0.30/0.46 @ ^ [X5: B] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F @ X5 ) @ M7 ) ) )
% 0.30/0.46 @ ( top_top @ ( refine1665802226e_nres @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_le_shift
% 0.30/0.46 thf(fact_233_bind__sim__select__rule,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,M: refine1665802226e_nres @ B,F4: B > ( refine1665802226e_nres @ A ),Psi: A > $o,F: B > ( refine1665802226e_nres @ C ),Phi: C > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M @ F4 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) )
% 0.30/0.46 => ( ! [X3: B] :
% 0.30/0.46 ( ( refine1102455758nofail @ B @ M )
% 0.30/0.46 => ( ( refine1315500908_inres @ B @ M @ X3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F4 @ X3 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ C ) @ ( F @ X3 ) @ ( refine605929679le_RES @ C @ ( collect @ C @ Phi ) ) ) ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( refine1665802226e_nres @ C ) @ ( refine463715084e_bind @ B @ C @ M @ F ) @ ( refine605929679le_RES @ C @ ( collect @ C @ Phi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_sim_select_rule
% 0.30/0.46 thf(fact_234_top__apply,axiom,
% 0.30/0.46 ! [C: $tType,D3: $tType] :
% 0.30/0.46 ( ( top @ C )
% 0.30/0.46 => ( ( top_top @ ( D3 > C ) )
% 0.30/0.46 = ( ^ [X5: D3] : ( top_top @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_apply
% 0.30/0.46 thf(fact_235_subset__empty,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( A5
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_empty
% 0.30/0.46 thf(fact_236_empty__subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A5 ) ).
% 0.30/0.46
% 0.30/0.46 % empty_subsetI
% 0.30/0.46 thf(fact_237_inf__top__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1561333602nf_top @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( top_top @ A ) @ X4 )
% 0.30/0.46 = X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_top_left
% 0.30/0.46 thf(fact_238_inf__top__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1561333602nf_top @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ( ( inf_inf @ A @ X4 @ ( top_top @ A ) )
% 0.30/0.46 = X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_top_right
% 0.30/0.46 thf(fact_239_inf__eq__top__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1561333602nf_top @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( ( inf_inf @ A @ X4 @ Y3 )
% 0.30/0.46 = ( top_top @ A ) )
% 0.30/0.46 = ( ( X4
% 0.30/0.46 = ( top_top @ A ) )
% 0.30/0.46 & ( Y3
% 0.30/0.46 = ( top_top @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_eq_top_iff
% 0.30/0.46 thf(fact_240_top__eq__inf__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1561333602nf_top @ A )
% 0.30/0.46 => ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( ( top_top @ A )
% 0.30/0.46 = ( inf_inf @ A @ X4 @ Y3 ) )
% 0.30/0.46 = ( ( X4
% 0.30/0.46 = ( top_top @ A ) )
% 0.30/0.46 & ( Y3
% 0.30/0.46 = ( top_top @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_eq_inf_iff
% 0.30/0.46 thf(fact_241_inf__top_Oeq__neutr__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1561333602nf_top @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( inf_inf @ A @ A2 @ B2 )
% 0.30/0.46 = ( top_top @ A ) )
% 0.30/0.46 = ( ( A2
% 0.30/0.46 = ( top_top @ A ) )
% 0.30/0.46 & ( B2
% 0.30/0.46 = ( top_top @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_top.eq_neutr_iff
% 0.30/0.46 thf(fact_242_inf__top_Oleft__neutral,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1561333602nf_top @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ ( top_top @ A ) @ A2 )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_top.left_neutral
% 0.30/0.46 thf(fact_243_inf__top_Oneutr__eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1561333602nf_top @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( top_top @ A )
% 0.30/0.46 = ( inf_inf @ A @ A2 @ B2 ) )
% 0.30/0.46 = ( ( A2
% 0.30/0.46 = ( top_top @ A ) )
% 0.30/0.46 & ( B2
% 0.30/0.46 = ( top_top @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_top.neutr_eq_iff
% 0.30/0.46 thf(fact_244_inf__top_Oright__neutral,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1561333602nf_top @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( inf_inf @ A @ A2 @ ( top_top @ A ) )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_top.right_neutral
% 0.30/0.46 thf(fact_245_inres__simps_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,X: set @ B] :
% 0.30/0.46 ( ( refine1315500908_inres @ B @ ( refine605929679le_RES @ B @ X ) )
% 0.30/0.46 = ( ^ [X5: B] : ( member @ B @ X5 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inres_simps(2)
% 0.30/0.46 thf(fact_246_nres__order__simps_I4_J,axiom,
% 0.30/0.46 ! [D3: $tType,M4: refine1665802226e_nres @ D3] :
% 0.30/0.46 ( ( ord_less_eq @ ( refine1665802226e_nres @ D3 ) @ ( top_top @ ( refine1665802226e_nres @ D3 ) ) @ M4 )
% 0.30/0.46 = ( M4
% 0.30/0.46 = ( top_top @ ( refine1665802226e_nres @ D3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nres_order_simps(4)
% 0.30/0.46 thf(fact_247_bind__FAIL,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: B > ( refine1665802226e_nres @ A )] :
% 0.30/0.46 ( ( refine463715084e_bind @ B @ A @ ( top_top @ ( refine1665802226e_nres @ B ) ) @ F )
% 0.30/0.46 = ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_FAIL
% 0.30/0.46 thf(fact_248_inres__simps_I3_J,axiom,
% 0.30/0.46 ! [C: $tType,X4: C] :
% 0.30/0.46 ( ( refine1315500908_inres @ C @ ( refine1687780735RETURN @ C @ X4 ) )
% 0.30/0.46 = ( ^ [Y5: C,Z: C] : ( Y5 = Z )
% 0.30/0.46 @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inres_simps(3)
% 0.30/0.46 thf(fact_249_nofail__simps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ~ ( refine1102455758nofail @ A @ ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nofail_simps(1)
% 0.30/0.46 thf(fact_250_nres__more__simps_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,X: set @ A] :
% 0.30/0.47 ( ( ( bot_bot @ ( refine1665802226e_nres @ A ) )
% 0.30/0.47 = ( refine605929679le_RES @ A @ X ) )
% 0.30/0.47 = ( X
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nres_more_simps(1)
% 0.30/0.47
% 0.30/0.47 % Type constructors (57)
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bounded_lattice @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice_1,axiom,
% 0.30/0.47 bounded_lattice @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice_2,axiom,
% 0.30/0.47 bounded_lattice @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice_3,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Obounded__lattice_4,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( bounded_lattice @ A8 )
% 0.30/0.47 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Obounded__semilattice__inf__top,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( bounded_lattice @ A8 )
% 0.30/0.47 => ( bounde1561333602nf_top @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( bounded_lattice @ A8 )
% 0.30/0.47 => ( bounded_lattice_bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( semilattice_inf @ A8 )
% 0.30/0.47 => ( semilattice_inf @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( order_bot @ A8 )
% 0.30/0.47 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( preorder @ A8 )
% 0.30/0.47 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( lattice @ A8 )
% 0.30/0.47 => ( lattice @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( order @ A8 )
% 0.30/0.47 => ( order @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Otop,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( top @ A8 )
% 0.30/0.47 => ( top @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( ord @ A8 )
% 0.30/0.47 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.47 ! [A7: $tType,A8: $tType] :
% 0.30/0.47 ( ( bot @ A8 )
% 0.30/0.47 => ( bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_5,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bounde1561333602nf_top @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_6,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bounded_lattice_bot @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_7,axiom,
% 0.30/0.47 ! [A7: $tType] : ( semilattice_inf @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Oorder__bot_8,axiom,
% 0.30/0.47 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_9,axiom,
% 0.30/0.47 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Lattices_Olattice_10,axiom,
% 0.30/0.47 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Oorder_11,axiom,
% 0.30/0.47 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Otop_12,axiom,
% 0.30/0.47 ! [A7: $tType] : ( top @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Oord_13,axiom,
% 0.30/0.47 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Set_Oset___Orderings_Obot_14,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_15,axiom,
% 0.30/0.47 bounde1561333602nf_top @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_16,axiom,
% 0.30/0.47 bounded_lattice_bot @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_17,axiom,
% 0.30/0.47 semilattice_inf @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Oorder__bot_18,axiom,
% 0.30/0.47 order_bot @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_19,axiom,
% 0.30/0.47 preorder @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.30/0.47 linorder @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Lattices_Olattice_20,axiom,
% 0.30/0.47 lattice @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_21,axiom,
% 0.30/0.47 order @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Otop_22,axiom,
% 0.30/0.47 top @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Oord_23,axiom,
% 0.30/0.47 ord @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_HOL_Obool___Orderings_Obot_24,axiom,
% 0.30/0.47 bot @ $o ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Lattices_Obounded__semilattice__inf__top_25,axiom,
% 0.30/0.47 bounde1561333602nf_top @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice__bot_26,axiom,
% 0.30/0.47 bounded_lattice_bot @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Lattices_Osemilattice__inf_27,axiom,
% 0.30/0.47 semilattice_inf @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_28,axiom,
% 0.30/0.47 order_bot @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_29,axiom,
% 0.30/0.47 preorder @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_30,axiom,
% 0.30/0.47 linorder @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Lattices_Olattice_31,axiom,
% 0.30/0.47 lattice @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oorder_32,axiom,
% 0.30/0.47 order @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Orderings_Otop_33,axiom,
% 0.30/0.47 top @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oord_34,axiom,
% 0.30/0.47 ord @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Product__Type_Ounit___Orderings_Obot_35,axiom,
% 0.30/0.47 bot @ product_unit ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__semilattice__inf__top_36,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bounde1561333602nf_top @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice__bot_37,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bounded_lattice_bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Osemilattice__inf_38,axiom,
% 0.30/0.47 ! [A7: $tType] : ( semilattice_inf @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_39,axiom,
% 0.30/0.47 ! [A7: $tType] : ( order_bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_40,axiom,
% 0.30/0.47 ! [A7: $tType] : ( preorder @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Olattice_41,axiom,
% 0.30/0.47 ! [A7: $tType] : ( lattice @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_42,axiom,
% 0.30/0.47 ! [A7: $tType] : ( order @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_43,axiom,
% 0.30/0.47 ! [A7: $tType] : ( top @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_44,axiom,
% 0.30/0.47 ! [A7: $tType] : ( ord @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_45,axiom,
% 0.30/0.47 ! [A7: $tType] : ( bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Helper facts (3)
% 0.30/0.47 thf(help_If_3_1_T,axiom,
% 0.30/0.47 ! [P: $o] :
% 0.30/0.47 ( ( P = $true )
% 0.30/0.47 | ( P = $false ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_2_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X4: A,Y3: A] :
% 0.30/0.47 ( ( if @ A @ $false @ X4 @ Y3 )
% 0.30/0.47 = Y3 ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_1_1_T,axiom,
% 0.30/0.47 ! [A: $tType,X4: A,Y3: A] :
% 0.30/0.47 ( ( if @ A @ $true @ X4 @ Y3 )
% 0.30/0.47 = X4 ) ).
% 0.30/0.47
% 0.30/0.47 % Conjectures (1)
% 0.30/0.47 thf(conj_0,conjecture,
% 0.30/0.47 ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2
% 0.30/0.47 @ ( refine605929679le_RES @ a
% 0.30/0.47 @ ( collect @ a
% 0.30/0.47 @ ^ [V3: a] :
% 0.30/0.47 ( ( p @ V3 )
% 0.30/0.47 & ( q @ V3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 2.82/1.58 ---- Embedded in THF ---
% 2.82/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.82/1.58 %%% Generated on Tue Feb 24 08:28:32 EST 2026
% 2.82/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.82/1.58 %%% Logic specification used:
% 2.82/1.58 %%% thf(spec, logic, $$dhol).
% 2.82/1.58
% 2.82/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.c73FR42ERP/DTF2DTF2203.p
% 2.82/1.58 thf(ty_t_Refine__Basic__Mirabelle__tqojlsrkwy_Onres, type, refine1665802226e_nres: ($tType > $tType)).
% 2.82/1.58 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.82/1.58 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.82/1.58 thf(ty_tf_a, type, a: $tType).
% 2.82/1.58 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_cl_Lattices_Obounded__semilattice__inf__top, type, bounde1561333602nf_top: (!> [A:$tType]: ($o))).
% 2.82/1.58 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.82/1.58 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.82/1.58 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.82/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.82/1.58 thf(sy_c_Orderings_Oorder__class_OGreatest, type, order_Greatest: (!> [A:$tType]: (((A > $o) > A)))).
% 2.82/1.58 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.82/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_ORETURN, type, refine1687780735RETURN: (!> [A:$tType]: ((A > (refine1665802226e_nres @ A))))).
% 2.82/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Obind, type, refine463715084e_bind: (!> [B:$tType,A:$tType]: (((refine1665802226e_nres @ B) > ((B > (refine1665802226e_nres @ A)) > (refine1665802226e_nres @ A)))))).
% 2.82/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Oinres, type, refine1315500908_inres: (!> [A:$tType]: (((refine1665802226e_nres @ A) > (A > $o))))).
% 2.82/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onf__inres, type, refine406925620_inres: (!> [A:$tType]: (((refine1665802226e_nres @ A) > (A > $o))))).
% 2.82/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onofail, type, refine1102455758nofail: (!> [A:$tType]: (((refine1665802226e_nres @ A) > $o)))).
% 2.82/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_OFAILi, type, refine1767639642_FAILi: (!> [A:$tType]: ((refine1665802226e_nres @ A)))).
% 2.82/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_ORES, type, refine605929679le_RES: (!> [A:$tType]: (((set @ A) > (refine1665802226e_nres @ A))))).
% 2.82/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_Orec__nres, type, refine1442219249c_nres: (!> [C:$tType,A:$tType]: ((C > (((set @ A) > C) > ((refine1665802226e_nres @ A) > C)))))).
% 2.82/1.58 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Othe__RES, type, refine1672542526he_RES: (!> [A:$tType]: (((refine1665802226e_nres @ A) > (set @ A))))).
% 2.82/1.58 thf(sy_c_Relation_OPowp, type, powp: (!> [A:$tType]: (((A > $o) > ((set @ A) > $o))))).
% 2.82/1.58 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.82/1.58 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.82/1.58 thf(sy_v_A, type, a2: (refine1665802226e_nres @ a)).
% 2.82/1.58 thf(sy_v_P, type, p: (a > $o)).
% 2.82/1.58 thf(sy_v_Q, type, q: (a > $o)).
% 2.82/1.58 thf(fact_0_nres__more__simps_I4_J, axiom, (! [A:$tType,X:(set @ A),Y:(set @ A)]: (((((refine605929679le_RES @ A) @ X) = ((refine605929679le_RES @ A) @ Y)) = (X = Y))))).
% 2.82/1.58 thf(fact_1_nres_Oinject, axiom, (! [A:$tType,X2:(set @ A),Y2:(set @ A)]: (((((refine605929679le_RES @ A) @ X2) = ((refine605929679le_RES @ A) @ Y2)) = (X2 = Y2))))).
% 2.82/1.58 thf(fact_2_assms_I2_J, axiom, (((ord_less_eq @ (refine1665802226e_nres @ a)) @ a2) @ ((refine605929679le_RES @ a) @ ((collect @ a) @ q)))).
% 2.82/1.58 thf(fact_3_assms_I1_J, axiom, (((ord_less_eq @ (refine1665802226e_nres @ a)) @ a2) @ ((refine605929679le_RES @ a) @ ((collect @ a) @ p)))).
% 2.82/1.58 thf(fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062, axiom, (((ord_less_eq @ (refine1665802226e_nres @ a)) @ a2) @ (((inf_inf @ (refine1665802226e_nres @ a)) @ ((refine605929679le_RES @ a) @ ((collect @ a) @ p))) @ ((refine605929679le_RES @ a) @ ((collect @ a) @ q))))).
% 2.82/1.58 thf(fact_5_if__rule, axiom, (! [A:$tType,B2:$o,S1:(refine1665802226e_nres @ A),Phi:(A > $o),S2:(refine1665802226e_nres @ A)]: (((B2 => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ S1) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi)))) => (((~ (B2)) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ S2) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((((if @ (refine1665802226e_nres @ A)) @ B2) @ S1) @ S2)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi)))))))).
% 2.82/1.58 thf(fact_6_RES__rule, axiom, (! [A:$tType,S:(set @ A),Phi:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ S) => (Phi @ X3)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ S)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))))))).
% 2.82/1.58 thf(fact_7_SPEC__iff, axiom, (! [A:$tType,P:(refine1665802226e_nres @ A),Q:(A > $o),R:(A > $o)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ P) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ (^ [S3:A]: (((Q @ S3) => (R @ S3))))))) => ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ P) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ (^ [S3:A]: (((~ ((Q @ S3))) => (~ ((R @ S3))))))))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ P) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ (^ [S3:A]: (((Q @ S3) = (R @ S3)))))))))))).
% 2.82/1.58 thf(fact_8_SPEC__rule, axiom, (! [A:$tType,Phi:(A > $o),Phi2:(A > $o)]: (((! [X3:A]: (((Phi @ X3) => (Phi2 @ X3)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi2))))))).
% 2.82/1.58 thf(fact_9_SPEC__trans, axiom, (! [A:$tType,X4:(refine1665802226e_nres @ A),Y3:(refine1665802226e_nres @ A),Postcond:(A > $o)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ X4) @ Y3) => ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ Y3) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Postcond))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ X4) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Postcond)))))))).
% 2.82/1.58 thf(fact_10_lhs__step__If, axiom, (! [A:$tType]: (((ord @ A) => (! [B2:$o,T:A,M:A,E:A]: (((B2 => (((ord_less_eq @ A) @ T) @ M)) => (((~ (B2)) => (((ord_less_eq @ A) @ E) @ M)) => (((ord_less_eq @ A) @ ((((if @ A) @ B2) @ T) @ E)) @ M))))))))).
% 2.82/1.58 thf(fact_11_use__spec__rule, axiom, (! [A:$tType,M:(refine1665802226e_nres @ A),Psi:(A > $o),Phi:(A > $o)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Psi))) => ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ (^ [S3:A]: (((Psi @ S3) => (Phi @ S3))))))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi)))))))).
% 2.82/1.58 thf(fact_12_SPEC__cons__rule, axiom, (! [A:$tType,M:(refine1665802226e_nres @ A),Phi:(A > $o),Psi:(A > $o)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) => ((! [X3:A]: (((Phi @ X3) => (Psi @ X3)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Psi)))))))).
% 2.82/1.58 thf(fact_13_order__mono__setup_Orefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X4:A]: ((((ord_less_eq @ A) @ X4) @ X4))))))).
% 2.82/1.58 thf(fact_14_the__RES_Osimps, axiom, (! [A:$tType,X:(set @ A)]: ((((refine1672542526he_RES @ A) @ ((refine605929679le_RES @ A) @ X)) = X)))).
% 2.82/1.58 thf(fact_15_nf__inres__RES, axiom, (! [A:$tType,X:(set @ A),X4:A]: (((((refine406925620_inres @ A) @ ((refine605929679le_RES @ A) @ X)) @ X4) = (((member @ A) @ X4) @ X))))).
% 2.82/1.58 thf(fact_16_nf__inres__SPEC, axiom, (! [A:$tType,Phi:(A > $o),X4:A]: (((((refine406925620_inres @ A) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) @ X4) = (Phi @ X4))))).
% 2.82/1.58 thf(fact_17_nres_Osimps_I7_J, axiom, (! [C:$tType,A:$tType,F1:C,F2:((set @ A) > C),X2:(set @ A)]: (((((((refine1442219249c_nres @ C) @ A) @ F1) @ F2) @ ((refine605929679le_RES @ A) @ X2)) = (F2 @ X2))))).
% 2.82/1.58 thf(fact_18_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X4:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X4)) @ (G @ X4))))))))).
% 2.82/1.58 thf(fact_19_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X4:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X4)) @ (G @ X4))))))))).
% 2.82/1.58 thf(fact_20_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.82/1.58 thf(fact_21_Refine__Misc_Oif__mono, axiom, (! [A:$tType]: (((ord @ A) => (! [B2:$o,M1:A,M12:A,M2:A,M22:A]: (((B2 => (((ord_less_eq @ A) @ M1) @ M12)) => (((~ (B2)) => (((ord_less_eq @ A) @ M2) @ M22)) => (((ord_less_eq @ A) @ ((((if @ A) @ B2) @ M1) @ M2)) @ ((((if @ A) @ B2) @ M12) @ M22)))))))))).
% 2.82/1.58 thf(fact_22_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F3:(A > B),G2:(A > B)]: ((! [X5:A]: ((((ord_less_eq @ B) @ (F3 @ X5)) @ (G2 @ X5))))))))))).
% 2.82/1.58 thf(fact_23_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.82/1.58 thf(fact_24_le__infD2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2)) => (((ord_less_eq @ A) @ A2) @ C2)))))))).
% 2.82/1.58 thf(fact_25_le__infD1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.82/1.58 thf(fact_26_inf__leI, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((! [X3:A]: (((((ord_less_eq @ A) @ X3) @ A2) => ((((ord_less_eq @ A) @ X3) @ B2) => (((ord_less_eq @ A) @ X3) @ C2))))) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C2)))))))).
% 2.82/1.58 thf(fact_27_less__eq__nres_Osimps_I2_J, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ A2)) @ ((refine605929679le_RES @ A) @ B2)) = (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 2.82/1.58 thf(fact_28_nres__order__simps_I5_J, axiom, (! [E2:$tType,X:(set @ E2),Y:(set @ E2)]: (((((ord_less_eq @ (refine1665802226e_nres @ E2)) @ ((refine605929679le_RES @ E2) @ X)) @ ((refine605929679le_RES @ E2) @ Y)) = (((ord_less_eq @ (set @ E2)) @ X) @ Y))))).
% 2.82/1.58 thf(fact_29_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))))))))).
% 2.82/1.58 thf(fact_30_order__mono__setup_Omono__if, axiom, (! [A:$tType]: (((preorder @ A) => (! [T:A,T2:A,E:A,E3:A,B2:$o]: (((((ord_less_eq @ A) @ T) @ T2) => ((((ord_less_eq @ A) @ E) @ E3) => (((ord_less_eq @ A) @ ((((if @ A) @ B2) @ T) @ E)) @ ((((if @ A) @ B2) @ T2) @ E3)))))))))).
% 2.82/1.58 thf(fact_31_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.82/1.58 thf(fact_32_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z:A]: ((Y5 = Z))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ B3) @ A3) & (((ord_less_eq @ A) @ A3) @ B3))))))))).
% 2.82/1.58 thf(fact_33_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.82/1.58 thf(fact_34_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((P @ A4) @ B4)))) => ((! [A4:A,B4:A]: ((((P @ B4) @ A4) => ((P @ A4) @ B4)))) => ((P @ A2) @ B2))))))))).
% 2.82/1.58 thf(fact_35_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.82/1.58 thf(fact_36_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X4:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ Z2) => (((ord_less_eq @ A) @ X4) @ Z2))))))))).
% 2.82/1.58 thf(fact_37_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.82/1.58 thf(fact_38_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.82/1.58 thf(fact_39_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.82/1.58 thf(fact_40_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z:A]: ((Y5 = Z))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) & (((ord_less_eq @ A) @ B3) @ A3))))))))).
% 2.82/1.58 thf(fact_41_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y3:A,X4:A]: (((((ord_less_eq @ A) @ Y3) @ X4) => ((((ord_less_eq @ A) @ X4) @ Y3) = (X4 = Y3))))))))).
% 2.82/1.58 thf(fact_42_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.82/1.58 thf(fact_43_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X5:A]: ((((member @ A) @ X5) @ A5)))) = A5)))).
% 2.82/1.58 thf(fact_44_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.82/1.58 thf(fact_45_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.82/1.58 thf(fact_46_le__cases3, axiom, (! [A:$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))))))))))))))))).
% 2.82/1.58 thf(fact_47_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.82/1.58 thf(fact_48_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X4:A,Y3:A]: (((~ ((((ord_less_eq @ A) @ X4) @ Y3))) => (((ord_less_eq @ A) @ Y3) @ X4)))))))).
% 2.82/1.58 thf(fact_49_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X4:A,Y3:A]: (((X4 = Y3) => (((ord_less_eq @ A) @ X4) @ Y3)))))))).
% 2.82/1.58 thf(fact_50_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) | (((ord_less_eq @ A) @ Y3) @ X4)))))))).
% 2.82/1.58 thf(fact_51_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ X4) => (X4 = Y3))))))))).
% 2.82/1.58 thf(fact_52_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z:A]: ((Y5 = Z))) = (^ [X5:A,Y6:A]: (((((ord_less_eq @ A) @ X5) @ Y6) & (((ord_less_eq @ A) @ Y6) @ X5))))))))).
% 2.82/1.58 thf(fact_53_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,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C2)))))))))).
% 2.82/1.58 thf(fact_54_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,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.82/1.58 thf(fact_55_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,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ C) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C2)))))))))).
% 2.82/1.58 thf(fact_56_inf_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2)) = ((((ord_less_eq @ A) @ A2) @ B2) & (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.82/1.58 thf(fact_57_le__inf__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X4) @ (((inf_inf @ A) @ Y3) @ Z2)) = ((((ord_less_eq @ A) @ X4) @ Y3) & (((ord_less_eq @ A) @ X4) @ Z2))))))))).
% 2.82/1.58 thf(fact_58_inf__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F3:(A > B),G2:(A > B),X5:A]: ((((inf_inf @ B) @ (F3 @ X5)) @ (G2 @ X5))))))))).
% 2.82/1.58 thf(fact_59_inf_Oidem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 2.82/1.58 thf(fact_60_inf__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A]: (((((inf_inf @ A) @ X4) @ X4) = X4))))))).
% 2.82/1.58 thf(fact_61_inf_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B2)) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.82/1.58 thf(fact_62_inf__left__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y3:A]: (((((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ X4) @ Y3)) = (((inf_inf @ A) @ X4) @ Y3)))))))).
% 2.82/1.58 thf(fact_63_inf_Oright__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.82/1.58 thf(fact_64_inf__right__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y3:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X4) @ Y3)) @ Y3) = (((inf_inf @ A) @ X4) @ Y3)))))))).
% 2.82/1.58 thf(fact_65_inf__nres_Osimps_I3_J, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((inf_inf @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ A2)) @ ((refine605929679le_RES @ A) @ B2)) = ((refine605929679le_RES @ A) @ (((inf_inf @ (set @ A)) @ A2) @ B2)))))).
% 2.82/1.58 thf(fact_66_inf__left__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y3:A,Z2:A]: (((((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ Y3) @ Z2)) = (((inf_inf @ A) @ Y3) @ (((inf_inf @ A) @ X4) @ Z2))))))))).
% 2.82/1.58 thf(fact_67_inf_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B2:A,A2:A,C2:A]: (((((inf_inf @ A) @ B2) @ (((inf_inf @ A) @ A2) @ C2)) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2))))))))).
% 2.82/1.58 thf(fact_68_inf__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [X5:A,Y6:A]: ((((inf_inf @ A) @ Y6) @ X5)))))))).
% 2.82/1.58 thf(fact_69_inf_Ocommute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [A3:A,B3:A]: ((((inf_inf @ A) @ B3) @ A3)))))))).
% 2.82/1.58 thf(fact_70_inf__assoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y3:A,Z2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X4) @ Y3)) @ Z2) = (((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ Y3) @ Z2))))))))).
% 2.82/1.58 thf(fact_71_inf_Oassoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C2) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2))))))))).
% 2.82/1.58 thf(fact_72_boolean__algebra__cancel_Oinf2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B5:A,K:A,B2:A,A2:A]: (((B5 = (((inf_inf @ A) @ K) @ B2)) => ((((inf_inf @ A) @ A2) @ B5) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 2.82/1.58 thf(fact_73_boolean__algebra__cancel_Oinf1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A5:A,K:A,A2:A,B2:A]: (((A5 = (((inf_inf @ A) @ K) @ A2)) => ((((inf_inf @ A) @ A5) @ B2) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 2.82/1.58 thf(fact_74_inf__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F3:(A > B),G2:(A > B),X5:A]: ((((inf_inf @ B) @ (F3 @ X5)) @ (G2 @ X5))))))))).
% 2.82/1.58 thf(fact_75_inf__sup__aci_I1_J, axiom, (! [A:$tType]: (((lattice @ A) => ((inf_inf @ A) = (^ [X5:A,Y6:A]: ((((inf_inf @ A) @ Y6) @ X5)))))))).
% 2.82/1.58 thf(fact_76_inf__sup__aci_I2_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X4:A,Y3:A,Z2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X4) @ Y3)) @ Z2) = (((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ Y3) @ Z2))))))))).
% 2.82/1.58 thf(fact_77_inf__sup__aci_I3_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X4:A,Y3:A,Z2:A]: (((((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ Y3) @ Z2)) = (((inf_inf @ A) @ Y3) @ (((inf_inf @ A) @ X4) @ Z2))))))))).
% 2.82/1.58 thf(fact_78_inf__sup__aci_I4_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X4:A,Y3:A]: (((((inf_inf @ A) @ X4) @ (((inf_inf @ A) @ X4) @ Y3)) = (((inf_inf @ A) @ X4) @ Y3)))))))).
% 2.82/1.58 thf(fact_79_inf__sup__ord_I2_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X4:A,Y3:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X4) @ Y3)) @ Y3))))))).
% 2.82/1.58 thf(fact_80_inf__sup__ord_I1_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X4:A,Y3:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X4) @ Y3)) @ X4))))))).
% 2.82/1.58 thf(fact_81_inf__le1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y3:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X4) @ Y3)) @ X4))))))).
% 2.82/1.58 thf(fact_82_inf__le2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y3:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X4) @ Y3)) @ Y3))))))).
% 2.82/1.58 thf(fact_83_le__infE, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ X4) @ (((inf_inf @ A) @ A2) @ B2)) => (~ (((((ord_less_eq @ A) @ X4) @ A2) => (~ ((((ord_less_eq @ A) @ X4) @ B2))))))))))))).
% 2.82/1.58 thf(fact_84_le__infI, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ X4) @ A2) => ((((ord_less_eq @ A) @ X4) @ B2) => (((ord_less_eq @ A) @ X4) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 2.82/1.58 thf(fact_85_inf__mono, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,C2:A,B2:A,D:A]: (((((ord_less_eq @ A) @ A2) @ C2) => ((((ord_less_eq @ A) @ B2) @ D) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ (((inf_inf @ A) @ C2) @ D)))))))))).
% 2.82/1.58 thf(fact_86_le__infI1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,X4:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ X4) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ X4)))))))).
% 2.82/1.58 thf(fact_87_le__infI2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B2:A,X4:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ X4) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ X4)))))))).
% 2.82/1.58 thf(fact_88_inf_OorderE, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (A2 = (((inf_inf @ A) @ A2) @ B2))))))))).
% 2.82/1.58 thf(fact_89_inf_OorderI, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((A2 = (((inf_inf @ A) @ A2) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.82/1.58 thf(fact_90_inf__unique, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [F:(A > (A > A)),X4:A,Y3:A]: (((! [X3:A,Y4:A]: ((((ord_less_eq @ A) @ ((F @ X3) @ Y4)) @ X3))) => ((! [X3:A,Y4:A]: ((((ord_less_eq @ A) @ ((F @ X3) @ Y4)) @ Y4))) => ((! [X3:A,Y4:A,Z3:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => ((((ord_less_eq @ A) @ X3) @ Z3) => (((ord_less_eq @ A) @ X3) @ ((F @ Y4) @ Z3)))))) => ((((inf_inf @ A) @ X4) @ Y3) = ((F @ X4) @ Y3))))))))))).
% 2.82/1.58 thf(fact_91_le__iff__inf, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((ord_less_eq @ A) = (^ [X5:A,Y6:A]: (((((inf_inf @ A) @ X5) @ Y6) = X5)))))))).
% 2.82/1.58 thf(fact_92_inf_Oabsorb1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((inf_inf @ A) @ A2) @ B2) = A2)))))))).
% 2.82/1.58 thf(fact_93_inf_Oabsorb2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((inf_inf @ A) @ A2) @ B2) = B2)))))))).
% 2.82/1.58 thf(fact_94_inf__absorb1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => ((((inf_inf @ A) @ X4) @ Y3) = X4)))))))).
% 2.82/1.58 thf(fact_95_inf__absorb2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [Y3:A,X4:A]: (((((ord_less_eq @ A) @ Y3) @ X4) => ((((inf_inf @ A) @ X4) @ Y3) = Y3)))))))).
% 2.82/1.58 thf(fact_96_inf_OboundedE, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2)) => (~ (((((ord_less_eq @ A) @ A2) @ B2) => (~ ((((ord_less_eq @ A) @ A2) @ C2))))))))))))).
% 2.82/1.58 thf(fact_97_inf_OboundedI, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ A2) @ C2) => (((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2)))))))))).
% 2.82/1.58 thf(fact_98_inf__greatest, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X4:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => ((((ord_less_eq @ A) @ X4) @ Z2) => (((ord_less_eq @ A) @ X4) @ (((inf_inf @ A) @ Y3) @ Z2)))))))))).
% 2.82/1.58 thf(fact_99_inf_Oorder__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((ord_less_eq @ A) = (^ [A3:A,B3:A]: ((A3 = (((inf_inf @ A) @ A3) @ B3))))))))).
% 2.82/1.58 thf(fact_100_inf_Ocobounded1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ A2))))))).
% 2.82/1.58 thf(fact_101_inf_Ocobounded2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2))))))).
% 2.82/1.58 thf(fact_102_inf_Oabsorb__iff1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((ord_less_eq @ A) = (^ [A3:A,B3:A]: (((((inf_inf @ A) @ A3) @ B3) = A3)))))))).
% 2.82/1.58 thf(fact_103_inf_Oabsorb__iff2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((ord_less_eq @ A) = (^ [B3:A,A3:A]: (((((inf_inf @ A) @ A3) @ B3) = B3)))))))).
% 2.82/1.58 thf(fact_104_inf_OcoboundedI1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ C2) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C2)))))))).
% 2.82/1.58 thf(fact_105_inf_OcoboundedI2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B2:A,C2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C2)))))))).
% 2.82/1.58 thf(fact_106_subsetI, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A5) => (((member @ A) @ X3) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A5) @ B5))))).
% 2.82/1.58 thf(fact_107_Int__subset__iff, axiom, (! [A:$tType,C3:(set @ A),A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C3) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) = ((((ord_less_eq @ (set @ A)) @ C3) @ A5) & (((ord_less_eq @ (set @ A)) @ C3) @ B5)))))).
% 2.82/1.58 thf(fact_108_subset__antisym, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A5) => (A5 = B5)))))).
% 2.82/1.58 thf(fact_109_Collect__subset, axiom, (! [A:$tType,A5:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X5:A]: (((((member @ A) @ X5) @ A5) & (P @ X5)))))) @ A5)))).
% 2.82/1.58 thf(fact_110_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X5:A]: ((((member @ A) @ X5) @ A6)))) @ (^ [X5:A]: ((((member @ A) @ X5) @ B6)))))))))).
% 2.82/1.58 thf(fact_111_pred__subset__eq, axiom, (! [A:$tType,R:(set @ A),S:(set @ A)]: (((((ord_less_eq @ (A > $o)) @ (^ [X5:A]: ((((member @ A) @ X5) @ R)))) @ (^ [X5:A]: ((((member @ A) @ X5) @ S)))) = (((ord_less_eq @ (set @ A)) @ R) @ S))))).
% 2.82/1.58 thf(fact_112_conj__subset__def, axiom, (! [A:$tType,A5:(set @ A),P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A5) @ ((collect @ A) @ (^ [X5:A]: (((P @ X5) & (Q @ X5)))))) = ((((ord_less_eq @ (set @ A)) @ A5) @ ((collect @ A) @ P)) & (((ord_less_eq @ (set @ A)) @ A5) @ ((collect @ A) @ Q))))))).
% 2.82/1.58 thf(fact_113_IntI, axiom, (! [A:$tType,C2:A,A5:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ A5) => ((((member @ A) @ C2) @ B5) => (((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A5) @ B5))))))).
% 2.82/1.58 thf(fact_114_Int__iff, axiom, (! [A:$tType,C2:A,A5:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) = ((((member @ A) @ C2) @ A5) & (((member @ A) @ C2) @ B5)))))).
% 2.82/1.58 thf(fact_115_predicate1I, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (A > $o)) @ P) @ Q))))).
% 2.82/1.58 thf(fact_116_IntE, axiom, (! [A:$tType,C2:A,A5:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) => (~ (((((member @ A) @ C2) @ A5) => (~ ((((member @ A) @ C2) @ B5)))))))))).
% 2.82/1.58 thf(fact_117_IntD1, axiom, (! [A:$tType,C2:A,A5:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) => (((member @ A) @ C2) @ A5))))).
% 2.82/1.58 thf(fact_118_IntD2, axiom, (! [A:$tType,C2:A,A5:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) => (((member @ A) @ C2) @ B5))))).
% 2.82/1.58 thf(fact_119_Int__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((collect @ A) @ (^ [X5:A]: (((((member @ A) @ X5) @ A6) & (((member @ A) @ X5) @ B6))))))))))).
% 2.82/1.58 thf(fact_120_Int__assoc, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) @ C3) = (((inf_inf @ (set @ A)) @ A5) @ (((inf_inf @ (set @ A)) @ B5) @ C3)))))).
% 2.82/1.58 thf(fact_121_Int__absorb, axiom, (! [A:$tType,A5:(set @ A)]: (((((inf_inf @ (set @ A)) @ A5) @ A5) = A5)))).
% 2.82/1.58 thf(fact_122_Int__Collect, axiom, (! [A:$tType,X4:A,A5:(set @ A),P:(A > $o)]: (((((member @ A) @ X4) @ (((inf_inf @ (set @ A)) @ A5) @ ((collect @ A) @ P))) = ((((member @ A) @ X4) @ A5) & (P @ X4)))))).
% 2.82/1.58 thf(fact_123_Int__commute, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((((inf_inf @ (set @ A)) @ B6) @ A6))))))).
% 2.82/1.58 thf(fact_124_inf__set__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: (((collect @ A) @ (((inf_inf @ (A > $o)) @ (^ [X5:A]: ((((member @ A) @ X5) @ A6)))) @ (^ [X5:A]: ((((member @ A) @ X5) @ B6))))))))))).
% 2.82/1.58 thf(fact_125_inf__Int__eq, axiom, (! [A:$tType,R:(set @ A),S:(set @ A)]: (((((inf_inf @ (A > $o)) @ (^ [X5:A]: ((((member @ A) @ X5) @ R)))) @ (^ [X5:A]: ((((member @ A) @ X5) @ S)))) = (^ [X5:A]: ((((member @ A) @ X5) @ (((inf_inf @ (set @ A)) @ R) @ S)))))))).
% 2.82/1.58 thf(fact_126_Collect__conj__eq, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X5:A]: (((P @ X5) & (Q @ X5))))) = (((inf_inf @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.82/1.58 thf(fact_127_Int__left__absorb, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((inf_inf @ (set @ A)) @ A5) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) = (((inf_inf @ (set @ A)) @ A5) @ B5))))).
% 2.82/1.58 thf(fact_128_Int__left__commute, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A5) @ (((inf_inf @ (set @ A)) @ B5) @ C3)) = (((inf_inf @ (set @ A)) @ B5) @ (((inf_inf @ (set @ A)) @ A5) @ C3)))))).
% 2.82/1.58 thf(fact_129_predicate1D, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o),X4:A]: (((((ord_less_eq @ (A > $o)) @ P) @ Q) => ((P @ X4) => (Q @ X4)))))).
% 2.82/1.58 thf(fact_130_rev__predicate1D, axiom, (! [A:$tType,P:(A > $o),X4:A,Q:(A > $o)]: (((P @ X4) => ((((ord_less_eq @ (A > $o)) @ P) @ Q) => (Q @ X4)))))).
% 2.82/1.58 thf(fact_131_Int__Collect__mono, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((! [X3:A]: (((((member @ A) @ X3) @ A5) => ((P @ X3) => (Q @ X3))))) => (((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A5) @ ((collect @ A) @ P))) @ (((inf_inf @ (set @ A)) @ B5) @ ((collect @ A) @ Q)))))))).
% 2.82/1.58 thf(fact_132_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X5:A]: (((P @ X5) => (Q @ X5)))))))).
% 2.82/1.58 thf(fact_133_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y5:(set @ A),Z:(set @ A)]: ((Y5 = Z))) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))).
% 2.82/1.58 thf(fact_134_subset__trans, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C3) => (((ord_less_eq @ (set @ A)) @ A5) @ C3)))))).
% 2.82/1.58 thf(fact_135_Int__greatest, axiom, (! [A:$tType,C3:(set @ A),A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C3) @ A5) => ((((ord_less_eq @ (set @ A)) @ C3) @ B5) => (((ord_less_eq @ (set @ A)) @ C3) @ (((inf_inf @ (set @ A)) @ A5) @ B5))))))).
% 2.82/1.58 thf(fact_136_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.82/1.58 thf(fact_137_subset__refl, axiom, (! [A:$tType,A5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A5) @ A5)))).
% 2.82/1.58 thf(fact_138_Int__absorb2, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((inf_inf @ (set @ A)) @ A5) @ B5) = A5))))).
% 2.82/1.58 thf(fact_139_Int__absorb1, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B5) @ A5) => ((((inf_inf @ (set @ A)) @ A5) @ B5) = B5))))).
% 2.82/1.58 thf(fact_140_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A6) => (((member @ A) @ T3) @ B6)))))))))).
% 2.82/1.58 thf(fact_141_equalityD2, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A5))))).
% 2.82/1.58 thf(fact_142_equalityD1, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (((ord_less_eq @ (set @ A)) @ A5) @ B5))))).
% 2.82/1.58 thf(fact_143_Int__lower2, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) @ B5)))).
% 2.82/1.58 thf(fact_144_Int__lower1, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) @ A5)))).
% 2.82/1.58 thf(fact_145_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [X5:A]: (((((member @ A) @ X5) @ A6) => (((member @ A) @ X5) @ B6)))))))))).
% 2.82/1.58 thf(fact_146_equalityE, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A5)))))))))).
% 2.82/1.58 thf(fact_147_Int__mono, axiom, (! [A:$tType,A5:(set @ A),C3:(set @ A),B5:(set @ A),D2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ C3) => ((((ord_less_eq @ (set @ A)) @ B5) @ D2) => (((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A5) @ B5)) @ (((inf_inf @ (set @ A)) @ C3) @ D2))))))).
% 2.82/1.58 thf(fact_148_subsetD, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((member @ A) @ C2) @ A5) => (((member @ A) @ C2) @ B5)))))).
% 2.82/1.58 thf(fact_149_in__mono, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),X4:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((member @ A) @ X4) @ A5) => (((member @ A) @ X4) @ B5)))))).
% 2.82/1.58 thf(fact_150_inter__eq__subsetI, axiom, (! [A:$tType,S:(set @ A),S4:(set @ A),A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ S) @ S4) => (((((inf_inf @ (set @ A)) @ A5) @ S4) = (((inf_inf @ (set @ A)) @ B5) @ S4)) => ((((inf_inf @ (set @ A)) @ A5) @ S) = (((inf_inf @ (set @ A)) @ B5) @ S))))))).
% 2.82/1.58 thf(fact_151_subset__Collect__iff, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B5) @ A5) => ((((ord_less_eq @ (set @ A)) @ B5) @ ((collect @ A) @ (^ [X5:A]: (((((member @ A) @ X5) @ A5) & (P @ X5)))))) = (! [X5:A]: (((((member @ A) @ X5) @ B5) => (P @ X5))))))))).
% 2.82/1.58 thf(fact_152_subset__CollectI, axiom, (! [A:$tType,B5:(set @ A),A5:(set @ A),Q:(A > $o),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B5) @ A5) => ((! [X3:A]: (((((member @ A) @ X3) @ B5) => ((Q @ X3) => (P @ X3))))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X5:A]: (((((member @ A) @ X5) @ B5) & (Q @ X5)))))) @ ((collect @ A) @ (^ [X5:A]: (((((member @ A) @ X5) @ A5) & (P @ X5))))))))))).
% 2.82/1.58 thf(fact_153_Collect__restrict, axiom, (! [A:$tType,X:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X5:A]: (((((member @ A) @ X5) @ X) & (P @ X5)))))) @ X)))).
% 2.82/1.58 thf(fact_154_inf1I, axiom, (! [A:$tType,A5:(A > $o),X4:A,B5:(A > $o)]: (((A5 @ X4) => ((B5 @ X4) => ((((inf_inf @ (A > $o)) @ A5) @ B5) @ X4)))))).
% 2.82/1.58 thf(fact_155_inf1E, axiom, (! [A:$tType,A5:(A > $o),B5:(A > $o),X4:A]: ((((((inf_inf @ (A > $o)) @ A5) @ B5) @ X4) => (~ (((A5 @ X4) => (~ ((B5 @ X4)))))))))).
% 2.82/1.58 thf(fact_156_inf1D1, axiom, (! [A:$tType,A5:(A > $o),B5:(A > $o),X4:A]: ((((((inf_inf @ (A > $o)) @ A5) @ B5) @ X4) => (A5 @ X4))))).
% 2.82/1.58 thf(fact_157_inf1D2, axiom, (! [A:$tType,A5:(A > $o),B5:(A > $o),X4:A]: ((((((inf_inf @ (A > $o)) @ A5) @ B5) @ X4) => (B5 @ X4))))).
% 2.82/1.58 thf(fact_158_ord__eq__le__eq__trans, axiom, (! [A:$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)))))))))).
% 2.82/1.58 thf(fact_159_subset__Collect__conv, axiom, (! [A:$tType,S:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ S) @ ((collect @ A) @ P)) = (! [X5:A]: (((((member @ A) @ X5) @ S) => (P @ X5)))))))).
% 2.82/1.58 thf(fact_160_prop__restrict, axiom, (! [A:$tType,X4:A,Z4:(set @ A),X:(set @ A),P:(A > $o)]: (((((member @ A) @ X4) @ Z4) => ((((ord_less_eq @ (set @ A)) @ Z4) @ ((collect @ A) @ (^ [X5:A]: (((((member @ A) @ X5) @ X) & (P @ X5)))))) => (P @ X4)))))).
% 2.82/1.58 thf(fact_161_Powp__mono, axiom, (! [A:$tType,A5:(A > $o),B5:(A > $o)]: (((((ord_less_eq @ (A > $o)) @ A5) @ B5) => (((ord_less_eq @ ((set @ A) > $o)) @ ((powp @ A) @ A5)) @ ((powp @ A) @ B5)))))).
% 2.82/1.58 thf(fact_162_inf__nres_Oelims, axiom, (! [A:$tType,X4:(refine1665802226e_nres @ A),Xa:(refine1665802226e_nres @ A),Y3:(refine1665802226e_nres @ A)]: ((((((inf_inf @ (refine1665802226e_nres @ A)) @ X4) @ Xa) = Y3) => (((Xa = (refine1767639642_FAILi @ A)) => (Y3 != X4)) => (((X4 = (refine1767639642_FAILi @ A)) => (! [V:(set @ A)]: (((Xa = ((refine605929679le_RES @ A) @ V)) => (Y3 != ((refine605929679le_RES @ A) @ V)))))) => (~ ((! [A4:(set @ A)]: (((X4 = ((refine605929679le_RES @ A) @ A4)) => (! [B4:(set @ A)]: (((Xa = ((refine605929679le_RES @ A) @ B4)) => (Y3 != ((refine605929679le_RES @ A) @ (((inf_inf @ (set @ A)) @ A4) @ B4))))))))))))))))).
% 2.82/1.58 thf(fact_163_GreatestI2__order, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X4:A,Q:(A > $o)]: (((P @ X4) => ((! [Y4:A]: (((P @ Y4) => (((ord_less_eq @ A) @ Y4) @ X4)))) => ((! [X3:A]: (((P @ X3) => ((! [Y7:A]: (((P @ Y7) => (((ord_less_eq @ A) @ Y7) @ X3)))) => (Q @ X3))))) => (Q @ ((order_Greatest @ A) @ P))))))))))).
% 2.82/1.58 thf(fact_164_inf__nres_Osimps_I1_J, axiom, (! [A:$tType,X4:(refine1665802226e_nres @ A)]: (((((inf_inf @ (refine1665802226e_nres @ A)) @ X4) @ (refine1767639642_FAILi @ A)) = X4)))).
% 2.82/1.58 thf(fact_165_nres_Odistinct_I1_J, axiom, (! [A:$tType,X2:(set @ A)]: (((refine1767639642_FAILi @ A) != ((refine605929679le_RES @ A) @ X2))))).
% 2.82/1.58 thf(fact_166_nres_Oinduct, axiom, (! [A:$tType,P:((refine1665802226e_nres @ A) > $o),Nres:(refine1665802226e_nres @ A)]: (((P @ (refine1767639642_FAILi @ A)) => ((! [X3:(set @ A)]: ((P @ ((refine605929679le_RES @ A) @ X3)))) => (P @ Nres)))))).
% 2.82/1.58 thf(fact_167_nres_Oexhaust, axiom, (! [A:$tType,Y3:(refine1665802226e_nres @ A)]: (((Y3 != (refine1767639642_FAILi @ A)) => (~ ((! [X22:(set @ A)]: ((Y3 != ((refine605929679le_RES @ A) @ X22)))))))))).
% 2.82/1.58 thf(fact_168_sup__nres_Oinduct, axiom, (! [A:$tType,P:((refine1665802226e_nres @ A) > ((refine1665802226e_nres @ A) > $o)),A0:(refine1665802226e_nres @ A),A1:(refine1665802226e_nres @ A)]: (((! [Uu:(refine1665802226e_nres @ A)]: (((P @ Uu) @ (refine1767639642_FAILi @ A)))) => ((! [V:(set @ A)]: (((P @ (refine1767639642_FAILi @ A)) @ ((refine605929679le_RES @ A) @ V)))) => ((! [A4:(set @ A),B4:(set @ A)]: (((P @ ((refine605929679le_RES @ A) @ A4)) @ ((refine605929679le_RES @ A) @ B4)))) => ((P @ A0) @ A1))))))).
% 2.82/1.58 thf(fact_169_less__nres_Oinduct, axiom, (! [A:$tType,P:((refine1665802226e_nres @ A) > ((refine1665802226e_nres @ A) > $o)),A0:(refine1665802226e_nres @ A),A1:(refine1665802226e_nres @ A)]: (((! [X_1:(refine1665802226e_nres @ A)]: (((P @ (refine1767639642_FAILi @ A)) @ X_1))) => ((! [Uv:(set @ A)]: (((P @ ((refine605929679le_RES @ A) @ Uv)) @ (refine1767639642_FAILi @ A)))) => ((! [A4:(set @ A),B4:(set @ A)]: (((P @ ((refine605929679le_RES @ A) @ A4)) @ ((refine605929679le_RES @ A) @ B4)))) => ((P @ A0) @ A1))))))).
% 2.82/1.58 thf(fact_170_less__eq__nres_Oinduct, axiom, (! [A:$tType,P:((refine1665802226e_nres @ A) > ((refine1665802226e_nres @ A) > $o)),A0:(refine1665802226e_nres @ A),A1:(refine1665802226e_nres @ A)]: (((! [Uu:(refine1665802226e_nres @ A)]: (((P @ Uu) @ (refine1767639642_FAILi @ A)))) => ((! [A4:(set @ A),B4:(set @ A)]: (((P @ ((refine605929679le_RES @ A) @ A4)) @ ((refine605929679le_RES @ A) @ B4)))) => ((! [Uv:(set @ A)]: (((P @ (refine1767639642_FAILi @ A)) @ ((refine605929679le_RES @ A) @ Uv)))) => ((P @ A0) @ A1))))))).
% 2.82/1.58 thf(fact_171_less__eq__nres_Osimps_I1_J, axiom, (! [A:$tType,Uu2:(refine1665802226e_nres @ A)]: ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ Uu2) @ (refine1767639642_FAILi @ A))))).
% 2.82/1.58 thf(fact_172_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)))).
% 2.82/1.58 thf(fact_173_less__eq__nres_Osimps_I3_J, axiom, (! [A:$tType,Uv2:(set @ A)]: ((~ ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ (refine1767639642_FAILi @ A)) @ ((refine605929679le_RES @ A) @ Uv2))))))).
% 2.82/1.58 thf(fact_174_inf__nres_Osimps_I2_J, axiom, (! [A:$tType,V2:(set @ A)]: (((((inf_inf @ (refine1665802226e_nres @ A)) @ (refine1767639642_FAILi @ A)) @ ((refine605929679le_RES @ A) @ V2)) = ((refine605929679le_RES @ A) @ V2))))).
% 2.82/1.58 thf(fact_175_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)))))))))).
% 2.82/1.58 thf(fact_176_less__eq__nres_Oelims_I2_J, axiom, (! [A:$tType,X4:(refine1665802226e_nres @ A),Xa:(refine1665802226e_nres @ A)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ X4) @ Xa) => ((Xa != (refine1767639642_FAILi @ A)) => (~ ((! [A4:(set @ A)]: (((X4 = ((refine605929679le_RES @ A) @ A4)) => (! [B4:(set @ A)]: (((Xa = ((refine605929679le_RES @ A) @ B4)) => (~ ((((ord_less_eq @ (set @ A)) @ A4) @ B4)))))))))))))))).
% 2.82/1.58 thf(fact_177_less__eq__nres_Oelims_I3_J, axiom, (! [A:$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)))))))))))).
% 2.82/1.58 thf(fact_178_Greatest__equality, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X4:A]: (((P @ X4) => ((! [Y4:A]: (((P @ Y4) => (((ord_less_eq @ A) @ Y4) @ X4)))) => (((order_Greatest @ A) @ P) = X4))))))))).
% 2.82/1.58 thf(fact_179_the__RES__inv, axiom, (! [A:$tType,M:(refine1665802226e_nres @ A)]: ((((refine1102455758nofail @ A) @ M) => (((refine605929679le_RES @ A) @ ((refine1672542526he_RES @ A) @ M)) = M))))).
% 2.82/1.58 thf(fact_180_relprop__triggers_I6_J, axiom, (! [I:$tType,R:(set @ I),R2:(set @ I)]: (((((ord_less_eq @ (set @ I)) @ R) @ R2) => (((ord_less_eq @ (set @ I)) @ R) @ R2))))).
% 2.82/1.58 thf(fact_181_inf__RETURN__SPEC_I1_J, axiom, (! [A:$tType,X4:A,Phi:(A > $o)]: (((((inf_inf @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X4)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) = ((refine605929679le_RES @ A) @ ((collect @ A) @ (^ [Y6:A]: (((Y6 = X4) & (Phi @ X4)))))))))).
% 2.82/1.58 thf(fact_182_nres__more__simps_I6_J, axiom, (! [A:$tType,X4:A,Y3:A]: (((((refine1687780735RETURN @ A) @ X4) = ((refine1687780735RETURN @ A) @ Y3)) = (X4 = Y3))))).
% 2.82/1.58 thf(fact_183_nofail__simps_I2_J, axiom, (! [B:$tType,X:(set @ B)]: (((refine1102455758nofail @ B) @ ((refine605929679le_RES @ B) @ X))))).
% 2.82/1.58 thf(fact_184_nres__order__simps_I20_J, axiom, (! [W:$tType,X4:W,Y3:W]: (((((ord_less_eq @ (refine1665802226e_nres @ W)) @ ((refine1687780735RETURN @ W) @ X4)) @ ((refine1687780735RETURN @ W) @ Y3)) = (X4 = Y3))))).
% 2.82/1.58 thf(fact_185_nofail__simps_I3_J, axiom, (! [C:$tType,X4:C]: (((refine1102455758nofail @ C) @ ((refine1687780735RETURN @ C) @ X4))))).
% 2.82/1.58 thf(fact_186_nres__order__simps_I21_J, axiom, (! [X6:$tType,X4:X6,Y:(set @ X6)]: (((((ord_less_eq @ (refine1665802226e_nres @ X6)) @ ((refine1687780735RETURN @ X6) @ X4)) @ ((refine605929679le_RES @ X6) @ Y)) = (((member @ X6) @ X4) @ Y))))).
% 2.82/1.58 thf(fact_187_inf__RETURN__SPEC_I2_J, axiom, (! [A:$tType,Phi:(A > $o),X4:A]: (((((inf_inf @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) @ ((refine1687780735RETURN @ A) @ X4)) = ((refine605929679le_RES @ A) @ ((collect @ A) @ (^ [Y6:A]: (((Y6 = X4) & (Phi @ X4)))))))))).
% 2.82/1.58 thf(fact_188_pwD1, axiom, (! [A:$tType,S:(refine1665802226e_nres @ A),S4:(refine1665802226e_nres @ A)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ S) @ S4) => (((refine1102455758nofail @ A) @ S4) => ((refine1102455758nofail @ A) @ S)))))).
% 2.82/1.58 thf(fact_189_le__nofailI, axiom, (! [A:$tType,M3:(refine1665802226e_nres @ A),M4:(refine1665802226e_nres @ A)]: (((((refine1102455758nofail @ A) @ M3) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ M4) @ M3)) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ M4) @ M3))))).
% 2.82/1.58 thf(fact_190_nofail__antimono__fun, axiom, (! [B:$tType,A:$tType,F:(A > (refine1665802226e_nres @ B)),G:(A > (refine1665802226e_nres @ B)),X4:A]: (((((ord_less_eq @ (A > (refine1665802226e_nres @ B))) @ F) @ G) => (((refine1102455758nofail @ B) @ (G @ X4)) => ((refine1102455758nofail @ B) @ (F @ X4))))))).
% 2.82/1.58 thf(fact_191_nofail__RES__conv, axiom, (! [A:$tType]: (((refine1102455758nofail @ A) = (^ [M5:(refine1665802226e_nres @ A)]: ((? [M6:(set @ A)]: ((M5 = ((refine605929679le_RES @ A) @ M6)))))))))).
% 2.82/1.58 thf(fact_192_SPEC__eq__is__RETURN_I1_J, axiom, (! [A:$tType,X4:A]: ((((refine605929679le_RES @ A) @ ((collect @ A) @ ((^ [Y5:A,Z:A]: ((Y5 = Z))) @ X4))) = ((refine1687780735RETURN @ A) @ X4))))).
% 2.82/1.58 thf(fact_193_RETURN__SPEC__conv, axiom, (! [A:$tType]: (((refine1687780735RETURN @ A) = (^ [R3:A]: (((refine605929679le_RES @ A) @ ((collect @ A) @ (^ [X5:A]: ((X5 = R3))))))))))).
% 2.82/1.58 thf(fact_194_SPEC__eq__is__RETURN_I2_J, axiom, (! [B:$tType,Y3:B]: ((((refine605929679le_RES @ B) @ ((collect @ B) @ (^ [X5:B]: ((X5 = Y3))))) = ((refine1687780735RETURN @ B) @ Y3))))).
% 2.82/1.58 thf(fact_195_pw__inf__nofail, axiom, (! [A:$tType,A2:(refine1665802226e_nres @ A),B2:(refine1665802226e_nres @ A)]: ((((refine1102455758nofail @ A) @ (((inf_inf @ (refine1665802226e_nres @ A)) @ A2) @ B2)) = (((refine1102455758nofail @ A) @ A2) | ((refine1102455758nofail @ A) @ B2)))))).
% 2.82/1.58 thf(fact_196_le__RES__nofailI, axiom, (! [A:$tType,A2:(refine1665802226e_nres @ A),X4:(set @ A)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ A2) @ ((refine605929679le_RES @ A) @ X4)) => ((refine1102455758nofail @ A) @ A2))))).
% 2.82/1.58 thf(fact_197_RETURN__rule, axiom, (! [A:$tType,Phi:(A > $o),X4:A]: (((Phi @ X4) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X4)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))))))).
% 2.82/1.58 thf(fact_198_lhs__step__RES, axiom, (! [A:$tType,X:(set @ A),M:(refine1665802226e_nres @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ X) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X3)) @ M)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ X)) @ M))))).
% 2.82/1.58 thf(fact_199_RETURN__to__SPEC__rule, axiom, (! [A:$tType,M:(refine1665802226e_nres @ A),V2:A]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ ((^ [Y5:A,Z:A]: ((Y5 = Z))) @ V2)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine1687780735RETURN @ A) @ V2)))))).
% 2.82/1.58 thf(fact_200_lhs__step__SPEC, axiom, (! [A:$tType,Phi:(A > $o),M:(refine1665802226e_nres @ A)]: (((! [X3:A]: (((Phi @ X3) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X3)) @ M)))) => (((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) @ M))))).
% 2.82/1.58 thf(fact_201_lhs__step__bind, axiom, (! [A:$tType,B:$tType,M7:(refine1665802226e_nres @ B),M:(refine1665802226e_nres @ A),F:(A > (refine1665802226e_nres @ B))]: (((((refine1102455758nofail @ B) @ M7) => ((refine1102455758nofail @ A) @ M)) => ((! [X3:A]: (((((refine406925620_inres @ A) @ M) @ X3) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ (F @ X3)) @ M7)))) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ ((((refine463715084e_bind @ A) @ B) @ M) @ F)) @ M7)))))).
% 2.82/1.58 thf(fact_202_inf__RETURN__RES_I2_J, axiom, (! [A:$tType,X4:A,X:(set @ A)]: ((((((member @ A) @ X4) @ X) => ((((inf_inf @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ X)) @ ((refine1687780735RETURN @ A) @ X4)) = ((refine1687780735RETURN @ A) @ X4))) & ((~ ((((member @ A) @ X4) @ X))) => ((((inf_inf @ (refine1665802226e_nres @ A)) @ ((refine605929679le_RES @ A) @ X)) @ ((refine1687780735RETURN @ A) @ X4)) = (bot_bot @ (refine1665802226e_nres @ A)))))))).
% 2.82/1.58 thf(fact_203_inf__RETURN__RES_I1_J, axiom, (! [A:$tType,X4:A,X:(set @ A)]: ((((((member @ A) @ X4) @ X) => ((((inf_inf @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X4)) @ ((refine605929679le_RES @ A) @ X)) = ((refine1687780735RETURN @ A) @ X4))) & ((~ ((((member @ A) @ X4) @ X))) => ((((inf_inf @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X4)) @ ((refine605929679le_RES @ A) @ X)) = (bot_bot @ (refine1665802226e_nres @ A)))))))).
% 2.82/1.58 thf(fact_204_bot__apply, axiom, (! [C:$tType,D3:$tType]: (((bot @ C) => ((bot_bot @ (D3 > C)) = (^ [X5:D3]: ((bot_bot @ C)))))))).
% 2.82/1.58 thf(fact_205_nres__monad3, axiom, (! [B:$tType,A:$tType,C:$tType,M4:(refine1665802226e_nres @ C),F:(C > (refine1665802226e_nres @ B)),G:(B > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ B) @ A) @ ((((refine463715084e_bind @ C) @ B) @ M4) @ F)) @ G) = ((((refine463715084e_bind @ C) @ A) @ M4) @ (^ [X5:C]: (((((refine463715084e_bind @ B) @ A) @ (F @ X5)) @ G)))))))).
% 2.82/1.58 thf(fact_206_If__bind__distrib, axiom, (! [B:$tType,A:$tType,B2:$o,T:(refine1665802226e_nres @ A),E:(refine1665802226e_nres @ A),F:(A > (refine1665802226e_nres @ B))]: (((B2 => (((((refine463715084e_bind @ A) @ B) @ ((((if @ (refine1665802226e_nres @ A)) @ B2) @ T) @ E)) @ F) = ((((refine463715084e_bind @ A) @ B) @ T) @ F))) & ((~ (B2)) => (((((refine463715084e_bind @ A) @ B) @ ((((if @ (refine1665802226e_nres @ A)) @ B2) @ T) @ E)) @ F) = ((((refine463715084e_bind @ A) @ B) @ E) @ F))))))).
% 2.82/1.58 thf(fact_207_inf__bot__right, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X4:A]: (((((inf_inf @ A) @ X4) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 2.82/1.58 thf(fact_208_inf__bot__left, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X4:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X4) = (bot_bot @ A)))))))).
% 2.82/1.58 thf(fact_209_nres__monad2, axiom, (! [A:$tType,M4:(refine1665802226e_nres @ A)]: ((((((refine463715084e_bind @ A) @ A) @ M4) @ (refine1687780735RETURN @ A)) = M4)))).
% 2.82/1.58 thf(fact_210_nres__monad1, axiom, (! [A:$tType,B:$tType,X4:B,F:(B > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ B) @ A) @ ((refine1687780735RETURN @ B) @ X4)) @ F) = (F @ X4))))).
% 2.82/1.58 thf(fact_211_nres__order__simps_I2_J, axiom, (! [B:$tType,M4:(refine1665802226e_nres @ B)]: (((((ord_less_eq @ (refine1665802226e_nres @ B)) @ M4) @ (bot_bot @ (refine1665802226e_nres @ B))) = (M4 = (bot_bot @ (refine1665802226e_nres @ B))))))).
% 2.82/1.58 thf(fact_212_bind__SUCCEED, axiom, (! [B:$tType,A:$tType,F:(B > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ B) @ A) @ (bot_bot @ (refine1665802226e_nres @ B))) @ F) = (bot_bot @ (refine1665802226e_nres @ A)))))).
% 2.82/1.58 thf(fact_213_nofail__simps_I4_J, axiom, (! [D3:$tType]: (((refine1102455758nofail @ D3) @ (bot_bot @ (refine1665802226e_nres @ D3)))))).
% 2.82/1.58 thf(fact_214_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J, axiom, (! [B:$tType,A:$tType,M4:(refine1665802226e_nres @ A),M3:(refine1665802226e_nres @ A),F:(A > (refine1665802226e_nres @ B)),F4:(A > (refine1665802226e_nres @ B))]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M4) @ M3) => ((! [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) @ M3) @ F4))))))).
% 2.82/1.58 thf(fact_215_bind__cong, axiom, (! [B:$tType,A:$tType,M:(refine1665802226e_nres @ A),M7:(refine1665802226e_nres @ A),F:(A > (refine1665802226e_nres @ B)),F4:(A > (refine1665802226e_nres @ B))]: (((M = M7) => ((! [X3:A]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X3)) @ M7) => ((F @ X3) = (F4 @ X3))))) => (((((refine463715084e_bind @ A) @ B) @ M) @ F) = ((((refine463715084e_bind @ A) @ B) @ M7) @ F4))))))).
% 2.82/1.58 thf(fact_216_pw__RES__bind__choose_I1_J, axiom, (! [A:$tType,B:$tType,X:(set @ B),F:(B > (refine1665802226e_nres @ A))]: ((((refine1102455758nofail @ A) @ ((((refine463715084e_bind @ B) @ A) @ ((refine605929679le_RES @ B) @ X)) @ F)) = (! [X5:B]: (((((member @ B) @ X5) @ X) => ((refine1102455758nofail @ A) @ (F @ X5))))))))).
% 2.82/1.58 thf(fact_217_let__to__bind__conv, axiom, (! [A:$tType,B:$tType]: (((^ [S3:B,F3:(B > (refine1665802226e_nres @ A))]: ((F3 @ S3))) = (^ [X5:B]: ((((refine463715084e_bind @ B) @ A) @ ((refine1687780735RETURN @ B) @ X5)))))))).
% 2.82/1.58 thf(fact_218_nres__inequalities_I5_J, axiom, (! [C:$tType,X4:C]: (((bot_bot @ (refine1665802226e_nres @ C)) != ((refine1687780735RETURN @ C) @ X4))))).
% 2.82/1.58 thf(fact_219_le__SPEC__bindI, axiom, (! [B:$tType,A:$tType,Phi:(A > $o),X4:A,M:(refine1665802226e_nres @ B),F:(A > (refine1665802226e_nres @ B))]: (((Phi @ X4) => ((((ord_less_eq @ (refine1665802226e_nres @ B)) @ M) @ (F @ X4)) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ M) @ ((((refine463715084e_bind @ A) @ B) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) @ F))))))).
% 2.82/1.58 thf(fact_220_RES__bind__choose, axiom, (! [B:$tType,A:$tType,X4:A,X:(set @ A),M:(refine1665802226e_nres @ B),F:(A > (refine1665802226e_nres @ B))]: (((((member @ A) @ X4) @ X) => ((((ord_less_eq @ (refine1665802226e_nres @ B)) @ M) @ (F @ X4)) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ M) @ ((((refine463715084e_bind @ A) @ B) @ ((refine605929679le_RES @ A) @ X)) @ F))))))).
% 2.82/1.58 thf(fact_221_SUCCEED__rule, axiom, (! [A:$tType,Phi:(A > $o)]: ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ (bot_bot @ (refine1665802226e_nres @ A))) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi)))))).
% 2.82/1.58 thf(fact_222_ibind__strict_I1_J, axiom, (! [A:$tType,F:(product_unit > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ product_unit) @ A) @ (bot_bot @ (refine1665802226e_nres @ product_unit))) @ F) = (bot_bot @ (refine1665802226e_nres @ A)))))).
% 2.82/1.58 thf(fact_223_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X5:A]: ((bot_bot @ B)))))))).
% 2.82/1.58 thf(fact_224_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) => (A2 = (bot_bot @ A))))))))).
% 2.82/1.58 thf(fact_225_bot_Oextremum__unique, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) = (A2 = (bot_bot @ A))))))))).
% 2.82/1.58 thf(fact_226_bot_Oextremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A2))))))).
% 2.82/1.58 thf(fact_227_nres__order__simps_I1_J, axiom, (! [A:$tType,M4:(refine1665802226e_nres @ A)]: ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ (bot_bot @ (refine1665802226e_nres @ A))) @ M4)))).
% 2.82/1.58 thf(fact_228_bind__rule__complete, axiom, (! [A:$tType,B:$tType,M4:(refine1665802226e_nres @ B),F:(B > (refine1665802226e_nres @ A)),Phi:(A > $o)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((((refine463715084e_bind @ B) @ A) @ M4) @ F)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) = (((ord_less_eq @ (refine1665802226e_nres @ B)) @ M4) @ ((refine605929679le_RES @ B) @ ((collect @ B) @ (^ [X5:B]: ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ (F @ X5)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi)))))))))))).
% 2.82/1.58 thf(fact_229_specify__left, axiom, (! [A:$tType,B:$tType,M:(refine1665802226e_nres @ A),Phi:(A > $o),F:(A > (refine1665802226e_nres @ B)),M4:(refine1665802226e_nres @ B)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Phi))) => ((! [X3:A]: (((Phi @ X3) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ (F @ X3)) @ M4)))) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ ((((refine463715084e_bind @ A) @ B) @ M) @ F)) @ M4)))))).
% 2.82/1.58 thf(fact_230_bind__rule, axiom, (! [A:$tType,B:$tType,M4:(refine1665802226e_nres @ A),F:(A > (refine1665802226e_nres @ B)),Phi:(B > $o)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ M4) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ (^ [X5:A]: ((((ord_less_eq @ (refine1665802226e_nres @ B)) @ (F @ X5)) @ ((refine605929679le_RES @ B) @ ((collect @ B) @ Phi)))))))) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ ((((refine463715084e_bind @ A) @ B) @ M4) @ F)) @ ((refine605929679le_RES @ B) @ ((collect @ B) @ Phi))))))).
% 2.82/1.58 thf(fact_231_bind__le__nofailI, axiom, (! [A:$tType,B:$tType,M:(refine1665802226e_nres @ A),F:(A > (refine1665802226e_nres @ B)),M7:(refine1665802226e_nres @ B)]: ((((refine1102455758nofail @ A) @ M) => ((! [X3:A]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((refine1687780735RETURN @ A) @ X3)) @ M) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ (F @ X3)) @ M7)))) => (((ord_less_eq @ (refine1665802226e_nres @ B)) @ ((((refine463715084e_bind @ A) @ B) @ M) @ F)) @ M7)))))).
% 2.82/1.58 thf(fact_232_bind__le__shift, axiom, (! [A:$tType,B:$tType,M:(refine1665802226e_nres @ B),F:(B > (refine1665802226e_nres @ A)),M7:(refine1665802226e_nres @ A)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((((refine463715084e_bind @ B) @ A) @ M) @ F)) @ M7) = (((ord_less_eq @ (refine1665802226e_nres @ B)) @ M) @ ((((if @ (refine1665802226e_nres @ B)) @ ((refine1102455758nofail @ A) @ M7)) @ ((refine605929679le_RES @ B) @ ((collect @ B) @ (^ [X5:B]: ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ (F @ X5)) @ M7)))))) @ (top_top @ (refine1665802226e_nres @ B)))))))).
% 2.82/1.58 thf(fact_233_bind__sim__select__rule, axiom, (! [A:$tType,B:$tType,C:$tType,M:(refine1665802226e_nres @ B),F4:(B > (refine1665802226e_nres @ A)),Psi:(A > $o),F:(B > (refine1665802226e_nres @ C)),Phi:(C > $o)]: (((((ord_less_eq @ (refine1665802226e_nres @ A)) @ ((((refine463715084e_bind @ B) @ A) @ M) @ F4)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Psi))) => ((! [X3:B]: ((((refine1102455758nofail @ B) @ M) => ((((refine1315500908_inres @ B) @ M) @ X3) => ((((ord_less_eq @ (refine1665802226e_nres @ A)) @ (F4 @ X3)) @ ((refine605929679le_RES @ A) @ ((collect @ A) @ Psi))) => (((ord_less_eq @ (refine1665802226e_nres @ C)) @ (F @ X3)) @ ((refine605929679le_RES @ C) @ ((collect @ C) @ Phi)))))))) => (((ord_less_eq @ (refine1665802226e_nres @ C)) @ ((((refine463715084e_bind @ B) @ C) @ M) @ F)) @ ((refine605929679le_RES @ C) @ ((collect @ C) @ Phi)))))))).
% 2.82/1.58 thf(fact_234_top__apply, axiom, (! [C:$tType,D3:$tType]: (((top @ C) => ((top_top @ (D3 > C)) = (^ [X5:D3]: ((top_top @ C)))))))).
% 2.82/1.58 thf(fact_235_subset__empty, axiom, (! [A:$tType,A5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ (bot_bot @ (set @ A))) = (A5 = (bot_bot @ (set @ A))))))).
% 2.82/1.58 thf(fact_236_empty__subsetI, axiom, (! [A:$tType,A5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A5)))).
% 2.82/1.58 thf(fact_237_inf__top__left, axiom, (! [A:$tType]: (((bounde1561333602nf_top @ A) => (! [X4:A]: (((((inf_inf @ A) @ (top_top @ A)) @ X4) = X4))))))).
% 2.82/1.58 thf(fact_238_inf__top__right, axiom, (! [A:$tType]: (((bounde1561333602nf_top @ A) => (! [X4:A]: (((((inf_inf @ A) @ X4) @ (top_top @ A)) = X4))))))).
% 2.82/1.58 thf(fact_239_inf__eq__top__iff, axiom, (! [A:$tType]: (((bounde1561333602nf_top @ A) => (! [X4:A,Y3:A]: ((((((inf_inf @ A) @ X4) @ Y3) = (top_top @ A)) = ((X4 = (top_top @ A)) & (Y3 = (top_top @ A)))))))))).
% 2.82/1.58 thf(fact_240_top__eq__inf__iff, axiom, (! [A:$tType]: (((bounde1561333602nf_top @ A) => (! [X4:A,Y3:A]: ((((top_top @ A) = (((inf_inf @ A) @ X4) @ Y3)) = ((X4 = (top_top @ A)) & (Y3 = (top_top @ A)))))))))).
% 2.82/1.58 thf(fact_241_inf__top_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1561333602nf_top @ A) => (! [A2:A,B2:A]: ((((((inf_inf @ A) @ A2) @ B2) = (top_top @ A)) = ((A2 = (top_top @ A)) & (B2 = (top_top @ A)))))))))).
% 2.82/1.58 thf(fact_242_inf__top_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1561333602nf_top @ A) => (! [A2:A]: (((((inf_inf @ A) @ (top_top @ A)) @ A2) = A2))))))).
% 2.82/1.58 thf(fact_243_inf__top_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1561333602nf_top @ A) => (! [A2:A,B2:A]: ((((top_top @ A) = (((inf_inf @ A) @ A2) @ B2)) = ((A2 = (top_top @ A)) & (B2 = (top_top @ A)))))))))).
% 2.82/1.58 thf(fact_244_inf__top_Oright__neutral, axiom, (! [A:$tType]: (((bounde1561333602nf_top @ A) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ (top_top @ A)) = A2))))))).
% 2.82/1.58 thf(fact_245_inres__simps_I2_J, axiom, (! [B:$tType,X:(set @ B)]: ((((refine1315500908_inres @ B) @ ((refine605929679le_RES @ B) @ X)) = (^ [X5:B]: ((((member @ B) @ X5) @ X))))))).
% 2.82/1.58 thf(fact_246_nres__order__simps_I4_J, axiom, (! [D3:$tType,M4:(refine1665802226e_nres @ D3)]: (((((ord_less_eq @ (refine1665802226e_nres @ D3)) @ (top_top @ (refine1665802226e_nres @ D3))) @ M4) = (M4 = (top_top @ (refine1665802226e_nres @ D3))))))).
% 2.82/1.58 thf(fact_247_bind__FAIL, axiom, (! [B:$tType,A:$tType,F:(B > (refine1665802226e_nres @ A))]: ((((((refine463715084e_bind @ B) @ A) @ (top_top @ (refine1665802226e_nres @ B))) @ F) = (top_top @ (refine1665802226e_nres @ A)))))).
% 2.82/1.58 thf(fact_248_inres__simps_I3_J, axiom, (! [C:$tType,X4:C]: ((((refine1315500908_inres @ C) @ ((refine1687780735RETURN @ C) @ X4)) = ((^ [Y5:C,Z:C]: ((Y5 = Z))) @ X4))))).
% 2.82/1.58 thf(fact_249_nofail__simps_I1_J, axiom, (! [A:$tType]: ((~ (((refine1102455758nofail @ A) @ (top_top @ (refine1665802226e_nres @ A)))))))).
% 2.82/1.58 thf(fact_250_nres__more__simps_I1_J, axiom, (! [A:$tType,X:(set @ A)]: ((((bot_bot @ (refine1665802226e_nres @ A)) = ((refine605929679le_RES @ A) @ X)) = (X = (bot_bot @ (set @ A))))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice, axiom, (! [A7:$tType]: ((bounded_lattice @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice_1, axiom, (bounded_lattice @ product_unit)).
% 2.82/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__lattice_2, axiom, (bounded_lattice @ $o)).
% 2.82/1.58 thf(tcon_Set_Oset___Lattices_Obounded__lattice_3, axiom, (! [A7:$tType]: ((bounded_lattice @ (set @ A7))))).
% 2.82/1.58 thf(tcon_fun___Lattices_Obounded__lattice_4, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounded_lattice @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Lattices_Obounded__semilattice__inf__top, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounde1561333602nf_top @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounded_lattice_bot @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A7:$tType,A8:$tType]: (((semilattice_inf @ A8) => (semilattice_inf @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A7:$tType,A8:$tType]: (((order_bot @ A8) => (order_bot @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Lattices_Olattice, axiom, (! [A7:$tType,A8:$tType]: (((lattice @ A8) => (lattice @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Orderings_Otop, axiom, (! [A7:$tType,A8:$tType]: (((top @ A8) => (top @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A8:$tType]: (((bot @ A8) => (bot @ (A7 > A8)))))).
% 2.82/1.58 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_5, axiom, (! [A7:$tType]: ((bounde1561333602nf_top @ (set @ A7))))).
% 2.82/1.58 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_6, axiom, (! [A7:$tType]: ((bounded_lattice_bot @ (set @ A7))))).
% 2.82/1.58 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_7, axiom, (! [A7:$tType]: ((semilattice_inf @ (set @ A7))))).
% 2.82/1.58 thf(tcon_Set_Oset___Orderings_Oorder__bot_8, axiom, (! [A7:$tType]: ((order_bot @ (set @ A7))))).
% 2.82/1.58 thf(tcon_Set_Oset___Orderings_Opreorder_9, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 2.82/1.58 thf(tcon_Set_Oset___Lattices_Olattice_10, axiom, (! [A7:$tType]: ((lattice @ (set @ A7))))).
% 2.82/1.58 thf(tcon_Set_Oset___Orderings_Oorder_11, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 2.82/1.58 thf(tcon_Set_Oset___Orderings_Otop_12, axiom, (! [A7:$tType]: ((top @ (set @ A7))))).
% 2.82/1.58 thf(tcon_Set_Oset___Orderings_Oord_13, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.82/1.58 thf(tcon_Set_Oset___Orderings_Obot_14, axiom, (! [A7:$tType]: ((bot @ (set @ A7))))).
% 2.82/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_15, axiom, (bounde1561333602nf_top @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_16, axiom, (bounded_lattice_bot @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_17, axiom, (semilattice_inf @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Orderings_Oorder__bot_18, axiom, (order_bot @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Orderings_Opreorder_19, axiom, (preorder @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Lattices_Olattice_20, axiom, (lattice @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_21, axiom, (order @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Orderings_Otop_22, axiom, (top @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Orderings_Oord_23, axiom, (ord @ $o)).
% 2.82/1.58 thf(tcon_HOL_Obool___Orderings_Obot_24, axiom, (bot @ $o)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Lattices_Obounded__semilattice__inf__top_25, axiom, (bounde1561333602nf_top @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice__bot_26, axiom, (bounded_lattice_bot @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Lattices_Osemilattice__inf_27, axiom, (semilattice_inf @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_28, axiom, (order_bot @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_29, axiom, (preorder @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_30, axiom, (linorder @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Lattices_Olattice_31, axiom, (lattice @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Orderings_Oorder_32, axiom, (order @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Orderings_Otop_33, axiom, (top @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Orderings_Oord_34, axiom, (ord @ product_unit)).
% 2.82/1.58 thf(tcon_Product__Type_Ounit___Orderings_Obot_35, axiom, (bot @ product_unit)).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__semilattice__inf__top_36, axiom, (! [A7:$tType]: ((bounde1561333602nf_top @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice__bot_37, axiom, (! [A7:$tType]: ((bounded_lattice_bot @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Osemilattice__inf_38, axiom, (! [A7:$tType]: ((semilattice_inf @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_39, axiom, (! [A7:$tType]: ((order_bot @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_40, axiom, (! [A7:$tType]: ((preorder @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Olattice_41, axiom, (! [A7:$tType]: ((lattice @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_42, axiom, (! [A7:$tType]: ((order @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_43, axiom, (! [A7:$tType]: ((top @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_44, axiom, (! [A7:$tType]: ((ord @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_45, axiom, (! [A7:$tType]: ((bot @ (refine1665802226e_nres @ A7))))).
% 2.82/1.58 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.82/1.58 thf(help_If_2_1_T, axiom, (! [A:$tType,X4:A,Y3:A]: ((((((if @ A) @ $false) @ X4) @ Y3) = Y3)))).
% 2.82/1.58 thf(help_If_1_1_T, axiom, (! [A:$tType,X4:A,Y3:A]: ((((((if @ A) @ $true) @ X4) @ Y3) = X4)))).
% 2.82/1.58 thf(conj_0, conjecture, (((ord_less_eq @ (refine1665802226e_nres @ a)) @ a2) @ ((refine605929679le_RES @ a) @ ((collect @ a) @ (^ [V3:a]: (((p @ V3) & (q @ V3)))))))).
% 2.82/1.58 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.c73FR42ERP/DTF2DTF2203.p
% 2.82/1.58 ------------------------
% 3.04/1.61 ---- Cleaned THF ---
% 3.04/1.61 thf(ty_t_Refine__Basic__Mirabelle__tqojlsrkwy_Onres,type,
% 3.04/1.61 refine1665802226e_nres: $tType > $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_Product__Type_Ounit,type,
% 3.04/1.61 product_unit: $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_Set_Oset,type,
% 3.04/1.61 set: $tType > $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_tf_a,type,
% 3.04/1.61 a: $tType ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Lattices_Obounded__lattice,type,
% 3.04/1.61 bounded_lattice:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_HOL_Otype,type,
% 3.04/1.61 type:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Obot,type,
% 3.04/1.61 bot:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Oord,type,
% 3.04/1.61 ord:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Otop,type,
% 3.04/1.61 top:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Oorder,type,
% 3.04/1.61 order:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Lattices_Olattice,type,
% 3.04/1.61 lattice:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Olinorder,type,
% 3.04/1.61 linorder:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Opreorder,type,
% 3.04/1.61 preorder:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Oorder__bot,type,
% 3.04/1.61 order_bot:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 3.04/1.61 semilattice_inf:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 3.04/1.61 bounded_lattice_bot:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Lattices_Obounded__semilattice__inf__top,type,
% 3.04/1.61 bounde1561333602nf_top:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_If,type,
% 3.04/1.61 if:
% 3.04/1.61 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 3.04/1.61 inf_inf:
% 3.04/1.61 !>[A: $tType] : ( A > A > A ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.04/1.61 bot_bot:
% 3.04/1.61 !>[A: $tType] : A ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.04/1.61 ord_less_eq:
% 3.04/1.61 !>[A: $tType] : ( A > A > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 3.04/1.61 order_Greatest:
% 3.04/1.61 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Orderings_Otop__class_Otop,type,
% 3.04/1.61 top_top:
% 3.04/1.61 !>[A: $tType] : A ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_ORETURN,type,
% 3.04/1.61 refine1687780735RETURN:
% 3.04/1.61 !>[A: $tType] : ( A > ( refine1665802226e_nres @ A ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Obind,type,
% 3.04/1.61 refine463715084e_bind:
% 3.04/1.61 !>[B: $tType,A: $tType] : ( ( refine1665802226e_nres @ B ) > ( B > ( refine1665802226e_nres @ A ) ) > ( refine1665802226e_nres @ A ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Oinres,type,
% 3.04/1.61 refine1315500908_inres:
% 3.04/1.61 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > A > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onf__inres,type,
% 3.04/1.61 refine406925620_inres:
% 3.04/1.61 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > A > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onofail,type,
% 3.04/1.61 refine1102455758nofail:
% 3.04/1.61 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_OFAILi,type,
% 3.04/1.61 refine1767639642_FAILi:
% 3.04/1.61 !>[A: $tType] : ( refine1665802226e_nres @ A ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_ORES,type,
% 3.04/1.61 refine605929679le_RES:
% 3.04/1.61 !>[A: $tType] : ( ( set @ A ) > ( refine1665802226e_nres @ A ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Onres_Orec__nres,type,
% 3.04/1.61 refine1442219249c_nres:
% 3.04/1.61 !>[C: $tType,A: $tType] : ( C > ( ( set @ A ) > C ) > ( refine1665802226e_nres @ A ) > C ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Refine__Basic__Mirabelle__tqojlsrkwy_Othe__RES,type,
% 3.04/1.61 refine1672542526he_RES:
% 3.04/1.61 !>[A: $tType] : ( ( refine1665802226e_nres @ A ) > ( set @ A ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Relation_OPowp,type,
% 3.04/1.61 powp:
% 3.04/1.61 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Set_OCollect,type,
% 3.04/1.61 collect:
% 3.04/1.61 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_member,type,
% 3.04/1.61 member:
% 3.04/1.61 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_v_A,type,
% 3.04/1.61 a2: refine1665802226e_nres @ a ).
% 3.04/1.61
% 3.04/1.61 thf(sy_v_P,type,
% 3.04/1.61 p: a > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_v_Q,type,
% 3.04/1.61 q: a > $o ).
% 3.04/1.61
% 3.04/1.61 thf(fact_0_nres__more__simps_I4_J,axiom,
% 3.04/1.61 ! [A: $tType,X: set @ A,Y: set @ A] :
% 3.04/1.61 ( ( ( refine605929679le_RES @ A @ X )
% 3.04/1.61 = ( refine605929679le_RES @ A @ Y ) )
% 3.04/1.61 = ( X = Y ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_1_nres_Oinject,axiom,
% 3.04/1.61 ! [A: $tType,X2: set @ A,Y2: set @ A] :
% 3.04/1.61 ( ( ( refine605929679le_RES @ A @ X2 )
% 3.04/1.61 = ( refine605929679le_RES @ A @ Y2 ) )
% 3.04/1.61 = ( X2 = Y2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_2_assms_I2_J,axiom,
% 3.04/1.61 ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( refine605929679le_RES @ a @ ( collect @ a @ q ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_3_assms_I1_J,axiom,
% 3.04/1.61 ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( refine605929679le_RES @ a @ ( collect @ a @ p ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062,axiom,
% 3.04/1.61 ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( inf_inf @ ( refine1665802226e_nres @ a ) @ ( refine605929679le_RES @ a @ ( collect @ a @ p ) ) @ ( refine605929679le_RES @ a @ ( collect @ a @ q ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_5_if__rule,axiom,
% 3.04/1.61 ! [A: $tType,B2: $o,S1: refine1665802226e_nres @ A,Phi: A > $o,S2: refine1665802226e_nres @ A] :
% 3.04/1.61 ( ( B2
% 3.04/1.61 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S1 @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) )
% 3.04/1.61 => ( ( ~ B2
% 3.04/1.61 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S2 @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) )
% 3.04/1.61 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( if @ ( refine1665802226e_nres @ A ) @ B2 @ S1 @ S2 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_6_RES__rule,axiom,
% 3.04/1.61 ! [A: $tType,S: set @ A,Phi: A > $o] :
% 3.04/1.61 ( ! [X3: A] :
% 3.04/1.61 ( ( member @ A @ X3 @ S )
% 3.04/1.61 => ( Phi @ X3 ) )
% 3.04/1.61 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ S ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_7_SPEC__iff,axiom,
% 3.04/1.61 ! [A: $tType,P: refine1665802226e_nres @ A,Q: A > $o,R: A > $o] :
% 3.04/1.61 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ P
% 3.04/1.61 @ ( refine605929679le_RES @ A
% 3.04/1.61 @ ( collect @ A
% 3.04/1.61 @ ^ [S3: A] :
% 3.04/1.61 ( ( Q @ S3 )
% 3.04/1.61 => ( R @ S3 ) ) ) ) )
% 3.04/1.61 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ P
% 3.04/1.61 @ ( refine605929679le_RES @ A
% 3.04/1.61 @ ( collect @ A
% 3.04/1.61 @ ^ [S3: A] :
% 3.04/1.61 ( ~ ( Q @ S3 )
% 3.04/1.61 => ~ ( R @ S3 ) ) ) ) )
% 3.04/1.61 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ P
% 3.04/1.61 @ ( refine605929679le_RES @ A
% 3.04/1.61 @ ( collect @ A
% 3.04/1.61 @ ^ [S3: A] :
% 3.04/1.61 ( ( Q @ S3 )
% 3.04/1.61 = ( R @ S3 ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_8_SPEC__rule,axiom,
% 3.04/1.61 ! [A: $tType,Phi: A > $o,Phi2: A > $o] :
% 3.04/1.61 ( ! [X3: A] :
% 3.04/1.61 ( ( Phi @ X3 )
% 3.04/1.61 => ( Phi2 @ X3 ) )
% 3.04/1.61 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_9_SPEC__trans,axiom,
% 3.04/1.61 ! [A: $tType,X4: refine1665802226e_nres @ A,Y3: refine1665802226e_nres @ A,Postcond: A > $o] :
% 3.04/1.61 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Y3 )
% 3.04/1.61 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ Y3 @ ( refine605929679le_RES @ A @ ( collect @ A @ Postcond ) ) )
% 3.04/1.61 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ ( refine605929679le_RES @ A @ ( collect @ A @ Postcond ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_10_lhs__step__If,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ord @ A )
% 3.04/1.61 => ! [B2: $o,T: A,M: A,E: A] :
% 3.04/1.61 ( ( B2
% 3.04/1.61 => ( ord_less_eq @ A @ T @ M ) )
% 3.04/1.61 => ( ( ~ B2
% 3.04/1.61 => ( ord_less_eq @ A @ E @ M ) )
% 3.04/1.61 => ( ord_less_eq @ A @ ( if @ A @ B2 @ T @ E ) @ M ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_11_use__spec__rule,axiom,
% 3.04/1.61 ! [A: $tType,M: refine1665802226e_nres @ A,Psi: A > $o,Phi: A > $o] :
% 3.04/1.61 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) )
% 3.04/1.61 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M
% 3.04/1.61 @ ( refine605929679le_RES @ A
% 3.04/1.61 @ ( collect @ A
% 3.04/1.61 @ ^ [S3: A] :
% 3.04/1.61 ( ( Psi @ S3 )
% 3.04/1.61 => ( Phi @ S3 ) ) ) ) )
% 3.04/1.61 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_12_SPEC__cons__rule,axiom,
% 3.04/1.61 ! [A: $tType,M: refine1665802226e_nres @ A,Phi: A > $o,Psi: A > $o] :
% 3.04/1.61 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 3.04/1.61 => ( ! [X3: A] :
% 3.04/1.61 ( ( Phi @ X3 )
% 3.04/1.61 => ( Psi @ X3 ) )
% 3.04/1.61 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_13_order__mono__setup_Orefl,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( preorder @ A )
% 3.04/1.61 => ! [X4: A] : ( ord_less_eq @ A @ X4 @ X4 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_14_the__RES_Osimps,axiom,
% 3.04/1.61 ! [A: $tType,X: set @ A] :
% 3.04/1.61 ( ( refine1672542526he_RES @ A @ ( refine605929679le_RES @ A @ X ) )
% 3.04/1.61 = X ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_15_nf__inres__RES,axiom,
% 3.04/1.61 ! [A: $tType,X: set @ A,X4: A] :
% 3.04/1.61 ( ( refine406925620_inres @ A @ ( refine605929679le_RES @ A @ X ) @ X4 )
% 3.04/1.61 = ( member @ A @ X4 @ X ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_16_nf__inres__SPEC,axiom,
% 3.04/1.61 ! [A: $tType,Phi: A > $o,X4: A] :
% 3.04/1.61 ( ( refine406925620_inres @ A @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ X4 )
% 3.04/1.61 = ( Phi @ X4 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_17_nres_Osimps_I7_J,axiom,
% 3.04/1.61 ! [C: $tType,A: $tType,F1: C,F2: ( set @ A ) > C,X2: set @ A] :
% 3.04/1.61 ( ( refine1442219249c_nres @ C @ A @ F1 @ F2 @ ( refine605929679le_RES @ A @ X2 ) )
% 3.04/1.61 = ( F2 @ X2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_18_le__funD,axiom,
% 3.04/1.61 ! [B: $tType,A: $tType] :
% 3.04/1.61 ( ( ord @ B )
% 3.04/1.61 => ! [F: A > B,G: A > B,X4: A] :
% 3.04/1.61 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 3.04/1.61 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_19_le__funE,axiom,
% 3.04/1.61 ! [B: $tType,A: $tType] :
% 3.04/1.61 ( ( ord @ B )
% 3.04/1.61 => ! [F: A > B,G: A > B,X4: A] :
% 3.04/1.61 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 3.04/1.61 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_20_le__funI,axiom,
% 3.04/1.61 ! [B: $tType,A: $tType] :
% 3.04/1.61 ( ( ord @ B )
% 3.04/1.61 => ! [F: A > B,G: A > B] :
% 3.04/1.61 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 3.04/1.61 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_21_Refine__Misc_Oif__mono,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ord @ A )
% 3.04/1.61 => ! [B2: $o,M1: A,M12: A,M2: A,M22: A] :
% 3.04/1.61 ( ( B2
% 3.04/1.61 => ( ord_less_eq @ A @ M1 @ M12 ) )
% 3.04/1.61 => ( ( ~ B2
% 3.04/1.61 => ( ord_less_eq @ A @ M2 @ M22 ) )
% 3.04/1.61 => ( ord_less_eq @ A @ ( if @ A @ B2 @ M1 @ M2 ) @ ( if @ A @ B2 @ M12 @ M22 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_22_le__fun__def,axiom,
% 3.04/1.61 ! [B: $tType,A: $tType] :
% 3.04/1.61 ( ( ord @ B )
% 3.04/1.61 => ( ( ord_less_eq @ ( A > B ) )
% 3.04/1.61 = ( ^ [F3: A > B,G2: A > B] :
% 3.04/1.61 ! [X5: A] : ( ord_less_eq @ B @ ( F3 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_23_order__subst1,axiom,
% 3.04/1.61 ! [A: $tType,B: $tType] :
% 3.04/1.61 ( ( ( order @ B )
% 3.04/1.61 & ( order @ A ) )
% 3.04/1.61 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 3.04/1.61 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 3.04/1.61 => ( ! [X3: B,Y4: B] :
% 3.04/1.61 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 3.04/1.61 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.04/1.61 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_24_le__infD2,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( semilattice_inf @ A )
% 3.04/1.61 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 3.04/1.61 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_25_le__infD1,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( semilattice_inf @ A )
% 3.04/1.61 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 3.04/1.61 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_26_inf__leI,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( semilattice_inf @ A )
% 3.04/1.61 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.61 ( ! [X3: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ X3 @ A2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ X3 @ B2 )
% 3.04/1.61 => ( ord_less_eq @ A @ X3 @ C2 ) ) )
% 3.04/1.61 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_27_less__eq__nres_Osimps_I2_J,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ A2 ) @ ( refine605929679le_RES @ A @ B2 ) )
% 3.04/1.61 = ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_28_nres__order__simps_I5_J,axiom,
% 3.04/1.61 ! [E2: $tType,X: set @ E2,Y: set @ E2] :
% 3.04/1.61 ( ( ord_less_eq @ ( refine1665802226e_nres @ E2 ) @ ( refine605929679le_RES @ E2 @ X ) @ ( refine605929679le_RES @ E2 @ Y ) )
% 3.04/1.61 = ( ord_less_eq @ ( set @ E2 ) @ X @ Y ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_29_order__mono__setup_Omono__let,axiom,
% 3.04/1.61 ! [A: $tType,B: $tType] :
% 3.04/1.61 ( ( preorder @ A )
% 3.04/1.61 => ! [F: B > A,F4: B > A,X4: B] :
% 3.04/1.61 ( ! [X3: B] : ( ord_less_eq @ A @ ( F @ X3 ) @ ( F4 @ X3 ) )
% 3.04/1.61 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F4 @ X4 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_30_order__mono__setup_Omono__if,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( preorder @ A )
% 3.04/1.61 => ! [T: A,T2: A,E: A,E3: A,B2: $o] :
% 3.04/1.61 ( ( ord_less_eq @ A @ T @ T2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ E @ E3 )
% 3.04/1.61 => ( ord_less_eq @ A @ ( if @ A @ B2 @ T @ E ) @ ( if @ A @ B2 @ T2 @ E3 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_31_dual__order_Oantisym,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [B2: A,A2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.61 => ( A2 = B2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_32_dual__order_Oeq__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 3.04/1.61 = ( ^ [A3: A,B3: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ B3 @ A3 )
% 3.04/1.61 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_33_dual__order_Otrans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [B2: A,A2: A,C2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 3.04/1.61 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_34_linorder__wlog,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( linorder @ A )
% 3.04/1.61 => ! [P: A > A > $o,A2: A,B2: A] :
% 3.04/1.61 ( ! [A4: A,B4: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A4 @ B4 )
% 3.04/1.61 => ( P @ A4 @ B4 ) )
% 3.04/1.61 => ( ! [A4: A,B4: A] :
% 3.04/1.61 ( ( P @ B4 @ A4 )
% 3.04/1.61 => ( P @ A4 @ B4 ) )
% 3.04/1.61 => ( P @ A2 @ B2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_35_dual__order_Orefl,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_36_order__trans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( preorder @ A )
% 3.04/1.61 => ! [X4: A,Y3: A,Z2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 3.04/1.61 => ( ord_less_eq @ A @ X4 @ Z2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_37_order__class_Oorder_Oantisym,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [A2: A,B2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.04/1.61 => ( A2 = B2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_38_ord__le__eq__trans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ord @ A )
% 3.04/1.61 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.61 => ( ( B2 = C2 )
% 3.04/1.61 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_39_ord__eq__le__trans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ord @ A )
% 3.04/1.61 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.61 ( ( A2 = B2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.04/1.61 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_40_order__class_Oorder_Oeq__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 3.04/1.61 = ( ^ [A3: A,B3: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A3 @ B3 )
% 3.04/1.61 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_41_antisym__conv,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [Y3: A,X4: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ Y3 @ X4 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.04/1.61 = ( X4 = Y3 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_42_mem__Collect__eq,axiom,
% 3.04/1.61 ! [A: $tType,A2: A,P: A > $o] :
% 3.04/1.61 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.04/1.61 = ( P @ A2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_43_Collect__mem__eq,axiom,
% 3.04/1.61 ! [A: $tType,A5: set @ A] :
% 3.04/1.61 ( ( collect @ A
% 3.04/1.61 @ ^ [X5: A] : ( member @ A @ X5 @ A5 ) )
% 3.04/1.61 = A5 ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_44_Collect__cong,axiom,
% 3.04/1.61 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.04/1.61 ( ! [X3: A] :
% 3.04/1.61 ( ( P @ X3 )
% 3.04/1.61 = ( Q @ X3 ) )
% 3.04/1.61 => ( ( collect @ A @ P )
% 3.04/1.61 = ( collect @ A @ Q ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_45_ext,axiom,
% 3.04/1.61 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.04/1.61 ( ! [X3: A] :
% 3.04/1.61 ( ( F @ X3 )
% 3.04/1.61 = ( G @ X3 ) )
% 3.04/1.61 => ( F = G ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_46_le__cases3,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( linorder @ A )
% 3.04/1.61 => ! [X4: A,Y3: A,Z2: A] :
% 3.04/1.61 ( ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 3.04/1.61 => ( ( ( ord_less_eq @ A @ Y3 @ X4 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ X4 @ Z2 ) )
% 3.04/1.61 => ( ( ( ord_less_eq @ A @ X4 @ Z2 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 3.04/1.61 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ Y3 @ X4 ) )
% 3.04/1.61 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ Z2 @ X4 ) )
% 3.04/1.61 => ~ ( ( ord_less_eq @ A @ Z2 @ X4 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_47_order_Otrans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.04/1.61 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_48_le__cases,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( linorder @ A )
% 3.04/1.61 => ! [X4: A,Y3: A] :
% 3.04/1.61 ( ~ ( ord_less_eq @ A @ X4 @ Y3 )
% 3.04/1.61 => ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_49_eq__refl,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( preorder @ A )
% 3.04/1.61 => ! [X4: A,Y3: A] :
% 3.04/1.61 ( ( X4 = Y3 )
% 3.04/1.61 => ( ord_less_eq @ A @ X4 @ Y3 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_50_linear,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( linorder @ A )
% 3.04/1.61 => ! [X4: A,Y3: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.04/1.61 | ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_51_antisym,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [X4: A,Y3: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ Y3 @ X4 )
% 3.04/1.61 => ( X4 = Y3 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_52_eq__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 3.04/1.61 = ( ^ [X5: A,Y6: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ X5 @ Y6 )
% 3.04/1.61 & ( ord_less_eq @ A @ Y6 @ X5 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_53_ord__le__eq__subst,axiom,
% 3.04/1.61 ! [A: $tType,B: $tType] :
% 3.04/1.61 ( ( ( ord @ B )
% 3.04/1.61 & ( ord @ A ) )
% 3.04/1.61 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.61 => ( ( ( F @ B2 )
% 3.04/1.61 = C2 )
% 3.04/1.61 => ( ! [X3: A,Y4: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 3.04/1.61 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.04/1.61 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_54_ord__eq__le__subst,axiom,
% 3.04/1.61 ! [A: $tType,B: $tType] :
% 3.04/1.61 ( ( ( ord @ B )
% 3.04/1.61 & ( ord @ A ) )
% 3.04/1.61 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 3.04/1.61 ( ( A2
% 3.04/1.61 = ( F @ B2 ) )
% 3.04/1.61 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 3.04/1.61 => ( ! [X3: B,Y4: B] :
% 3.04/1.61 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 3.04/1.61 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.04/1.61 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_55_order__subst2,axiom,
% 3.04/1.61 ! [A: $tType,C: $tType] :
% 3.04/1.61 ( ( ( order @ C )
% 3.04/1.61 & ( order @ A ) )
% 3.04/1.61 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.61 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 3.04/1.61 => ( ! [X3: A,Y4: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 3.04/1.61 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.04/1.61 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_56_inf_Obounded__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( semilattice_inf @ A )
% 3.04/1.61 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 3.04/1.61 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.61 & ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_57_le__inf__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( semilattice_inf @ A )
% 3.04/1.61 => ! [X4: A,Y3: A,Z2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 3.04/1.61 = ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.04/1.62 & ( ord_less_eq @ A @ X4 @ Z2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_58_inf__apply,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ B )
% 3.04/1.62 => ( ( inf_inf @ ( A > B ) )
% 3.04/1.62 = ( ^ [F3: A > B,G2: A > B,X5: A] : ( inf_inf @ B @ ( F3 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_59_inf_Oidem,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ A2 @ A2 )
% 3.04/1.62 = A2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_60_inf__idem,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A] :
% 3.04/1.62 ( ( inf_inf @ A @ X4 @ X4 )
% 3.04/1.62 = X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_61_inf_Oleft__idem,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 3.04/1.62 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_62_inf__left__idem,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] :
% 3.04/1.62 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ X4 @ Y3 ) )
% 3.04/1.62 = ( inf_inf @ A @ X4 @ Y3 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_63_inf_Oright__idem,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 3.04/1.62 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_64_inf__right__idem,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] :
% 3.04/1.62 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Y3 )
% 3.04/1.62 = ( inf_inf @ A @ X4 @ Y3 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_65_inf__nres_Osimps_I3_J,axiom,
% 3.04/1.62 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 3.04/1.62 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ A2 ) @ ( refine605929679le_RES @ A @ B2 ) )
% 3.04/1.62 = ( refine605929679le_RES @ A @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_66_inf__left__commute,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,Y3: A,Z2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 3.04/1.62 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X4 @ Z2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_67_inf_Oleft__commute,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [B2: A,A2: A,C2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C2 ) )
% 3.04/1.62 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_68_inf__commute,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ( ( inf_inf @ A )
% 3.04/1.62 = ( ^ [X5: A,Y6: A] : ( inf_inf @ A @ Y6 @ X5 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_69_inf_Ocommute,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ( ( inf_inf @ A )
% 3.04/1.62 = ( ^ [A3: A,B3: A] : ( inf_inf @ A @ B3 @ A3 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_70_inf__assoc,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,Y3: A,Z2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Z2 )
% 3.04/1.62 = ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_71_inf_Oassoc,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 )
% 3.04/1.62 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_72_boolean__algebra__cancel_Oinf2,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [B5: A,K: A,B2: A,A2: A] :
% 3.04/1.62 ( ( B5
% 3.04/1.62 = ( inf_inf @ A @ K @ B2 ) )
% 3.04/1.62 => ( ( inf_inf @ A @ A2 @ B5 )
% 3.04/1.62 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_73_boolean__algebra__cancel_Oinf1,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A5: A,K: A,A2: A,B2: A] :
% 3.04/1.62 ( ( A5
% 3.04/1.62 = ( inf_inf @ A @ K @ A2 ) )
% 3.04/1.62 => ( ( inf_inf @ A @ A5 @ B2 )
% 3.04/1.62 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_74_inf__fun__def,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ B )
% 3.04/1.62 => ( ( inf_inf @ ( A > B ) )
% 3.04/1.62 = ( ^ [F3: A > B,G2: A > B,X5: A] : ( inf_inf @ B @ ( F3 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_75_inf__sup__aci_I1_J,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( lattice @ A )
% 3.04/1.62 => ( ( inf_inf @ A )
% 3.04/1.62 = ( ^ [X5: A,Y6: A] : ( inf_inf @ A @ Y6 @ X5 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_76_inf__sup__aci_I2_J,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( lattice @ A )
% 3.04/1.62 => ! [X4: A,Y3: A,Z2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Z2 )
% 3.04/1.62 = ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_77_inf__sup__aci_I3_J,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( lattice @ A )
% 3.04/1.62 => ! [X4: A,Y3: A,Z2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 3.04/1.62 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X4 @ Z2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_78_inf__sup__aci_I4_J,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( lattice @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] :
% 3.04/1.62 ( ( inf_inf @ A @ X4 @ ( inf_inf @ A @ X4 @ Y3 ) )
% 3.04/1.62 = ( inf_inf @ A @ X4 @ Y3 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_79_inf__sup__ord_I2_J,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( lattice @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Y3 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_80_inf__sup__ord_I1_J,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( lattice @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_81_inf__le1,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_82_inf__le2,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X4 @ Y3 ) @ Y3 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_83_le__infE,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,A2: A,B2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ X4 @ ( inf_inf @ A @ A2 @ B2 ) )
% 3.04/1.62 => ~ ( ( ord_less_eq @ A @ X4 @ A2 )
% 3.04/1.62 => ~ ( ord_less_eq @ A @ X4 @ B2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_84_le__infI,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,A2: A,B2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ X4 @ A2 )
% 3.04/1.62 => ( ( ord_less_eq @ A @ X4 @ B2 )
% 3.04/1.62 => ( ord_less_eq @ A @ X4 @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_85_inf__mono,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,C2: A,B2: A,D: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ A2 @ C2 )
% 3.04/1.62 => ( ( ord_less_eq @ A @ B2 @ D )
% 3.04/1.62 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ ( inf_inf @ A @ C2 @ D ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_86_le__infI1,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,X4: A,B2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ A2 @ X4 )
% 3.04/1.62 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ X4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_87_le__infI2,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [B2: A,X4: A,A2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ B2 @ X4 )
% 3.04/1.62 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ X4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_88_inf_OorderE,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.62 => ( A2
% 3.04/1.62 = ( inf_inf @ A @ A2 @ B2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_89_inf_OorderI,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A] :
% 3.04/1.62 ( ( A2
% 3.04/1.62 = ( inf_inf @ A @ A2 @ B2 ) )
% 3.04/1.62 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_90_inf__unique,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [F: A > A > A,X4: A,Y3: A] :
% 3.04/1.62 ( ! [X3: A,Y4: A] : ( ord_less_eq @ A @ ( F @ X3 @ Y4 ) @ X3 )
% 3.04/1.62 => ( ! [X3: A,Y4: A] : ( ord_less_eq @ A @ ( F @ X3 @ Y4 ) @ Y4 )
% 3.04/1.62 => ( ! [X3: A,Y4: A,Z3: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 3.04/1.62 => ( ( ord_less_eq @ A @ X3 @ Z3 )
% 3.04/1.62 => ( ord_less_eq @ A @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 3.04/1.62 => ( ( inf_inf @ A @ X4 @ Y3 )
% 3.04/1.62 = ( F @ X4 @ Y3 ) ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_91_le__iff__inf,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ( ( ord_less_eq @ A )
% 3.04/1.62 = ( ^ [X5: A,Y6: A] :
% 3.04/1.62 ( ( inf_inf @ A @ X5 @ Y6 )
% 3.04/1.62 = X5 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_92_inf_Oabsorb1,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.62 => ( ( inf_inf @ A @ A2 @ B2 )
% 3.04/1.62 = A2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_93_inf_Oabsorb2,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [B2: A,A2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.04/1.62 => ( ( inf_inf @ A @ A2 @ B2 )
% 3.04/1.62 = B2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_94_inf__absorb1,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.04/1.62 => ( ( inf_inf @ A @ X4 @ Y3 )
% 3.04/1.62 = X4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_95_inf__absorb2,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [Y3: A,X4: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ Y3 @ X4 )
% 3.04/1.62 => ( ( inf_inf @ A @ X4 @ Y3 )
% 3.04/1.62 = Y3 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_96_inf_OboundedE,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 3.04/1.62 => ~ ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.62 => ~ ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_97_inf_OboundedI,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A,C2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.04/1.62 => ( ( ord_less_eq @ A @ A2 @ C2 )
% 3.04/1.62 => ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_98_inf__greatest,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [X4: A,Y3: A,Z2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 3.04/1.62 => ( ( ord_less_eq @ A @ X4 @ Z2 )
% 3.04/1.62 => ( ord_less_eq @ A @ X4 @ ( inf_inf @ A @ Y3 @ Z2 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_99_inf_Oorder__iff,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ( ( ord_less_eq @ A )
% 3.04/1.62 = ( ^ [A3: A,B3: A] :
% 3.04/1.62 ( A3
% 3.04/1.62 = ( inf_inf @ A @ A3 @ B3 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_100_inf_Ocobounded1,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ A2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_101_inf_Ocobounded2,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_102_inf_Oabsorb__iff1,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ( ( ord_less_eq @ A )
% 3.04/1.62 = ( ^ [A3: A,B3: A] :
% 3.04/1.62 ( ( inf_inf @ A @ A3 @ B3 )
% 3.04/1.62 = A3 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_103_inf_Oabsorb__iff2,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ( ( ord_less_eq @ A )
% 3.04/1.62 = ( ^ [B3: A,A3: A] :
% 3.04/1.62 ( ( inf_inf @ A @ A3 @ B3 )
% 3.04/1.62 = B3 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_104_inf_OcoboundedI1,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [A2: A,C2: A,B2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ A2 @ C2 )
% 3.04/1.62 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_105_inf_OcoboundedI2,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A )
% 3.04/1.62 => ! [B2: A,C2: A,A2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.04/1.62 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_106_subsetI,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ! [X3: A] :
% 3.04/1.62 ( ( member @ A @ X3 @ A5 )
% 3.04/1.62 => ( member @ A @ X3 @ B5 ) )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_107_Int__subset__iff,axiom,
% 3.04/1.62 ! [A: $tType,C3: set @ A,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ C3 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 3.04/1.62 = ( ( ord_less_eq @ ( set @ A ) @ C3 @ A5 )
% 3.04/1.62 & ( ord_less_eq @ ( set @ A ) @ C3 @ B5 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_108_subset__antisym,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 3.04/1.62 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 3.04/1.62 => ( A5 = B5 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_109_Collect__subset,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,P: A > $o] :
% 3.04/1.62 ( ord_less_eq @ ( set @ A )
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ A5 )
% 3.04/1.62 & ( P @ X5 ) ) )
% 3.04/1.62 @ A5 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_110_less__eq__set__def,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) )
% 3.04/1.62 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.04/1.62 ( ord_less_eq @ ( A > $o )
% 3.04/1.62 @ ^ [X5: A] : ( member @ A @ X5 @ A6 )
% 3.04/1.62 @ ^ [X5: A] : ( member @ A @ X5 @ B6 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_111_pred__subset__eq,axiom,
% 3.04/1.62 ! [A: $tType,R: set @ A,S: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( A > $o )
% 3.04/1.62 @ ^ [X5: A] : ( member @ A @ X5 @ R )
% 3.04/1.62 @ ^ [X5: A] : ( member @ A @ X5 @ S ) )
% 3.04/1.62 = ( ord_less_eq @ ( set @ A ) @ R @ S ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_112_conj__subset__def,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,P: A > $o,Q: A > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A5
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [X5: A] :
% 3.04/1.62 ( ( P @ X5 )
% 3.04/1.62 & ( Q @ X5 ) ) ) )
% 3.04/1.62 = ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( collect @ A @ P ) )
% 3.04/1.62 & ( ord_less_eq @ ( set @ A ) @ A5 @ ( collect @ A @ Q ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_113_IntI,axiom,
% 3.04/1.62 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( member @ A @ C2 @ A5 )
% 3.04/1.62 => ( ( member @ A @ C2 @ B5 )
% 3.04/1.62 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_114_Int__iff,axiom,
% 3.04/1.62 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 3.04/1.62 = ( ( member @ A @ C2 @ A5 )
% 3.04/1.62 & ( member @ A @ C2 @ B5 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_115_predicate1I,axiom,
% 3.04/1.62 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.04/1.62 ( ! [X3: A] :
% 3.04/1.62 ( ( P @ X3 )
% 3.04/1.62 => ( Q @ X3 ) )
% 3.04/1.62 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_116_IntE,axiom,
% 3.04/1.62 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 3.04/1.62 => ~ ( ( member @ A @ C2 @ A5 )
% 3.04/1.62 => ~ ( member @ A @ C2 @ B5 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_117_IntD1,axiom,
% 3.04/1.62 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 3.04/1.62 => ( member @ A @ C2 @ A5 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_118_IntD2,axiom,
% 3.04/1.62 ! [A: $tType,C2: A,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 3.04/1.62 => ( member @ A @ C2 @ B5 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_119_Int__def,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( inf_inf @ ( set @ A ) )
% 3.04/1.62 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.04/1.62 ( collect @ A
% 3.04/1.62 @ ^ [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ A6 )
% 3.04/1.62 & ( member @ A @ X5 @ B6 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_120_Int__assoc,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A,C3: set @ A] :
% 3.04/1.62 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) @ C3 )
% 3.04/1.62 = ( inf_inf @ ( set @ A ) @ A5 @ ( inf_inf @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_121_Int__absorb,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A] :
% 3.04/1.62 ( ( inf_inf @ ( set @ A ) @ A5 @ A5 )
% 3.04/1.62 = A5 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_122_Int__Collect,axiom,
% 3.04/1.62 ! [A: $tType,X4: A,A5: set @ A,P: A > $o] :
% 3.04/1.62 ( ( member @ A @ X4 @ ( inf_inf @ ( set @ A ) @ A5 @ ( collect @ A @ P ) ) )
% 3.04/1.62 = ( ( member @ A @ X4 @ A5 )
% 3.04/1.62 & ( P @ X4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_123_Int__commute,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( inf_inf @ ( set @ A ) )
% 3.04/1.62 = ( ^ [A6: set @ A,B6: set @ A] : ( inf_inf @ ( set @ A ) @ B6 @ A6 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_124_inf__set__def,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( inf_inf @ ( set @ A ) )
% 3.04/1.62 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.04/1.62 ( collect @ A
% 3.04/1.62 @ ( inf_inf @ ( A > $o )
% 3.04/1.62 @ ^ [X5: A] : ( member @ A @ X5 @ A6 )
% 3.04/1.62 @ ^ [X5: A] : ( member @ A @ X5 @ B6 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_125_inf__Int__eq,axiom,
% 3.04/1.62 ! [A: $tType,R: set @ A,S: set @ A] :
% 3.04/1.62 ( ( inf_inf @ ( A > $o )
% 3.04/1.62 @ ^ [X5: A] : ( member @ A @ X5 @ R )
% 3.04/1.62 @ ^ [X5: A] : ( member @ A @ X5 @ S ) )
% 3.04/1.62 = ( ^ [X5: A] : ( member @ A @ X5 @ ( inf_inf @ ( set @ A ) @ R @ S ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_126_Collect__conj__eq,axiom,
% 3.04/1.62 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.04/1.62 ( ( collect @ A
% 3.04/1.62 @ ^ [X5: A] :
% 3.04/1.62 ( ( P @ X5 )
% 3.04/1.62 & ( Q @ X5 ) ) )
% 3.04/1.62 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_127_Int__left__absorb,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( inf_inf @ ( set @ A ) @ A5 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) )
% 3.04/1.62 = ( inf_inf @ ( set @ A ) @ A5 @ B5 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_128_Int__left__commute,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A,C3: set @ A] :
% 3.04/1.62 ( ( inf_inf @ ( set @ A ) @ A5 @ ( inf_inf @ ( set @ A ) @ B5 @ C3 ) )
% 3.04/1.62 = ( inf_inf @ ( set @ A ) @ B5 @ ( inf_inf @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_129_predicate1D,axiom,
% 3.04/1.62 ! [A: $tType,P: A > $o,Q: A > $o,X4: A] :
% 3.04/1.62 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 3.04/1.62 => ( ( P @ X4 )
% 3.04/1.62 => ( Q @ X4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_130_rev__predicate1D,axiom,
% 3.04/1.62 ! [A: $tType,P: A > $o,X4: A,Q: A > $o] :
% 3.04/1.62 ( ( P @ X4 )
% 3.04/1.62 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 3.04/1.62 => ( Q @ X4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_131_Int__Collect__mono,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A,P: A > $o,Q: A > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 3.04/1.62 => ( ! [X3: A] :
% 3.04/1.62 ( ( member @ A @ X3 @ A5 )
% 3.04/1.62 => ( ( P @ X3 )
% 3.04/1.62 => ( Q @ X3 ) ) )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ ( collect @ A @ P ) ) @ ( inf_inf @ ( set @ A ) @ B5 @ ( collect @ A @ Q ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_132_Collect__mono__iff,axiom,
% 3.04/1.62 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 3.04/1.62 = ( ! [X5: A] :
% 3.04/1.62 ( ( P @ X5 )
% 3.04/1.62 => ( Q @ X5 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_133_set__eq__subset,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( ^ [Y5: set @ A,Z: set @ A] : ( Y5 = Z ) )
% 3.04/1.62 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 3.04/1.62 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_134_subset__trans,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A,C3: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 3.04/1.62 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C3 )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_135_Int__greatest,axiom,
% 3.04/1.62 ! [A: $tType,C3: set @ A,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ C3 @ A5 )
% 3.04/1.62 => ( ( ord_less_eq @ ( set @ A ) @ C3 @ B5 )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A ) @ C3 @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_136_Collect__mono,axiom,
% 3.04/1.62 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.04/1.62 ( ! [X3: A] :
% 3.04/1.62 ( ( P @ X3 )
% 3.04/1.62 => ( Q @ X3 ) )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_137_subset__refl,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ A5 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_138_Int__absorb2,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 3.04/1.62 => ( ( inf_inf @ ( set @ A ) @ A5 @ B5 )
% 3.04/1.62 = A5 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_139_Int__absorb1,axiom,
% 3.04/1.62 ! [A: $tType,B5: set @ A,A5: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 3.04/1.62 => ( ( inf_inf @ ( set @ A ) @ A5 @ B5 )
% 3.04/1.62 = B5 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_140_subset__iff,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) )
% 3.04/1.62 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.04/1.62 ! [T3: A] :
% 3.04/1.62 ( ( member @ A @ T3 @ A6 )
% 3.04/1.62 => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_141_equalityD2,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( A5 = B5 )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_142_equalityD1,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( A5 = B5 )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_143_Int__lower2,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) @ B5 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_144_Int__lower1,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) @ A5 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_145_subset__eq,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) )
% 3.04/1.62 = ( ^ [A6: set @ A,B6: set @ A] :
% 3.04/1.62 ! [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ A6 )
% 3.04/1.62 => ( member @ A @ X5 @ B6 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_146_equalityE,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( A5 = B5 )
% 3.04/1.62 => ~ ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 3.04/1.62 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_147_Int__mono,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,C3: set @ A,B5: set @ A,D2: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A5 @ C3 )
% 3.04/1.62 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ D2 )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A5 @ B5 ) @ ( inf_inf @ ( set @ A ) @ C3 @ D2 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_148_subsetD,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A,C2: A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 3.04/1.62 => ( ( member @ A @ C2 @ A5 )
% 3.04/1.62 => ( member @ A @ C2 @ B5 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_149_in__mono,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A,B5: set @ A,X4: A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 3.04/1.62 => ( ( member @ A @ X4 @ A5 )
% 3.04/1.62 => ( member @ A @ X4 @ B5 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_150_inter__eq__subsetI,axiom,
% 3.04/1.62 ! [A: $tType,S: set @ A,S4: set @ A,A5: set @ A,B5: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ S @ S4 )
% 3.04/1.62 => ( ( ( inf_inf @ ( set @ A ) @ A5 @ S4 )
% 3.04/1.62 = ( inf_inf @ ( set @ A ) @ B5 @ S4 ) )
% 3.04/1.62 => ( ( inf_inf @ ( set @ A ) @ A5 @ S )
% 3.04/1.62 = ( inf_inf @ ( set @ A ) @ B5 @ S ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_151_subset__Collect__iff,axiom,
% 3.04/1.62 ! [A: $tType,B5: set @ A,A5: set @ A,P: A > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 3.04/1.62 => ( ( ord_less_eq @ ( set @ A ) @ B5
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ A5 )
% 3.04/1.62 & ( P @ X5 ) ) ) )
% 3.04/1.62 = ( ! [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ B5 )
% 3.04/1.62 => ( P @ X5 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_152_subset__CollectI,axiom,
% 3.04/1.62 ! [A: $tType,B5: set @ A,A5: set @ A,Q: A > $o,P: A > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 3.04/1.62 => ( ! [X3: A] :
% 3.04/1.62 ( ( member @ A @ X3 @ B5 )
% 3.04/1.62 => ( ( Q @ X3 )
% 3.04/1.62 => ( P @ X3 ) ) )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A )
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ B5 )
% 3.04/1.62 & ( Q @ X5 ) ) )
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ A5 )
% 3.04/1.62 & ( P @ X5 ) ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_153_Collect__restrict,axiom,
% 3.04/1.62 ! [A: $tType,X: set @ A,P: A > $o] :
% 3.04/1.62 ( ord_less_eq @ ( set @ A )
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ X )
% 3.04/1.62 & ( P @ X5 ) ) )
% 3.04/1.62 @ X ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_154_inf1I,axiom,
% 3.04/1.62 ! [A: $tType,A5: A > $o,X4: A,B5: A > $o] :
% 3.04/1.62 ( ( A5 @ X4 )
% 3.04/1.62 => ( ( B5 @ X4 )
% 3.04/1.62 => ( inf_inf @ ( A > $o ) @ A5 @ B5 @ X4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_155_inf1E,axiom,
% 3.04/1.62 ! [A: $tType,A5: A > $o,B5: A > $o,X4: A] :
% 3.04/1.62 ( ( inf_inf @ ( A > $o ) @ A5 @ B5 @ X4 )
% 3.04/1.62 => ~ ( ( A5 @ X4 )
% 3.04/1.62 => ~ ( B5 @ X4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_156_inf1D1,axiom,
% 3.04/1.62 ! [A: $tType,A5: A > $o,B5: A > $o,X4: A] :
% 3.04/1.62 ( ( inf_inf @ ( A > $o ) @ A5 @ B5 @ X4 )
% 3.04/1.62 => ( A5 @ X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_157_inf1D2,axiom,
% 3.04/1.62 ! [A: $tType,A5: A > $o,B5: A > $o,X4: A] :
% 3.04/1.62 ( ( inf_inf @ ( A > $o ) @ A5 @ B5 @ X4 )
% 3.04/1.62 => ( B5 @ X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_158_ord__eq__le__eq__trans,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( ord @ A )
% 3.04/1.62 => ! [A2: A,B2: A,C2: A,D: A] :
% 3.04/1.62 ( ( A2 = B2 )
% 3.04/1.62 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.04/1.62 => ( ( C2 = D )
% 3.04/1.62 => ( ord_less_eq @ A @ A2 @ D ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_159_subset__Collect__conv,axiom,
% 3.04/1.62 ! [A: $tType,S: set @ A,P: A > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 3.04/1.62 = ( ! [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ S )
% 3.04/1.62 => ( P @ X5 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_160_prop__restrict,axiom,
% 3.04/1.62 ! [A: $tType,X4: A,Z4: set @ A,X: set @ A,P: A > $o] :
% 3.04/1.62 ( ( member @ A @ X4 @ Z4 )
% 3.04/1.62 => ( ( ord_less_eq @ ( set @ A ) @ Z4
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [X5: A] :
% 3.04/1.62 ( ( member @ A @ X5 @ X )
% 3.04/1.62 & ( P @ X5 ) ) ) )
% 3.04/1.62 => ( P @ X4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_161_Powp__mono,axiom,
% 3.04/1.62 ! [A: $tType,A5: A > $o,B5: A > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( A > $o ) @ A5 @ B5 )
% 3.04/1.62 => ( ord_less_eq @ ( ( set @ A ) > $o ) @ ( powp @ A @ A5 ) @ ( powp @ A @ B5 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_162_inf__nres_Oelims,axiom,
% 3.04/1.62 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A,Y3: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 3.04/1.62 = Y3 )
% 3.04/1.62 => ( ( ( Xa
% 3.04/1.62 = ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ( Y3 != X4 ) )
% 3.04/1.62 => ( ( ( X4
% 3.04/1.62 = ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ! [V: set @ A] :
% 3.04/1.62 ( ( Xa
% 3.04/1.62 = ( refine605929679le_RES @ A @ V ) )
% 3.04/1.62 => ( Y3
% 3.04/1.62 != ( refine605929679le_RES @ A @ V ) ) ) )
% 3.04/1.62 => ~ ! [A4: set @ A] :
% 3.04/1.62 ( ( X4
% 3.04/1.62 = ( refine605929679le_RES @ A @ A4 ) )
% 3.04/1.62 => ! [B4: set @ A] :
% 3.04/1.62 ( ( Xa
% 3.04/1.62 = ( refine605929679le_RES @ A @ B4 ) )
% 3.04/1.62 => ( Y3
% 3.04/1.62 != ( refine605929679le_RES @ A @ ( inf_inf @ ( set @ A ) @ A4 @ B4 ) ) ) ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_163_GreatestI2__order,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( order @ A )
% 3.04/1.62 => ! [P: A > $o,X4: A,Q: A > $o] :
% 3.04/1.62 ( ( P @ X4 )
% 3.04/1.62 => ( ! [Y4: A] :
% 3.04/1.62 ( ( P @ Y4 )
% 3.04/1.62 => ( ord_less_eq @ A @ Y4 @ X4 ) )
% 3.04/1.62 => ( ! [X3: A] :
% 3.04/1.62 ( ( P @ X3 )
% 3.04/1.62 => ( ! [Y7: A] :
% 3.04/1.62 ( ( P @ Y7 )
% 3.04/1.62 => ( ord_less_eq @ A @ Y7 @ X3 ) )
% 3.04/1.62 => ( Q @ X3 ) ) )
% 3.04/1.62 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_164_inf__nres_Osimps_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,X4: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ X4 @ ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 = X4 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_165_nres_Odistinct_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,X2: set @ A] :
% 3.04/1.62 ( ( refine1767639642_FAILi @ A )
% 3.04/1.62 != ( refine605929679le_RES @ A @ X2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_166_nres_Oinduct,axiom,
% 3.04/1.62 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > $o,Nres: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( P @ ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ( ! [X3: set @ A] : ( P @ ( refine605929679le_RES @ A @ X3 ) )
% 3.04/1.62 => ( P @ Nres ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_167_nres_Oexhaust,axiom,
% 3.04/1.62 ! [A: $tType,Y3: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( Y3
% 3.04/1.62 != ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ~ ! [X22: set @ A] :
% 3.04/1.62 ( Y3
% 3.04/1.62 != ( refine605929679le_RES @ A @ X22 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_168_sup__nres_Oinduct,axiom,
% 3.04/1.62 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ! [Uu: refine1665802226e_nres @ A] : ( P @ Uu @ ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ( ! [V: set @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ V ) )
% 3.04/1.62 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 3.04/1.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_169_less__nres_Oinduct,axiom,
% 3.04/1.62 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ! [X_1: refine1665802226e_nres @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ X_1 )
% 3.04/1.62 => ( ! [Uv: set @ A] : ( P @ ( refine605929679le_RES @ A @ Uv ) @ ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 3.04/1.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_170_less__eq__nres_Oinduct,axiom,
% 3.04/1.62 ! [A: $tType,P: ( refine1665802226e_nres @ A ) > ( refine1665802226e_nres @ A ) > $o,A0: refine1665802226e_nres @ A,A1: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ! [Uu: refine1665802226e_nres @ A] : ( P @ Uu @ ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ( ! [A4: set @ A,B4: set @ A] : ( P @ ( refine605929679le_RES @ A @ A4 ) @ ( refine605929679le_RES @ A @ B4 ) )
% 3.04/1.62 => ( ! [Uv: set @ A] : ( P @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ Uv ) )
% 3.04/1.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_171_less__eq__nres_Osimps_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,Uu2: refine1665802226e_nres @ A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ Uu2 @ ( refine1767639642_FAILi @ A ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_172_nres_Osimps_I6_J,axiom,
% 3.04/1.62 ! [A: $tType,C: $tType,F1: C,F2: ( set @ A ) > C] :
% 3.04/1.62 ( ( refine1442219249c_nres @ C @ A @ F1 @ F2 @ ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 = F1 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_173_less__eq__nres_Osimps_I3_J,axiom,
% 3.04/1.62 ! [A: $tType,Uv2: set @ A] :
% 3.04/1.62 ~ ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ Uv2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_174_inf__nres_Osimps_I2_J,axiom,
% 3.04/1.62 ! [A: $tType,V2: set @ A] :
% 3.04/1.62 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine1767639642_FAILi @ A ) @ ( refine605929679le_RES @ A @ V2 ) )
% 3.04/1.62 = ( refine605929679le_RES @ A @ V2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_175_less__eq__nres_Oelims_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A,Y3: $o] :
% 3.04/1.62 ( ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 3.04/1.62 = Y3 )
% 3.04/1.62 => ( ( ( Xa
% 3.04/1.62 = ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ~ Y3 )
% 3.04/1.62 => ( ! [A4: set @ A] :
% 3.04/1.62 ( ( X4
% 3.04/1.62 = ( refine605929679le_RES @ A @ A4 ) )
% 3.04/1.62 => ! [B4: set @ A] :
% 3.04/1.62 ( ( Xa
% 3.04/1.62 = ( refine605929679le_RES @ A @ B4 ) )
% 3.04/1.62 => ( Y3
% 3.04/1.62 = ( ~ ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ) )
% 3.04/1.62 => ~ ( ( X4
% 3.04/1.62 = ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ( ? [Uv: set @ A] :
% 3.04/1.62 ( Xa
% 3.04/1.62 = ( refine605929679le_RES @ A @ Uv ) )
% 3.04/1.62 => Y3 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_176_less__eq__nres_Oelims_I2_J,axiom,
% 3.04/1.62 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 3.04/1.62 => ( ( Xa
% 3.04/1.62 != ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ~ ! [A4: set @ A] :
% 3.04/1.62 ( ( X4
% 3.04/1.62 = ( refine605929679le_RES @ A @ A4 ) )
% 3.04/1.62 => ! [B4: set @ A] :
% 3.04/1.62 ( ( Xa
% 3.04/1.62 = ( refine605929679le_RES @ A @ B4 ) )
% 3.04/1.62 => ~ ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_177_less__eq__nres_Oelims_I3_J,axiom,
% 3.04/1.62 ! [A: $tType,X4: refine1665802226e_nres @ A,Xa: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ~ ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ X4 @ Xa )
% 3.04/1.62 => ( ! [A4: set @ A] :
% 3.04/1.62 ( ( X4
% 3.04/1.62 = ( refine605929679le_RES @ A @ A4 ) )
% 3.04/1.62 => ! [B4: set @ A] :
% 3.04/1.62 ( ( Xa
% 3.04/1.62 = ( refine605929679le_RES @ A @ B4 ) )
% 3.04/1.62 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) )
% 3.04/1.62 => ~ ( ( X4
% 3.04/1.62 = ( refine1767639642_FAILi @ A ) )
% 3.04/1.62 => ! [Uv: set @ A] :
% 3.04/1.62 ( Xa
% 3.04/1.62 != ( refine605929679le_RES @ A @ Uv ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_178_Greatest__equality,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( order @ A )
% 3.04/1.62 => ! [P: A > $o,X4: A] :
% 3.04/1.62 ( ( P @ X4 )
% 3.04/1.62 => ( ! [Y4: A] :
% 3.04/1.62 ( ( P @ Y4 )
% 3.04/1.62 => ( ord_less_eq @ A @ Y4 @ X4 ) )
% 3.04/1.62 => ( ( order_Greatest @ A @ P )
% 3.04/1.62 = X4 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_179_the__RES__inv,axiom,
% 3.04/1.62 ! [A: $tType,M: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( refine1102455758nofail @ A @ M )
% 3.04/1.62 => ( ( refine605929679le_RES @ A @ ( refine1672542526he_RES @ A @ M ) )
% 3.04/1.62 = M ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_180_relprop__triggers_I6_J,axiom,
% 3.04/1.62 ! [I: $tType,R: set @ I,R2: set @ I] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ I ) @ R @ R2 )
% 3.04/1.62 => ( ord_less_eq @ ( set @ I ) @ R @ R2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_181_inf__RETURN__SPEC_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,X4: A,Phi: A > $o] :
% 3.04/1.62 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 3.04/1.62 = ( refine605929679le_RES @ A
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [Y6: A] :
% 3.04/1.62 ( ( Y6 = X4 )
% 3.04/1.62 & ( Phi @ X4 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_182_nres__more__simps_I6_J,axiom,
% 3.04/1.62 ! [A: $tType,X4: A,Y3: A] :
% 3.04/1.62 ( ( ( refine1687780735RETURN @ A @ X4 )
% 3.04/1.62 = ( refine1687780735RETURN @ A @ Y3 ) )
% 3.04/1.62 = ( X4 = Y3 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_183_nofail__simps_I2_J,axiom,
% 3.04/1.62 ! [B: $tType,X: set @ B] : ( refine1102455758nofail @ B @ ( refine605929679le_RES @ B @ X ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_184_nres__order__simps_I20_J,axiom,
% 3.04/1.62 ! [W: $tType,X4: W,Y3: W] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ W ) @ ( refine1687780735RETURN @ W @ X4 ) @ ( refine1687780735RETURN @ W @ Y3 ) )
% 3.04/1.62 = ( X4 = Y3 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_185_nofail__simps_I3_J,axiom,
% 3.04/1.62 ! [C: $tType,X4: C] : ( refine1102455758nofail @ C @ ( refine1687780735RETURN @ C @ X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_186_nres__order__simps_I21_J,axiom,
% 3.04/1.62 ! [X6: $tType,X4: X6,Y: set @ X6] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ X6 ) @ ( refine1687780735RETURN @ X6 @ X4 ) @ ( refine605929679le_RES @ X6 @ Y ) )
% 3.04/1.62 = ( member @ X6 @ X4 @ Y ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_187_inf__RETURN__SPEC_I2_J,axiom,
% 3.04/1.62 ! [A: $tType,Phi: A > $o,X4: A] :
% 3.04/1.62 ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ ( refine1687780735RETURN @ A @ X4 ) )
% 3.04/1.62 = ( refine605929679le_RES @ A
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [Y6: A] :
% 3.04/1.62 ( ( Y6 = X4 )
% 3.04/1.62 & ( Phi @ X4 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_188_pwD1,axiom,
% 3.04/1.62 ! [A: $tType,S: refine1665802226e_nres @ A,S4: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ S @ S4 )
% 3.04/1.62 => ( ( refine1102455758nofail @ A @ S4 )
% 3.04/1.62 => ( refine1102455758nofail @ A @ S ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_189_le__nofailI,axiom,
% 3.04/1.62 ! [A: $tType,M3: refine1665802226e_nres @ A,M4: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( ( refine1102455758nofail @ A @ M3 )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M3 ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M3 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_190_nofail__antimono__fun,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType,F: A > ( refine1665802226e_nres @ B ),G: A > ( refine1665802226e_nres @ B ),X4: A] :
% 3.04/1.62 ( ( ord_less_eq @ ( A > ( refine1665802226e_nres @ B ) ) @ F @ G )
% 3.04/1.62 => ( ( refine1102455758nofail @ B @ ( G @ X4 ) )
% 3.04/1.62 => ( refine1102455758nofail @ B @ ( F @ X4 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_191_nofail__RES__conv,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( refine1102455758nofail @ A )
% 3.04/1.62 = ( ^ [M5: refine1665802226e_nres @ A] :
% 3.04/1.62 ? [M6: set @ A] :
% 3.04/1.62 ( M5
% 3.04/1.62 = ( refine605929679le_RES @ A @ M6 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_192_SPEC__eq__is__RETURN_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,X4: A] :
% 3.04/1.62 ( ( refine605929679le_RES @ A
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ( ^ [Y5: A,Z: A] : ( Y5 = Z )
% 3.04/1.62 @ X4 ) ) )
% 3.04/1.62 = ( refine1687780735RETURN @ A @ X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_193_RETURN__SPEC__conv,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( refine1687780735RETURN @ A )
% 3.04/1.62 = ( ^ [R3: A] :
% 3.04/1.62 ( refine605929679le_RES @ A
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [X5: A] : ( X5 = R3 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_194_SPEC__eq__is__RETURN_I2_J,axiom,
% 3.04/1.62 ! [B: $tType,Y3: B] :
% 3.04/1.62 ( ( refine605929679le_RES @ B
% 3.04/1.62 @ ( collect @ B
% 3.04/1.62 @ ^ [X5: B] : ( X5 = Y3 ) ) )
% 3.04/1.62 = ( refine1687780735RETURN @ B @ Y3 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_195_pw__inf__nofail,axiom,
% 3.04/1.62 ! [A: $tType,A2: refine1665802226e_nres @ A,B2: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( refine1102455758nofail @ A @ ( inf_inf @ ( refine1665802226e_nres @ A ) @ A2 @ B2 ) )
% 3.04/1.62 = ( ( refine1102455758nofail @ A @ A2 )
% 3.04/1.62 | ( refine1102455758nofail @ A @ B2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_196_le__RES__nofailI,axiom,
% 3.04/1.62 ! [A: $tType,A2: refine1665802226e_nres @ A,X4: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ A2 @ ( refine605929679le_RES @ A @ X4 ) )
% 3.04/1.62 => ( refine1102455758nofail @ A @ A2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_197_RETURN__rule,axiom,
% 3.04/1.62 ! [A: $tType,Phi: A > $o,X4: A] :
% 3.04/1.62 ( ( Phi @ X4 )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_198_lhs__step__RES,axiom,
% 3.04/1.62 ! [A: $tType,X: set @ A,M: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ! [X3: A] :
% 3.04/1.62 ( ( member @ A @ X3 @ X )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ X ) @ M ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_199_RETURN__to__SPEC__rule,axiom,
% 3.04/1.62 ! [A: $tType,M: refine1665802226e_nres @ A,V2: A] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M
% 3.04/1.62 @ ( refine605929679le_RES @ A
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ( ^ [Y5: A,Z: A] : ( Y5 = Z )
% 3.04/1.62 @ V2 ) ) ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine1687780735RETURN @ A @ V2 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_200_lhs__step__SPEC,axiom,
% 3.04/1.62 ! [A: $tType,Phi: A > $o,M: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ! [X3: A] :
% 3.04/1.62 ( ( Phi @ X3 )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ M ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_201_lhs__step__bind,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType,M7: refine1665802226e_nres @ B,M: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B )] :
% 3.04/1.62 ( ( ( refine1102455758nofail @ B @ M7 )
% 3.04/1.62 => ( refine1102455758nofail @ A @ M ) )
% 3.04/1.62 => ( ! [X3: A] :
% 3.04/1.62 ( ( refine406925620_inres @ A @ M @ X3 )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ M7 ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M @ F ) @ M7 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_202_inf__RETURN__RES_I2_J,axiom,
% 3.04/1.62 ! [A: $tType,X4: A,X: set @ A] :
% 3.04/1.62 ( ( ( member @ A @ X4 @ X )
% 3.04/1.62 => ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ X ) @ ( refine1687780735RETURN @ A @ X4 ) )
% 3.04/1.62 = ( refine1687780735RETURN @ A @ X4 ) ) )
% 3.04/1.62 & ( ~ ( member @ A @ X4 @ X )
% 3.04/1.62 => ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine605929679le_RES @ A @ X ) @ ( refine1687780735RETURN @ A @ X4 ) )
% 3.04/1.62 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_203_inf__RETURN__RES_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,X4: A,X: set @ A] :
% 3.04/1.62 ( ( ( member @ A @ X4 @ X )
% 3.04/1.62 => ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ X ) )
% 3.04/1.62 = ( refine1687780735RETURN @ A @ X4 ) ) )
% 3.04/1.62 & ( ~ ( member @ A @ X4 @ X )
% 3.04/1.62 => ( ( inf_inf @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X4 ) @ ( refine605929679le_RES @ A @ X ) )
% 3.04/1.62 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_204_bot__apply,axiom,
% 3.04/1.62 ! [C: $tType,D3: $tType] :
% 3.04/1.62 ( ( bot @ C )
% 3.04/1.62 => ( ( bot_bot @ ( D3 > C ) )
% 3.04/1.62 = ( ^ [X5: D3] : ( bot_bot @ C ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_205_nres__monad3,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType,C: $tType,M4: refine1665802226e_nres @ C,F: C > ( refine1665802226e_nres @ B ),G: B > ( refine1665802226e_nres @ A )] :
% 3.04/1.62 ( ( refine463715084e_bind @ B @ A @ ( refine463715084e_bind @ C @ B @ M4 @ F ) @ G )
% 3.04/1.62 = ( refine463715084e_bind @ C @ A @ M4
% 3.04/1.62 @ ^ [X5: C] : ( refine463715084e_bind @ B @ A @ ( F @ X5 ) @ G ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_206_If__bind__distrib,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType,B2: $o,T: refine1665802226e_nres @ A,E: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B )] :
% 3.04/1.62 ( ( B2
% 3.04/1.62 => ( ( refine463715084e_bind @ A @ B @ ( if @ ( refine1665802226e_nres @ A ) @ B2 @ T @ E ) @ F )
% 3.04/1.62 = ( refine463715084e_bind @ A @ B @ T @ F ) ) )
% 3.04/1.62 & ( ~ B2
% 3.04/1.62 => ( ( refine463715084e_bind @ A @ B @ ( if @ ( refine1665802226e_nres @ A ) @ B2 @ T @ E ) @ F )
% 3.04/1.62 = ( refine463715084e_bind @ A @ B @ E @ F ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_207_inf__bot__right,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounded_lattice_bot @ A )
% 3.04/1.62 => ! [X4: A] :
% 3.04/1.62 ( ( inf_inf @ A @ X4 @ ( bot_bot @ A ) )
% 3.04/1.62 = ( bot_bot @ A ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_208_inf__bot__left,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounded_lattice_bot @ A )
% 3.04/1.62 => ! [X4: A] :
% 3.04/1.62 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X4 )
% 3.04/1.62 = ( bot_bot @ A ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_209_nres__monad2,axiom,
% 3.04/1.62 ! [A: $tType,M4: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( refine463715084e_bind @ A @ A @ M4 @ ( refine1687780735RETURN @ A ) )
% 3.04/1.62 = M4 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_210_nres__monad1,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType,X4: B,F: B > ( refine1665802226e_nres @ A )] :
% 3.04/1.62 ( ( refine463715084e_bind @ B @ A @ ( refine1687780735RETURN @ B @ X4 ) @ F )
% 3.04/1.62 = ( F @ X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_211_nres__order__simps_I2_J,axiom,
% 3.04/1.62 ! [B: $tType,M4: refine1665802226e_nres @ B] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M4 @ ( bot_bot @ ( refine1665802226e_nres @ B ) ) )
% 3.04/1.62 = ( M4
% 3.04/1.62 = ( bot_bot @ ( refine1665802226e_nres @ B ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_212_bind__SUCCEED,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType,F: B > ( refine1665802226e_nres @ A )] :
% 3.04/1.62 ( ( refine463715084e_bind @ B @ A @ ( bot_bot @ ( refine1665802226e_nres @ B ) ) @ F )
% 3.04/1.62 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_213_nofail__simps_I4_J,axiom,
% 3.04/1.62 ! [D3: $tType] : ( refine1102455758nofail @ D3 @ ( bot_bot @ ( refine1665802226e_nres @ D3 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_214_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType,M4: refine1665802226e_nres @ A,M3: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4 @ M3 )
% 3.04/1.62 => ( ! [X3: A] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M4 )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ ( F4 @ X3 ) ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M4 @ F ) @ ( refine463715084e_bind @ A @ B @ M3 @ F4 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_215_bind__cong,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType,M: refine1665802226e_nres @ A,M7: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),F4: A > ( refine1665802226e_nres @ B )] :
% 3.04/1.62 ( ( M = M7 )
% 3.04/1.62 => ( ! [X3: A] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M7 )
% 3.04/1.62 => ( ( F @ X3 )
% 3.04/1.62 = ( F4 @ X3 ) ) )
% 3.04/1.62 => ( ( refine463715084e_bind @ A @ B @ M @ F )
% 3.04/1.62 = ( refine463715084e_bind @ A @ B @ M7 @ F4 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_216_pw__RES__bind__choose_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType,X: set @ B,F: B > ( refine1665802226e_nres @ A )] :
% 3.04/1.62 ( ( refine1102455758nofail @ A @ ( refine463715084e_bind @ B @ A @ ( refine605929679le_RES @ B @ X ) @ F ) )
% 3.04/1.62 = ( ! [X5: B] :
% 3.04/1.62 ( ( member @ B @ X5 @ X )
% 3.04/1.62 => ( refine1102455758nofail @ A @ ( F @ X5 ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_217_let__to__bind__conv,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType] :
% 3.04/1.62 ( ( ^ [S3: B,F3: B > ( refine1665802226e_nres @ A )] : ( F3 @ S3 ) )
% 3.04/1.62 = ( ^ [X5: B] : ( refine463715084e_bind @ B @ A @ ( refine1687780735RETURN @ B @ X5 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_218_nres__inequalities_I5_J,axiom,
% 3.04/1.62 ! [C: $tType,X4: C] :
% 3.04/1.62 ( ( bot_bot @ ( refine1665802226e_nres @ C ) )
% 3.04/1.62 != ( refine1687780735RETURN @ C @ X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_219_le__SPEC__bindI,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType,Phi: A > $o,X4: A,M: refine1665802226e_nres @ B,F: A > ( refine1665802226e_nres @ B )] :
% 3.04/1.62 ( ( Phi @ X4 )
% 3.04/1.62 => ( ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M @ ( F @ X4 ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M @ ( refine463715084e_bind @ A @ B @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) @ F ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_220_RES__bind__choose,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType,X4: A,X: set @ A,M: refine1665802226e_nres @ B,F: A > ( refine1665802226e_nres @ B )] :
% 3.04/1.62 ( ( member @ A @ X4 @ X )
% 3.04/1.62 => ( ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M @ ( F @ X4 ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M @ ( refine463715084e_bind @ A @ B @ ( refine605929679le_RES @ A @ X ) @ F ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_221_SUCCEED__rule,axiom,
% 3.04/1.62 ! [A: $tType,Phi: A > $o] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_222_ibind__strict_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,F: product_unit > ( refine1665802226e_nres @ A )] :
% 3.04/1.62 ( ( refine463715084e_bind @ product_unit @ A @ ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) @ F )
% 3.04/1.62 = ( bot_bot @ ( refine1665802226e_nres @ A ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_223_bot__fun__def,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType] :
% 3.04/1.62 ( ( bot @ B )
% 3.04/1.62 => ( ( bot_bot @ ( A > B ) )
% 3.04/1.62 = ( ^ [X5: A] : ( bot_bot @ B ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_224_bot_Oextremum__uniqueI,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( order_bot @ A )
% 3.04/1.62 => ! [A2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 3.04/1.62 => ( A2
% 3.04/1.62 = ( bot_bot @ A ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_225_bot_Oextremum__unique,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( order_bot @ A )
% 3.04/1.62 => ! [A2: A] :
% 3.04/1.62 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 3.04/1.62 = ( A2
% 3.04/1.62 = ( bot_bot @ A ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_226_bot_Oextremum,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( order_bot @ A )
% 3.04/1.62 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_227_nres__order__simps_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,M4: refine1665802226e_nres @ A] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( bot_bot @ ( refine1665802226e_nres @ A ) ) @ M4 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_228_bind__rule__complete,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType,M4: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A ),Phi: A > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M4 @ F ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 3.04/1.62 = ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M4
% 3.04/1.62 @ ( refine605929679le_RES @ B
% 3.04/1.62 @ ( collect @ B
% 3.04/1.62 @ ^ [X5: B] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F @ X5 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_229_specify__left,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType,M: refine1665802226e_nres @ A,Phi: A > $o,F: A > ( refine1665802226e_nres @ B ),M4: refine1665802226e_nres @ B] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M @ ( refine605929679le_RES @ A @ ( collect @ A @ Phi ) ) )
% 3.04/1.62 => ( ! [X3: A] :
% 3.04/1.62 ( ( Phi @ X3 )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ M4 ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M @ F ) @ M4 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_230_bind__rule,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType,M4: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),Phi: B > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ M4
% 3.04/1.62 @ ( refine605929679le_RES @ A
% 3.04/1.62 @ ( collect @ A
% 3.04/1.62 @ ^ [X5: A] : ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X5 ) @ ( refine605929679le_RES @ B @ ( collect @ B @ Phi ) ) ) ) ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M4 @ F ) @ ( refine605929679le_RES @ B @ ( collect @ B @ Phi ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_231_bind__le__nofailI,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType,M: refine1665802226e_nres @ A,F: A > ( refine1665802226e_nres @ B ),M7: refine1665802226e_nres @ B] :
% 3.04/1.62 ( ( refine1102455758nofail @ A @ M )
% 3.04/1.62 => ( ! [X3: A] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine1687780735RETURN @ A @ X3 ) @ M )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( F @ X3 ) @ M7 ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ ( refine463715084e_bind @ A @ B @ M @ F ) @ M7 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_232_bind__le__shift,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType,M: refine1665802226e_nres @ B,F: B > ( refine1665802226e_nres @ A ),M7: refine1665802226e_nres @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M @ F ) @ M7 )
% 3.04/1.62 = ( ord_less_eq @ ( refine1665802226e_nres @ B ) @ M
% 3.04/1.62 @ ( if @ ( refine1665802226e_nres @ B ) @ ( refine1102455758nofail @ A @ M7 )
% 3.04/1.62 @ ( refine605929679le_RES @ B
% 3.04/1.62 @ ( collect @ B
% 3.04/1.62 @ ^ [X5: B] : ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F @ X5 ) @ M7 ) ) )
% 3.04/1.62 @ ( top_top @ ( refine1665802226e_nres @ B ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_233_bind__sim__select__rule,axiom,
% 3.04/1.62 ! [A: $tType,B: $tType,C: $tType,M: refine1665802226e_nres @ B,F4: B > ( refine1665802226e_nres @ A ),Psi: A > $o,F: B > ( refine1665802226e_nres @ C ),Phi: C > $o] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( refine463715084e_bind @ B @ A @ M @ F4 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) )
% 3.04/1.62 => ( ! [X3: B] :
% 3.04/1.62 ( ( refine1102455758nofail @ B @ M )
% 3.04/1.62 => ( ( refine1315500908_inres @ B @ M @ X3 )
% 3.04/1.62 => ( ( ord_less_eq @ ( refine1665802226e_nres @ A ) @ ( F4 @ X3 ) @ ( refine605929679le_RES @ A @ ( collect @ A @ Psi ) ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ C ) @ ( F @ X3 ) @ ( refine605929679le_RES @ C @ ( collect @ C @ Phi ) ) ) ) ) )
% 3.04/1.62 => ( ord_less_eq @ ( refine1665802226e_nres @ C ) @ ( refine463715084e_bind @ B @ C @ M @ F ) @ ( refine605929679le_RES @ C @ ( collect @ C @ Phi ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_234_top__apply,axiom,
% 3.04/1.62 ! [C: $tType,D3: $tType] :
% 3.04/1.62 ( ( top @ C )
% 3.04/1.62 => ( ( top_top @ ( D3 > C ) )
% 3.04/1.62 = ( ^ [X5: D3] : ( top_top @ C ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_235_subset__empty,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A] :
% 3.04/1.62 ( ( ord_less_eq @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 3.04/1.62 = ( A5
% 3.04/1.62 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_236_empty__subsetI,axiom,
% 3.04/1.62 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A5 ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_237_inf__top__left,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounde1561333602nf_top @ A )
% 3.04/1.62 => ! [X4: A] :
% 3.04/1.62 ( ( inf_inf @ A @ ( top_top @ A ) @ X4 )
% 3.04/1.62 = X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_238_inf__top__right,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounde1561333602nf_top @ A )
% 3.04/1.62 => ! [X4: A] :
% 3.04/1.62 ( ( inf_inf @ A @ X4 @ ( top_top @ A ) )
% 3.04/1.62 = X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_239_inf__eq__top__iff,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounde1561333602nf_top @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] :
% 3.04/1.62 ( ( ( inf_inf @ A @ X4 @ Y3 )
% 3.04/1.62 = ( top_top @ A ) )
% 3.04/1.62 = ( ( X4
% 3.04/1.62 = ( top_top @ A ) )
% 3.04/1.62 & ( Y3
% 3.04/1.62 = ( top_top @ A ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_240_top__eq__inf__iff,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounde1561333602nf_top @ A )
% 3.04/1.62 => ! [X4: A,Y3: A] :
% 3.04/1.62 ( ( ( top_top @ A )
% 3.04/1.62 = ( inf_inf @ A @ X4 @ Y3 ) )
% 3.04/1.62 = ( ( X4
% 3.04/1.62 = ( top_top @ A ) )
% 3.04/1.62 & ( Y3
% 3.04/1.62 = ( top_top @ A ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_241_inf__top_Oeq__neutr__iff,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounde1561333602nf_top @ A )
% 3.04/1.62 => ! [A2: A,B2: A] :
% 3.04/1.62 ( ( ( inf_inf @ A @ A2 @ B2 )
% 3.04/1.62 = ( top_top @ A ) )
% 3.04/1.62 = ( ( A2
% 3.04/1.62 = ( top_top @ A ) )
% 3.04/1.62 & ( B2
% 3.04/1.62 = ( top_top @ A ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_242_inf__top_Oleft__neutral,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounde1561333602nf_top @ A )
% 3.04/1.62 => ! [A2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ ( top_top @ A ) @ A2 )
% 3.04/1.62 = A2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_243_inf__top_Oneutr__eq__iff,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounde1561333602nf_top @ A )
% 3.04/1.62 => ! [A2: A,B2: A] :
% 3.04/1.62 ( ( ( top_top @ A )
% 3.04/1.62 = ( inf_inf @ A @ A2 @ B2 ) )
% 3.04/1.62 = ( ( A2
% 3.04/1.62 = ( top_top @ A ) )
% 3.04/1.62 & ( B2
% 3.04/1.62 = ( top_top @ A ) ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_244_inf__top_Oright__neutral,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ( ( bounde1561333602nf_top @ A )
% 3.04/1.62 => ! [A2: A] :
% 3.04/1.62 ( ( inf_inf @ A @ A2 @ ( top_top @ A ) )
% 3.04/1.62 = A2 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_245_inres__simps_I2_J,axiom,
% 3.04/1.62 ! [B: $tType,X: set @ B] :
% 3.04/1.62 ( ( refine1315500908_inres @ B @ ( refine605929679le_RES @ B @ X ) )
% 3.04/1.62 = ( ^ [X5: B] : ( member @ B @ X5 @ X ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_246_nres__order__simps_I4_J,axiom,
% 3.04/1.62 ! [D3: $tType,M4: refine1665802226e_nres @ D3] :
% 3.04/1.62 ( ( ord_less_eq @ ( refine1665802226e_nres @ D3 ) @ ( top_top @ ( refine1665802226e_nres @ D3 ) ) @ M4 )
% 3.04/1.62 = ( M4
% 3.04/1.62 = ( top_top @ ( refine1665802226e_nres @ D3 ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_247_bind__FAIL,axiom,
% 3.04/1.62 ! [B: $tType,A: $tType,F: B > ( refine1665802226e_nres @ A )] :
% 3.04/1.62 ( ( refine463715084e_bind @ B @ A @ ( top_top @ ( refine1665802226e_nres @ B ) ) @ F )
% 3.04/1.62 = ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_248_inres__simps_I3_J,axiom,
% 3.04/1.62 ! [C: $tType,X4: C] :
% 3.04/1.62 ( ( refine1315500908_inres @ C @ ( refine1687780735RETURN @ C @ X4 ) )
% 3.04/1.62 = ( ^ [Y5: C,Z: C] : ( Y5 = Z )
% 3.04/1.62 @ X4 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_249_nofail__simps_I1_J,axiom,
% 3.04/1.62 ! [A: $tType] :
% 3.04/1.62 ~ ( refine1102455758nofail @ A @ ( top_top @ ( refine1665802226e_nres @ A ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(fact_250_nres__more__simps_I1_J,axiom,
% 3.04/1.62 ! [A: $tType,X: set @ A] :
% 3.04/1.62 ( ( ( bot_bot @ ( refine1665802226e_nres @ A ) )
% 3.04/1.62 = ( refine605929679le_RES @ A @ X ) )
% 3.04/1.62 = ( X
% 3.04/1.62 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice,axiom,
% 3.04/1.62 ! [A7: $tType] : ( bounded_lattice @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice_1,axiom,
% 3.04/1.62 bounded_lattice @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Lattices_Obounded__lattice_2,axiom,
% 3.04/1.62 bounded_lattice @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Lattices_Obounded__lattice_3,axiom,
% 3.04/1.62 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Lattices_Obounded__lattice_4,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( bounded_lattice @ A8 )
% 3.04/1.62 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Lattices_Obounded__semilattice__inf__top,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( bounded_lattice @ A8 )
% 3.04/1.62 => ( bounde1561333602nf_top @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( bounded_lattice @ A8 )
% 3.04/1.62 => ( bounded_lattice_bot @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( semilattice_inf @ A8 )
% 3.04/1.62 => ( semilattice_inf @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( order_bot @ A8 )
% 3.04/1.62 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( preorder @ A8 )
% 3.04/1.62 => ( preorder @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Lattices_Olattice,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( lattice @ A8 )
% 3.04/1.62 => ( lattice @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( order @ A8 )
% 3.04/1.62 => ( order @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Orderings_Otop,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( top @ A8 )
% 3.04/1.62 => ( top @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Orderings_Oord,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( ord @ A8 )
% 3.04/1.62 => ( ord @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_fun___Orderings_Obot,axiom,
% 3.04/1.62 ! [A7: $tType,A8: $tType] :
% 3.04/1.62 ( ( bot @ A8 )
% 3.04/1.62 => ( bot @ ( A7 > A8 ) ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_5,axiom,
% 3.04/1.62 ! [A7: $tType] : ( bounde1561333602nf_top @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_6,axiom,
% 3.04/1.62 ! [A7: $tType] : ( bounded_lattice_bot @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_7,axiom,
% 3.04/1.62 ! [A7: $tType] : ( semilattice_inf @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Orderings_Oorder__bot_8,axiom,
% 3.04/1.62 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Orderings_Opreorder_9,axiom,
% 3.04/1.62 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Lattices_Olattice_10,axiom,
% 3.04/1.62 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Orderings_Oorder_11,axiom,
% 3.04/1.62 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Orderings_Otop_12,axiom,
% 3.04/1.62 ! [A7: $tType] : ( top @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Orderings_Oord_13,axiom,
% 3.04/1.62 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Set_Oset___Orderings_Obot_14,axiom,
% 3.04/1.62 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_15,axiom,
% 3.04/1.62 bounde1561333602nf_top @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_16,axiom,
% 3.04/1.62 bounded_lattice_bot @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_17,axiom,
% 3.04/1.62 semilattice_inf @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Orderings_Oorder__bot_18,axiom,
% 3.04/1.62 order_bot @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Orderings_Opreorder_19,axiom,
% 3.04/1.62 preorder @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 3.04/1.62 linorder @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Lattices_Olattice_20,axiom,
% 3.04/1.62 lattice @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Orderings_Oorder_21,axiom,
% 3.04/1.62 order @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Orderings_Otop_22,axiom,
% 3.04/1.62 top @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Orderings_Oord_23,axiom,
% 3.04/1.62 ord @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_HOL_Obool___Orderings_Obot_24,axiom,
% 3.04/1.62 bot @ $o ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Lattices_Obounded__semilattice__inf__top_25,axiom,
% 3.04/1.62 bounde1561333602nf_top @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Lattices_Obounded__lattice__bot_26,axiom,
% 3.04/1.62 bounded_lattice_bot @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Lattices_Osemilattice__inf_27,axiom,
% 3.04/1.62 semilattice_inf @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_28,axiom,
% 3.04/1.62 order_bot @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_29,axiom,
% 3.04/1.62 preorder @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_30,axiom,
% 3.04/1.62 linorder @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Lattices_Olattice_31,axiom,
% 3.04/1.62 lattice @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Orderings_Oorder_32,axiom,
% 3.04/1.62 order @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Orderings_Otop_33,axiom,
% 3.04/1.62 top @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Orderings_Oord_34,axiom,
% 3.04/1.62 ord @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Product__Type_Ounit___Orderings_Obot_35,axiom,
% 3.04/1.62 bot @ product_unit ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__semilattice__inf__top_36,axiom,
% 3.04/1.62 ! [A7: $tType] : ( bounde1561333602nf_top @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice__bot_37,axiom,
% 3.04/1.62 ! [A7: $tType] : ( bounded_lattice_bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Osemilattice__inf_38,axiom,
% 3.04/1.62 ! [A7: $tType] : ( semilattice_inf @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_39,axiom,
% 3.04/1.62 ! [A7: $tType] : ( order_bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_40,axiom,
% 3.04/1.62 ! [A7: $tType] : ( preorder @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Olattice_41,axiom,
% 3.04/1.62 ! [A7: $tType] : ( lattice @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_42,axiom,
% 3.04/1.62 ! [A7: $tType] : ( order @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_43,axiom,
% 3.04/1.62 ! [A7: $tType] : ( top @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_44,axiom,
% 3.04/1.62 ! [A7: $tType] : ( ord @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_45,axiom,
% 3.04/1.62 ! [A7: $tType] : ( bot @ ( refine1665802226e_nres @ A7 ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(help_If_3_1_T,axiom,
% 3.04/1.62 ! [P: $o] :
% 3.04/1.62 ( ( P = $true )
% 3.04/1.62 | ( P = $false ) ) ).
% 3.04/1.62
% 3.04/1.62 thf(help_If_2_1_T,axiom,
% 3.04/1.62 ! [A: $tType,X4: A,Y3: A] :
% 3.04/1.62 ( ( if @ A @ $false @ X4 @ Y3 )
% 3.04/1.62 = Y3 ) ).
% 3.04/1.62
% 3.04/1.62 thf(help_If_1_1_T,axiom,
% 3.04/1.62 ! [A: $tType,X4: A,Y3: A] :
% 3.04/1.62 ( ( if @ A @ $true @ X4 @ Y3 )
% 3.04/1.62 = X4 ) ).
% 3.04/1.62
% 3.04/1.62 thf(conj_0,conjecture,
% 3.04/1.62 ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2
% 3.04/1.62 @ ( refine605929679le_RES @ a
% 3.04/1.62 @ ( collect @ a
% 3.04/1.62 @ ^ [V3: a] :
% 3.04/1.62 ( ( p @ V3 )
% 3.04/1.62 & ( q @ V3 ) ) ) ) ) ).
% 3.04/1.62 ------------------------
% 3.04/1.63 % (2391)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/183Mi)
% 3.04/1.63 % (2392)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_2203 for (2999ds/4Mi)
% 3.04/1.63 % (2393)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_2203 for (2999ds/27Mi)
% 3.04/1.63 % (2395)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_2203 for (2999ds/2Mi)
% 3.04/1.63 % (2396)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_2203 for (2999ds/275Mi)
% 3.04/1.64 % (2395)Instruction limit reached!
% 3.04/1.64 % (2395)------------------------------
% 3.04/1.64 % (2395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.64 % (2395)Termination reason: Unknown
% 3.04/1.64 % (2395)Termination phase: shuffling
% 3.04/1.64
% 3.04/1.64 % (2395)Memory used [KB]: 1279
% 3.04/1.64 % (2395)Time elapsed: 0.002 s
% 3.04/1.64 % (2395)Instructions burned: 2 (million)
% 3.04/1.64 % (2395)------------------------------
% 3.04/1.64 % (2395)------------------------------
% 3.04/1.64 % (2397)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/18Mi)
% 3.04/1.64 % (2392)Instruction limit reached!
% 3.04/1.64 % (2392)------------------------------
% 3.04/1.64 % (2392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.64 % (2392)Termination reason: Unknown
% 3.04/1.64 % (2392)Termination phase: shuffling
% 3.04/1.64
% 3.04/1.64 % (2392)Memory used [KB]: 1407
% 3.04/1.64 % (2392)Time elapsed: 0.003 s
% 3.04/1.64 % (2392)Instructions burned: 5 (million)
% 3.04/1.64 % (2392)------------------------------
% 3.04/1.64 % (2392)------------------------------
% 3.04/1.64 % (2394)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/2Mi)
% 3.04/1.64 % (2394)Instruction limit reached!
% 3.04/1.64 % (2394)------------------------------
% 3.04/1.64 % (2394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.64 % (2394)Termination reason: Unknown
% 3.04/1.64 % (2394)Termination phase: shuffling
% 3.04/1.64
% 3.04/1.64 % (2394)Memory used [KB]: 1407
% 3.04/1.64 % (2394)Time elapsed: 0.003 s
% 3.04/1.64 % (2394)Instructions burned: 3 (million)
% 3.04/1.64 % (2394)------------------------------
% 3.04/1.64 % (2394)------------------------------
% 3.04/1.64 % (2397)Instruction limit reached!
% 3.04/1.64 % (2397)------------------------------
% 3.04/1.64 % (2397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.64 % (2397)Termination reason: Unknown
% 3.04/1.64 % (2397)Termination phase: shuffling
% 3.04/1.64
% 3.04/1.64 % (2397)Memory used [KB]: 1663
% 3.04/1.64 % (2397)Time elapsed: 0.008 s
% 3.04/1.64 % (2397)Instructions burned: 19 (million)
% 3.04/1.64 % (2397)------------------------------
% 3.04/1.64 % (2397)------------------------------
% 3.04/1.64 % (2393)Instruction limit reached!
% 3.04/1.64 % (2393)------------------------------
% 3.04/1.64 % (2393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.64 % (2393)Termination reason: Unknown
% 3.04/1.64 % (2393)Termination phase: Property scanning
% 3.04/1.64
% 3.04/1.64 % (2393)Memory used [KB]: 1791
% 3.04/1.64 % (2393)Time elapsed: 0.010 s
% 3.04/1.64 % (2393)Instructions burned: 27 (million)
% 3.04/1.64 % (2393)------------------------------
% 3.04/1.64 % (2393)------------------------------
% 3.04/1.64 % (2398)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/3Mi)
% 3.04/1.65 % (2399)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_2203 for (2999ds/37Mi)
% 3.04/1.65 % (2398)Instruction limit reached!
% 3.04/1.65 % (2398)------------------------------
% 3.04/1.65 % (2398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.65 % (2398)Termination reason: Unknown
% 3.04/1.65 % (2398)Termination phase: shuffling
% 3.04/1.65
% 3.04/1.65 % (2398)Memory used [KB]: 1407
% 3.04/1.65 % (2398)Time elapsed: 0.002 s
% 3.04/1.65 % (2398)Instructions burned: 3 (million)
% 3.04/1.65 % (2398)------------------------------
% 3.04/1.65 % (2398)------------------------------
% 3.04/1.65 % (2400)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_2203 for (2999ds/15Mi)
% 3.04/1.65 % (2402)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_2203 for (2999ds/1041Mi)
% 3.04/1.65 % (2403)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/7Mi)
% 3.04/1.66 % (2400)Instruction limit reached!
% 3.04/1.66 % (2400)------------------------------
% 3.04/1.66 % (2400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.66 % (2400)Termination reason: Unknown
% 3.04/1.66 % (2400)Termination phase: shuffling
% 3.04/1.66
% 3.04/1.66 % (2400)Memory used [KB]: 1663
% 3.04/1.66 % (2400)Time elapsed: 0.007 s
% 3.04/1.66 % (2400)Instructions burned: 17 (million)
% 3.04/1.66 % (2400)------------------------------
% 3.04/1.66 % (2400)------------------------------
% 3.04/1.66 % (2399)Instruction limit reached!
% 3.04/1.66 % (2399)------------------------------
% 3.04/1.66 % (2399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.66 % (2399)Termination reason: Unknown
% 3.04/1.66 % (2399)Termination phase: Property scanning
% 3.04/1.66
% 3.04/1.66 % (2399)Memory used [KB]: 2046
% 3.04/1.66 % (2399)Time elapsed: 0.012 s
% 3.04/1.66 % (2399)Instructions burned: 40 (million)
% 3.04/1.66 % (2399)------------------------------
% 3.04/1.66 % (2399)------------------------------
% 3.04/1.66 % (2403)Instruction limit reached!
% 3.04/1.66 % (2403)------------------------------
% 3.04/1.66 % (2403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.66 % (2403)Termination reason: Unknown
% 3.04/1.66 % (2403)Termination phase: shuffling
% 3.04/1.66
% 3.04/1.66 % (2403)Memory used [KB]: 1535
% 3.04/1.66 % (2403)Time elapsed: 0.004 s
% 3.04/1.66 % (2403)Instructions burned: 9 (million)
% 3.04/1.66 % (2403)------------------------------
% 3.04/1.66 % (2403)------------------------------
% 3.04/1.66 % (2401)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_2203 for (2999ds/3Mi)
% 3.04/1.66 % (2401)Instruction limit reached!
% 3.04/1.66 % (2401)------------------------------
% 3.04/1.66 % (2401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.66 % (2401)Termination reason: Unknown
% 3.04/1.66 % (2401)Termination phase: shuffling
% 3.04/1.66
% 3.04/1.66 % (2401)Memory used [KB]: 1407
% 3.04/1.66 % (2401)Time elapsed: 0.003 s
% 3.04/1.66 % (2401)Instructions burned: 3 (million)
% 3.04/1.66 % (2401)------------------------------
% 3.04/1.66 % (2401)------------------------------
% 3.04/1.67 % (2404)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/16Mi)
% 3.04/1.67 % (2405)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_2203 for (2999ds/3Mi)
% 3.04/1.67 % (2406)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_2203 for (2999ds/3Mi)
% 3.04/1.67 % (2405)Instruction limit reached!
% 3.04/1.67 % (2405)------------------------------
% 3.04/1.67 % (2405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.67 % (2405)Termination reason: Unknown
% 3.04/1.67 % (2405)Termination phase: shuffling
% 3.04/1.67
% 3.04/1.67 % (2405)Memory used [KB]: 1407
% 3.04/1.67 % (2405)Time elapsed: 0.003 s
% 3.04/1.67 % (2405)Instructions burned: 5 (million)
% 3.04/1.67 % (2405)------------------------------
% 3.04/1.67 % (2405)------------------------------
% 3.04/1.67 % (2406)Instruction limit reached!
% 3.04/1.67 % (2406)------------------------------
% 3.04/1.67 % (2406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.67 % (2406)Termination reason: Unknown
% 3.04/1.67 % (2406)Termination phase: shuffling
% 3.04/1.67
% 3.04/1.67 % (2406)Memory used [KB]: 1407
% 3.04/1.67 % (2406)Time elapsed: 0.003 s
% 3.04/1.67 % (2406)Instructions burned: 5 (million)
% 3.04/1.67 % (2406)------------------------------
% 3.04/1.67 % (2406)------------------------------
% 3.04/1.67 % (2404)Instruction limit reached!
% 3.04/1.67 % (2404)------------------------------
% 3.04/1.67 % (2404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.67 % (2404)Termination reason: Unknown
% 3.04/1.67 % (2404)Termination phase: shuffling
% 3.04/1.67
% 3.04/1.67 % (2404)Memory used [KB]: 1663
% 3.04/1.67 % (2404)Time elapsed: 0.007 s
% 3.04/1.67 % (2404)Instructions burned: 17 (million)
% 3.04/1.67 % (2404)------------------------------
% 3.04/1.67 % (2404)------------------------------
% 3.04/1.67 % (2407)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/7Mi)
% 3.04/1.67 % (2407)Instruction limit reached!
% 3.04/1.67 % (2407)------------------------------
% 3.04/1.67 % (2407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.67 % (2407)Termination reason: Unknown
% 3.04/1.67 % (2407)Termination phase: shuffling
% 3.04/1.67
% 3.04/1.67 % (2407)Memory used [KB]: 1407
% 3.04/1.67 % (2407)Time elapsed: 0.006 s
% 3.04/1.67 % (2407)Instructions burned: 7 (million)
% 3.04/1.67 % (2407)------------------------------
% 3.04/1.67 % (2407)------------------------------
% 3.04/1.68 % (2408)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/3Mi)
% 3.04/1.68 % (2408)Instruction limit reached!
% 3.04/1.68 % (2408)------------------------------
% 3.04/1.68 % (2408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.68 % (2408)Termination reason: Unknown
% 3.04/1.68 % (2408)Termination phase: shuffling
% 3.04/1.68
% 3.04/1.68 % (2408)Memory used [KB]: 1407
% 3.04/1.68 % (2408)Time elapsed: 0.002 s
% 3.04/1.68 % (2408)Instructions burned: 3 (million)
% 3.04/1.68 % (2408)------------------------------
% 3.04/1.68 % (2408)------------------------------
% 3.04/1.68 % (2409)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/4Mi)
% 3.04/1.68 % (2410)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/18Mi)
% 3.04/1.68 % (2409)Instruction limit reached!
% 3.04/1.68 % (2409)------------------------------
% 3.04/1.68 % (2409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.68 % (2409)Termination reason: Unknown
% 3.04/1.68 % (2409)Termination phase: shuffling
% 3.04/1.68
% 3.04/1.68 % (2409)Memory used [KB]: 1407
% 3.04/1.68 % (2409)Time elapsed: 0.003 s
% 3.04/1.68 % (2409)Instructions burned: 6 (million)
% 3.04/1.68 % (2409)------------------------------
% 3.04/1.68 % (2409)------------------------------
% 3.04/1.68 % (2411)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/710Mi)
% 3.04/1.69 % (2410)Instruction limit reached!
% 3.04/1.69 % (2410)------------------------------
% 3.04/1.69 % (2410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.69 % (2410)Termination reason: Unknown
% 3.04/1.69 % (2410)Termination phase: shuffling
% 3.04/1.69
% 3.04/1.69 % (2410)Memory used [KB]: 1663
% 3.04/1.69 % (2410)Time elapsed: 0.007 s
% 3.04/1.69 % (2410)Instructions burned: 18 (million)
% 3.04/1.69 % (2410)------------------------------
% 3.04/1.69 % (2410)------------------------------
% 3.04/1.69 % (2412)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/6Mi)
% 3.04/1.69 % (2412)Instruction limit reached!
% 3.04/1.69 % (2412)------------------------------
% 3.04/1.69 % (2412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.69 % (2412)Termination reason: Unknown
% 3.04/1.69 % (2412)Termination phase: shuffling
% 3.04/1.69
% 3.04/1.69 % (2412)Memory used [KB]: 1407
% 3.04/1.69 % (2412)Time elapsed: 0.003 s
% 3.04/1.69 % (2412)Instructions burned: 6 (million)
% 3.04/1.69 % (2412)------------------------------
% 3.04/1.69 % (2412)------------------------------
% 3.04/1.69 % (2413)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_2203 for (2999ds/902Mi)
% 3.04/1.69 % (2391)Instruction limit reached!
% 3.04/1.69 % (2391)------------------------------
% 3.04/1.69 % (2391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.69 % (2391)Termination reason: Unknown
% 3.04/1.69 % (2391)Termination phase: Saturation
% 3.04/1.69
% 3.04/1.69 % (2391)Memory used [KB]: 7164
% 3.04/1.69 % (2391)Time elapsed: 0.057 s
% 3.04/1.69 % (2391)Instructions burned: 183 (million)
% 3.04/1.69 % (2391)------------------------------
% 3.04/1.69 % (2391)------------------------------
% 3.04/1.70 % (2414)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_2203 for (2999ds/21Mi)
% 3.06/1.70 % (2415)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/5Mi)
% 3.06/1.70 % (2416)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_2203 for (2999ds/6Mi)
% 3.06/1.70 % (2415)Instruction limit reached!
% 3.06/1.70 % (2415)------------------------------
% 3.06/1.70 % (2415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.70 % (2415)Termination reason: Unknown
% 3.06/1.70 % (2415)Termination phase: shuffling
% 3.06/1.70
% 3.06/1.70 % (2415)Memory used [KB]: 1407
% 3.06/1.70 % (2415)Time elapsed: 0.003 s
% 3.06/1.70 % (2415)Instructions burned: 7 (million)
% 3.06/1.70 % (2415)------------------------------
% 3.06/1.70 % (2415)------------------------------
% 3.06/1.70 % (2416)Instruction limit reached!
% 3.06/1.70 % (2416)------------------------------
% 3.06/1.70 % (2416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.70 % (2416)Termination reason: Unknown
% 3.06/1.70 % (2416)Termination phase: shuffling
% 3.06/1.70
% 3.06/1.70 % (2416)Memory used [KB]: 1407
% 3.06/1.70 % (2416)Time elapsed: 0.003 s
% 3.06/1.70 % (2416)Instructions burned: 6 (million)
% 3.06/1.70 % (2416)------------------------------
% 3.06/1.70 % (2416)------------------------------
% 3.06/1.70 % (2414)Instruction limit reached!
% 3.06/1.70 % (2414)------------------------------
% 3.06/1.70 % (2414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.70 % (2414)Termination reason: Unknown
% 3.06/1.70 % (2414)Termination phase: shuffling
% 3.06/1.70
% 3.06/1.70 % (2414)Memory used [KB]: 1791
% 3.06/1.70 % (2414)Time elapsed: 0.008 s
% 3.06/1.70 % (2414)Instructions burned: 21 (million)
% 3.06/1.70 % (2414)------------------------------
% 3.06/1.70 % (2414)------------------------------
% 3.06/1.71 % (2421)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/377Mi)
% 3.06/1.71 % (2422)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_2203 for (2999ds/779Mi)
% 3.06/1.71 % (2424)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_2203 for (2999ds/19Mi)
% 3.06/1.72 % (2424)Instruction limit reached!
% 3.06/1.72 % (2424)------------------------------
% 3.06/1.72 % (2424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.72 % (2424)Termination reason: Unknown
% 3.06/1.72 % (2424)Termination phase: shuffling
% 3.06/1.72
% 3.06/1.72 % (2424)Memory used [KB]: 1663
% 3.06/1.72 % (2424)Time elapsed: 0.007 s
% 3.06/1.72 % (2424)Instructions burned: 20 (million)
% 3.06/1.72 % (2424)------------------------------
% 3.06/1.72 % (2424)------------------------------
% 3.06/1.72 % (2396)Instruction limit reached!
% 3.06/1.72 % (2396)------------------------------
% 3.06/1.72 % (2396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.72 % (2396)Termination reason: Unknown
% 3.06/1.72 % (2396)Termination phase: Saturation
% 3.06/1.72
% 3.06/1.72 % (2396)Memory used [KB]: 7036
% 3.06/1.72 % (2396)Time elapsed: 0.088 s
% 3.06/1.72 % (2396)Instructions burned: 276 (million)
% 3.06/1.72 % (2396)------------------------------
% 3.06/1.72 % (2396)------------------------------
% 3.06/1.73 % (2431)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/879Mi)
% 3.06/1.73 % (2433)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2203 for (2999ds/17Mi)
% 3.06/1.74 % (2433)Instruction limit reached!
% 3.06/1.74 % (2433)------------------------------
% 3.06/1.74 % (2433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.74 % (2433)Termination reason: Unknown
% 3.06/1.74 % (2433)Termination phase: shuffling
% 3.06/1.74
% 3.06/1.74 % (2433)Memory used [KB]: 1663
% 3.06/1.74 % (2433)Time elapsed: 0.007 s
% 3.06/1.74 % (2433)Instructions burned: 18 (million)
% 3.06/1.74 % (2433)------------------------------
% 3.06/1.74 % (2433)------------------------------
% 3.06/1.75 % (2440)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2203 for (2998ds/3Mi)
% 3.06/1.75 % (2440)Instruction limit reached!
% 3.06/1.75 % (2440)------------------------------
% 3.06/1.75 % (2440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.75 % (2440)Termination reason: Unknown
% 3.06/1.75 % (2440)Termination phase: shuffling
% 3.06/1.75
% 3.06/1.75 % (2440)Memory used [KB]: 1407
% 3.06/1.75 % (2440)Time elapsed: 0.003 s
% 3.06/1.75 % (2440)Instructions burned: 5 (million)
% 3.06/1.75 % (2440)------------------------------
% 3.06/1.75 % (2440)------------------------------
% 3.06/1.76 % (2446)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2203 for (2998ds/30Mi)
% 3.06/1.77 % (2446)Instruction limit reached!
% 3.06/1.77 % (2446)------------------------------
% 3.06/1.77 % (2446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.77 % (2446)Termination reason: Unknown
% 3.06/1.77 % (2446)Termination phase: Property scanning
% 3.06/1.77
% 3.06/1.77 % (2446)Memory used [KB]: 1791
% 3.06/1.77 % (2446)Time elapsed: 0.011 s
% 3.06/1.77 % (2446)Instructions burned: 32 (million)
% 3.06/1.77 % (2446)------------------------------
% 3.06/1.77 % (2446)------------------------------
% 3.06/1.77 % (2431)First to succeed.
% 3.06/1.77 % (2431)Refutation found. Thanks to Tanya!
% 3.06/1.77 % SZS status Theorem for DTF2THF_2203
% 3.06/1.77 % SZS output start Proof for DTF2THF_2203
% 3.06/1.77 thf(type_def_6, type, refine1665802226e_nres: ($tType) > $tType).
% 3.06/1.77 thf(type_def_7, type, set: ($tType) > $tType).
% 3.06/1.77 thf(type_def_8, type, a: $tType).
% 3.06/1.77 thf(type_def_9, type, product_unit: $tType).
% 3.06/1.77 thf(func_def_0, type, refine1665802226e_nres: ($tType) > $tType).
% 3.06/1.77 thf(func_def_1, type, product_unit: $tType).
% 3.06/1.77 thf(func_def_2, type, set: ($tType) > $tType).
% 3.06/1.77 thf(func_def_3, type, a: $tType).
% 3.06/1.77 thf(func_def_4, type, bounded_lattice: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_5, type, type: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_6, type, bot: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_7, type, ord: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_8, type, top: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_9, type, order: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_10, type, lattice: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_11, type, linorder: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_12, type, preorder: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_13, type, order_bot: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_14, type, semilattice_inf: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_15, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_16, type, bounde1561333602nf_top: !>[X0: $tType]:($o)).
% 3.06/1.77 thf(func_def_17, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.06/1.77 thf(func_def_18, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.06/1.77 thf(func_def_19, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.06/1.77 thf(func_def_20, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.06/1.77 thf(func_def_21, type, order_Greatest: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_22, type, top_top: !>[X0: $tType]:(X0)).
% 3.06/1.77 thf(func_def_23, type, refine1687780735RETURN: !>[X0: $tType]:(X0 > refine1665802226e_nres @ X0)).
% 3.06/1.77 thf(func_def_24, type, refine463715084e_bind: !>[X0: $tType, X1: $tType]:(refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1)).
% 3.06/1.77 thf(func_def_25, type, refine1315500908_inres: !>[X0: $tType]:(refine1665802226e_nres @ X0 > X0 > $o)).
% 3.06/1.77 thf(func_def_26, type, refine406925620_inres: !>[X0: $tType]:(refine1665802226e_nres @ X0 > X0 > $o)).
% 3.06/1.77 thf(func_def_27, type, refine1102455758nofail: !>[X0: $tType]:(refine1665802226e_nres @ X0 > $o)).
% 3.06/1.77 thf(func_def_28, type, refine1767639642_FAILi: !>[X0: $tType]:(refine1665802226e_nres @ X0)).
% 3.06/1.77 thf(func_def_29, type, refine605929679le_RES: !>[X0: $tType]:(set @ X0 > refine1665802226e_nres @ X0)).
% 3.06/1.77 thf(func_def_30, type, refine1442219249c_nres: !>[X0: $tType, X1: $tType]:(X0 > (set @ X1 > X0) > refine1665802226e_nres @ X1 > X0)).
% 3.06/1.77 thf(func_def_31, type, refine1672542526he_RES: !>[X0: $tType]:(refine1665802226e_nres @ X0 > set @ X0)).
% 3.06/1.77 thf(func_def_32, type, powp: !>[X0: $tType]:((X0 > $o) > set @ X0 > $o)).
% 3.06/1.77 thf(func_def_33, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.06/1.77 thf(func_def_34, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.06/1.77 thf(func_def_35, type, a2: refine1665802226e_nres @ a).
% 3.06/1.77 thf(func_def_36, type, p: a > $o).
% 3.06/1.77 thf(func_def_37, type, q: a > $o).
% 3.06/1.77 thf(func_def_52, type, sK0: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_53, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > $o) > (X1 > refine1665802226e_nres @ X2) > (X0 > $o) > (X1 > refine1665802226e_nres @ X0) > refine1665802226e_nres @ X1 > X1)).
% 3.06/1.77 thf(func_def_54, type, sK2: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_55, type, sK3: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 3.06/1.77 thf(func_def_56, type, sK4: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_57, type, sK5: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > set @ X0 > X0)).
% 3.06/1.77 thf(func_def_58, type, sK6: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > set @ X0 > X0)).
% 3.06/1.77 thf(func_def_59, type, sK7: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_60, type, sK8: !>[X0: $tType, X1: $tType]:(refine1665802226e_nres @ X1 > (X0 > refine1665802226e_nres @ X1) > (X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_61, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.06/1.77 thf(func_def_62, type, sK10: !>[X0: $tType]:(refine1665802226e_nres @ X0 > (X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_63, type, sK11: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_65, type, sK13: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_66, type, sK14: !>[X0: $tType]:(refine1665802226e_nres @ X0 > set @ X0)).
% 3.06/1.77 thf(func_def_67, type, sK15: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 3.06/1.77 thf(func_def_68, type, sK16: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > refine1665802226e_nres @ X0) > X1)).
% 3.06/1.77 thf(func_def_69, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > refine1665802226e_nres @ X0) > set @ X1 > set @ X0)).
% 3.06/1.77 thf(func_def_70, type, sK18: !>[X0: $tType, X1: $tType]:((X1 > refine1665802226e_nres @ X0) > X1 > set @ X0)).
% 3.06/1.77 thf(func_def_71, type, sK19: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 3.06/1.77 thf(f1280,plain,(
% 3.06/1.77 $false),
% 3.06/1.77 inference(subsumption_resolution,[status(thm)],[f1279,f1025])).
% 3.06/1.77 thf(f1025,plain,(
% 3.06/1.77 ($true != (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0)))))))),
% 3.06/1.77 inference(cnf_transformation,[status(thm)],[f885])).
% 3.06/1.77 thf(f885,plain,(
% 3.06/1.77 ($true != (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0)))))))),
% 3.06/1.77 inference(flattening,[status(thm)],[f536])).
% 3.06/1.77 thf(f536,plain,(
% 3.06/1.77 ~($true = (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0)))))))),
% 3.06/1.77 inference(fool_elimination,[status(thm)],[f535])).
% 3.06/1.77 thf(f535,plain,(
% 3.06/1.77 ~(ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[X0 : a] : ((q @ X0) & (p @ X0))))))),
% 3.06/1.77 inference(rectify,[status(thm)],[f313])).
% 3.06/1.77 thf(f313,negated_conjecture,(
% 3.06/1.77 ~(ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[X89 : a] : ((q @ X89) & (p @ X89))))))),
% 3.06/1.77 inference(negated_conjecture,[status(cth)],[f312])).
% 3.06/1.77 thf(f312,conjecture,(
% 3.06/1.77 (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[X89 : a] : ((q @ X89) & (p @ X89))))))),
% 3.06/1.77 file('/export/starexec/sandbox2/tmp/tmp.c73FR42ERP/DTF2THF_2203.p',conj_0)).
% 3.06/1.77 thf(f1279,plain,(
% 3.06/1.77 ($true = (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0)))))))),
% 3.06/1.77 inference(forward_demodulation,[status(thm)],[f1278,f1042])).
% 3.06/1.77 thf(f1042,plain,(
% 3.06/1.77 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (((collect @ X0 @ (^[Y0 : X0]: ((X1 @ Y0) & (X2 @ Y0)))) = (inf_inf @ set @ X0 @ (collect @ X0 @ X1) @ (collect @ X0 @ X2)))) )),
% 3.06/1.77 inference(cnf_transformation,[status(thm)],[f530])).
% 3.06/1.77 thf(f530,plain,(
% 3.06/1.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((collect @ X0 @ (^[Y0 : X0]: ((X1 @ Y0) & (X2 @ Y0)))) = (inf_inf @ set @ X0 @ (collect @ X0 @ X1) @ (collect @ X0 @ X2)))),
% 3.06/1.77 inference(fool_elimination,[status(thm)],[f529])).
% 3.06/1.77 thf(f529,plain,(
% 3.06/1.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((inf_inf @ set @ X0 @ (collect @ X0 @ X1) @ (collect @ X0 @ X2)) = (collect @ X0 @ (^[X3 : X0] : ((X2 @ X3) & (X1 @ X3)))))),
% 3.06/1.77 inference(rectify,[status(thm)],[f127])).
% 3.06/1.77 thf(f127,axiom,(
% 3.06/1.77 ! [X0 : $tType,X13 : X0 > $o,X14 : X0 > $o] : ((inf_inf @ set @ X0 @ (collect @ X0 @ X13) @ (collect @ X0 @ X14)) = (collect @ X0 @ (^[X35 : X0] : ((X14 @ X35) & (X13 @ X35)))))),
% 3.06/1.77 file('/export/starexec/sandbox2/tmp/tmp.c73FR42ERP/DTF2THF_2203.p',fact_126_Collect__conj__eq)).
% 3.06/1.77 thf(f1278,plain,(
% 3.06/1.77 ($true = (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (inf_inf @ set @ a @ (collect @ a @ p) @ (collect @ a @ q)))))),
% 3.06/1.77 inference(backward_demodulation,[status(thm)],[f1071,f1086])).
% 3.06/1.77 thf(f1086,plain,(
% 3.06/1.77 ( ! [X0 : $tType,X2 : set @ X0,X1 : set @ X0] : (((refine605929679le_RES @ X0 @ (inf_inf @ set @ X0 @ X1 @ X2)) = (inf_inf @ refine1665802226e_nres @ X0 @ (refine605929679le_RES @ X0 @ X1) @ (refine605929679le_RES @ X0 @ X2)))) )),
% 3.06/1.77 inference(cnf_transformation,[status(thm)],[f888])).
% 3.06/1.77 thf(f888,plain,(
% 3.06/1.77 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((refine605929679le_RES @ X0 @ (inf_inf @ set @ X0 @ X1 @ X2)) = (inf_inf @ refine1665802226e_nres @ X0 @ (refine605929679le_RES @ X0 @ X1) @ (refine605929679le_RES @ X0 @ X2)))),
% 3.06/1.77 inference(rectify,[status(thm)],[f66])).
% 3.06/1.77 thf(f66,axiom,(
% 3.06/1.77 ! [X0 : $tType,X36 : set @ X0,X7 : set @ X0] : ((inf_inf @ refine1665802226e_nres @ X0 @ (refine605929679le_RES @ X0 @ X36) @ (refine605929679le_RES @ X0 @ X7)) = (refine605929679le_RES @ X0 @ (inf_inf @ set @ X0 @ X36 @ X7)))),
% 3.06/1.77 file('/export/starexec/sandbox2/tmp/tmp.c73FR42ERP/DTF2THF_2203.p',fact_65_inf__nres_Osimps_I3_J)).
% 3.06/1.77 thf(f1071,plain,(
% 3.06/1.77 ((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (inf_inf @ refine1665802226e_nres @ a @ (refine605929679le_RES @ a @ (collect @ a @ p)) @ (refine605929679le_RES @ a @ (collect @ a @ q)))) = $true)),
% 3.06/1.77 inference(cnf_transformation,[status(thm)],[f552])).
% 3.06/1.77 thf(f552,plain,(
% 3.06/1.77 ((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (inf_inf @ refine1665802226e_nres @ a @ (refine605929679le_RES @ a @ (collect @ a @ p)) @ (refine605929679le_RES @ a @ (collect @ a @ q)))) = $true)),
% 3.06/1.77 inference(fool_elimination,[status(thm)],[f551])).
% 3.06/1.77 thf(f551,plain,(
% 3.06/1.77 (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (inf_inf @ refine1665802226e_nres @ a @ (refine605929679le_RES @ a @ (collect @ a @ p)) @ (refine605929679le_RES @ a @ (collect @ a @ q))))),
% 3.06/1.77 inference(rectify,[status(thm)],[f5])).
% 3.06/1.77 thf(f5,axiom,(
% 3.06/1.77 (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (inf_inf @ refine1665802226e_nres @ a @ (refine605929679le_RES @ a @ (collect @ a @ p)) @ (refine605929679le_RES @ a @ (collect @ a @ q))))),
% 3.06/1.77 file('/export/starexec/sandbox2/tmp/tmp.c73FR42ERP/DTF2THF_2203.p',fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062)).
% 3.06/1.77 % SZS output end Proof for DTF2THF_2203
% 3.06/1.77 % (2431)------------------------------
% 3.06/1.77 % (2431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.77 % (2431)Termination reason: Refutation
% 3.06/1.77
% 3.06/1.77 % (2431)Memory used [KB]: 6780
% 3.06/1.77 % (2431)Time elapsed: 0.044 s
% 3.06/1.77 % (2431)Instructions burned: 132 (million)
% 3.06/1.77 % (2431)------------------------------
% 3.06/1.77 % (2431)------------------------------
% 3.06/1.77 % (2390)Success in time 0.14 s
%------------------------------------------------------------------------------