%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP164^1 : 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 : n024.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 08:56:04 AM UTC 2026
% Result : Theorem 2.13s 1.31s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 3 ~; 0 |; 0 &; 12 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 116 ( 114 usr; 7 con; 0-3 aty)
% Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
refine787176636t_unit: $tType ).
thf(type_def_7,type,
refine424419629nres_a: $tType ).
thf(type_def_8,type,
set_Product_unit: $tType ).
thf(type_def_9,type,
set_a: $tType ).
thf(type_def_10,type,
set_Pr451126599t_unit: $tType ).
thf(type_def_11,type,
set_Pr1720557880unit_a: $tType ).
thf(type_def_12,type,
set_Pr1628433942t_unit: $tType ).
thf(type_def_13,type,
set_Product_prod_a_a: $tType ).
thf(type_def_14,type,
product_unit: $tType ).
thf(type_def_15,type,
produc971140967t_unit: $tType ).
thf(type_def_16,type,
a: $tType ).
thf(type_def_17,type,
produc884009688unit_a: $tType ).
thf(type_def_18,type,
produc1767851702t_unit: $tType ).
thf(type_def_19,type,
product_prod_a_a: $tType ).
thf(func_def_0,type,
set_Pr451126599t_unit: $tType ).
thf(func_def_1,type,
refine787176636t_unit: $tType ).
thf(func_def_2,type,
produc971140967t_unit: $tType ).
thf(func_def_3,type,
set_Pr1628433942t_unit: $tType ).
thf(func_def_4,type,
set_Pr1720557880unit_a: $tType ).
thf(func_def_5,type,
refine424419629nres_a: $tType ).
thf(func_def_6,type,
produc1767851702t_unit: $tType ).
thf(func_def_7,type,
produc884009688unit_a: $tType ).
thf(func_def_8,type,
set_Product_prod_a_a: $tType ).
thf(func_def_9,type,
set_Product_unit: $tType ).
thf(func_def_10,type,
product_prod_a_a: $tType ).
thf(func_def_11,type,
product_unit: $tType ).
thf(func_def_12,type,
set_a: $tType ).
thf(func_def_13,type,
a: $tType ).
thf(func_def_14,type,
if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(func_def_15,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_16,type,
bot_bo658782032t_unit: refine787176636t_unit ).
thf(func_def_17,type,
bot_bo529555393nres_a: refine424419629nres_a ).
thf(func_def_18,type,
bot_bo1087887705t_unit: set_Product_unit ).
thf(func_def_19,type,
bot_bot_set_a: set_a ).
thf(func_def_20,type,
ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
thf(func_def_21,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_22,type,
ord_le2035129575t_unit: set_Pr451126599t_unit > set_Pr451126599t_unit > $o ).
thf(func_def_23,type,
ord_le2070001880unit_a: set_Pr1720557880unit_a > set_Pr1720557880unit_a > $o ).
thf(func_def_24,type,
ord_le1977877942t_unit: set_Pr1628433942t_unit > set_Pr1628433942t_unit > $o ).
thf(func_def_25,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_26,type,
ord_le1023748749t_unit: set_Product_unit > set_Product_unit > $o ).
thf(func_def_27,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_28,type,
order_453013155t_unit: ( refine787176636t_unit > $o ) > refine787176636t_unit ).
thf(func_def_29,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(func_def_30,type,
top_to177290092t_unit: refine787176636t_unit ).
thf(func_def_31,type,
top_to231829469nres_a: refine424419629nres_a ).
thf(func_def_32,type,
partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o ).
thf(func_def_33,type,
partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_34,type,
produc1076565719t_unit: product_unit > product_unit > produc971140967t_unit ).
thf(func_def_35,type,
produc1799512520unit_a: product_unit > a > produc884009688unit_a ).
thf(func_def_36,type,
produc1776699686t_unit: a > product_unit > produc1767851702t_unit ).
thf(func_def_37,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(func_def_38,type,
refine1420258419t_unit: product_unit > refine787176636t_unit ).
thf(func_def_39,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(func_def_40,type,
refine838861686t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(func_def_41,type,
refine364464487unit_a: set_Pr1720557880unit_a > refine787176636t_unit > refine424419629nres_a ).
thf(func_def_42,type,
refine341651653t_unit: set_Pr1628433942t_unit > refine424419629nres_a > refine787176636t_unit ).
thf(func_def_43,type,
refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_44,type,
refine681446406t_unit: refine787176636t_unit > ( product_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_45,type,
refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_46,type,
refine96995669t_unit: refine424419629nres_a > ( a > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_47,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_48,type,
refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(func_def_49,type,
refine2043866374unit_a: set_Pr1720557880unit_a > refine424419629nres_a > refine787176636t_unit ).
thf(func_def_50,type,
refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a ).
thf(func_def_51,type,
refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_52,type,
refine558004794t_unit: refine787176636t_unit > product_unit > $o ).
thf(func_def_53,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(func_def_54,type,
refine983493746t_unit: refine787176636t_unit > product_unit > $o ).
thf(func_def_55,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(func_def_56,type,
refine579265252t_unit: refine787176636t_unit > $o ).
thf(func_def_57,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(func_def_58,type,
refine1777164439t_unit: set_Product_unit > refine787176636t_unit ).
thf(func_def_59,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(func_def_60,type,
refine230495195t_unit: ( refine787176636t_unit > refine787176636t_unit ) > ( refine787176636t_unit > refine787176636t_unit ) > $o ).
thf(func_def_61,type,
refine2089046860nres_a: ( refine787176636t_unit > refine424419629nres_a ) > ( refine424419629nres_a > refine787176636t_unit ) > $o ).
thf(func_def_62,type,
refine327276970t_unit: ( refine424419629nres_a > refine787176636t_unit ) > ( refine787176636t_unit > refine424419629nres_a ) > $o ).
thf(func_def_63,type,
refine2004812827nres_a: ( refine424419629nres_a > refine424419629nres_a ) > ( refine424419629nres_a > refine424419629nres_a ) > $o ).
thf(func_def_64,type,
domain2090798924t_unit: set_Pr451126599t_unit > set_Product_unit ).
thf(func_def_65,type,
domain822362941unit_a: set_Pr1720557880unit_a > set_Product_unit ).
thf(func_def_66,type,
domain799550107t_unit: set_Pr1628433942t_unit > set_a ).
thf(func_def_67,type,
domain_a_a: set_Product_prod_a_a > set_a ).
thf(func_def_68,type,
single330234563t_unit: set_Pr451126599t_unit > $o ).
thf(func_def_69,type,
single249782708unit_a: set_Pr1720557880unit_a > $o ).
thf(func_def_70,type,
single226969874t_unit: set_Pr1628433942t_unit > $o ).
thf(func_def_71,type,
single_valued_a_a: set_Product_prod_a_a > $o ).
thf(func_def_72,type,
collec797068754t_unit: ( produc971140967t_unit > $o ) > set_Pr451126599t_unit ).
thf(func_def_73,type,
collec535904323unit_a: ( produc884009688unit_a > $o ) > set_Pr1720557880unit_a ).
thf(func_def_74,type,
collec1419746337t_unit: ( produc1767851702t_unit > $o ) > set_Pr1628433942t_unit ).
thf(func_def_75,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(func_def_76,type,
collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).
thf(func_def_77,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_78,type,
insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_79,type,
insert_a: a > set_a > set_a ).
thf(func_def_80,type,
member1423014800t_unit: produc971140967t_unit > set_Pr451126599t_unit > $o ).
thf(func_def_81,type,
member1211819009unit_a: produc884009688unit_a > set_Pr1720557880unit_a > $o ).
thf(func_def_82,type,
member2095661023t_unit: produc1767851702t_unit > set_Pr1628433942t_unit > $o ).
thf(func_def_83,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_84,type,
member_Product_unit: product_unit > set_Product_unit > $o ).
thf(func_def_85,type,
member_a: a > set_a > $o ).
thf(func_def_86,type,
f: product_unit > refine424419629nres_a ).
thf(func_def_99,type,
sK0: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_100,type,
sK1: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_101,type,
sK2: refine787176636t_unit > refine787176636t_unit > product_unit ).
thf(func_def_102,type,
sK3: refine424419629nres_a > ( product_unit > refine424419629nres_a ) > refine787176636t_unit > product_unit ).
thf(func_def_103,type,
sK4: ( refine787176636t_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_104,type,
sK5: ( refine787176636t_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_105,type,
sK6: ( refine787176636t_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_106,type,
sK7: ( refine787176636t_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_107,type,
sK8: ( refine424419629nres_a > refine787176636t_unit ) > refine424419629nres_a ).
thf(func_def_108,type,
sK9: ( refine424419629nres_a > refine787176636t_unit ) > refine424419629nres_a ).
thf(func_def_109,type,
sK10: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > product_unit ).
thf(func_def_110,type,
sK11: refine787176636t_unit > refine787176636t_unit > product_unit ).
thf(func_def_111,type,
sK12: ( refine424419629nres_a > refine787176636t_unit ) > refine424419629nres_a ).
thf(func_def_112,type,
sK13: ( refine424419629nres_a > refine787176636t_unit ) > refine424419629nres_a ).
thf(func_def_113,type,
sK14: ( product_unit > refine424419629nres_a ) > ( product_unit > refine424419629nres_a ) > refine787176636t_unit > product_unit ).
thf(func_def_114,type,
sK15: refine787176636t_unit > refine424419629nres_a > ( product_unit > refine424419629nres_a ) > product_unit ).
thf(func_def_115,type,
sK16: ( refine787176636t_unit > refine424419629nres_a ) > refine787176636t_unit ).
thf(func_def_116,type,
sK17: ( refine787176636t_unit > refine424419629nres_a ) > refine787176636t_unit ).
thf(func_def_117,type,
sK18: ( refine787176636t_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_118,type,
sK19: ( refine787176636t_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_119,type,
sK20: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_120,type,
sK21: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_121,type,
sK22: ( refine787176636t_unit > refine424419629nres_a ) > refine787176636t_unit ).
thf(func_def_122,type,
sK23: ( refine787176636t_unit > refine424419629nres_a ) > refine787176636t_unit ).
thf(func_def_123,type,
sK24: ( refine787176636t_unit > refine424419629nres_a ) > refine787176636t_unit ).
thf(func_def_124,type,
sK25: ( refine787176636t_unit > refine424419629nres_a ) > refine787176636t_unit ).
thf(func_def_125,type,
sK26: ( refine787176636t_unit > refine424419629nres_a ) > refine787176636t_unit ).
thf(func_def_126,type,
sK27: ( refine787176636t_unit > refine424419629nres_a ) > refine787176636t_unit ).
thf(func_def_127,type,
sK28: ( refine424419629nres_a > refine787176636t_unit ) > refine424419629nres_a ).
thf(func_def_128,type,
sK29: ( refine424419629nres_a > refine787176636t_unit ) > refine424419629nres_a ).
thf(func_def_129,type,
sK30: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_130,type,
sK31: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_131,type,
sK32: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_132,type,
sK33: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_133,type,
sK34: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > ( product_unit > refine424419629nres_a ) > product_unit ).
thf(func_def_134,type,
sK35: ( refine787176636t_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_135,type,
sK36: ( refine787176636t_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_136,type,
sK37: ( refine424419629nres_a > refine787176636t_unit ) > refine424419629nres_a ).
thf(func_def_137,type,
sK38: ( refine424419629nres_a > refine787176636t_unit ) > refine424419629nres_a ).
thf(func_def_138,type,
sK39: refine787176636t_unit > refine787176636t_unit > product_unit ).
thf(func_def_140,type,
ph41:
!>[X0: $tType] : X0 ).
thf(f1358,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1254,f1219]) ).
thf(f1219,plain,
! [X0: product_unit > refine424419629nres_a] :
( bot_bo529555393nres_a
= ( refine119808503unit_a @ bot_bo658782032t_unit @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: product_unit > refine424419629nres_a] :
( bot_bo529555393nres_a
= ( refine119808503unit_a @ bot_bo658782032t_unit @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.D2qxee7X2B/DTF2THF_9718.p',fact_3_bind__SUCCEED) ).
thf(f1254,plain,
( bot_bo529555393nres_a
!= ( refine119808503unit_a @ bot_bo658782032t_unit @ f ) ),
inference(cnf_transformation,[status(thm)],[f951]) ).
thf(f951,plain,
( bot_bo529555393nres_a
!= ( refine119808503unit_a @ bot_bo658782032t_unit @ f ) ),
inference(flattening,[status(thm)],[f359]) ).
thf(f359,negated_conjecture,
( bot_bo529555393nres_a
!= ( refine119808503unit_a @ bot_bo658782032t_unit @ f ) ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f358,conjecture,
( bot_bo529555393nres_a
= ( refine119808503unit_a @ bot_bo658782032t_unit @ f ) ),
file('/export/starexec/sandbox2/tmp/tmp.D2qxee7X2B/DTF2THF_9718.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP164^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 03:28:25 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : ITP164^1 : TPTP v9.2.1. Released v7.5.0.
% 0.07/0.32 % Domain : Interactive Theorem Proving
% 0.07/0.32 % Problem : Sledgehammer Refine_Basic problem prob_743__3591834_1
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English :
% 0.07/0.32
% 0.07/0.32 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.07/0.32 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Des21]
% 0.07/0.32 % Names : Refine_Basic/prob_743__3591834_1 [Des21]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.07/0.32 % Syntax : Number of formulae : 445 ( 175 unt; 87 typ; 0 def)
% 0.07/0.32 % Number of atoms : 1137 ( 343 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 6 ( 3 avg)
% 0.07/0.32 % Number of connectives : 2801 ( 20 ~; 1 |; 48 &;2266 @)
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% 0.07/0.32 insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.07/0.32 insert_a: a > set_a > set_a ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
% 0.07/0.32 member1423014800t_unit: produc971140967t_unit > set_Pr451126599t_unit > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mtf__a_J,type,
% 0.07/0.32 member1211819009unit_a: produc884009688unit_a > set_Pr1720557880unit_a > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Ounit_J,type,
% 0.07/0.32 member2095661023t_unit: produc1767851702t_unit > set_Pr1628433942t_unit > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.07/0.32 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_member_001t__Product____Type__Ounit,type,
% 0.07/0.32 member_Product_unit: product_unit > set_Product_unit > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_member_001tf__a,type,
% 0.07/0.32 member_a: a > set_a > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_f,type,
% 0.07/0.32 f: product_unit > refine424419629nres_a ).
% 0.07/0.32
% 0.07/0.32 % Relevant facts (352)
% 0.07/0.32 thf(fact_0_bind__SUCCEED,axiom,
% 0.07/0.32 ! [F: product_unit > refine787176636t_unit] :
% 0.07/0.32 ( ( refine681446406t_unit @ bot_bo658782032t_unit @ F )
% 0.07/0.32 = bot_bo658782032t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % bind_SUCCEED
% 0.07/0.32 thf(fact_1_bind__SUCCEED,axiom,
% 0.07/0.32 ! [F: a > refine787176636t_unit] :
% 0.07/0.32 ( ( refine96995669t_unit @ bot_bo529555393nres_a @ F )
% 0.07/0.32 = bot_bo658782032t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % bind_SUCCEED
% 0.07/0.32 thf(fact_2_bind__SUCCEED,axiom,
% 0.07/0.32 ! [F: a > refine424419629nres_a] :
% 0.07/0.32 ( ( refine436832838nd_a_a @ bot_bo529555393nres_a @ F )
% 0.07/0.32 = bot_bo529555393nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % bind_SUCCEED
% 0.07/0.32 thf(fact_3_bind__SUCCEED,axiom,
% 0.07/0.32 ! [F: product_unit > refine424419629nres_a] :
% 0.07/0.32 ( ( refine119808503unit_a @ bot_bo658782032t_unit @ F )
% 0.07/0.32 = bot_bo529555393nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % bind_SUCCEED
% 0.07/0.32 thf(fact_4_nres__monad1,axiom,
% 0.07/0.32 ! [X: product_unit,F: product_unit > refine787176636t_unit] :
% 0.07/0.32 ( ( refine681446406t_unit @ ( refine1420258419t_unit @ X ) @ F )
% 0.07/0.32 = ( F @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_monad1
% 0.07/0.32 thf(fact_5_nres__monad1,axiom,
% 0.07/0.32 ! [X: a,F: a > refine424419629nres_a] :
% 0.07/0.32 ( ( refine436832838nd_a_a @ ( refine2063221604TURN_a @ X ) @ F )
% 0.07/0.32 = ( F @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_monad1
% 0.07/0.32 thf(fact_6_nres__monad1,axiom,
% 0.07/0.32 ! [X: a,F: a > refine787176636t_unit] :
% 0.07/0.32 ( ( refine96995669t_unit @ ( refine2063221604TURN_a @ X ) @ F )
% 0.07/0.32 = ( F @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_monad1
% 0.07/0.32 thf(fact_7_nres__monad1,axiom,
% 0.07/0.32 ! [X: product_unit,F: product_unit > refine424419629nres_a] :
% 0.07/0.32 ( ( refine119808503unit_a @ ( refine1420258419t_unit @ X ) @ F )
% 0.07/0.32 = ( F @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_monad1
% 0.07/0.32 thf(fact_8_nres__monad2,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit] :
% 0.07/0.32 ( ( refine681446406t_unit @ M @ refine1420258419t_unit )
% 0.07/0.32 = M ) ).
% 0.07/0.32
% 0.07/0.32 % nres_monad2
% 0.07/0.32 thf(fact_9_nres__monad2,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a] :
% 0.07/0.32 ( ( refine436832838nd_a_a @ M @ refine2063221604TURN_a )
% 0.07/0.32 = M ) ).
% 0.07/0.32
% 0.07/0.32 % nres_monad2
% 0.07/0.32 thf(fact_10_abs__fun__strict,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( refine838861686t_unit @ R @ bot_bo658782032t_unit )
% 0.07/0.32 = bot_bo658782032t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_strict
% 0.07/0.32 thf(fact_11_abs__fun__strict,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( refine364464487unit_a @ R @ bot_bo658782032t_unit )
% 0.07/0.32 = bot_bo529555393nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_strict
% 0.07/0.32 thf(fact_12_abs__fun__strict,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( refine341651653t_unit @ R @ bot_bo529555393nres_a )
% 0.07/0.32 = bot_bo658782032t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_strict
% 0.07/0.32 thf(fact_13_abs__fun__strict,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a] :
% 0.07/0.32 ( ( refine1136779702un_a_a @ R @ bot_bo529555393nres_a )
% 0.07/0.32 = bot_bo529555393nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_strict
% 0.07/0.32 thf(fact_14_conc__fun__strict,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( refine944483349t_unit @ R @ bot_bo658782032t_unit )
% 0.07/0.32 = bot_bo658782032t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_strict
% 0.07/0.32 thf(fact_15_conc__fun__strict,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( refine2021053540t_unit @ R @ bot_bo658782032t_unit )
% 0.07/0.32 = bot_bo529555393nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_strict
% 0.07/0.32 thf(fact_16_conc__fun__strict,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( refine2043866374unit_a @ R @ bot_bo529555393nres_a )
% 0.07/0.32 = bot_bo658782032t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_strict
% 0.07/0.32 thf(fact_17_conc__fun__strict,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a] :
% 0.07/0.32 ( ( refine1441824853un_a_a @ R @ bot_bo529555393nres_a )
% 0.07/0.32 = bot_bo529555393nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_strict
% 0.07/0.32 thf(fact_18_nres__inequalities_I5_J,axiom,
% 0.07/0.32 ! [X: product_unit] :
% 0.07/0.32 ( bot_bo658782032t_unit
% 0.07/0.32 != ( refine1420258419t_unit @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_inequalities(5)
% 0.07/0.32 thf(fact_19_nres__inequalities_I5_J,axiom,
% 0.07/0.32 ! [X: a] :
% 0.07/0.32 ( bot_bo529555393nres_a
% 0.07/0.32 != ( refine2063221604TURN_a @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_inequalities(5)
% 0.07/0.32 thf(fact_20_inres__simps_I4_J,axiom,
% 0.07/0.32 ( ( refine558004794t_unit @ bot_bo658782032t_unit )
% 0.07/0.32 = ( ^ [Uu: product_unit] : $false ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_simps(4)
% 0.07/0.32 thf(fact_21_inres__simps_I4_J,axiom,
% 0.07/0.32 ( ( refine1001002027nres_a @ bot_bo529555393nres_a )
% 0.07/0.32 = ( ^ [Uu: a] : $false ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_simps(4)
% 0.07/0.32 thf(fact_22_nres__order__simps_I2_J,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ M @ bot_bo658782032t_unit )
% 0.07/0.32 = ( M = bot_bo658782032t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(2)
% 0.07/0.32 thf(fact_23_nres__order__simps_I2_J,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ M @ bot_bo529555393nres_a )
% 0.07/0.32 = ( M = bot_bo529555393nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(2)
% 0.07/0.32 thf(fact_24_nofail__simps_I4_J,axiom,
% 0.07/0.32 refine579265252t_unit @ bot_bo658782032t_unit ).
% 0.07/0.32
% 0.07/0.32 % nofail_simps(4)
% 0.07/0.32 thf(fact_25_nofail__simps_I4_J,axiom,
% 0.07/0.32 refine412683989fail_a @ bot_bo529555393nres_a ).
% 0.07/0.32
% 0.07/0.32 % nofail_simps(4)
% 0.07/0.32 thf(fact_26_bind__FAIL,axiom,
% 0.07/0.32 ! [F: product_unit > refine424419629nres_a] :
% 0.07/0.32 ( ( refine119808503unit_a @ top_to177290092t_unit @ F )
% 0.07/0.32 = top_to231829469nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % bind_FAIL
% 0.07/0.32 thf(fact_27_bind__FAIL,axiom,
% 0.07/0.32 ! [F: a > refine424419629nres_a] :
% 0.07/0.32 ( ( refine436832838nd_a_a @ top_to231829469nres_a @ F )
% 0.07/0.32 = top_to231829469nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % bind_FAIL
% 0.07/0.32 thf(fact_28_bind__FAIL,axiom,
% 0.07/0.32 ! [F: a > refine787176636t_unit] :
% 0.07/0.32 ( ( refine96995669t_unit @ top_to231829469nres_a @ F )
% 0.07/0.32 = top_to177290092t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % bind_FAIL
% 0.07/0.32 thf(fact_29_bind__FAIL,axiom,
% 0.07/0.32 ! [F: product_unit > refine787176636t_unit] :
% 0.07/0.32 ( ( refine681446406t_unit @ top_to177290092t_unit @ F )
% 0.07/0.32 = top_to177290092t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % bind_FAIL
% 0.07/0.32 thf(fact_30_nres__order__simps_I1_J,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ M ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(1)
% 0.07/0.32 thf(fact_31_nres__order__simps_I1_J,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ M ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(1)
% 0.07/0.32 thf(fact_32_nres__more__simps_I6_J,axiom,
% 0.07/0.32 ! [X: product_unit,Y: product_unit] :
% 0.07/0.32 ( ( ( refine1420258419t_unit @ X )
% 0.07/0.32 = ( refine1420258419t_unit @ Y ) )
% 0.07/0.32 = ( X = Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(6)
% 0.07/0.32 thf(fact_33_nres__more__simps_I6_J,axiom,
% 0.07/0.32 ! [X: a,Y: a] :
% 0.07/0.32 ( ( ( refine2063221604TURN_a @ X )
% 0.07/0.32 = ( refine2063221604TURN_a @ Y ) )
% 0.07/0.32 = ( X = Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(6)
% 0.07/0.32 thf(fact_34_nres__order__simps_I4_J,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M )
% 0.07/0.32 = ( M = top_to231829469nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(4)
% 0.07/0.32 thf(fact_35_nres__order__simps_I4_J,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ M )
% 0.07/0.32 = ( M = top_to177290092t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(4)
% 0.07/0.32 thf(fact_36_nofail__simps_I1_J,axiom,
% 0.07/0.32 ~ ( refine412683989fail_a @ top_to231829469nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % nofail_simps(1)
% 0.07/0.32 thf(fact_37_nofail__simps_I1_J,axiom,
% 0.07/0.32 ~ ( refine579265252t_unit @ top_to177290092t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % nofail_simps(1)
% 0.07/0.32 thf(fact_38_inres__simps_I1_J,axiom,
% 0.07/0.32 ( ( refine1001002027nres_a @ top_to231829469nres_a )
% 0.07/0.32 = ( ^ [Uu: a] : $true ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_simps(1)
% 0.07/0.32 thf(fact_39_inres__simps_I1_J,axiom,
% 0.07/0.32 ( ( refine558004794t_unit @ top_to177290092t_unit )
% 0.07/0.32 = ( ^ [Uu: product_unit] : $true ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_simps(1)
% 0.07/0.32 thf(fact_40_conc__fun__fail__iff_I2_J,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( top_to231829469nres_a
% 0.07/0.32 = ( refine1441824853un_a_a @ R @ S ) )
% 0.07/0.32 = ( S = top_to231829469nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_fail_iff(2)
% 0.07/0.32 thf(fact_41_conc__fun__fail__iff_I2_J,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( top_to177290092t_unit
% 0.07/0.32 = ( refine2043866374unit_a @ R @ S ) )
% 0.07/0.32 = ( S = top_to231829469nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_fail_iff(2)
% 0.07/0.32 thf(fact_42_conc__fun__fail__iff_I2_J,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( top_to231829469nres_a
% 0.07/0.32 = ( refine2021053540t_unit @ R @ S ) )
% 0.07/0.32 = ( S = top_to177290092t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_fail_iff(2)
% 0.07/0.32 thf(fact_43_conc__fun__fail__iff_I2_J,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( top_to177290092t_unit
% 0.07/0.32 = ( refine944483349t_unit @ R @ S ) )
% 0.07/0.32 = ( S = top_to177290092t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_fail_iff(2)
% 0.07/0.32 thf(fact_44_conc__fun__fail__iff_I1_J,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( ( refine1441824853un_a_a @ R @ S )
% 0.07/0.32 = top_to231829469nres_a )
% 0.07/0.32 = ( S = top_to231829469nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_fail_iff(1)
% 0.07/0.32 thf(fact_45_conc__fun__fail__iff_I1_J,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( ( refine2043866374unit_a @ R @ S )
% 0.07/0.32 = top_to177290092t_unit )
% 0.07/0.32 = ( S = top_to231829469nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_fail_iff(1)
% 0.07/0.32 thf(fact_46_conc__fun__fail__iff_I1_J,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( ( refine2021053540t_unit @ R @ S )
% 0.07/0.32 = top_to231829469nres_a )
% 0.07/0.32 = ( S = top_to177290092t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_fail_iff(1)
% 0.07/0.32 thf(fact_47_conc__fun__fail__iff_I1_J,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( ( refine944483349t_unit @ R @ S )
% 0.07/0.32 = top_to177290092t_unit )
% 0.07/0.32 = ( S = top_to177290092t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_fail_iff(1)
% 0.07/0.32 thf(fact_48_conc__fun__FAIL,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a] :
% 0.07/0.32 ( ( refine1441824853un_a_a @ R @ top_to231829469nres_a )
% 0.07/0.32 = top_to231829469nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_FAIL
% 0.07/0.32 thf(fact_49_conc__fun__FAIL,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( refine2043866374unit_a @ R @ top_to231829469nres_a )
% 0.07/0.32 = top_to177290092t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_FAIL
% 0.07/0.32 thf(fact_50_conc__fun__FAIL,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( refine2021053540t_unit @ R @ top_to177290092t_unit )
% 0.07/0.32 = top_to231829469nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_FAIL
% 0.07/0.32 thf(fact_51_conc__fun__FAIL,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( refine944483349t_unit @ R @ top_to177290092t_unit )
% 0.07/0.32 = top_to177290092t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_FAIL
% 0.07/0.32 thf(fact_52_nres__order__simps_I20_J,axiom,
% 0.07/0.32 ! [X: product_unit,Y: product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X ) @ ( refine1420258419t_unit @ Y ) )
% 0.07/0.32 = ( X = Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(20)
% 0.07/0.32 thf(fact_53_nres__order__simps_I20_J,axiom,
% 0.07/0.32 ! [X: a,Y: a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine2063221604TURN_a @ Y ) )
% 0.07/0.32 = ( X = Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(20)
% 0.07/0.32 thf(fact_54_abs__fun__simps_I1_J,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a] :
% 0.07/0.32 ( ( refine1136779702un_a_a @ R @ top_to231829469nres_a )
% 0.07/0.32 = top_to231829469nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_simps(1)
% 0.07/0.32 thf(fact_55_abs__fun__simps_I1_J,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( refine341651653t_unit @ R @ top_to231829469nres_a )
% 0.07/0.32 = top_to177290092t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_simps(1)
% 0.07/0.32 thf(fact_56_abs__fun__simps_I1_J,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( refine364464487unit_a @ R @ top_to177290092t_unit )
% 0.07/0.32 = top_to231829469nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_simps(1)
% 0.07/0.32 thf(fact_57_abs__fun__simps_I1_J,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( refine838861686t_unit @ R @ top_to177290092t_unit )
% 0.07/0.32 = top_to177290092t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_simps(1)
% 0.07/0.32 thf(fact_58_nofail__simps_I3_J,axiom,
% 0.07/0.32 ! [X: product_unit] : ( refine579265252t_unit @ ( refine1420258419t_unit @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nofail_simps(3)
% 0.07/0.32 thf(fact_59_nofail__simps_I3_J,axiom,
% 0.07/0.32 ! [X: a] : ( refine412683989fail_a @ ( refine2063221604TURN_a @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nofail_simps(3)
% 0.07/0.32 thf(fact_60_inres__simps_I3_J,axiom,
% 0.07/0.32 ! [X: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ ( refine1420258419t_unit @ X ) )
% 0.07/0.32 = ( ^ [Y2: product_unit,Z: product_unit] : ( Y2 = Z )
% 0.07/0.32 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_simps(3)
% 0.07/0.32 thf(fact_61_inres__simps_I3_J,axiom,
% 0.07/0.32 ! [X: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ ( refine2063221604TURN_a @ X ) )
% 0.07/0.32 = ( ^ [Y2: a,Z: a] : ( Y2 = Z )
% 0.07/0.32 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_simps(3)
% 0.07/0.32 thf(fact_62_intro__nofail_I2_J,axiom,
% 0.07/0.32 ! [S: refine424419629nres_a] :
% 0.07/0.32 ( ( top_to231829469nres_a != S )
% 0.07/0.32 = ( refine412683989fail_a @ S ) ) ).
% 0.07/0.32
% 0.07/0.32 % intro_nofail(2)
% 0.07/0.32 thf(fact_63_intro__nofail_I2_J,axiom,
% 0.07/0.32 ! [S: refine787176636t_unit] :
% 0.07/0.32 ( ( top_to177290092t_unit != S )
% 0.07/0.32 = ( refine579265252t_unit @ S ) ) ).
% 0.07/0.32
% 0.07/0.32 % intro_nofail(2)
% 0.07/0.32 thf(fact_64_nres__order__simps_I3_J,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a] : ( ord_le519537037nres_a @ M @ top_to231829469nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(3)
% 0.07/0.32 thf(fact_65_nres__order__simps_I3_J,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit] : ( ord_le1051254044t_unit @ M @ top_to177290092t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(3)
% 0.07/0.32 thf(fact_66_nres__inequalities_I3_J,axiom,
% 0.07/0.32 ! [X: product_unit] :
% 0.07/0.32 ( top_to177290092t_unit
% 0.07/0.32 != ( refine1420258419t_unit @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_inequalities(3)
% 0.07/0.32 thf(fact_67_nres__inequalities_I3_J,axiom,
% 0.07/0.32 ! [X: a] :
% 0.07/0.32 ( top_to231829469nres_a
% 0.07/0.32 != ( refine2063221604TURN_a @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_inequalities(3)
% 0.07/0.32 thf(fact_68_abs__trans__additional_I1_J,axiom,
% 0.07/0.32 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_a,C: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A @ B )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ B ) @ C )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ A ) @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans_additional(1)
% 0.07/0.32 thf(fact_69_abs__trans__additional_I1_J,axiom,
% 0.07/0.32 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Pr1628433942t_unit,C: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A @ B )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ B ) @ C )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ A ) @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans_additional(1)
% 0.07/0.32 thf(fact_70_abs__trans__additional_I1_J,axiom,
% 0.07/0.32 ! [A: refine787176636t_unit,B: refine787176636t_unit,R: set_Pr1720557880unit_a,C: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A @ B )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ B ) @ C )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ A ) @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans_additional(1)
% 0.07/0.32 thf(fact_71_abs__trans__additional_I1_J,axiom,
% 0.07/0.32 ! [A: refine787176636t_unit,B: refine787176636t_unit,R: set_Pr451126599t_unit,C: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A @ B )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ B ) @ C )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ A ) @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans_additional(1)
% 0.07/0.32 thf(fact_72_conc__trans__additional_I1_J,axiom,
% 0.07/0.32 ! [A: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ B ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B @ C )
% 0.07/0.32 => ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans_additional(1)
% 0.07/0.32 thf(fact_73_conc__trans__additional_I1_J,axiom,
% 0.07/0.32 ! [A: refine787176636t_unit,R: set_Pr1720557880unit_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ R @ B ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B @ C )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ R @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans_additional(1)
% 0.07/0.32 thf(fact_74_conc__trans__additional_I1_J,axiom,
% 0.07/0.32 ! [A: refine424419629nres_a,R: set_Pr1628433942t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ R @ B ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.07/0.32 => ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ R @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans_additional(1)
% 0.07/0.32 thf(fact_75_conc__trans__additional_I1_J,axiom,
% 0.07/0.32 ! [A: refine787176636t_unit,R: set_Pr451126599t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ R @ B ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ R @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans_additional(1)
% 0.07/0.32 thf(fact_76_order__subst1,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_77_order__subst1,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,F: refine787176636t_unit > refine424419629nres_a,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_78_order__subst1,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,F: refine424419629nres_a > refine787176636t_unit,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_79_order__subst1,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_80_order__subst1,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_81_order__subst1,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,F: set_a > refine787176636t_unit,B2: set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_82_order__subst1,axiom,
% 0.07/0.32 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_83_order__subst1,axiom,
% 0.07/0.32 ! [A2: set_a,F: refine787176636t_unit > set_a,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_84_order__subst1,axiom,
% 0.07/0.32 ! [A2: set_a,F: set_a > set_a,B2: set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_85_order__subst1,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,F: set_Pr451126599t_unit > refine424419629nres_a,B2: set_Pr451126599t_unit,C2: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le2035129575t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: set_Pr451126599t_unit,Y3: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( ord_le2035129575t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_86_order__subst2,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_87_order__subst2,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_88_order__subst2,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_89_order__subst2,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_90_order__subst2,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_91_order__subst2,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_92_order__subst2,axiom,
% 0.07/0.32 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_93_order__subst2,axiom,
% 0.07/0.32 ! [A2: set_a,B2: set_a,F: set_a > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_94_order__subst2,axiom,
% 0.07/0.32 ! [A2: set_a,B2: set_a,F: set_a > set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_95_order__subst2,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_Pr451126599t_unit,C2: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le2035129575t_unit @ ( F @ B2 ) @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le2035129575t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le2035129575t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_96_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_97_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,F: refine424419629nres_a > refine787176636t_unit,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_98_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,F: refine787176636t_unit > refine424419629nres_a,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_99_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_100_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_101_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: set_a,F: refine787176636t_unit > set_a,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_102_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C2: set_a] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_103_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,F: set_a > refine787176636t_unit,B2: set_a,C2: set_a] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_104_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: set_a,F: set_a > set_a,B2: set_a,C2: set_a] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_105_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A2: set_Pr451126599t_unit,F: refine424419629nres_a > set_Pr451126599t_unit,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le2035129575t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le2035129575t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_106_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_107_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_108_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_109_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_110_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_111_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_112_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_113_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: set_a,B2: set_a,F: set_a > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_114_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: set_a,B2: set_a,F: set_a > set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: set_a,Y3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_115_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_Pr451126599t_unit,C2: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C2 )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le2035129575t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le2035129575t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_116_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_Pr451126599t_unit,Z: set_Pr451126599t_unit] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [X3: set_Pr451126599t_unit,Y4: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( ord_le2035129575t_unit @ X3 @ Y4 )
% 0.07/0.32 & ( ord_le2035129575t_unit @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_117_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_Pr1720557880unit_a,Z: set_Pr1720557880unit_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [X3: set_Pr1720557880unit_a,Y4: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( ord_le2070001880unit_a @ X3 @ Y4 )
% 0.07/0.32 & ( ord_le2070001880unit_a @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_118_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_Pr1628433942t_unit,Z: set_Pr1628433942t_unit] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [X3: set_Pr1628433942t_unit,Y4: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( ord_le1977877942t_unit @ X3 @ Y4 )
% 0.07/0.32 & ( ord_le1977877942t_unit @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_119_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [X3: set_Product_prod_a_a,Y4: set_Product_prod_a_a] :
% 0.07/0.32 ( ( ord_le1824328871od_a_a @ X3 @ Y4 )
% 0.07/0.32 & ( ord_le1824328871od_a_a @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_120_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [X3: set_a,Y4: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.07/0.32 & ( ord_less_eq_set_a @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_121_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: refine424419629nres_a,Z: refine424419629nres_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.07/0.32 & ( ord_le519537037nres_a @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_122_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: refine787176636t_unit,Z: refine787176636t_unit] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [X3: refine787176636t_unit,Y4: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X3 @ Y4 )
% 0.07/0.32 & ( ord_le1051254044t_unit @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_123_antisym,axiom,
% 0.07/0.32 ! [X: set_Pr451126599t_unit,Y: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( ord_le2035129575t_unit @ X @ Y )
% 0.07/0.32 => ( ( ord_le2035129575t_unit @ Y @ X )
% 0.07/0.32 => ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_124_antisym,axiom,
% 0.07/0.32 ! [X: set_Pr1720557880unit_a,Y: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( ord_le2070001880unit_a @ X @ Y )
% 0.07/0.32 => ( ( ord_le2070001880unit_a @ Y @ X )
% 0.07/0.32 => ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_125_antisym,axiom,
% 0.07/0.32 ! [X: set_Pr1628433942t_unit,Y: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( ord_le1977877942t_unit @ X @ Y )
% 0.07/0.32 => ( ( ord_le1977877942t_unit @ Y @ X )
% 0.07/0.32 => ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_126_antisym,axiom,
% 0.07/0.32 ! [X: set_Product_prod_a_a,Y: set_Product_prod_a_a] :
% 0.07/0.32 ( ( ord_le1824328871od_a_a @ X @ Y )
% 0.07/0.32 => ( ( ord_le1824328871od_a_a @ Y @ X )
% 0.07/0.32 => ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_127_antisym,axiom,
% 0.07/0.32 ! [X: set_a,Y: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ X @ Y )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ Y @ X )
% 0.07/0.32 => ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_128_antisym,axiom,
% 0.07/0.32 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X @ Y )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ Y @ X )
% 0.07/0.32 => ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_129_antisym,axiom,
% 0.07/0.32 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X @ Y )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ Y @ X )
% 0.07/0.32 => ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_130_eq__refl,axiom,
% 0.07/0.32 ! [X: set_Pr451126599t_unit,Y: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( X = Y )
% 0.07/0.32 => ( ord_le2035129575t_unit @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_131_eq__refl,axiom,
% 0.07/0.32 ! [X: set_Pr1720557880unit_a,Y: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( X = Y )
% 0.07/0.32 => ( ord_le2070001880unit_a @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_132_eq__refl,axiom,
% 0.07/0.32 ! [X: set_Pr1628433942t_unit,Y: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( X = Y )
% 0.07/0.32 => ( ord_le1977877942t_unit @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_133_eq__refl,axiom,
% 0.07/0.32 ! [X: set_Product_prod_a_a,Y: set_Product_prod_a_a] :
% 0.07/0.32 ( ( X = Y )
% 0.07/0.32 => ( ord_le1824328871od_a_a @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_134_eq__refl,axiom,
% 0.07/0.32 ! [X: set_a,Y: set_a] :
% 0.07/0.32 ( ( X = Y )
% 0.07/0.32 => ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_135_eq__refl,axiom,
% 0.07/0.32 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.07/0.32 ( ( X = Y )
% 0.07/0.32 => ( ord_le519537037nres_a @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_136_eq__refl,axiom,
% 0.07/0.32 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.07/0.32 ( ( X = Y )
% 0.07/0.32 => ( ord_le1051254044t_unit @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_137_order_Otrans,axiom,
% 0.07/0.32 ! [A2: set_Pr451126599t_unit,B2: set_Pr451126599t_unit,C2: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( ord_le2035129575t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le2035129575t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ord_le2035129575t_unit @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_138_order_Otrans,axiom,
% 0.07/0.32 ! [A2: set_Pr1720557880unit_a,B2: set_Pr1720557880unit_a,C2: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( ord_le2070001880unit_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le2070001880unit_a @ B2 @ C2 )
% 0.07/0.32 => ( ord_le2070001880unit_a @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_139_order_Otrans,axiom,
% 0.07/0.32 ! [A2: set_Pr1628433942t_unit,B2: set_Pr1628433942t_unit,C2: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( ord_le1977877942t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le1977877942t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ord_le1977877942t_unit @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_140_order_Otrans,axiom,
% 0.07/0.32 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.07/0.32 ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le1824328871od_a_a @ B2 @ C2 )
% 0.07/0.32 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_141_order_Otrans,axiom,
% 0.07/0.32 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.07/0.32 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_142_order_Otrans,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_143_order_Otrans,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_144_mem__Collect__eq,axiom,
% 0.07/0.32 ! [A2: produc971140967t_unit,P: produc971140967t_unit > $o] :
% 0.07/0.32 ( ( member1423014800t_unit @ A2 @ ( collec797068754t_unit @ P ) )
% 0.07/0.32 = ( P @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mem_Collect_eq
% 0.07/0.32 thf(fact_145_mem__Collect__eq,axiom,
% 0.07/0.32 ! [A2: produc884009688unit_a,P: produc884009688unit_a > $o] :
% 0.07/0.32 ( ( member1211819009unit_a @ A2 @ ( collec535904323unit_a @ P ) )
% 0.07/0.32 = ( P @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mem_Collect_eq
% 0.07/0.32 thf(fact_146_mem__Collect__eq,axiom,
% 0.07/0.32 ! [A2: produc1767851702t_unit,P: produc1767851702t_unit > $o] :
% 0.07/0.32 ( ( member2095661023t_unit @ A2 @ ( collec1419746337t_unit @ P ) )
% 0.07/0.32 = ( P @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mem_Collect_eq
% 0.07/0.32 thf(fact_147_mem__Collect__eq,axiom,
% 0.07/0.32 ! [A2: product_prod_a_a,P: product_prod_a_a > $o] :
% 0.07/0.32 ( ( member449909584od_a_a @ A2 @ ( collec645855634od_a_a @ P ) )
% 0.07/0.32 = ( P @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mem_Collect_eq
% 0.07/0.32 thf(fact_148_mem__Collect__eq,axiom,
% 0.07/0.32 ! [A2: product_unit,P: product_unit > $o] :
% 0.07/0.32 ( ( member_Product_unit @ A2 @ ( collect_Product_unit @ P ) )
% 0.07/0.32 = ( P @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mem_Collect_eq
% 0.07/0.32 thf(fact_149_mem__Collect__eq,axiom,
% 0.07/0.32 ! [A2: a,P: a > $o] :
% 0.07/0.32 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.07/0.32 = ( P @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mem_Collect_eq
% 0.07/0.32 thf(fact_150_Collect__mem__eq,axiom,
% 0.07/0.32 ! [A: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( collec797068754t_unit
% 0.07/0.32 @ ^ [X3: produc971140967t_unit] : ( member1423014800t_unit @ X3 @ A ) )
% 0.07/0.32 = A ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mem_eq
% 0.07/0.32 thf(fact_151_Collect__mem__eq,axiom,
% 0.07/0.32 ! [A: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( collec535904323unit_a
% 0.07/0.32 @ ^ [X3: produc884009688unit_a] : ( member1211819009unit_a @ X3 @ A ) )
% 0.07/0.32 = A ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mem_eq
% 0.07/0.32 thf(fact_152_Collect__mem__eq,axiom,
% 0.07/0.32 ! [A: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( collec1419746337t_unit
% 0.07/0.32 @ ^ [X3: produc1767851702t_unit] : ( member2095661023t_unit @ X3 @ A ) )
% 0.07/0.32 = A ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mem_eq
% 0.07/0.32 thf(fact_153_Collect__mem__eq,axiom,
% 0.07/0.32 ! [A: set_Product_prod_a_a] :
% 0.07/0.32 ( ( collec645855634od_a_a
% 0.07/0.32 @ ^ [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ A ) )
% 0.07/0.32 = A ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mem_eq
% 0.07/0.32 thf(fact_154_Collect__mem__eq,axiom,
% 0.07/0.32 ! [A: set_Product_unit] :
% 0.07/0.32 ( ( collect_Product_unit
% 0.07/0.32 @ ^ [X3: product_unit] : ( member_Product_unit @ X3 @ A ) )
% 0.07/0.32 = A ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mem_eq
% 0.07/0.32 thf(fact_155_Collect__mem__eq,axiom,
% 0.07/0.32 ! [A: set_a] :
% 0.07/0.32 ( ( collect_a
% 0.07/0.32 @ ^ [X3: a] : ( member_a @ X3 @ A ) )
% 0.07/0.32 = A ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mem_eq
% 0.07/0.32 thf(fact_156_Collect__cong,axiom,
% 0.07/0.32 ! [P: product_unit > $o,Q: product_unit > $o] :
% 0.07/0.32 ( ! [X2: product_unit] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 = ( Q @ X2 ) )
% 0.07/0.32 => ( ( collect_Product_unit @ P )
% 0.07/0.32 = ( collect_Product_unit @ Q ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_cong
% 0.07/0.32 thf(fact_157_Collect__cong,axiom,
% 0.07/0.32 ! [P: a > $o,Q: a > $o] :
% 0.07/0.32 ( ! [X2: a] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 = ( Q @ X2 ) )
% 0.07/0.32 => ( ( collect_a @ P )
% 0.07/0.32 = ( collect_a @ Q ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_cong
% 0.07/0.32 thf(fact_158_antisym__conv,axiom,
% 0.07/0.32 ! [Y: set_Pr451126599t_unit,X: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( ord_le2035129575t_unit @ Y @ X )
% 0.07/0.32 => ( ( ord_le2035129575t_unit @ X @ Y )
% 0.07/0.32 = ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_159_antisym__conv,axiom,
% 0.07/0.32 ! [Y: set_Pr1720557880unit_a,X: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( ord_le2070001880unit_a @ Y @ X )
% 0.07/0.32 => ( ( ord_le2070001880unit_a @ X @ Y )
% 0.07/0.32 = ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_160_antisym__conv,axiom,
% 0.07/0.32 ! [Y: set_Pr1628433942t_unit,X: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( ord_le1977877942t_unit @ Y @ X )
% 0.07/0.32 => ( ( ord_le1977877942t_unit @ X @ Y )
% 0.07/0.32 = ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_161_antisym__conv,axiom,
% 0.07/0.32 ! [Y: set_Product_prod_a_a,X: set_Product_prod_a_a] :
% 0.07/0.32 ( ( ord_le1824328871od_a_a @ Y @ X )
% 0.07/0.32 => ( ( ord_le1824328871od_a_a @ X @ Y )
% 0.07/0.32 = ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_162_antisym__conv,axiom,
% 0.07/0.32 ! [Y: set_a,X: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ Y @ X )
% 0.07/0.32 => ( ( ord_less_eq_set_a @ X @ Y )
% 0.07/0.32 = ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_163_antisym__conv,axiom,
% 0.07/0.32 ! [Y: refine424419629nres_a,X: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ Y @ X )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ X @ Y )
% 0.07/0.32 = ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_164_antisym__conv,axiom,
% 0.07/0.32 ! [Y: refine787176636t_unit,X: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ Y @ X )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ X @ Y )
% 0.07/0.32 = ( X = Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_165_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_Pr451126599t_unit,Z: set_Pr451126599t_unit] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [A3: set_Pr451126599t_unit,B3: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( ord_le2035129575t_unit @ A3 @ B3 )
% 0.07/0.32 & ( ord_le2035129575t_unit @ B3 @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_166_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_Pr1720557880unit_a,Z: set_Pr1720557880unit_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [A3: set_Pr1720557880unit_a,B3: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( ord_le2070001880unit_a @ A3 @ B3 )
% 0.07/0.32 & ( ord_le2070001880unit_a @ B3 @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_167_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_Pr1628433942t_unit,Z: set_Pr1628433942t_unit] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [A3: set_Pr1628433942t_unit,B3: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( ord_le1977877942t_unit @ A3 @ B3 )
% 0.07/0.32 & ( ord_le1977877942t_unit @ B3 @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_168_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [A3: set_Product_prod_a_a,B3: set_Product_prod_a_a] :
% 0.07/0.32 ( ( ord_le1824328871od_a_a @ A3 @ B3 )
% 0.07/0.32 & ( ord_le1824328871od_a_a @ B3 @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_169_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [A3: set_a,B3: set_a] :
% 0.07/0.32 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.07/0.32 & ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_170_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: refine424419629nres_a,Z: refine424419629nres_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 0.07/0.32 & ( ord_le519537037nres_a @ B3 @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_171_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: refine787176636t_unit,Z: refine787176636t_unit] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [A3: refine787176636t_unit,B3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A3 @ B3 )
% 0.07/0.32 & ( ord_le1051254044t_unit @ B3 @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_172_ord__eq__le__trans,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( A2 = B2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_trans
% 0.07/0.32 thf(fact_173_ord__eq__le__trans,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( A2 = B2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_trans
% 0.07/0.32 thf(fact_174_ord__le__eq__trans,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( B2 = C2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_trans
% 0.07/0.32 thf(fact_175_ord__le__eq__trans,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( B2 = C2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ A2 @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_trans
% 0.07/0.32 thf(fact_176_order__class_Oorder_Oantisym,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.07/0.32 => ( A2 = B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.antisym
% 0.07/0.32 thf(fact_177_order__class_Oorder_Oantisym,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit,B2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B2 @ A2 )
% 0.07/0.32 => ( A2 = B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.antisym
% 0.07/0.32 thf(fact_178_order__trans,axiom,
% 0.07/0.32 ! [X: refine424419629nres_a,Y: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X @ Y )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ Y @ Z2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ X @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_trans
% 0.07/0.32 thf(fact_179_order__trans,axiom,
% 0.07/0.32 ! [X: refine787176636t_unit,Y: refine787176636t_unit,Z2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X @ Y )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ Y @ Z2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ X @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_trans
% 0.07/0.32 thf(fact_180_dual__order_Orefl,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ A2 ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.refl
% 0.07/0.32 thf(fact_181_dual__order_Orefl,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit] : ( ord_le1051254044t_unit @ A2 @ A2 ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.refl
% 0.07/0.32 thf(fact_182_dual__order_Otrans,axiom,
% 0.07/0.32 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ C2 @ B2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ C2 @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.trans
% 0.07/0.32 thf(fact_183_dual__order_Otrans,axiom,
% 0.07/0.32 ! [B2: refine787176636t_unit,A2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ B2 @ A2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ C2 @ B2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ C2 @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.trans
% 0.07/0.32 thf(fact_184_top__greatest,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ top_to231829469nres_a ) ).
% 0.07/0.32
% 0.07/0.32 % top_greatest
% 0.07/0.32 thf(fact_185_top__greatest,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit] : ( ord_le1051254044t_unit @ A2 @ top_to177290092t_unit ) ).
% 0.07/0.32
% 0.07/0.32 % top_greatest
% 0.07/0.32 thf(fact_186_pwD1,axiom,
% 0.07/0.32 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ S @ S2 )
% 0.07/0.32 => ( ( refine412683989fail_a @ S2 )
% 0.07/0.32 => ( refine412683989fail_a @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pwD1
% 0.07/0.32 thf(fact_187_pwD1,axiom,
% 0.07/0.32 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ S @ S2 )
% 0.07/0.32 => ( ( refine579265252t_unit @ S2 )
% 0.07/0.32 => ( refine579265252t_unit @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pwD1
% 0.07/0.32 thf(fact_188_pwD2,axiom,
% 0.07/0.32 ! [S: refine424419629nres_a,S2: refine424419629nres_a,X: a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ S @ S2 )
% 0.07/0.32 => ( ( refine1001002027nres_a @ S @ X )
% 0.07/0.32 => ( refine1001002027nres_a @ S2 @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pwD2
% 0.07/0.32 thf(fact_189_pwD2,axiom,
% 0.07/0.32 ! [S: refine787176636t_unit,S2: refine787176636t_unit,X: product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ S @ S2 )
% 0.07/0.32 => ( ( refine558004794t_unit @ S @ X )
% 0.07/0.32 => ( refine558004794t_unit @ S2 @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pwD2
% 0.07/0.32 thf(fact_190_dual__order_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: refine424419629nres_a,Z: refine424419629nres_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ B3 @ A3 )
% 0.07/0.32 & ( ord_le519537037nres_a @ A3 @ B3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.eq_iff
% 0.07/0.32 thf(fact_191_dual__order_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: refine787176636t_unit,Z: refine787176636t_unit] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [A3: refine787176636t_unit,B3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ B3 @ A3 )
% 0.07/0.32 & ( ord_le1051254044t_unit @ A3 @ B3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.eq_iff
% 0.07/0.32 thf(fact_192_dual__order_Oantisym,axiom,
% 0.07/0.32 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.07/0.32 => ( A2 = B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.antisym
% 0.07/0.32 thf(fact_193_dual__order_Oantisym,axiom,
% 0.07/0.32 ! [B2: refine787176636t_unit,A2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ B2 @ A2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.07/0.32 => ( A2 = B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.antisym
% 0.07/0.32 thf(fact_194_pw__eqI,axiom,
% 0.07/0.32 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.07/0.32 ( ( ( refine412683989fail_a @ S )
% 0.07/0.32 = ( refine412683989fail_a @ S2 ) )
% 0.07/0.32 => ( ! [X2: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ S @ X2 )
% 0.07/0.32 = ( refine1001002027nres_a @ S2 @ X2 ) )
% 0.07/0.32 => ( S = S2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_eqI
% 0.07/0.32 thf(fact_195_pw__eqI,axiom,
% 0.07/0.32 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.07/0.32 ( ( ( refine579265252t_unit @ S )
% 0.07/0.32 = ( refine579265252t_unit @ S2 ) )
% 0.07/0.32 => ( ! [X2: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ S @ X2 )
% 0.07/0.32 = ( refine558004794t_unit @ S2 @ X2 ) )
% 0.07/0.32 => ( S = S2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_eqI
% 0.07/0.32 thf(fact_196_pw__leI,axiom,
% 0.07/0.32 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( ( refine412683989fail_a @ S2 )
% 0.07/0.32 => ( ( refine412683989fail_a @ S )
% 0.07/0.32 & ! [X2: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ S @ X2 )
% 0.07/0.32 => ( refine1001002027nres_a @ S2 @ X2 ) ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ S @ S2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_leI
% 0.07/0.32 thf(fact_197_pw__leI,axiom,
% 0.07/0.32 ! [S2: refine787176636t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( ( refine579265252t_unit @ S2 )
% 0.07/0.32 => ( ( refine579265252t_unit @ S )
% 0.07/0.32 & ! [X2: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ S @ X2 )
% 0.07/0.32 => ( refine558004794t_unit @ S2 @ X2 ) ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ S @ S2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_leI
% 0.07/0.32 thf(fact_198_pw__leI_H,axiom,
% 0.07/0.32 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( ( refine412683989fail_a @ S2 )
% 0.07/0.32 => ( refine412683989fail_a @ S ) )
% 0.07/0.32 => ( ! [X2: a] :
% 0.07/0.32 ( ( refine412683989fail_a @ S2 )
% 0.07/0.32 => ( ( refine1001002027nres_a @ S @ X2 )
% 0.07/0.32 => ( refine1001002027nres_a @ S2 @ X2 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ S @ S2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_leI'
% 0.07/0.32 thf(fact_199_pw__leI_H,axiom,
% 0.07/0.32 ! [S2: refine787176636t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( ( refine579265252t_unit @ S2 )
% 0.07/0.32 => ( refine579265252t_unit @ S ) )
% 0.07/0.32 => ( ! [X2: product_unit] :
% 0.07/0.32 ( ( refine579265252t_unit @ S2 )
% 0.07/0.32 => ( ( refine558004794t_unit @ S @ X2 )
% 0.07/0.32 => ( refine558004794t_unit @ S2 @ X2 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ S @ S2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_leI'
% 0.07/0.32 thf(fact_200_abs__trans,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a,C: refine424419629nres_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ C ) @ B )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R2 @ B ) @ A )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R2 @ ( refine1136779702un_a_a @ R @ C ) ) @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans
% 0.07/0.32 thf(fact_201_abs__trans,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a,C: refine424419629nres_a,B: refine424419629nres_a,R2: set_Pr1628433942t_unit,A: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ C ) @ B )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R2 @ B ) @ A )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R2 @ ( refine1136779702un_a_a @ R @ C ) ) @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans
% 0.07/0.32 thf(fact_202_abs__trans,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit,C: refine424419629nres_a,B: refine787176636t_unit,R2: set_Pr1720557880unit_a,A: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ C ) @ B )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R2 @ B ) @ A )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine364464487unit_a @ R2 @ ( refine341651653t_unit @ R @ C ) ) @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans
% 0.07/0.32 thf(fact_203_abs__trans,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit,C: refine424419629nres_a,B: refine787176636t_unit,R2: set_Pr451126599t_unit,A: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ C ) @ B )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R2 @ B ) @ A )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R2 @ ( refine341651653t_unit @ R @ C ) ) @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans
% 0.07/0.32 thf(fact_204_abs__trans,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a,C: refine787176636t_unit,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ C ) @ B )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R2 @ B ) @ A )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R2 @ ( refine364464487unit_a @ R @ C ) ) @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans
% 0.07/0.32 thf(fact_205_abs__trans,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a,C: refine787176636t_unit,B: refine424419629nres_a,R2: set_Pr1628433942t_unit,A: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ C ) @ B )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R2 @ B ) @ A )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R2 @ ( refine364464487unit_a @ R @ C ) ) @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans
% 0.07/0.32 thf(fact_206_abs__trans,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit,C: refine787176636t_unit,B: refine787176636t_unit,R2: set_Pr1720557880unit_a,A: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ C ) @ B )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R2 @ B ) @ A )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine364464487unit_a @ R2 @ ( refine838861686t_unit @ R @ C ) ) @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans
% 0.07/0.32 thf(fact_207_abs__trans,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit,C: refine787176636t_unit,B: refine787176636t_unit,R2: set_Pr451126599t_unit,A: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ C ) @ B )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R2 @ B ) @ A )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R2 @ ( refine838861686t_unit @ R @ C ) ) @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_trans
% 0.07/0.32 thf(fact_208_inres__def,axiom,
% 0.07/0.32 ( refine558004794t_unit
% 0.07/0.32 = ( ^ [S3: refine787176636t_unit,X3: product_unit] : ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ S3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_def
% 0.07/0.32 thf(fact_209_inres__def,axiom,
% 0.07/0.32 ( refine1001002027nres_a
% 0.07/0.32 = ( ^ [S3: refine424419629nres_a,X3: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ S3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_def
% 0.07/0.32 thf(fact_210_pw__eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: refine424419629nres_a,Z: refine424419629nres_a] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.07/0.32 ( ( ( refine412683989fail_a @ S3 )
% 0.07/0.32 = ( refine412683989fail_a @ S4 ) )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ S3 @ X3 )
% 0.07/0.32 = ( refine1001002027nres_a @ S4 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_eq_iff
% 0.07/0.32 thf(fact_211_pw__eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y2: refine787176636t_unit,Z: refine787176636t_unit] : ( Y2 = Z ) )
% 0.07/0.32 = ( ^ [S3: refine787176636t_unit,S4: refine787176636t_unit] :
% 0.07/0.32 ( ( ( refine579265252t_unit @ S3 )
% 0.07/0.32 = ( refine579265252t_unit @ S4 ) )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ S3 @ X3 )
% 0.07/0.32 = ( refine558004794t_unit @ S4 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_eq_iff
% 0.07/0.32 thf(fact_212_pw__le__iff,axiom,
% 0.07/0.32 ( ord_le519537037nres_a
% 0.07/0.32 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.07/0.32 ( ( refine412683989fail_a @ S4 )
% 0.07/0.32 => ( ( refine412683989fail_a @ S3 )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ S3 @ X3 )
% 0.07/0.32 => ( refine1001002027nres_a @ S4 @ X3 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_le_iff
% 0.07/0.32 thf(fact_213_pw__le__iff,axiom,
% 0.07/0.32 ( ord_le1051254044t_unit
% 0.07/0.32 = ( ^ [S3: refine787176636t_unit,S4: refine787176636t_unit] :
% 0.07/0.32 ( ( refine579265252t_unit @ S4 )
% 0.07/0.32 => ( ( refine579265252t_unit @ S3 )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ S3 @ X3 )
% 0.07/0.32 => ( refine558004794t_unit @ S4 @ X3 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_le_iff
% 0.07/0.32 thf(fact_214_conc__trans,axiom,
% 0.07/0.32 ! [C: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ B ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R2 @ A ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ ( refine1441824853un_a_a @ R2 @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans
% 0.07/0.32 thf(fact_215_conc__trans,axiom,
% 0.07/0.32 ! [C: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,R2: set_Pr1628433942t_unit,A: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ B ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B @ ( refine2021053540t_unit @ R2 @ A ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ ( refine2021053540t_unit @ R2 @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans
% 0.07/0.32 thf(fact_216_conc__trans,axiom,
% 0.07/0.32 ! [C: refine787176636t_unit,R: set_Pr1720557880unit_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ R @ B ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R2 @ A ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ R @ ( refine1441824853un_a_a @ R2 @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans
% 0.07/0.32 thf(fact_217_conc__trans,axiom,
% 0.07/0.32 ! [C: refine787176636t_unit,R: set_Pr1720557880unit_a,B: refine424419629nres_a,R2: set_Pr1628433942t_unit,A: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ R @ B ) )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ B @ ( refine2021053540t_unit @ R2 @ A ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ R @ ( refine2021053540t_unit @ R2 @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans
% 0.07/0.32 thf(fact_218_conc__trans,axiom,
% 0.07/0.32 ! [C: refine424419629nres_a,R: set_Pr1628433942t_unit,B: refine787176636t_unit,R2: set_Pr1720557880unit_a,A: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ R @ B ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B @ ( refine2043866374unit_a @ R2 @ A ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ R @ ( refine2043866374unit_a @ R2 @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans
% 0.07/0.32 thf(fact_219_conc__trans,axiom,
% 0.07/0.32 ! [C: refine424419629nres_a,R: set_Pr1628433942t_unit,B: refine787176636t_unit,R2: set_Pr451126599t_unit,A: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ R @ B ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B @ ( refine944483349t_unit @ R2 @ A ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ R @ ( refine944483349t_unit @ R2 @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans
% 0.07/0.32 thf(fact_220_conc__trans,axiom,
% 0.07/0.32 ! [C: refine787176636t_unit,R: set_Pr451126599t_unit,B: refine787176636t_unit,R2: set_Pr1720557880unit_a,A: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ R @ B ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B @ ( refine2043866374unit_a @ R2 @ A ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ R @ ( refine2043866374unit_a @ R2 @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans
% 0.07/0.32 thf(fact_221_conc__trans,axiom,
% 0.07/0.32 ! [C: refine787176636t_unit,R: set_Pr451126599t_unit,B: refine787176636t_unit,R2: set_Pr451126599t_unit,A: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ R @ B ) )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ B @ ( refine944483349t_unit @ R2 @ A ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ R @ ( refine944483349t_unit @ R2 @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_trans
% 0.07/0.32 thf(fact_222_le__nofailI,axiom,
% 0.07/0.32 ! [M2: refine424419629nres_a,M: refine424419629nres_a] :
% 0.07/0.32 ( ( ( refine412683989fail_a @ M2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ M @ M2 ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ M @ M2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_nofailI
% 0.07/0.32 thf(fact_223_le__nofailI,axiom,
% 0.07/0.32 ! [M2: refine787176636t_unit,M: refine787176636t_unit] :
% 0.07/0.32 ( ( ( refine579265252t_unit @ M2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ M @ M2 ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ M @ M2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_nofailI
% 0.07/0.32 thf(fact_224_top_Oextremum__unique,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A2 )
% 0.07/0.32 = ( A2 = top_to231829469nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % top.extremum_unique
% 0.07/0.32 thf(fact_225_top_Oextremum__unique,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A2 )
% 0.07/0.32 = ( A2 = top_to177290092t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % top.extremum_unique
% 0.07/0.32 thf(fact_226_pw__bind__leI,axiom,
% 0.07/0.32 ! [S: refine424419629nres_a,M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.07/0.32 ( ( ( refine412683989fail_a @ S )
% 0.07/0.32 => ( refine412683989fail_a @ M ) )
% 0.07/0.32 => ( ! [X2: a] :
% 0.07/0.32 ( ( refine412683989fail_a @ M )
% 0.07/0.32 => ( ( refine1001002027nres_a @ M @ X2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ S ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_leI
% 0.07/0.32 thf(fact_227_pw__bind__leI,axiom,
% 0.07/0.32 ! [S: refine787176636t_unit,M: refine424419629nres_a,F: a > refine787176636t_unit] :
% 0.07/0.32 ( ( ( refine579265252t_unit @ S )
% 0.07/0.32 => ( refine412683989fail_a @ M ) )
% 0.07/0.32 => ( ! [X2: a] :
% 0.07/0.32 ( ( refine412683989fail_a @ M )
% 0.07/0.32 => ( ( refine1001002027nres_a @ M @ X2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ S ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M @ F ) @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_leI
% 0.07/0.32 thf(fact_228_pw__bind__leI,axiom,
% 0.07/0.32 ! [S: refine424419629nres_a,M: refine787176636t_unit,F: product_unit > refine424419629nres_a] :
% 0.07/0.32 ( ( ( refine412683989fail_a @ S )
% 0.07/0.32 => ( refine579265252t_unit @ M ) )
% 0.07/0.32 => ( ! [X2: product_unit] :
% 0.07/0.32 ( ( refine579265252t_unit @ M )
% 0.07/0.32 => ( ( refine558004794t_unit @ M @ X2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ S ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine119808503unit_a @ M @ F ) @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_leI
% 0.07/0.32 thf(fact_229_pw__bind__leI,axiom,
% 0.07/0.32 ! [S: refine787176636t_unit,M: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 0.07/0.32 ( ( ( refine579265252t_unit @ S )
% 0.07/0.32 => ( refine579265252t_unit @ M ) )
% 0.07/0.32 => ( ! [X2: product_unit] :
% 0.07/0.32 ( ( refine579265252t_unit @ M )
% 0.07/0.32 => ( ( refine558004794t_unit @ M @ X2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ S ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M @ F ) @ S ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_leI
% 0.07/0.32 thf(fact_230_top_Oextremum__uniqueI,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A2 )
% 0.07/0.32 => ( A2 = top_to231829469nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % top.extremum_uniqueI
% 0.07/0.32 thf(fact_231_top_Oextremum__uniqueI,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A2 )
% 0.07/0.32 => ( A2 = top_to177290092t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % top.extremum_uniqueI
% 0.07/0.32 thf(fact_232_pw__bind__le__iff,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a,F: a > refine424419629nres_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ S )
% 0.07/0.32 = ( ( ( refine412683989fail_a @ S )
% 0.07/0.32 => ( refine412683989fail_a @ M ) )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( ( refine412683989fail_a @ M )
% 0.07/0.32 & ( refine1001002027nres_a @ M @ X3 ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X3 ) @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_le_iff
% 0.07/0.32 thf(fact_233_pw__bind__le__iff,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a,F: a > refine787176636t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M @ F ) @ S )
% 0.07/0.32 = ( ( ( refine579265252t_unit @ S )
% 0.07/0.32 => ( refine412683989fail_a @ M ) )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( ( refine412683989fail_a @ M )
% 0.07/0.32 & ( refine1001002027nres_a @ M @ X3 ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_le_iff
% 0.07/0.32 thf(fact_234_pw__bind__le__iff,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit,F: product_unit > refine424419629nres_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine119808503unit_a @ M @ F ) @ S )
% 0.07/0.32 = ( ( ( refine412683989fail_a @ S )
% 0.07/0.32 => ( refine579265252t_unit @ M ) )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( ( refine579265252t_unit @ M )
% 0.07/0.32 & ( refine558004794t_unit @ M @ X3 ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X3 ) @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_le_iff
% 0.07/0.32 thf(fact_235_pw__bind__le__iff,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit,F: product_unit > refine787176636t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M @ F ) @ S )
% 0.07/0.32 = ( ( ( refine579265252t_unit @ S )
% 0.07/0.32 => ( refine579265252t_unit @ M ) )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( ( refine579265252t_unit @ M )
% 0.07/0.32 & ( refine558004794t_unit @ M @ X3 ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ S ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_le_iff
% 0.07/0.32 thf(fact_236_pw__conc__nofail,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( refine412683989fail_a @ ( refine1441824853un_a_a @ R @ S ) )
% 0.07/0.32 = ( refine412683989fail_a @ S ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_conc_nofail
% 0.07/0.32 thf(fact_237_pw__conc__nofail,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 0.07/0.32 ( ( refine579265252t_unit @ ( refine2043866374unit_a @ R @ S ) )
% 0.07/0.32 = ( refine412683989fail_a @ S ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_conc_nofail
% 0.07/0.32 thf(fact_238_pw__conc__nofail,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( refine412683989fail_a @ ( refine2021053540t_unit @ R @ S ) )
% 0.07/0.32 = ( refine579265252t_unit @ S ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_conc_nofail
% 0.07/0.32 thf(fact_239_pw__conc__nofail,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.07/0.32 ( ( refine579265252t_unit @ ( refine944483349t_unit @ R @ S ) )
% 0.07/0.32 = ( refine579265252t_unit @ S ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_conc_nofail
% 0.07/0.32 thf(fact_240_not__nofail__inres,axiom,
% 0.07/0.32 ! [S: refine424419629nres_a,X: a] :
% 0.07/0.32 ( ~ ( refine412683989fail_a @ S )
% 0.07/0.32 => ( refine1001002027nres_a @ S @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % not_nofail_inres
% 0.07/0.32 thf(fact_241_not__nofail__inres,axiom,
% 0.07/0.32 ! [S: refine787176636t_unit,X: product_unit] :
% 0.07/0.32 ( ~ ( refine579265252t_unit @ S )
% 0.07/0.32 => ( refine558004794t_unit @ S @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % not_nofail_inres
% 0.07/0.32 thf(fact_242_bot_Oextremum__uniqueI,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ bot_bo529555393nres_a )
% 0.07/0.32 => ( A2 = bot_bo529555393nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot.extremum_uniqueI
% 0.07/0.32 thf(fact_243_bot_Oextremum__uniqueI,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ bot_bo658782032t_unit )
% 0.07/0.32 => ( A2 = bot_bo658782032t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot.extremum_uniqueI
% 0.07/0.32 thf(fact_244_bot_Oextremum__unique,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ A2 @ bot_bo529555393nres_a )
% 0.07/0.32 = ( A2 = bot_bo529555393nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot.extremum_unique
% 0.07/0.32 thf(fact_245_bot_Oextremum__unique,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ A2 @ bot_bo658782032t_unit )
% 0.07/0.32 = ( A2 = bot_bo658782032t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot.extremum_unique
% 0.07/0.32 thf(fact_246_bot_Oextremum,axiom,
% 0.07/0.32 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A2 ) ).
% 0.07/0.32
% 0.07/0.32 % bot.extremum
% 0.07/0.32 thf(fact_247_bot_Oextremum,axiom,
% 0.07/0.32 ! [A2: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ A2 ) ).
% 0.07/0.32
% 0.07/0.32 % bot.extremum
% 0.07/0.32 thf(fact_248_pw__bind__nofail,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.07/0.32 ( ( refine412683989fail_a @ ( refine436832838nd_a_a @ M @ F ) )
% 0.07/0.32 = ( ( refine412683989fail_a @ M )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ M @ X3 )
% 0.07/0.32 => ( refine412683989fail_a @ ( F @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_nofail
% 0.07/0.32 thf(fact_249_pw__bind__nofail,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a,F: a > refine787176636t_unit] :
% 0.07/0.32 ( ( refine579265252t_unit @ ( refine96995669t_unit @ M @ F ) )
% 0.07/0.32 = ( ( refine412683989fail_a @ M )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ M @ X3 )
% 0.07/0.32 => ( refine579265252t_unit @ ( F @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_nofail
% 0.07/0.32 thf(fact_250_pw__bind__nofail,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit,F: product_unit > refine424419629nres_a] :
% 0.07/0.32 ( ( refine412683989fail_a @ ( refine119808503unit_a @ M @ F ) )
% 0.07/0.32 = ( ( refine579265252t_unit @ M )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ M @ X3 )
% 0.07/0.32 => ( refine412683989fail_a @ ( F @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_nofail
% 0.07/0.32 thf(fact_251_pw__bind__nofail,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 0.07/0.32 ( ( refine579265252t_unit @ ( refine681446406t_unit @ M @ F ) )
% 0.07/0.32 = ( ( refine579265252t_unit @ M )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ M @ X3 )
% 0.07/0.32 => ( refine579265252t_unit @ ( F @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_bind_nofail
% 0.07/0.32 thf(fact_252_bind__cong,axiom,
% 0.07/0.32 ! [M3: refine787176636t_unit,M4: refine787176636t_unit,F: product_unit > refine424419629nres_a,F2: product_unit > refine424419629nres_a] :
% 0.07/0.32 ( ( M3 = M4 )
% 0.07/0.32 => ( ! [X2: product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X2 ) @ M4 )
% 0.07/0.32 => ( ( F @ X2 )
% 0.07/0.32 = ( F2 @ X2 ) ) )
% 0.07/0.32 => ( ( refine119808503unit_a @ M3 @ F )
% 0.07/0.32 = ( refine119808503unit_a @ M4 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % bind_cong
% 0.07/0.32 thf(fact_253_bind__cong,axiom,
% 0.07/0.32 ! [M3: refine787176636t_unit,M4: refine787176636t_unit,F: product_unit > refine787176636t_unit,F2: product_unit > refine787176636t_unit] :
% 0.07/0.32 ( ( M3 = M4 )
% 0.07/0.32 => ( ! [X2: product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X2 ) @ M4 )
% 0.07/0.32 => ( ( F @ X2 )
% 0.07/0.32 = ( F2 @ X2 ) ) )
% 0.07/0.32 => ( ( refine681446406t_unit @ M3 @ F )
% 0.07/0.32 = ( refine681446406t_unit @ M4 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % bind_cong
% 0.07/0.32 thf(fact_254_bind__cong,axiom,
% 0.07/0.32 ! [M3: refine424419629nres_a,M4: refine424419629nres_a,F: a > refine424419629nres_a,F2: a > refine424419629nres_a] :
% 0.07/0.32 ( ( M3 = M4 )
% 0.07/0.32 => ( ! [X2: a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M4 )
% 0.07/0.32 => ( ( F @ X2 )
% 0.07/0.32 = ( F2 @ X2 ) ) )
% 0.07/0.32 => ( ( refine436832838nd_a_a @ M3 @ F )
% 0.07/0.32 = ( refine436832838nd_a_a @ M4 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % bind_cong
% 0.07/0.32 thf(fact_255_bind__cong,axiom,
% 0.07/0.32 ! [M3: refine424419629nres_a,M4: refine424419629nres_a,F: a > refine787176636t_unit,F2: a > refine787176636t_unit] :
% 0.07/0.32 ( ( M3 = M4 )
% 0.07/0.32 => ( ! [X2: a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M4 )
% 0.07/0.32 => ( ( F @ X2 )
% 0.07/0.32 = ( F2 @ X2 ) ) )
% 0.07/0.32 => ( ( refine96995669t_unit @ M3 @ F )
% 0.07/0.32 = ( refine96995669t_unit @ M4 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % bind_cong
% 0.07/0.32 thf(fact_256_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit,M2: refine787176636t_unit,F: product_unit > refine424419629nres_a,F2: product_unit > refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ M @ M2 )
% 0.07/0.32 => ( ! [X2: product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X2 ) @ M )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F2 @ X2 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine119808503unit_a @ M @ F ) @ ( refine119808503unit_a @ M2 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.07/0.32 thf(fact_257_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit,M2: refine787176636t_unit,F: product_unit > refine787176636t_unit,F2: product_unit > refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ M @ M2 )
% 0.07/0.32 => ( ! [X2: product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X2 ) @ M )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F2 @ X2 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M @ F ) @ ( refine681446406t_unit @ M2 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.07/0.32 thf(fact_258_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a,M2: refine424419629nres_a,F: a > refine424419629nres_a,F2: a > refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ M @ M2 )
% 0.07/0.32 => ( ! [X2: a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F2 @ X2 ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ ( refine436832838nd_a_a @ M2 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.07/0.32 thf(fact_259_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a,M2: refine424419629nres_a,F: a > refine787176636t_unit,F2: a > refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ M @ M2 )
% 0.07/0.32 => ( ! [X2: a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F2 @ X2 ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M @ F ) @ ( refine96995669t_unit @ M2 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.07/0.32 thf(fact_260_nres__inequalities_I2_J,axiom,
% 0.07/0.32 top_to177290092t_unit != bot_bo658782032t_unit ).
% 0.07/0.32
% 0.07/0.32 % nres_inequalities(2)
% 0.07/0.32 thf(fact_261_nres__inequalities_I2_J,axiom,
% 0.07/0.32 top_to231829469nres_a != bot_bo529555393nres_a ).
% 0.07/0.32
% 0.07/0.32 % nres_inequalities(2)
% 0.07/0.32 thf(fact_262_nres__inequalities_I4_J,axiom,
% 0.07/0.32 bot_bo658782032t_unit != top_to177290092t_unit ).
% 0.07/0.32
% 0.07/0.32 % nres_inequalities(4)
% 0.07/0.32 thf(fact_263_nres__inequalities_I4_J,axiom,
% 0.07/0.32 bot_bo529555393nres_a != top_to231829469nres_a ).
% 0.07/0.32
% 0.07/0.32 % nres_inequalities(4)
% 0.07/0.32 thf(fact_264_order__mono__setup_Orefl,axiom,
% 0.07/0.32 ! [X: refine424419629nres_a] : ( ord_le519537037nres_a @ X @ X ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.refl
% 0.07/0.32 thf(fact_265_order__mono__setup_Orefl,axiom,
% 0.07/0.32 ! [X: refine787176636t_unit] : ( ord_le1051254044t_unit @ X @ X ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.refl
% 0.07/0.32 thf(fact_266_nf__inres__def,axiom,
% 0.07/0.32 ( refine1312857699nres_a
% 0.07/0.32 = ( ^ [M5: refine424419629nres_a,X3: a] :
% 0.07/0.32 ( ( refine412683989fail_a @ M5 )
% 0.07/0.32 & ( refine1001002027nres_a @ M5 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % nf_inres_def
% 0.07/0.32 thf(fact_267_nf__inres__def,axiom,
% 0.07/0.32 ( refine983493746t_unit
% 0.07/0.32 = ( ^ [M5: refine787176636t_unit,X3: product_unit] :
% 0.07/0.32 ( ( refine579265252t_unit @ M5 )
% 0.07/0.32 & ( refine558004794t_unit @ M5 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % nf_inres_def
% 0.07/0.32 thf(fact_268_meta__le__everything__if__top,axiom,
% 0.07/0.32 ! [M3: refine424419629nres_a,X: refine424419629nres_a] :
% 0.07/0.32 ( ( M3 = top_to231829469nres_a )
% 0.07/0.32 => ( ord_le519537037nres_a @ X @ M3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % meta_le_everything_if_top
% 0.07/0.32 thf(fact_269_meta__le__everything__if__top,axiom,
% 0.07/0.32 ! [M3: refine787176636t_unit,X: refine787176636t_unit] :
% 0.07/0.32 ( ( M3 = top_to177290092t_unit )
% 0.07/0.32 => ( ord_le1051254044t_unit @ X @ M3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % meta_le_everything_if_top
% 0.07/0.32 thf(fact_270_pw__flat__le__iff,axiom,
% 0.07/0.32 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.07/0.32 ( ( partia906949161nres_a @ bot_bo529555393nres_a @ S @ S2 )
% 0.07/0.32 = ( ? [X4: a] : ( refine1001002027nres_a @ S @ X4 )
% 0.07/0.32 => ( ( ( refine412683989fail_a @ S )
% 0.07/0.32 = ( refine412683989fail_a @ S2 ) )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ S @ X3 )
% 0.07/0.32 = ( refine1001002027nres_a @ S2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_flat_le_iff
% 0.07/0.32 thf(fact_271_pw__flat__le__iff,axiom,
% 0.07/0.32 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.07/0.32 ( ( partia1658438072t_unit @ bot_bo658782032t_unit @ S @ S2 )
% 0.07/0.32 = ( ? [X4: product_unit] : ( refine558004794t_unit @ S @ X4 )
% 0.07/0.32 => ( ( ( refine579265252t_unit @ S )
% 0.07/0.32 = ( refine579265252t_unit @ S2 ) )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ S @ X3 )
% 0.07/0.32 = ( refine558004794t_unit @ S2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_flat_le_iff
% 0.07/0.32 thf(fact_272_pw__abs__inres,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a,M: refine424419629nres_a,A2: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ ( refine1136779702un_a_a @ R @ M ) @ A2 )
% 0.07/0.32 = ( ( refine412683989fail_a @ ( refine1136779702un_a_a @ R @ M ) )
% 0.07/0.32 => ? [C3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ M @ C3 )
% 0.07/0.32 & ( member449909584od_a_a @ ( product_Pair_a_a @ C3 @ A2 ) @ R ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_abs_inres
% 0.07/0.32 thf(fact_273_pw__abs__inres,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit,M: refine424419629nres_a,A2: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ ( refine341651653t_unit @ R @ M ) @ A2 )
% 0.07/0.32 = ( ( refine579265252t_unit @ ( refine341651653t_unit @ R @ M ) )
% 0.07/0.32 => ? [C3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ M @ C3 )
% 0.07/0.32 & ( member2095661023t_unit @ ( produc1776699686t_unit @ C3 @ A2 ) @ R ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_abs_inres
% 0.07/0.32 thf(fact_274_pw__abs__inres,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a,M: refine787176636t_unit,A2: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ ( refine364464487unit_a @ R @ M ) @ A2 )
% 0.07/0.32 = ( ( refine412683989fail_a @ ( refine364464487unit_a @ R @ M ) )
% 0.07/0.32 => ? [C3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ M @ C3 )
% 0.07/0.32 & ( member1211819009unit_a @ ( produc1799512520unit_a @ C3 @ A2 ) @ R ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_abs_inres
% 0.07/0.32 thf(fact_275_pw__abs__inres,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit,M: refine787176636t_unit,A2: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ ( refine838861686t_unit @ R @ M ) @ A2 )
% 0.07/0.32 = ( ( refine579265252t_unit @ ( refine838861686t_unit @ R @ M ) )
% 0.07/0.32 => ? [C3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ M @ C3 )
% 0.07/0.32 & ( member1423014800t_unit @ ( produc1076565719t_unit @ C3 @ A2 ) @ R ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_abs_inres
% 0.07/0.32 thf(fact_276_pw__abs__nofail,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a,M: refine424419629nres_a] :
% 0.07/0.32 ( ( refine412683989fail_a @ ( refine1136779702un_a_a @ R @ M ) )
% 0.07/0.32 = ( ( refine412683989fail_a @ M )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ M @ X3 )
% 0.07/0.32 => ( member_a @ X3 @ ( domain_a_a @ R ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_abs_nofail
% 0.07/0.32 thf(fact_277_pw__abs__nofail,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit,M: refine424419629nres_a] :
% 0.07/0.32 ( ( refine579265252t_unit @ ( refine341651653t_unit @ R @ M ) )
% 0.07/0.32 = ( ( refine412683989fail_a @ M )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ M @ X3 )
% 0.07/0.32 => ( member_a @ X3 @ ( domain799550107t_unit @ R ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_abs_nofail
% 0.07/0.32 thf(fact_278_pw__abs__nofail,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a,M: refine787176636t_unit] :
% 0.07/0.32 ( ( refine412683989fail_a @ ( refine364464487unit_a @ R @ M ) )
% 0.07/0.32 = ( ( refine579265252t_unit @ M )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ M @ X3 )
% 0.07/0.32 => ( member_Product_unit @ X3 @ ( domain822362941unit_a @ R ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_abs_nofail
% 0.07/0.32 thf(fact_279_pw__abs__nofail,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit,M: refine787176636t_unit] :
% 0.07/0.32 ( ( refine579265252t_unit @ ( refine838861686t_unit @ R @ M ) )
% 0.07/0.32 = ( ( refine579265252t_unit @ M )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ M @ X3 )
% 0.07/0.32 => ( member_Product_unit @ X3 @ ( domain2090798924t_unit @ R ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_abs_nofail
% 0.07/0.32 thf(fact_280_conc__abs__swap,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a,M4: refine424419629nres_a,M3: refine424419629nres_a] :
% 0.07/0.32 ( ( single_valued_a_a @ R )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ M4 @ ( refine1441824853un_a_a @ R @ M3 ) )
% 0.07/0.32 = ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ M4 ) @ M3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_abs_swap
% 0.07/0.32 thf(fact_281_conc__abs__swap,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a,M4: refine787176636t_unit,M3: refine424419629nres_a] :
% 0.07/0.32 ( ( single249782708unit_a @ R )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ M4 @ ( refine2043866374unit_a @ R @ M3 ) )
% 0.07/0.32 = ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ M4 ) @ M3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_abs_swap
% 0.07/0.32 thf(fact_282_conc__abs__swap,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit,M4: refine424419629nres_a,M3: refine787176636t_unit] :
% 0.07/0.32 ( ( single226969874t_unit @ R )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ M4 @ ( refine2021053540t_unit @ R @ M3 ) )
% 0.07/0.32 = ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ M4 ) @ M3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_abs_swap
% 0.07/0.32 thf(fact_283_conc__abs__swap,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit,M4: refine787176636t_unit,M3: refine787176636t_unit] :
% 0.07/0.32 ( ( single330234563t_unit @ R )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ M4 @ ( refine944483349t_unit @ R @ M3 ) )
% 0.07/0.32 = ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ M4 ) @ M3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_abs_swap
% 0.07/0.32 thf(fact_284_pw__flat__ge__iff,axiom,
% 0.07/0.32 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.07/0.32 ( ( partia906949161nres_a @ top_to231829469nres_a @ S @ S2 )
% 0.07/0.32 = ( ( refine412683989fail_a @ S )
% 0.07/0.32 => ( ( refine412683989fail_a @ S2 )
% 0.07/0.32 & ! [X3: a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ S @ X3 )
% 0.07/0.32 = ( refine1001002027nres_a @ S2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_flat_ge_iff
% 0.07/0.32 thf(fact_285_pw__flat__ge__iff,axiom,
% 0.07/0.32 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.07/0.32 ( ( partia1658438072t_unit @ top_to177290092t_unit @ S @ S2 )
% 0.07/0.32 = ( ( refine579265252t_unit @ S )
% 0.07/0.32 => ( ( refine579265252t_unit @ S2 )
% 0.07/0.32 & ! [X3: product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ S @ X3 )
% 0.07/0.32 = ( refine558004794t_unit @ S2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % pw_flat_ge_iff
% 0.07/0.32 thf(fact_286_GreatestI2__order,axiom,
% 0.07/0.32 ! [P: refine424419629nres_a > $o,X: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ Y3 @ X ) )
% 0.07/0.32 => ( ! [X2: refine424419629nres_a] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 => ( ! [Y5: refine424419629nres_a] :
% 0.07/0.32 ( ( P @ Y5 )
% 0.07/0.32 => ( ord_le519537037nres_a @ Y5 @ X2 ) )
% 0.07/0.32 => ( Q @ X2 ) ) )
% 0.07/0.32 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % GreatestI2_order
% 0.07/0.32 thf(fact_287_GreatestI2__order,axiom,
% 0.07/0.32 ! [P: refine787176636t_unit > $o,X: refine787176636t_unit,Q: refine787176636t_unit > $o] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ Y3 @ X ) )
% 0.07/0.32 => ( ! [X2: refine787176636t_unit] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 => ( ! [Y5: refine787176636t_unit] :
% 0.07/0.32 ( ( P @ Y5 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ Y5 @ X2 ) )
% 0.07/0.32 => ( Q @ X2 ) ) )
% 0.07/0.32 => ( Q @ ( order_453013155t_unit @ P ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % GreatestI2_order
% 0.07/0.32 thf(fact_288_Greatest__equality,axiom,
% 0.07/0.32 ! [P: refine424419629nres_a > $o,X: refine424419629nres_a] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: refine424419629nres_a] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_le519537037nres_a @ Y3 @ X ) )
% 0.07/0.32 => ( ( order_1714329108nres_a @ P )
% 0.07/0.32 = X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Greatest_equality
% 0.07/0.32 thf(fact_289_Greatest__equality,axiom,
% 0.07/0.32 ! [P: refine787176636t_unit > $o,X: refine787176636t_unit] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: refine787176636t_unit] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ Y3 @ X ) )
% 0.07/0.32 => ( ( order_453013155t_unit @ P )
% 0.07/0.32 = X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Greatest_equality
% 0.07/0.32 thf(fact_290_Refine__Misc_Oif__mono,axiom,
% 0.07/0.32 ! [B2: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M22: refine424419629nres_a,M23: refine424419629nres_a] :
% 0.07/0.32 ( ( B2
% 0.07/0.32 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 0.07/0.32 => ( ( ~ B2
% 0.07/0.32 => ( ord_le519537037nres_a @ M22 @ M23 ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ M1 @ M22 ) @ ( if_Ref1724547303nres_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Misc.if_mono
% 0.07/0.32 thf(fact_291_Refine__Misc_Oif__mono,axiom,
% 0.07/0.32 ! [B2: $o,M1: refine787176636t_unit,M12: refine787176636t_unit,M22: refine787176636t_unit,M23: refine787176636t_unit] :
% 0.07/0.32 ( ( B2
% 0.07/0.32 => ( ord_le1051254044t_unit @ M1 @ M12 ) )
% 0.07/0.32 => ( ( ~ B2
% 0.07/0.32 => ( ord_le1051254044t_unit @ M22 @ M23 ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B2 @ M1 @ M22 ) @ ( if_Ref1369692790t_unit @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Misc.if_mono
% 0.07/0.32 thf(fact_292_flat__ord__compat_I1_J,axiom,
% 0.07/0.32 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.07/0.32 ( ( partia906949161nres_a @ bot_bo529555393nres_a @ X @ Y )
% 0.07/0.32 => ( ord_le519537037nres_a @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % flat_ord_compat(1)
% 0.07/0.32 thf(fact_293_flat__ord__compat_I1_J,axiom,
% 0.07/0.32 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.07/0.32 ( ( partia1658438072t_unit @ bot_bo658782032t_unit @ X @ Y )
% 0.07/0.32 => ( ord_le1051254044t_unit @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % flat_ord_compat(1)
% 0.07/0.32 thf(fact_294_flat__ord__compat_I2_J,axiom,
% 0.07/0.32 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.07/0.32 ( ( partia906949161nres_a @ top_to231829469nres_a @ X @ Y )
% 0.07/0.32 => ( ord_le519537037nres_a @ Y @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % flat_ord_compat(2)
% 0.07/0.32 thf(fact_295_flat__ord__compat_I2_J,axiom,
% 0.07/0.32 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.07/0.32 ( ( partia1658438072t_unit @ top_to177290092t_unit @ X @ Y )
% 0.07/0.32 => ( ord_le1051254044t_unit @ Y @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % flat_ord_compat(2)
% 0.07/0.32 thf(fact_296_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit,M2: refine787176636t_unit,F: product_unit > refine424419629nres_a,F2: product_unit > refine424419629nres_a] :
% 0.07/0.32 ( ( partia1658438072t_unit @ top_to177290092t_unit @ M @ M2 )
% 0.07/0.32 => ( ! [X2: product_unit] : ( partia906949161nres_a @ top_to231829469nres_a @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.07/0.32 => ( partia906949161nres_a @ top_to231829469nres_a @ ( refine119808503unit_a @ M @ F ) @ ( refine119808503unit_a @ M2 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(2)
% 0.07/0.32 thf(fact_297_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a,M2: refine424419629nres_a,F: a > refine424419629nres_a,F2: a > refine424419629nres_a] :
% 0.07/0.32 ( ( partia906949161nres_a @ top_to231829469nres_a @ M @ M2 )
% 0.07/0.32 => ( ! [X2: a] : ( partia906949161nres_a @ top_to231829469nres_a @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.07/0.32 => ( partia906949161nres_a @ top_to231829469nres_a @ ( refine436832838nd_a_a @ M @ F ) @ ( refine436832838nd_a_a @ M2 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(2)
% 0.07/0.32 thf(fact_298_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.07/0.32 ! [M: refine424419629nres_a,M2: refine424419629nres_a,F: a > refine787176636t_unit,F2: a > refine787176636t_unit] :
% 0.07/0.32 ( ( partia906949161nres_a @ top_to231829469nres_a @ M @ M2 )
% 0.07/0.32 => ( ! [X2: a] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.07/0.32 => ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine96995669t_unit @ M @ F ) @ ( refine96995669t_unit @ M2 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(2)
% 0.07/0.32 thf(fact_299_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.07/0.32 ! [M: refine787176636t_unit,M2: refine787176636t_unit,F: product_unit > refine787176636t_unit,F2: product_unit > refine787176636t_unit] :
% 0.07/0.32 ( ( partia1658438072t_unit @ top_to177290092t_unit @ M @ M2 )
% 0.07/0.32 => ( ! [X2: product_unit] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.07/0.32 => ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine681446406t_unit @ M @ F ) @ ( refine681446406t_unit @ M2 @ F2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(2)
% 0.07/0.32 thf(fact_300_conc__fun__R__mono,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a,R2: set_Product_prod_a_a,M: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1824328871od_a_a @ R @ R2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine1441824853un_a_a @ R @ M ) @ ( refine1441824853un_a_a @ R2 @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_R_mono
% 0.07/0.32 thf(fact_301_conc__fun__R__mono,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a,R2: set_Pr1720557880unit_a,M: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le2070001880unit_a @ R @ R2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine2043866374unit_a @ R @ M ) @ ( refine2043866374unit_a @ R2 @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_R_mono
% 0.07/0.32 thf(fact_302_conc__fun__R__mono,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit,R2: set_Pr1628433942t_unit,M: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1977877942t_unit @ R @ R2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( refine2021053540t_unit @ R @ M ) @ ( refine2021053540t_unit @ R2 @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_R_mono
% 0.07/0.32 thf(fact_303_conc__fun__R__mono,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit,R2: set_Pr451126599t_unit,M: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le2035129575t_unit @ R @ R2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( refine944483349t_unit @ R @ M ) @ ( refine944483349t_unit @ R2 @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % conc_fun_R_mono
% 0.07/0.32 thf(fact_304_order__mono__setup_Omono__if,axiom,
% 0.07/0.32 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B2: $o] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ T @ T2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ E @ E2 )
% 0.07/0.32 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ T @ E ) @ ( if_Ref1724547303nres_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_if
% 0.07/0.32 thf(fact_305_order__mono__setup_Omono__if,axiom,
% 0.07/0.32 ! [T: refine787176636t_unit,T2: refine787176636t_unit,E: refine787176636t_unit,E2: refine787176636t_unit,B2: $o] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ T @ T2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ E @ E2 )
% 0.07/0.32 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B2 @ T @ E ) @ ( if_Ref1369692790t_unit @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_if
% 0.07/0.32 thf(fact_306_ac__galois,axiom,
% 0.07/0.32 ! [R: set_Product_prod_a_a] :
% 0.07/0.32 ( ( single_valued_a_a @ R )
% 0.07/0.32 => ( refine2004812827nres_a @ ( refine1136779702un_a_a @ R ) @ ( refine1441824853un_a_a @ R ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ac_galois
% 0.07/0.32 thf(fact_307_ac__galois,axiom,
% 0.07/0.32 ! [R: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ( single249782708unit_a @ R )
% 0.07/0.32 => ( refine2089046860nres_a @ ( refine364464487unit_a @ R ) @ ( refine2043866374unit_a @ R ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ac_galois
% 0.07/0.32 thf(fact_308_ac__galois,axiom,
% 0.07/0.32 ! [R: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ( single226969874t_unit @ R )
% 0.07/0.32 => ( refine327276970t_unit @ ( refine341651653t_unit @ R ) @ ( refine2021053540t_unit @ R ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ac_galois
% 0.07/0.32 thf(fact_309_ac__galois,axiom,
% 0.07/0.32 ! [R: set_Pr451126599t_unit] :
% 0.07/0.32 ( ( single330234563t_unit @ R )
% 0.07/0.32 => ( refine230495195t_unit @ ( refine838861686t_unit @ R ) @ ( refine944483349t_unit @ R ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ac_galois
% 0.07/0.32 thf(fact_310_abs__fun__simps_I3_J,axiom,
% 0.07/0.32 ! [X5: set_a,R: set_Product_prod_a_a] :
% 0.07/0.32 ( ~ ( ord_less_eq_set_a @ X5 @ ( domain_a_a @ R ) )
% 0.07/0.32 => ( ( refine1136779702un_a_a @ R @ ( refine1198353288_RES_a @ X5 ) )
% 0.07/0.32 = top_to231829469nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_simps(3)
% 0.07/0.32 thf(fact_311_abs__fun__simps_I3_J,axiom,
% 0.07/0.32 ! [X5: set_a,R: set_Pr1628433942t_unit] :
% 0.07/0.32 ( ~ ( ord_less_eq_set_a @ X5 @ ( domain799550107t_unit @ R ) )
% 0.07/0.32 => ( ( refine341651653t_unit @ R @ ( refine1198353288_RES_a @ X5 ) )
% 0.07/0.32 = top_to177290092t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_simps(3)
% 0.07/0.32 thf(fact_312_abs__fun__simps_I3_J,axiom,
% 0.07/0.32 ! [X5: set_Product_unit,R: set_Pr1720557880unit_a] :
% 0.07/0.32 ( ~ ( ord_le1023748749t_unit @ X5 @ ( domain822362941unit_a @ R ) )
% 0.07/0.32 => ( ( refine364464487unit_a @ R @ ( refine1777164439t_unit @ X5 ) )
% 0.07/0.32 = top_to231829469nres_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_simps(3)
% 0.07/0.32 thf(fact_313_abs__fun__simps_I3_J,axiom,
% 0.07/0.32 ! [X5: set_Product_unit,R: set_Pr451126599t_unit] :
% 0.07/0.32 ( ~ ( ord_le1023748749t_unit @ X5 @ ( domain2090798924t_unit @ R ) )
% 0.07/0.32 => ( ( refine838861686t_unit @ R @ ( refine1777164439t_unit @ X5 ) )
% 0.07/0.32 = top_to177290092t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % abs_fun_simps(3)
% 0.07/0.32 thf(fact_314_inres__simps_I2_J,axiom,
% 0.07/0.32 ! [X5: set_a] :
% 0.07/0.32 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X5 ) )
% 0.07/0.32 = ( ^ [X3: a] : ( member_a @ X3 @ X5 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_simps(2)
% 0.07/0.32 thf(fact_315_inres__simps_I2_J,axiom,
% 0.07/0.32 ! [X5: set_Product_unit] :
% 0.07/0.32 ( ( refine558004794t_unit @ ( refine1777164439t_unit @ X5 ) )
% 0.07/0.32 = ( ^ [X3: product_unit] : ( member_Product_unit @ X3 @ X5 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % inres_simps(2)
% 0.07/0.32 thf(fact_316_nres__more__simps_I2_J,axiom,
% 0.07/0.32 ! [X5: set_Product_unit] :
% 0.07/0.32 ( ( ( refine1777164439t_unit @ X5 )
% 0.07/0.32 = bot_bo658782032t_unit )
% 0.07/0.32 = ( X5 = bot_bo1087887705t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(2)
% 0.07/0.32 thf(fact_317_nres__more__simps_I2_J,axiom,
% 0.07/0.32 ! [X5: set_a] :
% 0.07/0.32 ( ( ( refine1198353288_RES_a @ X5 )
% 0.07/0.32 = bot_bo529555393nres_a )
% 0.07/0.32 = ( X5 = bot_bot_set_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(2)
% 0.07/0.32 thf(fact_318_nres__more__simps_I1_J,axiom,
% 0.07/0.32 ! [X5: set_Product_unit] :
% 0.07/0.32 ( ( bot_bo658782032t_unit
% 0.07/0.32 = ( refine1777164439t_unit @ X5 ) )
% 0.07/0.32 = ( X5 = bot_bo1087887705t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(1)
% 0.07/0.32 thf(fact_319_nres__more__simps_I1_J,axiom,
% 0.07/0.32 ! [X5: set_a] :
% 0.07/0.32 ( ( bot_bo529555393nres_a
% 0.07/0.32 = ( refine1198353288_RES_a @ X5 ) )
% 0.07/0.32 = ( X5 = bot_bot_set_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(1)
% 0.07/0.32 thf(fact_320_nres__order__simps_I21_J,axiom,
% 0.07/0.32 ! [X: product_unit,Y6: set_Product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X ) @ ( refine1777164439t_unit @ Y6 ) )
% 0.07/0.32 = ( member_Product_unit @ X @ Y6 ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(21)
% 0.07/0.32 thf(fact_321_nres__order__simps_I21_J,axiom,
% 0.07/0.32 ! [X: a,Y6: set_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1198353288_RES_a @ Y6 ) )
% 0.07/0.32 = ( member_a @ X @ Y6 ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(21)
% 0.07/0.32 thf(fact_322_galois__connection__def,axiom,
% 0.07/0.32 ( refine2004812827nres_a
% 0.07/0.32 = ( ^ [Alpha: refine424419629nres_a > refine424419629nres_a,Gamma: refine424419629nres_a > refine424419629nres_a] :
% 0.07/0.32 ! [C3: refine424419629nres_a,A3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ C3 @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le519537037nres_a @ ( Alpha @ C3 ) @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_323_galois__connection__def,axiom,
% 0.07/0.32 ( refine327276970t_unit
% 0.07/0.32 = ( ^ [Alpha: refine424419629nres_a > refine787176636t_unit,Gamma: refine787176636t_unit > refine424419629nres_a] :
% 0.07/0.32 ! [C3: refine424419629nres_a,A3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ C3 @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le1051254044t_unit @ ( Alpha @ C3 ) @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_324_galois__connection__def,axiom,
% 0.07/0.32 ( refine2089046860nres_a
% 0.07/0.32 = ( ^ [Alpha: refine787176636t_unit > refine424419629nres_a,Gamma: refine424419629nres_a > refine787176636t_unit] :
% 0.07/0.32 ! [C3: refine787176636t_unit,A3: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ C3 @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le519537037nres_a @ ( Alpha @ C3 ) @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_325_galois__connection__def,axiom,
% 0.07/0.32 ( refine230495195t_unit
% 0.07/0.32 = ( ^ [Alpha: refine787176636t_unit > refine787176636t_unit,Gamma: refine787176636t_unit > refine787176636t_unit] :
% 0.07/0.32 ! [C3: refine787176636t_unit,A3: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ C3 @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le1051254044t_unit @ ( Alpha @ C3 ) @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_326_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma2: refine424419629nres_a > refine424419629nres_a,Alpha2: refine424419629nres_a > refine424419629nres_a] :
% 0.07/0.32 ( ! [C4: refine424419629nres_a,A4: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le519537037nres_a @ ( Alpha2 @ C4 ) @ A4 ) )
% 0.07/0.32 => ( refine2004812827nres_a @ Alpha2 @ Gamma2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_327_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma2: refine787176636t_unit > refine424419629nres_a,Alpha2: refine424419629nres_a > refine787176636t_unit] :
% 0.07/0.32 ( ! [C4: refine424419629nres_a,A4: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le1051254044t_unit @ ( Alpha2 @ C4 ) @ A4 ) )
% 0.07/0.32 => ( refine327276970t_unit @ Alpha2 @ Gamma2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_328_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma2: refine424419629nres_a > refine787176636t_unit,Alpha2: refine787176636t_unit > refine424419629nres_a] :
% 0.07/0.32 ( ! [C4: refine787176636t_unit,A4: refine424419629nres_a] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le519537037nres_a @ ( Alpha2 @ C4 ) @ A4 ) )
% 0.07/0.32 => ( refine2089046860nres_a @ Alpha2 @ Gamma2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_329_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma2: refine787176636t_unit > refine787176636t_unit,Alpha2: refine787176636t_unit > refine787176636t_unit] :
% 0.07/0.32 ( ! [C4: refine787176636t_unit,A4: refine787176636t_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le1051254044t_unit @ ( Alpha2 @ C4 ) @ A4 ) )
% 0.07/0.32 => ( refine230495195t_unit @ Alpha2 @ Gamma2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_330_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha2: refine424419629nres_a > refine424419629nres_a,Gamma2: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.07/0.32 ( ( refine2004812827nres_a @ Alpha2 @ Gamma2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ C2 @ ( Gamma2 @ A2 ) )
% 0.07/0.32 = ( ord_le519537037nres_a @ ( Alpha2 @ C2 ) @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_331_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha2: refine424419629nres_a > refine787176636t_unit,Gamma2: refine787176636t_unit > refine424419629nres_a,C2: refine424419629nres_a,A2: refine787176636t_unit] :
% 0.07/0.32 ( ( refine327276970t_unit @ Alpha2 @ Gamma2 )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ C2 @ ( Gamma2 @ A2 ) )
% 0.07/0.32 = ( ord_le1051254044t_unit @ ( Alpha2 @ C2 ) @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_332_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha2: refine787176636t_unit > refine424419629nres_a,Gamma2: refine424419629nres_a > refine787176636t_unit,C2: refine787176636t_unit,A2: refine424419629nres_a] :
% 0.07/0.32 ( ( refine2089046860nres_a @ Alpha2 @ Gamma2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ C2 @ ( Gamma2 @ A2 ) )
% 0.07/0.32 = ( ord_le519537037nres_a @ ( Alpha2 @ C2 ) @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_333_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha2: refine787176636t_unit > refine787176636t_unit,Gamma2: refine787176636t_unit > refine787176636t_unit,C2: refine787176636t_unit,A2: refine787176636t_unit] :
% 0.07/0.32 ( ( refine230495195t_unit @ Alpha2 @ Gamma2 )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ C2 @ ( Gamma2 @ A2 ) )
% 0.07/0.32 = ( ord_le1051254044t_unit @ ( Alpha2 @ C2 ) @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_334_nres__order__simps_I5_J,axiom,
% 0.07/0.32 ! [X5: set_a,Y6: set_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X5 ) @ ( refine1198353288_RES_a @ Y6 ) )
% 0.07/0.32 = ( ord_less_eq_set_a @ X5 @ Y6 ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(5)
% 0.07/0.32 thf(fact_335_nres__order__simps_I5_J,axiom,
% 0.07/0.32 ! [X5: set_Product_unit,Y6: set_Product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ X5 ) @ ( refine1777164439t_unit @ Y6 ) )
% 0.07/0.32 = ( ord_le1023748749t_unit @ X5 @ Y6 ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(5)
% 0.07/0.32 thf(fact_336_less__eq__nres_Osimps_I2_J,axiom,
% 0.07/0.32 ! [A2: set_a,B2: set_a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A2 ) @ ( refine1198353288_RES_a @ B2 ) )
% 0.07/0.32 = ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_eq_nres.simps(2)
% 0.07/0.32 thf(fact_337_less__eq__nres_Osimps_I2_J,axiom,
% 0.07/0.32 ! [A2: set_Product_unit,B2: set_Product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A2 ) @ ( refine1777164439t_unit @ B2 ) )
% 0.07/0.32 = ( ord_le1023748749t_unit @ A2 @ B2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_eq_nres.simps(2)
% 0.07/0.32 thf(fact_338_bot__nres__def,axiom,
% 0.07/0.32 ( bot_bo658782032t_unit
% 0.07/0.32 = ( refine1777164439t_unit @ bot_bo1087887705t_unit ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot_nres_def
% 0.07/0.32 thf(fact_339_bot__nres__def,axiom,
% 0.07/0.32 ( bot_bo529555393nres_a
% 0.07/0.32 = ( refine1198353288_RES_a @ bot_bot_set_a ) ) ).
% 0.07/0.32
% 0.07/0.32 % bot_nres_def
% 0.07/0.32 thf(fact_340_SPEC__cons__rule,axiom,
% 0.07/0.32 ! [M3: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ M3 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.07/0.32 => ( ! [X2: a] :
% 0.07/0.32 ( ( Phi @ X2 )
% 0.07/0.32 => ( Psi @ X2 ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ M3 @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % SPEC_cons_rule
% 0.07/0.32 thf(fact_341_SPEC__cons__rule,axiom,
% 0.07/0.32 ! [M3: refine787176636t_unit,Phi: product_unit > $o,Psi: product_unit > $o] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ M3 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) )
% 0.07/0.32 => ( ! [X2: product_unit] :
% 0.07/0.32 ( ( Phi @ X2 )
% 0.07/0.32 => ( Psi @ X2 ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ M3 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Psi ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % SPEC_cons_rule
% 0.07/0.32 thf(fact_342_SPEC__trans,axiom,
% 0.07/0.32 ! [X: refine424419629nres_a,Y: refine424419629nres_a,Postcond: a > $o] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ X @ Y )
% 0.07/0.32 => ( ( ord_le519537037nres_a @ Y @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 0.07/0.32 => ( ord_le519537037nres_a @ X @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % SPEC_trans
% 0.07/0.32 thf(fact_343_SPEC__trans,axiom,
% 0.07/0.32 ! [X: refine787176636t_unit,Y: refine787176636t_unit,Postcond: product_unit > $o] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ X @ Y )
% 0.07/0.32 => ( ( ord_le1051254044t_unit @ Y @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) )
% 0.07/0.32 => ( ord_le1051254044t_unit @ X @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % SPEC_trans
% 0.07/0.32 thf(fact_344_nres__order__simps_I22_J,axiom,
% 0.07/0.32 ! [X5: set_Product_unit,Y: product_unit] :
% 0.07/0.32 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ X5 ) @ ( refine1420258419t_unit @ Y ) )
% 0.07/0.32 = ( ord_le1023748749t_unit @ X5 @ ( insert_Product_unit @ Y @ bot_bo1087887705t_unit ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(22)
% 0.07/0.32 thf(fact_345_nres__order__simps_I22_J,axiom,
% 0.07/0.32 ! [X5: set_a,Y: a] :
% 0.07/0.32 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X5 ) @ ( refine2063221604TURN_a @ Y ) )
% 0.07/0.32 = ( ord_less_eq_set_a @ X5 @ ( insert_a @ Y @ bot_bot_set_a ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_order_simps(22)
% 0.07/0.32 thf(fact_346_nres__more__simps_I3_J,axiom,
% 0.07/0.32 ! [X5: set_Product_unit,X: product_unit] :
% 0.07/0.32 ( ( ( refine1777164439t_unit @ X5 )
% 0.07/0.32 = ( refine1420258419t_unit @ X ) )
% 0.07/0.32 = ( X5
% 0.07/0.32 = ( insert_Product_unit @ X @ bot_bo1087887705t_unit ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(3)
% 0.07/0.32 thf(fact_347_nres__more__simps_I3_J,axiom,
% 0.07/0.32 ! [X5: set_a,X: a] :
% 0.07/0.32 ( ( ( refine1198353288_RES_a @ X5 )
% 0.07/0.32 = ( refine2063221604TURN_a @ X ) )
% 0.07/0.32 = ( X5
% 0.07/0.32 = ( insert_a @ X @ bot_bot_set_a ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(3)
% 0.07/0.32 thf(fact_348_nres__more__simps_I5_J,axiom,
% 0.07/0.32 ! [X: product_unit,X5: set_Product_unit] :
% 0.07/0.32 ( ( ( refine1420258419t_unit @ X )
% 0.07/0.32 = ( refine1777164439t_unit @ X5 ) )
% 0.07/0.32 = ( ( insert_Product_unit @ X @ bot_bo1087887705t_unit )
% 0.07/0.32 = X5 ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(5)
% 0.07/0.32 thf(fact_349_nres__more__simps_I5_J,axiom,
% 0.07/0.32 ! [X: a,X5: set_a] :
% 0.07/0.32 ( ( ( refine2063221604TURN_a @ X )
% 0.07/0.32 = ( refine1198353288_RES_a @ X5 ) )
% 0.07/0.32 = ( ( insert_a @ X @ bot_bot_set_a )
% 0.07/0.32 = X5 ) ) ).
% 0.07/0.32
% 0.07/0.32 % nres_more_simps(5)
% 0.07/0.32 thf(fact_350_RETURN__def,axiom,
% 0.07/0.32 ( refine1420258419t_unit
% 0.07/0.32 = ( ^ [X3: product_unit] : ( refine1777164439t_unit @ ( insert_Product_unit @ X3 @ bot_bo1087887705t_unit ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RETURN_def
% 0.07/0.32 thf(fact_351_RETURN__def,axiom,
% 0.07/0.32 ( refine2063221604TURN_a
% 0.07/0.32 = ( ^ [X3: a] : ( refine1198353288_RES_a @ ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % RETURN_def
% 0.07/0.32
% 0.07/0.32 % Helper facts (5)
% 0.07/0.32 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.07/0.32 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.07/0.32 ( ( if_Ref1724547303nres_a @ $false @ X @ Y )
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% 0.07/0.32
% 0.07/0.32 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.07/0.32 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.07/0.32 ( ( if_Ref1724547303nres_a @ $true @ X @ Y )
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% 0.07/0.32 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
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% 0.07/0.32 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.07/0.32 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
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% 0.07/0.32 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
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% 0.07/0.32 ( ( if_Ref1369692790t_unit @ $true @ X @ Y )
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% 0.07/0.32
% 0.07/0.32 % Conjectures (1)
% 0.07/0.32 thf(conj_0,conjecture,
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% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.16/1.20 ---- Embedded in THF ---
% 0.16/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.16/1.21 %%% Generated on Tue Feb 24 03:28:26 EST 2026
% 0.16/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 0.16/1.21 %%% Logic specification used:
% 0.16/1.21 %%% thf(spec, logic, $$dhol).
% 0.16/1.21
% 0.16/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.D2qxee7X2B/DTF2DTF9718.p
% See solution above
% 0.16/1.21 ------------------------
% 0.16/1.25 ---- Cleaned THF ---
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% 0.16/1.25 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
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% 0.16/1.25 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Ounit_J_J,type,
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% 0.16/1.25 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
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% 0.16/1.25 thf(ty_n_t__Set__Oset_Itf__a_J,type,
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% 0.16/1.25 thf(ty_n_tf__a,type,
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% 0.16/1.25 thf(sy_c_Orderings_Obot__class_Obot_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
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% 0.16/1.25 thf(sy_c_Orderings_Obot__class_Obot_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
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% 0.16/1.25 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Ounit_J,type,
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% 0.16/1.25 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
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% 0.16/1.25 thf(sy_c_Partial__Function_Oflat__ord_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
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% 0.16/1.25 thf(sy_c_Product__Type_OPair_001tf__a_001t__Product____Type__Ounit,type,
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% 0.16/1.25 thf(sy_c_Product__Type_OPair_001tf__a_001tf__a,type,
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% 0.16/1.25 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001t__Product____Type__Ounit,type,
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% 0.16/1.25 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__a,type,
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% 0.16/1.25 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
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% 0.16/1.25 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001t__Product____Type__Ounit_001tf__a,type,
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% 0.16/1.25 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__a_001t__Product____Type__Ounit,type,
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% 0.16/1.25 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__a_001tf__a,type,
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% 0.16/1.25 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__a_001t__Product____Type__Ounit,type,
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% 0.16/1.25 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__a_001tf__a,type,
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% 0.16/1.25
% 0.16/1.25 thf(sy_c_Relation_Osingle__valued_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 0.16/1.25 single330234563t_unit: set_Pr451126599t_unit > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Relation_Osingle__valued_001t__Product____Type__Ounit_001tf__a,type,
% 0.16/1.25 single249782708unit_a: set_Pr1720557880unit_a > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Relation_Osingle__valued_001tf__a_001t__Product____Type__Ounit,type,
% 0.16/1.25 single226969874t_unit: set_Pr1628433942t_unit > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Relation_Osingle__valued_001tf__a_001tf__a,type,
% 0.16/1.25 single_valued_a_a: set_Product_prod_a_a > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
% 0.16/1.25 collec797068754t_unit: ( produc971140967t_unit > $o ) > set_Pr451126599t_unit ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mtf__a_J,type,
% 0.16/1.25 collec535904323unit_a: ( produc884009688unit_a > $o ) > set_Pr1720557880unit_a ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Ounit_J,type,
% 0.16/1.25 collec1419746337t_unit: ( produc1767851702t_unit > $o ) > set_Pr1628433942t_unit ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.16/1.25 collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Set_OCollect_001t__Product____Type__Ounit,type,
% 0.16/1.25 collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.16/1.25 collect_a: ( a > $o ) > set_a ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Set_Oinsert_001t__Product____Type__Ounit,type,
% 0.16/1.25 insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.16/1.25 insert_a: a > set_a > set_a ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
% 0.16/1.25 member1423014800t_unit: produc971140967t_unit > set_Pr451126599t_unit > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mtf__a_J,type,
% 0.16/1.25 member1211819009unit_a: produc884009688unit_a > set_Pr1720557880unit_a > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Ounit_J,type,
% 0.16/1.25 member2095661023t_unit: produc1767851702t_unit > set_Pr1628433942t_unit > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.16/1.25 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_member_001t__Product____Type__Ounit,type,
% 0.16/1.25 member_Product_unit: product_unit > set_Product_unit > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_c_member_001tf__a,type,
% 0.16/1.25 member_a: a > set_a > $o ).
% 0.16/1.25
% 0.16/1.25 thf(sy_v_f,type,
% 0.16/1.25 f: product_unit > refine424419629nres_a ).
% 0.16/1.25
% 0.16/1.25 thf(fact_0_bind__SUCCEED,axiom,
% 0.16/1.25 ! [F: product_unit > refine787176636t_unit] :
% 0.16/1.25 ( ( refine681446406t_unit @ bot_bo658782032t_unit @ F )
% 0.16/1.25 = bot_bo658782032t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_1_bind__SUCCEED,axiom,
% 0.16/1.25 ! [F: a > refine787176636t_unit] :
% 0.16/1.25 ( ( refine96995669t_unit @ bot_bo529555393nres_a @ F )
% 0.16/1.25 = bot_bo658782032t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_2_bind__SUCCEED,axiom,
% 0.16/1.25 ! [F: a > refine424419629nres_a] :
% 0.16/1.25 ( ( refine436832838nd_a_a @ bot_bo529555393nres_a @ F )
% 0.16/1.25 = bot_bo529555393nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_3_bind__SUCCEED,axiom,
% 0.16/1.25 ! [F: product_unit > refine424419629nres_a] :
% 0.16/1.25 ( ( refine119808503unit_a @ bot_bo658782032t_unit @ F )
% 0.16/1.25 = bot_bo529555393nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_4_nres__monad1,axiom,
% 0.16/1.25 ! [X: product_unit,F: product_unit > refine787176636t_unit] :
% 0.16/1.25 ( ( refine681446406t_unit @ ( refine1420258419t_unit @ X ) @ F )
% 0.16/1.25 = ( F @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_5_nres__monad1,axiom,
% 0.16/1.25 ! [X: a,F: a > refine424419629nres_a] :
% 0.16/1.25 ( ( refine436832838nd_a_a @ ( refine2063221604TURN_a @ X ) @ F )
% 0.16/1.25 = ( F @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_6_nres__monad1,axiom,
% 0.16/1.25 ! [X: a,F: a > refine787176636t_unit] :
% 0.16/1.25 ( ( refine96995669t_unit @ ( refine2063221604TURN_a @ X ) @ F )
% 0.16/1.25 = ( F @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_7_nres__monad1,axiom,
% 0.16/1.25 ! [X: product_unit,F: product_unit > refine424419629nres_a] :
% 0.16/1.25 ( ( refine119808503unit_a @ ( refine1420258419t_unit @ X ) @ F )
% 0.16/1.25 = ( F @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_8_nres__monad2,axiom,
% 0.16/1.25 ! [M: refine787176636t_unit] :
% 0.16/1.25 ( ( refine681446406t_unit @ M @ refine1420258419t_unit )
% 0.16/1.25 = M ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_9_nres__monad2,axiom,
% 0.16/1.25 ! [M: refine424419629nres_a] :
% 0.16/1.25 ( ( refine436832838nd_a_a @ M @ refine2063221604TURN_a )
% 0.16/1.25 = M ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_10_abs__fun__strict,axiom,
% 0.16/1.25 ! [R: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( refine838861686t_unit @ R @ bot_bo658782032t_unit )
% 0.16/1.25 = bot_bo658782032t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_11_abs__fun__strict,axiom,
% 0.16/1.25 ! [R: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( refine364464487unit_a @ R @ bot_bo658782032t_unit )
% 0.16/1.25 = bot_bo529555393nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_12_abs__fun__strict,axiom,
% 0.16/1.25 ! [R: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( refine341651653t_unit @ R @ bot_bo529555393nres_a )
% 0.16/1.25 = bot_bo658782032t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_13_abs__fun__strict,axiom,
% 0.16/1.25 ! [R: set_Product_prod_a_a] :
% 0.16/1.25 ( ( refine1136779702un_a_a @ R @ bot_bo529555393nres_a )
% 0.16/1.25 = bot_bo529555393nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_14_conc__fun__strict,axiom,
% 0.16/1.25 ! [R: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( refine944483349t_unit @ R @ bot_bo658782032t_unit )
% 0.16/1.25 = bot_bo658782032t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_15_conc__fun__strict,axiom,
% 0.16/1.25 ! [R: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( refine2021053540t_unit @ R @ bot_bo658782032t_unit )
% 0.16/1.25 = bot_bo529555393nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_16_conc__fun__strict,axiom,
% 0.16/1.25 ! [R: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( refine2043866374unit_a @ R @ bot_bo529555393nres_a )
% 0.16/1.25 = bot_bo658782032t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_17_conc__fun__strict,axiom,
% 0.16/1.25 ! [R: set_Product_prod_a_a] :
% 0.16/1.25 ( ( refine1441824853un_a_a @ R @ bot_bo529555393nres_a )
% 0.16/1.25 = bot_bo529555393nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_18_nres__inequalities_I5_J,axiom,
% 0.16/1.25 ! [X: product_unit] :
% 0.16/1.25 ( bot_bo658782032t_unit
% 0.16/1.25 != ( refine1420258419t_unit @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_19_nres__inequalities_I5_J,axiom,
% 0.16/1.25 ! [X: a] :
% 0.16/1.25 ( bot_bo529555393nres_a
% 0.16/1.25 != ( refine2063221604TURN_a @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_20_inres__simps_I4_J,axiom,
% 0.16/1.25 ( ( refine558004794t_unit @ bot_bo658782032t_unit )
% 0.16/1.25 = ( ^ [Uu: product_unit] : $false ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_21_inres__simps_I4_J,axiom,
% 0.16/1.25 ( ( refine1001002027nres_a @ bot_bo529555393nres_a )
% 0.16/1.25 = ( ^ [Uu: a] : $false ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_22_nres__order__simps_I2_J,axiom,
% 0.16/1.25 ! [M: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ M @ bot_bo658782032t_unit )
% 0.16/1.25 = ( M = bot_bo658782032t_unit ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_23_nres__order__simps_I2_J,axiom,
% 0.16/1.25 ! [M: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ M @ bot_bo529555393nres_a )
% 0.16/1.25 = ( M = bot_bo529555393nres_a ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_24_nofail__simps_I4_J,axiom,
% 0.16/1.25 refine579265252t_unit @ bot_bo658782032t_unit ).
% 0.16/1.25
% 0.16/1.25 thf(fact_25_nofail__simps_I4_J,axiom,
% 0.16/1.25 refine412683989fail_a @ bot_bo529555393nres_a ).
% 0.16/1.25
% 0.16/1.25 thf(fact_26_bind__FAIL,axiom,
% 0.16/1.25 ! [F: product_unit > refine424419629nres_a] :
% 0.16/1.25 ( ( refine119808503unit_a @ top_to177290092t_unit @ F )
% 0.16/1.25 = top_to231829469nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_27_bind__FAIL,axiom,
% 0.16/1.25 ! [F: a > refine424419629nres_a] :
% 0.16/1.25 ( ( refine436832838nd_a_a @ top_to231829469nres_a @ F )
% 0.16/1.25 = top_to231829469nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_28_bind__FAIL,axiom,
% 0.16/1.25 ! [F: a > refine787176636t_unit] :
% 0.16/1.25 ( ( refine96995669t_unit @ top_to231829469nres_a @ F )
% 0.16/1.25 = top_to177290092t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_29_bind__FAIL,axiom,
% 0.16/1.25 ! [F: product_unit > refine787176636t_unit] :
% 0.16/1.25 ( ( refine681446406t_unit @ top_to177290092t_unit @ F )
% 0.16/1.25 = top_to177290092t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_30_nres__order__simps_I1_J,axiom,
% 0.16/1.25 ! [M: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ M ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_31_nres__order__simps_I1_J,axiom,
% 0.16/1.25 ! [M: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ M ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_32_nres__more__simps_I6_J,axiom,
% 0.16/1.25 ! [X: product_unit,Y: product_unit] :
% 0.16/1.25 ( ( ( refine1420258419t_unit @ X )
% 0.16/1.25 = ( refine1420258419t_unit @ Y ) )
% 0.16/1.25 = ( X = Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_33_nres__more__simps_I6_J,axiom,
% 0.16/1.25 ! [X: a,Y: a] :
% 0.16/1.25 ( ( ( refine2063221604TURN_a @ X )
% 0.16/1.25 = ( refine2063221604TURN_a @ Y ) )
% 0.16/1.25 = ( X = Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_34_nres__order__simps_I4_J,axiom,
% 0.16/1.25 ! [M: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M )
% 0.16/1.25 = ( M = top_to231829469nres_a ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_35_nres__order__simps_I4_J,axiom,
% 0.16/1.25 ! [M: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ M )
% 0.16/1.25 = ( M = top_to177290092t_unit ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_36_nofail__simps_I1_J,axiom,
% 0.16/1.25 ~ ( refine412683989fail_a @ top_to231829469nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_37_nofail__simps_I1_J,axiom,
% 0.16/1.25 ~ ( refine579265252t_unit @ top_to177290092t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_38_inres__simps_I1_J,axiom,
% 0.16/1.25 ( ( refine1001002027nres_a @ top_to231829469nres_a )
% 0.16/1.25 = ( ^ [Uu: a] : $true ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_39_inres__simps_I1_J,axiom,
% 0.16/1.25 ( ( refine558004794t_unit @ top_to177290092t_unit )
% 0.16/1.25 = ( ^ [Uu: product_unit] : $true ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_40_conc__fun__fail__iff_I2_J,axiom,
% 0.16/1.25 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 0.16/1.25 ( ( top_to231829469nres_a
% 0.16/1.25 = ( refine1441824853un_a_a @ R @ S ) )
% 0.16/1.25 = ( S = top_to231829469nres_a ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_41_conc__fun__fail__iff_I2_J,axiom,
% 0.16/1.25 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 0.16/1.25 ( ( top_to177290092t_unit
% 0.16/1.25 = ( refine2043866374unit_a @ R @ S ) )
% 0.16/1.25 = ( S = top_to231829469nres_a ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_42_conc__fun__fail__iff_I2_J,axiom,
% 0.16/1.25 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 0.16/1.25 ( ( top_to231829469nres_a
% 0.16/1.25 = ( refine2021053540t_unit @ R @ S ) )
% 0.16/1.25 = ( S = top_to177290092t_unit ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_43_conc__fun__fail__iff_I2_J,axiom,
% 0.16/1.25 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.16/1.25 ( ( top_to177290092t_unit
% 0.16/1.25 = ( refine944483349t_unit @ R @ S ) )
% 0.16/1.25 = ( S = top_to177290092t_unit ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_44_conc__fun__fail__iff_I1_J,axiom,
% 0.16/1.25 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 0.16/1.25 ( ( ( refine1441824853un_a_a @ R @ S )
% 0.16/1.25 = top_to231829469nres_a )
% 0.16/1.25 = ( S = top_to231829469nres_a ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_45_conc__fun__fail__iff_I1_J,axiom,
% 0.16/1.25 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 0.16/1.25 ( ( ( refine2043866374unit_a @ R @ S )
% 0.16/1.25 = top_to177290092t_unit )
% 0.16/1.25 = ( S = top_to231829469nres_a ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_46_conc__fun__fail__iff_I1_J,axiom,
% 0.16/1.25 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 0.16/1.25 ( ( ( refine2021053540t_unit @ R @ S )
% 0.16/1.25 = top_to231829469nres_a )
% 0.16/1.25 = ( S = top_to177290092t_unit ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_47_conc__fun__fail__iff_I1_J,axiom,
% 0.16/1.25 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.16/1.25 ( ( ( refine944483349t_unit @ R @ S )
% 0.16/1.25 = top_to177290092t_unit )
% 0.16/1.25 = ( S = top_to177290092t_unit ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_48_conc__fun__FAIL,axiom,
% 0.16/1.25 ! [R: set_Product_prod_a_a] :
% 0.16/1.25 ( ( refine1441824853un_a_a @ R @ top_to231829469nres_a )
% 0.16/1.25 = top_to231829469nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_49_conc__fun__FAIL,axiom,
% 0.16/1.25 ! [R: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( refine2043866374unit_a @ R @ top_to231829469nres_a )
% 0.16/1.25 = top_to177290092t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_50_conc__fun__FAIL,axiom,
% 0.16/1.25 ! [R: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( refine2021053540t_unit @ R @ top_to177290092t_unit )
% 0.16/1.25 = top_to231829469nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_51_conc__fun__FAIL,axiom,
% 0.16/1.25 ! [R: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( refine944483349t_unit @ R @ top_to177290092t_unit )
% 0.16/1.25 = top_to177290092t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_52_nres__order__simps_I20_J,axiom,
% 0.16/1.25 ! [X: product_unit,Y: product_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X ) @ ( refine1420258419t_unit @ Y ) )
% 0.16/1.25 = ( X = Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_53_nres__order__simps_I20_J,axiom,
% 0.16/1.25 ! [X: a,Y: a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine2063221604TURN_a @ Y ) )
% 0.16/1.25 = ( X = Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_54_abs__fun__simps_I1_J,axiom,
% 0.16/1.25 ! [R: set_Product_prod_a_a] :
% 0.16/1.25 ( ( refine1136779702un_a_a @ R @ top_to231829469nres_a )
% 0.16/1.25 = top_to231829469nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_55_abs__fun__simps_I1_J,axiom,
% 0.16/1.25 ! [R: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( refine341651653t_unit @ R @ top_to231829469nres_a )
% 0.16/1.25 = top_to177290092t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_56_abs__fun__simps_I1_J,axiom,
% 0.16/1.25 ! [R: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( refine364464487unit_a @ R @ top_to177290092t_unit )
% 0.16/1.25 = top_to231829469nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_57_abs__fun__simps_I1_J,axiom,
% 0.16/1.25 ! [R: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( refine838861686t_unit @ R @ top_to177290092t_unit )
% 0.16/1.25 = top_to177290092t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_58_nofail__simps_I3_J,axiom,
% 0.16/1.25 ! [X: product_unit] : ( refine579265252t_unit @ ( refine1420258419t_unit @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_59_nofail__simps_I3_J,axiom,
% 0.16/1.25 ! [X: a] : ( refine412683989fail_a @ ( refine2063221604TURN_a @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_60_inres__simps_I3_J,axiom,
% 0.16/1.25 ! [X: product_unit] :
% 0.16/1.25 ( ( refine558004794t_unit @ ( refine1420258419t_unit @ X ) )
% 0.16/1.25 = ( ^ [Y2: product_unit,Z: product_unit] : ( Y2 = Z )
% 0.16/1.25 @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_61_inres__simps_I3_J,axiom,
% 0.16/1.25 ! [X: a] :
% 0.16/1.25 ( ( refine1001002027nres_a @ ( refine2063221604TURN_a @ X ) )
% 0.16/1.25 = ( ^ [Y2: a,Z: a] : ( Y2 = Z )
% 0.16/1.25 @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_62_intro__nofail_I2_J,axiom,
% 0.16/1.25 ! [S: refine424419629nres_a] :
% 0.16/1.25 ( ( top_to231829469nres_a != S )
% 0.16/1.25 = ( refine412683989fail_a @ S ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_63_intro__nofail_I2_J,axiom,
% 0.16/1.25 ! [S: refine787176636t_unit] :
% 0.16/1.25 ( ( top_to177290092t_unit != S )
% 0.16/1.25 = ( refine579265252t_unit @ S ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_64_nres__order__simps_I3_J,axiom,
% 0.16/1.25 ! [M: refine424419629nres_a] : ( ord_le519537037nres_a @ M @ top_to231829469nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_65_nres__order__simps_I3_J,axiom,
% 0.16/1.25 ! [M: refine787176636t_unit] : ( ord_le1051254044t_unit @ M @ top_to177290092t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_66_nres__inequalities_I3_J,axiom,
% 0.16/1.25 ! [X: product_unit] :
% 0.16/1.25 ( top_to177290092t_unit
% 0.16/1.25 != ( refine1420258419t_unit @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_67_nres__inequalities_I3_J,axiom,
% 0.16/1.25 ! [X: a] :
% 0.16/1.25 ( top_to231829469nres_a
% 0.16/1.25 != ( refine2063221604TURN_a @ X ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_68_abs__trans__additional_I1_J,axiom,
% 0.16/1.25 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_a,C: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A @ B )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ B ) @ C )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ A ) @ C ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_69_abs__trans__additional_I1_J,axiom,
% 0.16/1.25 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Pr1628433942t_unit,C: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A @ B )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ B ) @ C )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ A ) @ C ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_70_abs__trans__additional_I1_J,axiom,
% 0.16/1.25 ! [A: refine787176636t_unit,B: refine787176636t_unit,R: set_Pr1720557880unit_a,C: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A @ B )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ B ) @ C )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ A ) @ C ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_71_abs__trans__additional_I1_J,axiom,
% 0.16/1.25 ! [A: refine787176636t_unit,B: refine787176636t_unit,R: set_Pr451126599t_unit,C: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A @ B )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ B ) @ C )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ A ) @ C ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_72_conc__trans__additional_I1_J,axiom,
% 0.16/1.25 ! [A: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ B ) )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B @ C )
% 0.16/1.25 => ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ C ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_73_conc__trans__additional_I1_J,axiom,
% 0.16/1.25 ! [A: refine787176636t_unit,R: set_Pr1720557880unit_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ R @ B ) )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B @ C )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A @ ( refine2043866374unit_a @ R @ C ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_74_conc__trans__additional_I1_J,axiom,
% 0.16/1.25 ! [A: refine424419629nres_a,R: set_Pr1628433942t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ R @ B ) )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.16/1.25 => ( ord_le519537037nres_a @ A @ ( refine2021053540t_unit @ R @ C ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_75_conc__trans__additional_I1_J,axiom,
% 0.16/1.25 ! [A: refine787176636t_unit,R: set_Pr451126599t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ R @ B ) )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A @ ( refine944483349t_unit @ R @ C ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_76_order__subst1,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_77_order__subst1,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,F: refine787176636t_unit > refine424419629nres_a,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_78_order__subst1,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,F: refine424419629nres_a > refine787176636t_unit,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_79_order__subst1,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_80_order__subst1,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_81_order__subst1,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,F: set_a > refine787176636t_unit,B2: set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_82_order__subst1,axiom,
% 0.16/1.25 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_83_order__subst1,axiom,
% 0.16/1.25 ! [A2: set_a,F: refine787176636t_unit > set_a,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_84_order__subst1,axiom,
% 0.16/1.25 ! [A2: set_a,F: set_a > set_a,B2: set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_85_order__subst1,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,F: set_Pr451126599t_unit > refine424419629nres_a,B2: set_Pr451126599t_unit,C2: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le2035129575t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: set_Pr451126599t_unit,Y3: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( ord_le2035129575t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_86_order__subst2,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_87_order__subst2,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_88_order__subst2,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_89_order__subst2,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_90_order__subst2,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_91_order__subst2,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_92_order__subst2,axiom,
% 0.16/1.25 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_93_order__subst2,axiom,
% 0.16/1.25 ! [A2: set_a,B2: set_a,F: set_a > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_94_order__subst2,axiom,
% 0.16/1.25 ! [A2: set_a,B2: set_a,F: set_a > set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_95_order__subst2,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_Pr451126599t_unit,C2: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le2035129575t_unit @ ( F @ B2 ) @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le2035129575t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le2035129575t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_96_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_97_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,F: refine424419629nres_a > refine787176636t_unit,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_98_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,F: refine787176636t_unit > refine424419629nres_a,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_99_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_100_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_101_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: set_a,F: refine787176636t_unit > set_a,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_102_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C2: set_a] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_103_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,F: set_a > refine787176636t_unit,B2: set_a,C2: set_a] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_104_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: set_a,F: set_a > set_a,B2: set_a,C2: set_a] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_105_ord__eq__le__subst,axiom,
% 0.16/1.25 ! [A2: set_Pr451126599t_unit,F: refine424419629nres_a > set_Pr451126599t_unit,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( A2
% 0.16/1.25 = ( F @ B2 ) )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le2035129575t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le2035129575t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_106_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_107_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_108_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_109_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_110_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_111_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,F: refine787176636t_unit > set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_112_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_113_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: set_a,B2: set_a,F: set_a > refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_114_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: set_a,B2: set_a,F: set_a > set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: set_a,Y3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_115_ord__le__eq__subst,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_Pr451126599t_unit,C2: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ( F @ B2 )
% 0.16/1.25 = C2 )
% 0.16/1.25 => ( ! [X2: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X2 @ Y3 )
% 0.16/1.25 => ( ord_le2035129575t_unit @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/1.25 => ( ord_le2035129575t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_116_eq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_Pr451126599t_unit,Z: set_Pr451126599t_unit] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [X3: set_Pr451126599t_unit,Y4: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( ord_le2035129575t_unit @ X3 @ Y4 )
% 0.16/1.25 & ( ord_le2035129575t_unit @ Y4 @ X3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_117_eq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_Pr1720557880unit_a,Z: set_Pr1720557880unit_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [X3: set_Pr1720557880unit_a,Y4: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( ord_le2070001880unit_a @ X3 @ Y4 )
% 0.16/1.25 & ( ord_le2070001880unit_a @ Y4 @ X3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_118_eq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_Pr1628433942t_unit,Z: set_Pr1628433942t_unit] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [X3: set_Pr1628433942t_unit,Y4: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( ord_le1977877942t_unit @ X3 @ Y4 )
% 0.16/1.25 & ( ord_le1977877942t_unit @ Y4 @ X3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_119_eq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [X3: set_Product_prod_a_a,Y4: set_Product_prod_a_a] :
% 0.16/1.25 ( ( ord_le1824328871od_a_a @ X3 @ Y4 )
% 0.16/1.25 & ( ord_le1824328871od_a_a @ Y4 @ X3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_120_eq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [X3: set_a,Y4: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.16/1.25 & ( ord_less_eq_set_a @ Y4 @ X3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_121_eq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: refine424419629nres_a,Z: refine424419629nres_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.16/1.25 & ( ord_le519537037nres_a @ Y4 @ X3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_122_eq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: refine787176636t_unit,Z: refine787176636t_unit] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [X3: refine787176636t_unit,Y4: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X3 @ Y4 )
% 0.16/1.25 & ( ord_le1051254044t_unit @ Y4 @ X3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_123_antisym,axiom,
% 0.16/1.25 ! [X: set_Pr451126599t_unit,Y: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( ord_le2035129575t_unit @ X @ Y )
% 0.16/1.25 => ( ( ord_le2035129575t_unit @ Y @ X )
% 0.16/1.25 => ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_124_antisym,axiom,
% 0.16/1.25 ! [X: set_Pr1720557880unit_a,Y: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( ord_le2070001880unit_a @ X @ Y )
% 0.16/1.25 => ( ( ord_le2070001880unit_a @ Y @ X )
% 0.16/1.25 => ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_125_antisym,axiom,
% 0.16/1.25 ! [X: set_Pr1628433942t_unit,Y: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( ord_le1977877942t_unit @ X @ Y )
% 0.16/1.25 => ( ( ord_le1977877942t_unit @ Y @ X )
% 0.16/1.25 => ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_126_antisym,axiom,
% 0.16/1.25 ! [X: set_Product_prod_a_a,Y: set_Product_prod_a_a] :
% 0.16/1.25 ( ( ord_le1824328871od_a_a @ X @ Y )
% 0.16/1.25 => ( ( ord_le1824328871od_a_a @ Y @ X )
% 0.16/1.25 => ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_127_antisym,axiom,
% 0.16/1.25 ! [X: set_a,Y: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ X @ Y )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ Y @ X )
% 0.16/1.25 => ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_128_antisym,axiom,
% 0.16/1.25 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X @ Y )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ Y @ X )
% 0.16/1.25 => ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_129_antisym,axiom,
% 0.16/1.25 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X @ Y )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ Y @ X )
% 0.16/1.25 => ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_130_eq__refl,axiom,
% 0.16/1.25 ! [X: set_Pr451126599t_unit,Y: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( X = Y )
% 0.16/1.25 => ( ord_le2035129575t_unit @ X @ Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_131_eq__refl,axiom,
% 0.16/1.25 ! [X: set_Pr1720557880unit_a,Y: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( X = Y )
% 0.16/1.25 => ( ord_le2070001880unit_a @ X @ Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_132_eq__refl,axiom,
% 0.16/1.25 ! [X: set_Pr1628433942t_unit,Y: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( X = Y )
% 0.16/1.25 => ( ord_le1977877942t_unit @ X @ Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_133_eq__refl,axiom,
% 0.16/1.25 ! [X: set_Product_prod_a_a,Y: set_Product_prod_a_a] :
% 0.16/1.25 ( ( X = Y )
% 0.16/1.25 => ( ord_le1824328871od_a_a @ X @ Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_134_eq__refl,axiom,
% 0.16/1.25 ! [X: set_a,Y: set_a] :
% 0.16/1.25 ( ( X = Y )
% 0.16/1.25 => ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_135_eq__refl,axiom,
% 0.16/1.25 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.16/1.25 ( ( X = Y )
% 0.16/1.25 => ( ord_le519537037nres_a @ X @ Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_136_eq__refl,axiom,
% 0.16/1.25 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.16/1.25 ( ( X = Y )
% 0.16/1.25 => ( ord_le1051254044t_unit @ X @ Y ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_137_order_Otrans,axiom,
% 0.16/1.25 ! [A2: set_Pr451126599t_unit,B2: set_Pr451126599t_unit,C2: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( ord_le2035129575t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le2035129575t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ord_le2035129575t_unit @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_138_order_Otrans,axiom,
% 0.16/1.25 ! [A2: set_Pr1720557880unit_a,B2: set_Pr1720557880unit_a,C2: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( ord_le2070001880unit_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le2070001880unit_a @ B2 @ C2 )
% 0.16/1.25 => ( ord_le2070001880unit_a @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_139_order_Otrans,axiom,
% 0.16/1.25 ! [A2: set_Pr1628433942t_unit,B2: set_Pr1628433942t_unit,C2: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( ord_le1977877942t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le1977877942t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ord_le1977877942t_unit @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_140_order_Otrans,axiom,
% 0.16/1.25 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.16/1.25 ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le1824328871od_a_a @ B2 @ C2 )
% 0.16/1.25 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_141_order_Otrans,axiom,
% 0.16/1.25 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.16/1.25 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_142_order_Otrans,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_143_order_Otrans,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_144_mem__Collect__eq,axiom,
% 0.16/1.25 ! [A2: produc971140967t_unit,P: produc971140967t_unit > $o] :
% 0.16/1.25 ( ( member1423014800t_unit @ A2 @ ( collec797068754t_unit @ P ) )
% 0.16/1.25 = ( P @ A2 ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_145_mem__Collect__eq,axiom,
% 0.16/1.25 ! [A2: produc884009688unit_a,P: produc884009688unit_a > $o] :
% 0.16/1.25 ( ( member1211819009unit_a @ A2 @ ( collec535904323unit_a @ P ) )
% 0.16/1.25 = ( P @ A2 ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_146_mem__Collect__eq,axiom,
% 0.16/1.25 ! [A2: produc1767851702t_unit,P: produc1767851702t_unit > $o] :
% 0.16/1.25 ( ( member2095661023t_unit @ A2 @ ( collec1419746337t_unit @ P ) )
% 0.16/1.25 = ( P @ A2 ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_147_mem__Collect__eq,axiom,
% 0.16/1.25 ! [A2: product_prod_a_a,P: product_prod_a_a > $o] :
% 0.16/1.25 ( ( member449909584od_a_a @ A2 @ ( collec645855634od_a_a @ P ) )
% 0.16/1.25 = ( P @ A2 ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_148_mem__Collect__eq,axiom,
% 0.16/1.25 ! [A2: product_unit,P: product_unit > $o] :
% 0.16/1.25 ( ( member_Product_unit @ A2 @ ( collect_Product_unit @ P ) )
% 0.16/1.25 = ( P @ A2 ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_149_mem__Collect__eq,axiom,
% 0.16/1.25 ! [A2: a,P: a > $o] :
% 0.16/1.25 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.16/1.25 = ( P @ A2 ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_150_Collect__mem__eq,axiom,
% 0.16/1.25 ! [A: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( collec797068754t_unit
% 0.16/1.25 @ ^ [X3: produc971140967t_unit] : ( member1423014800t_unit @ X3 @ A ) )
% 0.16/1.25 = A ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_151_Collect__mem__eq,axiom,
% 0.16/1.25 ! [A: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( collec535904323unit_a
% 0.16/1.25 @ ^ [X3: produc884009688unit_a] : ( member1211819009unit_a @ X3 @ A ) )
% 0.16/1.25 = A ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_152_Collect__mem__eq,axiom,
% 0.16/1.25 ! [A: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( collec1419746337t_unit
% 0.16/1.25 @ ^ [X3: produc1767851702t_unit] : ( member2095661023t_unit @ X3 @ A ) )
% 0.16/1.25 = A ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_153_Collect__mem__eq,axiom,
% 0.16/1.25 ! [A: set_Product_prod_a_a] :
% 0.16/1.25 ( ( collec645855634od_a_a
% 0.16/1.25 @ ^ [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ A ) )
% 0.16/1.25 = A ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_154_Collect__mem__eq,axiom,
% 0.16/1.25 ! [A: set_Product_unit] :
% 0.16/1.25 ( ( collect_Product_unit
% 0.16/1.25 @ ^ [X3: product_unit] : ( member_Product_unit @ X3 @ A ) )
% 0.16/1.25 = A ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_155_Collect__mem__eq,axiom,
% 0.16/1.25 ! [A: set_a] :
% 0.16/1.25 ( ( collect_a
% 0.16/1.25 @ ^ [X3: a] : ( member_a @ X3 @ A ) )
% 0.16/1.25 = A ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_156_Collect__cong,axiom,
% 0.16/1.25 ! [P: product_unit > $o,Q: product_unit > $o] :
% 0.16/1.25 ( ! [X2: product_unit] :
% 0.16/1.25 ( ( P @ X2 )
% 0.16/1.25 = ( Q @ X2 ) )
% 0.16/1.25 => ( ( collect_Product_unit @ P )
% 0.16/1.25 = ( collect_Product_unit @ Q ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_157_Collect__cong,axiom,
% 0.16/1.25 ! [P: a > $o,Q: a > $o] :
% 0.16/1.25 ( ! [X2: a] :
% 0.16/1.25 ( ( P @ X2 )
% 0.16/1.25 = ( Q @ X2 ) )
% 0.16/1.25 => ( ( collect_a @ P )
% 0.16/1.25 = ( collect_a @ Q ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_158_antisym__conv,axiom,
% 0.16/1.25 ! [Y: set_Pr451126599t_unit,X: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( ord_le2035129575t_unit @ Y @ X )
% 0.16/1.25 => ( ( ord_le2035129575t_unit @ X @ Y )
% 0.16/1.25 = ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_159_antisym__conv,axiom,
% 0.16/1.25 ! [Y: set_Pr1720557880unit_a,X: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( ord_le2070001880unit_a @ Y @ X )
% 0.16/1.25 => ( ( ord_le2070001880unit_a @ X @ Y )
% 0.16/1.25 = ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_160_antisym__conv,axiom,
% 0.16/1.25 ! [Y: set_Pr1628433942t_unit,X: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( ord_le1977877942t_unit @ Y @ X )
% 0.16/1.25 => ( ( ord_le1977877942t_unit @ X @ Y )
% 0.16/1.25 = ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_161_antisym__conv,axiom,
% 0.16/1.25 ! [Y: set_Product_prod_a_a,X: set_Product_prod_a_a] :
% 0.16/1.25 ( ( ord_le1824328871od_a_a @ Y @ X )
% 0.16/1.25 => ( ( ord_le1824328871od_a_a @ X @ Y )
% 0.16/1.25 = ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_162_antisym__conv,axiom,
% 0.16/1.25 ! [Y: set_a,X: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ Y @ X )
% 0.16/1.25 => ( ( ord_less_eq_set_a @ X @ Y )
% 0.16/1.25 = ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_163_antisym__conv,axiom,
% 0.16/1.25 ! [Y: refine424419629nres_a,X: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ Y @ X )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ X @ Y )
% 0.16/1.25 = ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_164_antisym__conv,axiom,
% 0.16/1.25 ! [Y: refine787176636t_unit,X: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ Y @ X )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ X @ Y )
% 0.16/1.25 = ( X = Y ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_165_order__class_Oorder_Oeq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_Pr451126599t_unit,Z: set_Pr451126599t_unit] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [A3: set_Pr451126599t_unit,B3: set_Pr451126599t_unit] :
% 0.16/1.25 ( ( ord_le2035129575t_unit @ A3 @ B3 )
% 0.16/1.25 & ( ord_le2035129575t_unit @ B3 @ A3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_166_order__class_Oorder_Oeq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_Pr1720557880unit_a,Z: set_Pr1720557880unit_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [A3: set_Pr1720557880unit_a,B3: set_Pr1720557880unit_a] :
% 0.16/1.25 ( ( ord_le2070001880unit_a @ A3 @ B3 )
% 0.16/1.25 & ( ord_le2070001880unit_a @ B3 @ A3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_167_order__class_Oorder_Oeq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_Pr1628433942t_unit,Z: set_Pr1628433942t_unit] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [A3: set_Pr1628433942t_unit,B3: set_Pr1628433942t_unit] :
% 0.16/1.25 ( ( ord_le1977877942t_unit @ A3 @ B3 )
% 0.16/1.25 & ( ord_le1977877942t_unit @ B3 @ A3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_168_order__class_Oorder_Oeq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [A3: set_Product_prod_a_a,B3: set_Product_prod_a_a] :
% 0.16/1.25 ( ( ord_le1824328871od_a_a @ A3 @ B3 )
% 0.16/1.25 & ( ord_le1824328871od_a_a @ B3 @ A3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_169_order__class_Oorder_Oeq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: set_a,Z: set_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [A3: set_a,B3: set_a] :
% 0.16/1.25 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.16/1.25 & ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_170_order__class_Oorder_Oeq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: refine424419629nres_a,Z: refine424419629nres_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 0.16/1.25 & ( ord_le519537037nres_a @ B3 @ A3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_171_order__class_Oorder_Oeq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: refine787176636t_unit,Z: refine787176636t_unit] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [A3: refine787176636t_unit,B3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A3 @ B3 )
% 0.16/1.25 & ( ord_le1051254044t_unit @ B3 @ A3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_172_ord__eq__le__trans,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( A2 = B2 )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_173_ord__eq__le__trans,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( A2 = B2 )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B2 @ C2 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_174_ord__le__eq__trans,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( B2 = C2 )
% 0.16/1.25 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_175_ord__le__eq__trans,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( B2 = C2 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ A2 @ C2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_176_order__class_Oorder_Oantisym,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.16/1.25 => ( A2 = B2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_177_order__class_Oorder_Oantisym,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit,B2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ B2 @ A2 )
% 0.16/1.25 => ( A2 = B2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_178_order__trans,axiom,
% 0.16/1.25 ! [X: refine424419629nres_a,Y: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ X @ Y )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ Y @ Z2 )
% 0.16/1.25 => ( ord_le519537037nres_a @ X @ Z2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_179_order__trans,axiom,
% 0.16/1.25 ! [X: refine787176636t_unit,Y: refine787176636t_unit,Z2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ X @ Y )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ Y @ Z2 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ X @ Z2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_180_dual__order_Orefl,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ A2 ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_181_dual__order_Orefl,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit] : ( ord_le1051254044t_unit @ A2 @ A2 ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_182_dual__order_Otrans,axiom,
% 0.16/1.25 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ C2 @ B2 )
% 0.16/1.25 => ( ord_le519537037nres_a @ C2 @ A2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_183_dual__order_Otrans,axiom,
% 0.16/1.25 ! [B2: refine787176636t_unit,A2: refine787176636t_unit,C2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ B2 @ A2 )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ C2 @ B2 )
% 0.16/1.25 => ( ord_le1051254044t_unit @ C2 @ A2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_184_top__greatest,axiom,
% 0.16/1.25 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ top_to231829469nres_a ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_185_top__greatest,axiom,
% 0.16/1.25 ! [A2: refine787176636t_unit] : ( ord_le1051254044t_unit @ A2 @ top_to177290092t_unit ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_186_pwD1,axiom,
% 0.16/1.25 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ S @ S2 )
% 0.16/1.25 => ( ( refine412683989fail_a @ S2 )
% 0.16/1.25 => ( refine412683989fail_a @ S ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_187_pwD1,axiom,
% 0.16/1.25 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ S @ S2 )
% 0.16/1.25 => ( ( refine579265252t_unit @ S2 )
% 0.16/1.25 => ( refine579265252t_unit @ S ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_188_pwD2,axiom,
% 0.16/1.25 ! [S: refine424419629nres_a,S2: refine424419629nres_a,X: a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ S @ S2 )
% 0.16/1.25 => ( ( refine1001002027nres_a @ S @ X )
% 0.16/1.25 => ( refine1001002027nres_a @ S2 @ X ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_189_pwD2,axiom,
% 0.16/1.25 ! [S: refine787176636t_unit,S2: refine787176636t_unit,X: product_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ S @ S2 )
% 0.16/1.25 => ( ( refine558004794t_unit @ S @ X )
% 0.16/1.25 => ( refine558004794t_unit @ S2 @ X ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_190_dual__order_Oeq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: refine424419629nres_a,Z: refine424419629nres_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ B3 @ A3 )
% 0.16/1.25 & ( ord_le519537037nres_a @ A3 @ B3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_191_dual__order_Oeq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: refine787176636t_unit,Z: refine787176636t_unit] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [A3: refine787176636t_unit,B3: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ B3 @ A3 )
% 0.16/1.25 & ( ord_le1051254044t_unit @ A3 @ B3 ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_192_dual__order_Oantisym,axiom,
% 0.16/1.25 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.16/1.25 => ( A2 = B2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_193_dual__order_Oantisym,axiom,
% 0.16/1.25 ! [B2: refine787176636t_unit,A2: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ B2 @ A2 )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.16/1.25 => ( A2 = B2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_194_pw__eqI,axiom,
% 0.16/1.25 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.16/1.25 ( ( ( refine412683989fail_a @ S )
% 0.16/1.25 = ( refine412683989fail_a @ S2 ) )
% 0.16/1.25 => ( ! [X2: a] :
% 0.16/1.25 ( ( refine1001002027nres_a @ S @ X2 )
% 0.16/1.25 = ( refine1001002027nres_a @ S2 @ X2 ) )
% 0.16/1.25 => ( S = S2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_195_pw__eqI,axiom,
% 0.16/1.25 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.16/1.25 ( ( ( refine579265252t_unit @ S )
% 0.16/1.25 = ( refine579265252t_unit @ S2 ) )
% 0.16/1.25 => ( ! [X2: product_unit] :
% 0.16/1.25 ( ( refine558004794t_unit @ S @ X2 )
% 0.16/1.25 = ( refine558004794t_unit @ S2 @ X2 ) )
% 0.16/1.25 => ( S = S2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_196_pw__leI,axiom,
% 0.16/1.25 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 0.16/1.25 ( ( ( refine412683989fail_a @ S2 )
% 0.16/1.25 => ( ( refine412683989fail_a @ S )
% 0.16/1.25 & ! [X2: a] :
% 0.16/1.25 ( ( refine1001002027nres_a @ S @ X2 )
% 0.16/1.25 => ( refine1001002027nres_a @ S2 @ X2 ) ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ S @ S2 ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_197_pw__leI,axiom,
% 0.16/1.25 ! [S2: refine787176636t_unit,S: refine787176636t_unit] :
% 0.16/1.25 ( ( ( refine579265252t_unit @ S2 )
% 0.16/1.25 => ( ( refine579265252t_unit @ S )
% 0.16/1.25 & ! [X2: product_unit] :
% 0.16/1.25 ( ( refine558004794t_unit @ S @ X2 )
% 0.16/1.25 => ( refine558004794t_unit @ S2 @ X2 ) ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ S @ S2 ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_198_pw__leI_H,axiom,
% 0.16/1.25 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 0.16/1.25 ( ( ( refine412683989fail_a @ S2 )
% 0.16/1.25 => ( refine412683989fail_a @ S ) )
% 0.16/1.25 => ( ! [X2: a] :
% 0.16/1.25 ( ( refine412683989fail_a @ S2 )
% 0.16/1.25 => ( ( refine1001002027nres_a @ S @ X2 )
% 0.16/1.25 => ( refine1001002027nres_a @ S2 @ X2 ) ) )
% 0.16/1.25 => ( ord_le519537037nres_a @ S @ S2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_199_pw__leI_H,axiom,
% 0.16/1.25 ! [S2: refine787176636t_unit,S: refine787176636t_unit] :
% 0.16/1.25 ( ( ( refine579265252t_unit @ S2 )
% 0.16/1.25 => ( refine579265252t_unit @ S ) )
% 0.16/1.25 => ( ! [X2: product_unit] :
% 0.16/1.25 ( ( refine579265252t_unit @ S2 )
% 0.16/1.25 => ( ( refine558004794t_unit @ S @ X2 )
% 0.16/1.25 => ( refine558004794t_unit @ S2 @ X2 ) ) )
% 0.16/1.25 => ( ord_le1051254044t_unit @ S @ S2 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_200_abs__trans,axiom,
% 0.16/1.25 ! [R: set_Product_prod_a_a,C: refine424419629nres_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ C ) @ B )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R2 @ B ) @ A )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R2 @ ( refine1136779702un_a_a @ R @ C ) ) @ A ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_201_abs__trans,axiom,
% 0.16/1.25 ! [R: set_Product_prod_a_a,C: refine424419629nres_a,B: refine424419629nres_a,R2: set_Pr1628433942t_unit,A: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ C ) @ B )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R2 @ B ) @ A )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R2 @ ( refine1136779702un_a_a @ R @ C ) ) @ A ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_202_abs__trans,axiom,
% 0.16/1.25 ! [R: set_Pr1628433942t_unit,C: refine424419629nres_a,B: refine787176636t_unit,R2: set_Pr1720557880unit_a,A: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ C ) @ B )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R2 @ B ) @ A )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( refine364464487unit_a @ R2 @ ( refine341651653t_unit @ R @ C ) ) @ A ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_203_abs__trans,axiom,
% 0.16/1.25 ! [R: set_Pr1628433942t_unit,C: refine424419629nres_a,B: refine787176636t_unit,R2: set_Pr451126599t_unit,A: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ C ) @ B )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R2 @ B ) @ A )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R2 @ ( refine341651653t_unit @ R @ C ) ) @ A ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_204_abs__trans,axiom,
% 0.16/1.25 ! [R: set_Pr1720557880unit_a,C: refine787176636t_unit,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ C ) @ B )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R2 @ B ) @ A )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R2 @ ( refine364464487unit_a @ R @ C ) ) @ A ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_205_abs__trans,axiom,
% 0.16/1.25 ! [R: set_Pr1720557880unit_a,C: refine787176636t_unit,B: refine424419629nres_a,R2: set_Pr1628433942t_unit,A: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ C ) @ B )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R2 @ B ) @ A )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R2 @ ( refine364464487unit_a @ R @ C ) ) @ A ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_206_abs__trans,axiom,
% 0.16/1.25 ! [R: set_Pr451126599t_unit,C: refine787176636t_unit,B: refine787176636t_unit,R2: set_Pr1720557880unit_a,A: refine424419629nres_a] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ C ) @ B )
% 0.16/1.25 => ( ( ord_le519537037nres_a @ ( refine364464487unit_a @ R2 @ B ) @ A )
% 0.16/1.25 => ( ord_le519537037nres_a @ ( refine364464487unit_a @ R2 @ ( refine838861686t_unit @ R @ C ) ) @ A ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_207_abs__trans,axiom,
% 0.16/1.25 ! [R: set_Pr451126599t_unit,C: refine787176636t_unit,B: refine787176636t_unit,R2: set_Pr451126599t_unit,A: refine787176636t_unit] :
% 0.16/1.25 ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ C ) @ B )
% 0.16/1.25 => ( ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R2 @ B ) @ A )
% 0.16/1.25 => ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R2 @ ( refine838861686t_unit @ R @ C ) ) @ A ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_208_inres__def,axiom,
% 0.16/1.25 ( refine558004794t_unit
% 0.16/1.25 = ( ^ [S3: refine787176636t_unit,X3: product_unit] : ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ S3 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_209_inres__def,axiom,
% 0.16/1.25 ( refine1001002027nres_a
% 0.16/1.25 = ( ^ [S3: refine424419629nres_a,X3: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ S3 ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_210_pw__eq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: refine424419629nres_a,Z: refine424419629nres_a] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.16/1.25 ( ( ( refine412683989fail_a @ S3 )
% 0.16/1.25 = ( refine412683989fail_a @ S4 ) )
% 0.16/1.25 & ! [X3: a] :
% 0.16/1.25 ( ( refine1001002027nres_a @ S3 @ X3 )
% 0.16/1.25 = ( refine1001002027nres_a @ S4 @ X3 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_211_pw__eq__iff,axiom,
% 0.16/1.25 ( ( ^ [Y2: refine787176636t_unit,Z: refine787176636t_unit] : ( Y2 = Z ) )
% 0.16/1.25 = ( ^ [S3: refine787176636t_unit,S4: refine787176636t_unit] :
% 0.16/1.25 ( ( ( refine579265252t_unit @ S3 )
% 0.16/1.25 = ( refine579265252t_unit @ S4 ) )
% 0.16/1.25 & ! [X3: product_unit] :
% 0.16/1.25 ( ( refine558004794t_unit @ S3 @ X3 )
% 0.16/1.25 = ( refine558004794t_unit @ S4 @ X3 ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_212_pw__le__iff,axiom,
% 0.16/1.25 ( ord_le519537037nres_a
% 0.16/1.25 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.16/1.25 ( ( refine412683989fail_a @ S4 )
% 0.16/1.25 => ( ( refine412683989fail_a @ S3 )
% 0.16/1.25 & ! [X3: a] :
% 0.16/1.25 ( ( refine1001002027nres_a @ S3 @ X3 )
% 0.16/1.25 => ( refine1001002027nres_a @ S4 @ X3 ) ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_213_pw__le__iff,axiom,
% 0.16/1.25 ( ord_le1051254044t_unit
% 0.16/1.25 = ( ^ [S3: refine787176636t_unit,S4: refine787176636t_unit] :
% 0.16/1.25 ( ( refine579265252t_unit @ S4 )
% 0.16/1.25 => ( ( refine579265252t_unit @ S3 )
% 0.16/1.25 & ! [X3: product_unit] :
% 0.16/1.25 ( ( refine558004794t_unit @ S3 @ X3 )
% 0.16/1.25 => ( refine558004794t_unit @ S4 @ X3 ) ) ) ) ) ) ).
% 0.16/1.25
% 0.16/1.25 thf(fact_214_conc__trans,axiom,
% 0.16/1.26 ! [C: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ B ) )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R2 @ A ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ ( refine1441824853un_a_a @ R2 @ A ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_215_conc__trans,axiom,
% 0.16/1.26 ! [C: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,R2: set_Pr1628433942t_unit,A: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ B ) )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ B @ ( refine2021053540t_unit @ R2 @ A ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ ( refine2021053540t_unit @ R2 @ A ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_216_conc__trans,axiom,
% 0.16/1.26 ! [C: refine787176636t_unit,R: set_Pr1720557880unit_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ R @ B ) )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R2 @ A ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ R @ ( refine1441824853un_a_a @ R2 @ A ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_217_conc__trans,axiom,
% 0.16/1.26 ! [C: refine787176636t_unit,R: set_Pr1720557880unit_a,B: refine424419629nres_a,R2: set_Pr1628433942t_unit,A: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ R @ B ) )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ B @ ( refine2021053540t_unit @ R2 @ A ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ C @ ( refine2043866374unit_a @ R @ ( refine2021053540t_unit @ R2 @ A ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_218_conc__trans,axiom,
% 0.16/1.26 ! [C: refine424419629nres_a,R: set_Pr1628433942t_unit,B: refine787176636t_unit,R2: set_Pr1720557880unit_a,A: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ R @ B ) )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ B @ ( refine2043866374unit_a @ R2 @ A ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ R @ ( refine2043866374unit_a @ R2 @ A ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_219_conc__trans,axiom,
% 0.16/1.26 ! [C: refine424419629nres_a,R: set_Pr1628433942t_unit,B: refine787176636t_unit,R2: set_Pr451126599t_unit,A: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ R @ B ) )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ B @ ( refine944483349t_unit @ R2 @ A ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ C @ ( refine2021053540t_unit @ R @ ( refine944483349t_unit @ R2 @ A ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_220_conc__trans,axiom,
% 0.16/1.26 ! [C: refine787176636t_unit,R: set_Pr451126599t_unit,B: refine787176636t_unit,R2: set_Pr1720557880unit_a,A: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ R @ B ) )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ B @ ( refine2043866374unit_a @ R2 @ A ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ R @ ( refine2043866374unit_a @ R2 @ A ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_221_conc__trans,axiom,
% 0.16/1.26 ! [C: refine787176636t_unit,R: set_Pr451126599t_unit,B: refine787176636t_unit,R2: set_Pr451126599t_unit,A: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ R @ B ) )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ B @ ( refine944483349t_unit @ R2 @ A ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ C @ ( refine944483349t_unit @ R @ ( refine944483349t_unit @ R2 @ A ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_222_le__nofailI,axiom,
% 0.16/1.26 ! [M2: refine424419629nres_a,M: refine424419629nres_a] :
% 0.16/1.26 ( ( ( refine412683989fail_a @ M2 )
% 0.16/1.26 => ( ord_le519537037nres_a @ M @ M2 ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ M @ M2 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_223_le__nofailI,axiom,
% 0.16/1.26 ! [M2: refine787176636t_unit,M: refine787176636t_unit] :
% 0.16/1.26 ( ( ( refine579265252t_unit @ M2 )
% 0.16/1.26 => ( ord_le1051254044t_unit @ M @ M2 ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ M @ M2 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_224_top_Oextremum__unique,axiom,
% 0.16/1.26 ! [A2: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A2 )
% 0.16/1.26 = ( A2 = top_to231829469nres_a ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_225_top_Oextremum__unique,axiom,
% 0.16/1.26 ! [A2: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A2 )
% 0.16/1.26 = ( A2 = top_to177290092t_unit ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_226_pw__bind__leI,axiom,
% 0.16/1.26 ! [S: refine424419629nres_a,M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.16/1.26 ( ( ( refine412683989fail_a @ S )
% 0.16/1.26 => ( refine412683989fail_a @ M ) )
% 0.16/1.26 => ( ! [X2: a] :
% 0.16/1.26 ( ( refine412683989fail_a @ M )
% 0.16/1.26 => ( ( refine1001002027nres_a @ M @ X2 )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( F @ X2 ) @ S ) ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ S ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_227_pw__bind__leI,axiom,
% 0.16/1.26 ! [S: refine787176636t_unit,M: refine424419629nres_a,F: a > refine787176636t_unit] :
% 0.16/1.26 ( ( ( refine579265252t_unit @ S )
% 0.16/1.26 => ( refine412683989fail_a @ M ) )
% 0.16/1.26 => ( ! [X2: a] :
% 0.16/1.26 ( ( refine412683989fail_a @ M )
% 0.16/1.26 => ( ( refine1001002027nres_a @ M @ X2 )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ S ) ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M @ F ) @ S ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_228_pw__bind__leI,axiom,
% 0.16/1.26 ! [S: refine424419629nres_a,M: refine787176636t_unit,F: product_unit > refine424419629nres_a] :
% 0.16/1.26 ( ( ( refine412683989fail_a @ S )
% 0.16/1.26 => ( refine579265252t_unit @ M ) )
% 0.16/1.26 => ( ! [X2: product_unit] :
% 0.16/1.26 ( ( refine579265252t_unit @ M )
% 0.16/1.26 => ( ( refine558004794t_unit @ M @ X2 )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( F @ X2 ) @ S ) ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( refine119808503unit_a @ M @ F ) @ S ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_229_pw__bind__leI,axiom,
% 0.16/1.26 ! [S: refine787176636t_unit,M: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 0.16/1.26 ( ( ( refine579265252t_unit @ S )
% 0.16/1.26 => ( refine579265252t_unit @ M ) )
% 0.16/1.26 => ( ! [X2: product_unit] :
% 0.16/1.26 ( ( refine579265252t_unit @ M )
% 0.16/1.26 => ( ( refine558004794t_unit @ M @ X2 )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ S ) ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M @ F ) @ S ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_230_top_Oextremum__uniqueI,axiom,
% 0.16/1.26 ! [A2: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A2 )
% 0.16/1.26 => ( A2 = top_to231829469nres_a ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_231_top_Oextremum__uniqueI,axiom,
% 0.16/1.26 ! [A2: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A2 )
% 0.16/1.26 => ( A2 = top_to177290092t_unit ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_232_pw__bind__le__iff,axiom,
% 0.16/1.26 ! [M: refine424419629nres_a,F: a > refine424419629nres_a,S: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ S )
% 0.16/1.26 = ( ( ( refine412683989fail_a @ S )
% 0.16/1.26 => ( refine412683989fail_a @ M ) )
% 0.16/1.26 & ! [X3: a] :
% 0.16/1.26 ( ( ( refine412683989fail_a @ M )
% 0.16/1.26 & ( refine1001002027nres_a @ M @ X3 ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( F @ X3 ) @ S ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_233_pw__bind__le__iff,axiom,
% 0.16/1.26 ! [M: refine424419629nres_a,F: a > refine787176636t_unit,S: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M @ F ) @ S )
% 0.16/1.26 = ( ( ( refine579265252t_unit @ S )
% 0.16/1.26 => ( refine412683989fail_a @ M ) )
% 0.16/1.26 & ! [X3: a] :
% 0.16/1.26 ( ( ( refine412683989fail_a @ M )
% 0.16/1.26 & ( refine1001002027nres_a @ M @ X3 ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ S ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_234_pw__bind__le__iff,axiom,
% 0.16/1.26 ! [M: refine787176636t_unit,F: product_unit > refine424419629nres_a,S: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine119808503unit_a @ M @ F ) @ S )
% 0.16/1.26 = ( ( ( refine412683989fail_a @ S )
% 0.16/1.26 => ( refine579265252t_unit @ M ) )
% 0.16/1.26 & ! [X3: product_unit] :
% 0.16/1.26 ( ( ( refine579265252t_unit @ M )
% 0.16/1.26 & ( refine558004794t_unit @ M @ X3 ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( F @ X3 ) @ S ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_235_pw__bind__le__iff,axiom,
% 0.16/1.26 ! [M: refine787176636t_unit,F: product_unit > refine787176636t_unit,S: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M @ F ) @ S )
% 0.16/1.26 = ( ( ( refine579265252t_unit @ S )
% 0.16/1.26 => ( refine579265252t_unit @ M ) )
% 0.16/1.26 & ! [X3: product_unit] :
% 0.16/1.26 ( ( ( refine579265252t_unit @ M )
% 0.16/1.26 & ( refine558004794t_unit @ M @ X3 ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ S ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_236_pw__conc__nofail,axiom,
% 0.16/1.26 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 0.16/1.26 ( ( refine412683989fail_a @ ( refine1441824853un_a_a @ R @ S ) )
% 0.16/1.26 = ( refine412683989fail_a @ S ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_237_pw__conc__nofail,axiom,
% 0.16/1.26 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 0.16/1.26 ( ( refine579265252t_unit @ ( refine2043866374unit_a @ R @ S ) )
% 0.16/1.26 = ( refine412683989fail_a @ S ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_238_pw__conc__nofail,axiom,
% 0.16/1.26 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 0.16/1.26 ( ( refine412683989fail_a @ ( refine2021053540t_unit @ R @ S ) )
% 0.16/1.26 = ( refine579265252t_unit @ S ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_239_pw__conc__nofail,axiom,
% 0.16/1.26 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.16/1.26 ( ( refine579265252t_unit @ ( refine944483349t_unit @ R @ S ) )
% 0.16/1.26 = ( refine579265252t_unit @ S ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_240_not__nofail__inres,axiom,
% 0.16/1.26 ! [S: refine424419629nres_a,X: a] :
% 0.16/1.26 ( ~ ( refine412683989fail_a @ S )
% 0.16/1.26 => ( refine1001002027nres_a @ S @ X ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_241_not__nofail__inres,axiom,
% 0.16/1.26 ! [S: refine787176636t_unit,X: product_unit] :
% 0.16/1.26 ( ~ ( refine579265252t_unit @ S )
% 0.16/1.26 => ( refine558004794t_unit @ S @ X ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_242_bot_Oextremum__uniqueI,axiom,
% 0.16/1.26 ! [A2: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ A2 @ bot_bo529555393nres_a )
% 0.16/1.26 => ( A2 = bot_bo529555393nres_a ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_243_bot_Oextremum__uniqueI,axiom,
% 0.16/1.26 ! [A2: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ A2 @ bot_bo658782032t_unit )
% 0.16/1.26 => ( A2 = bot_bo658782032t_unit ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_244_bot_Oextremum__unique,axiom,
% 0.16/1.26 ! [A2: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ A2 @ bot_bo529555393nres_a )
% 0.16/1.26 = ( A2 = bot_bo529555393nres_a ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_245_bot_Oextremum__unique,axiom,
% 0.16/1.26 ! [A2: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ A2 @ bot_bo658782032t_unit )
% 0.16/1.26 = ( A2 = bot_bo658782032t_unit ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_246_bot_Oextremum,axiom,
% 0.16/1.26 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A2 ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_247_bot_Oextremum,axiom,
% 0.16/1.26 ! [A2: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ A2 ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_248_pw__bind__nofail,axiom,
% 0.16/1.26 ! [M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.16/1.26 ( ( refine412683989fail_a @ ( refine436832838nd_a_a @ M @ F ) )
% 0.16/1.26 = ( ( refine412683989fail_a @ M )
% 0.16/1.26 & ! [X3: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ M @ X3 )
% 0.16/1.26 => ( refine412683989fail_a @ ( F @ X3 ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_249_pw__bind__nofail,axiom,
% 0.16/1.26 ! [M: refine424419629nres_a,F: a > refine787176636t_unit] :
% 0.16/1.26 ( ( refine579265252t_unit @ ( refine96995669t_unit @ M @ F ) )
% 0.16/1.26 = ( ( refine412683989fail_a @ M )
% 0.16/1.26 & ! [X3: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ M @ X3 )
% 0.16/1.26 => ( refine579265252t_unit @ ( F @ X3 ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_250_pw__bind__nofail,axiom,
% 0.16/1.26 ! [M: refine787176636t_unit,F: product_unit > refine424419629nres_a] :
% 0.16/1.26 ( ( refine412683989fail_a @ ( refine119808503unit_a @ M @ F ) )
% 0.16/1.26 = ( ( refine579265252t_unit @ M )
% 0.16/1.26 & ! [X3: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ M @ X3 )
% 0.16/1.26 => ( refine412683989fail_a @ ( F @ X3 ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_251_pw__bind__nofail,axiom,
% 0.16/1.26 ! [M: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 0.16/1.26 ( ( refine579265252t_unit @ ( refine681446406t_unit @ M @ F ) )
% 0.16/1.26 = ( ( refine579265252t_unit @ M )
% 0.16/1.26 & ! [X3: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ M @ X3 )
% 0.16/1.26 => ( refine579265252t_unit @ ( F @ X3 ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_252_bind__cong,axiom,
% 0.16/1.26 ! [M3: refine787176636t_unit,M4: refine787176636t_unit,F: product_unit > refine424419629nres_a,F2: product_unit > refine424419629nres_a] :
% 0.16/1.26 ( ( M3 = M4 )
% 0.16/1.26 => ( ! [X2: product_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X2 ) @ M4 )
% 0.16/1.26 => ( ( F @ X2 )
% 0.16/1.26 = ( F2 @ X2 ) ) )
% 0.16/1.26 => ( ( refine119808503unit_a @ M3 @ F )
% 0.16/1.26 = ( refine119808503unit_a @ M4 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_253_bind__cong,axiom,
% 0.16/1.26 ! [M3: refine787176636t_unit,M4: refine787176636t_unit,F: product_unit > refine787176636t_unit,F2: product_unit > refine787176636t_unit] :
% 0.16/1.26 ( ( M3 = M4 )
% 0.16/1.26 => ( ! [X2: product_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X2 ) @ M4 )
% 0.16/1.26 => ( ( F @ X2 )
% 0.16/1.26 = ( F2 @ X2 ) ) )
% 0.16/1.26 => ( ( refine681446406t_unit @ M3 @ F )
% 0.16/1.26 = ( refine681446406t_unit @ M4 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_254_bind__cong,axiom,
% 0.16/1.26 ! [M3: refine424419629nres_a,M4: refine424419629nres_a,F: a > refine424419629nres_a,F2: a > refine424419629nres_a] :
% 0.16/1.26 ( ( M3 = M4 )
% 0.16/1.26 => ( ! [X2: a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M4 )
% 0.16/1.26 => ( ( F @ X2 )
% 0.16/1.26 = ( F2 @ X2 ) ) )
% 0.16/1.26 => ( ( refine436832838nd_a_a @ M3 @ F )
% 0.16/1.26 = ( refine436832838nd_a_a @ M4 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_255_bind__cong,axiom,
% 0.16/1.26 ! [M3: refine424419629nres_a,M4: refine424419629nres_a,F: a > refine787176636t_unit,F2: a > refine787176636t_unit] :
% 0.16/1.26 ( ( M3 = M4 )
% 0.16/1.26 => ( ! [X2: a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M4 )
% 0.16/1.26 => ( ( F @ X2 )
% 0.16/1.26 = ( F2 @ X2 ) ) )
% 0.16/1.26 => ( ( refine96995669t_unit @ M3 @ F )
% 0.16/1.26 = ( refine96995669t_unit @ M4 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_256_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.16/1.26 ! [M: refine787176636t_unit,M2: refine787176636t_unit,F: product_unit > refine424419629nres_a,F2: product_unit > refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ M @ M2 )
% 0.16/1.26 => ( ! [X2: product_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X2 ) @ M )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F2 @ X2 ) ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( refine119808503unit_a @ M @ F ) @ ( refine119808503unit_a @ M2 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_257_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.16/1.26 ! [M: refine787176636t_unit,M2: refine787176636t_unit,F: product_unit > refine787176636t_unit,F2: product_unit > refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ M @ M2 )
% 0.16/1.26 => ( ! [X2: product_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X2 ) @ M )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F2 @ X2 ) ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M @ F ) @ ( refine681446406t_unit @ M2 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_258_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.16/1.26 ! [M: refine424419629nres_a,M2: refine424419629nres_a,F: a > refine424419629nres_a,F2: a > refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ M @ M2 )
% 0.16/1.26 => ( ! [X2: a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F2 @ X2 ) ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ ( refine436832838nd_a_a @ M2 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_259_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.16/1.26 ! [M: refine424419629nres_a,M2: refine424419629nres_a,F: a > refine787176636t_unit,F2: a > refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ M @ M2 )
% 0.16/1.26 => ( ! [X2: a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( F @ X2 ) @ ( F2 @ X2 ) ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M @ F ) @ ( refine96995669t_unit @ M2 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_260_nres__inequalities_I2_J,axiom,
% 0.16/1.26 top_to177290092t_unit != bot_bo658782032t_unit ).
% 0.16/1.26
% 0.16/1.26 thf(fact_261_nres__inequalities_I2_J,axiom,
% 0.16/1.26 top_to231829469nres_a != bot_bo529555393nres_a ).
% 0.16/1.26
% 0.16/1.26 thf(fact_262_nres__inequalities_I4_J,axiom,
% 0.16/1.26 bot_bo658782032t_unit != top_to177290092t_unit ).
% 0.16/1.26
% 0.16/1.26 thf(fact_263_nres__inequalities_I4_J,axiom,
% 0.16/1.26 bot_bo529555393nres_a != top_to231829469nres_a ).
% 0.16/1.26
% 0.16/1.26 thf(fact_264_order__mono__setup_Orefl,axiom,
% 0.16/1.26 ! [X: refine424419629nres_a] : ( ord_le519537037nres_a @ X @ X ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_265_order__mono__setup_Orefl,axiom,
% 0.16/1.26 ! [X: refine787176636t_unit] : ( ord_le1051254044t_unit @ X @ X ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_266_nf__inres__def,axiom,
% 0.16/1.26 ( refine1312857699nres_a
% 0.16/1.26 = ( ^ [M5: refine424419629nres_a,X3: a] :
% 0.16/1.26 ( ( refine412683989fail_a @ M5 )
% 0.16/1.26 & ( refine1001002027nres_a @ M5 @ X3 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_267_nf__inres__def,axiom,
% 0.16/1.26 ( refine983493746t_unit
% 0.16/1.26 = ( ^ [M5: refine787176636t_unit,X3: product_unit] :
% 0.16/1.26 ( ( refine579265252t_unit @ M5 )
% 0.16/1.26 & ( refine558004794t_unit @ M5 @ X3 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_268_meta__le__everything__if__top,axiom,
% 0.16/1.26 ! [M3: refine424419629nres_a,X: refine424419629nres_a] :
% 0.16/1.26 ( ( M3 = top_to231829469nres_a )
% 0.16/1.26 => ( ord_le519537037nres_a @ X @ M3 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_269_meta__le__everything__if__top,axiom,
% 0.16/1.26 ! [M3: refine787176636t_unit,X: refine787176636t_unit] :
% 0.16/1.26 ( ( M3 = top_to177290092t_unit )
% 0.16/1.26 => ( ord_le1051254044t_unit @ X @ M3 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_270_pw__flat__le__iff,axiom,
% 0.16/1.26 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.16/1.26 ( ( partia906949161nres_a @ bot_bo529555393nres_a @ S @ S2 )
% 0.16/1.26 = ( ? [X4: a] : ( refine1001002027nres_a @ S @ X4 )
% 0.16/1.26 => ( ( ( refine412683989fail_a @ S )
% 0.16/1.26 = ( refine412683989fail_a @ S2 ) )
% 0.16/1.26 & ! [X3: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ S @ X3 )
% 0.16/1.26 = ( refine1001002027nres_a @ S2 @ X3 ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_271_pw__flat__le__iff,axiom,
% 0.16/1.26 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.16/1.26 ( ( partia1658438072t_unit @ bot_bo658782032t_unit @ S @ S2 )
% 0.16/1.26 = ( ? [X4: product_unit] : ( refine558004794t_unit @ S @ X4 )
% 0.16/1.26 => ( ( ( refine579265252t_unit @ S )
% 0.16/1.26 = ( refine579265252t_unit @ S2 ) )
% 0.16/1.26 & ! [X3: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ S @ X3 )
% 0.16/1.26 = ( refine558004794t_unit @ S2 @ X3 ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_272_pw__abs__inres,axiom,
% 0.16/1.26 ! [R: set_Product_prod_a_a,M: refine424419629nres_a,A2: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ ( refine1136779702un_a_a @ R @ M ) @ A2 )
% 0.16/1.26 = ( ( refine412683989fail_a @ ( refine1136779702un_a_a @ R @ M ) )
% 0.16/1.26 => ? [C3: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ M @ C3 )
% 0.16/1.26 & ( member449909584od_a_a @ ( product_Pair_a_a @ C3 @ A2 ) @ R ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_273_pw__abs__inres,axiom,
% 0.16/1.26 ! [R: set_Pr1628433942t_unit,M: refine424419629nres_a,A2: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ ( refine341651653t_unit @ R @ M ) @ A2 )
% 0.16/1.26 = ( ( refine579265252t_unit @ ( refine341651653t_unit @ R @ M ) )
% 0.16/1.26 => ? [C3: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ M @ C3 )
% 0.16/1.26 & ( member2095661023t_unit @ ( produc1776699686t_unit @ C3 @ A2 ) @ R ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_274_pw__abs__inres,axiom,
% 0.16/1.26 ! [R: set_Pr1720557880unit_a,M: refine787176636t_unit,A2: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ ( refine364464487unit_a @ R @ M ) @ A2 )
% 0.16/1.26 = ( ( refine412683989fail_a @ ( refine364464487unit_a @ R @ M ) )
% 0.16/1.26 => ? [C3: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ M @ C3 )
% 0.16/1.26 & ( member1211819009unit_a @ ( produc1799512520unit_a @ C3 @ A2 ) @ R ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_275_pw__abs__inres,axiom,
% 0.16/1.26 ! [R: set_Pr451126599t_unit,M: refine787176636t_unit,A2: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ ( refine838861686t_unit @ R @ M ) @ A2 )
% 0.16/1.26 = ( ( refine579265252t_unit @ ( refine838861686t_unit @ R @ M ) )
% 0.16/1.26 => ? [C3: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ M @ C3 )
% 0.16/1.26 & ( member1423014800t_unit @ ( produc1076565719t_unit @ C3 @ A2 ) @ R ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_276_pw__abs__nofail,axiom,
% 0.16/1.26 ! [R: set_Product_prod_a_a,M: refine424419629nres_a] :
% 0.16/1.26 ( ( refine412683989fail_a @ ( refine1136779702un_a_a @ R @ M ) )
% 0.16/1.26 = ( ( refine412683989fail_a @ M )
% 0.16/1.26 & ! [X3: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ M @ X3 )
% 0.16/1.26 => ( member_a @ X3 @ ( domain_a_a @ R ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_277_pw__abs__nofail,axiom,
% 0.16/1.26 ! [R: set_Pr1628433942t_unit,M: refine424419629nres_a] :
% 0.16/1.26 ( ( refine579265252t_unit @ ( refine341651653t_unit @ R @ M ) )
% 0.16/1.26 = ( ( refine412683989fail_a @ M )
% 0.16/1.26 & ! [X3: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ M @ X3 )
% 0.16/1.26 => ( member_a @ X3 @ ( domain799550107t_unit @ R ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_278_pw__abs__nofail,axiom,
% 0.16/1.26 ! [R: set_Pr1720557880unit_a,M: refine787176636t_unit] :
% 0.16/1.26 ( ( refine412683989fail_a @ ( refine364464487unit_a @ R @ M ) )
% 0.16/1.26 = ( ( refine579265252t_unit @ M )
% 0.16/1.26 & ! [X3: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ M @ X3 )
% 0.16/1.26 => ( member_Product_unit @ X3 @ ( domain822362941unit_a @ R ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_279_pw__abs__nofail,axiom,
% 0.16/1.26 ! [R: set_Pr451126599t_unit,M: refine787176636t_unit] :
% 0.16/1.26 ( ( refine579265252t_unit @ ( refine838861686t_unit @ R @ M ) )
% 0.16/1.26 = ( ( refine579265252t_unit @ M )
% 0.16/1.26 & ! [X3: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ M @ X3 )
% 0.16/1.26 => ( member_Product_unit @ X3 @ ( domain2090798924t_unit @ R ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_280_conc__abs__swap,axiom,
% 0.16/1.26 ! [R: set_Product_prod_a_a,M4: refine424419629nres_a,M3: refine424419629nres_a] :
% 0.16/1.26 ( ( single_valued_a_a @ R )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ M4 @ ( refine1441824853un_a_a @ R @ M3 ) )
% 0.16/1.26 = ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ M4 ) @ M3 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_281_conc__abs__swap,axiom,
% 0.16/1.26 ! [R: set_Pr1720557880unit_a,M4: refine787176636t_unit,M3: refine424419629nres_a] :
% 0.16/1.26 ( ( single249782708unit_a @ R )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ M4 @ ( refine2043866374unit_a @ R @ M3 ) )
% 0.16/1.26 = ( ord_le519537037nres_a @ ( refine364464487unit_a @ R @ M4 ) @ M3 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_282_conc__abs__swap,axiom,
% 0.16/1.26 ! [R: set_Pr1628433942t_unit,M4: refine424419629nres_a,M3: refine787176636t_unit] :
% 0.16/1.26 ( ( single226969874t_unit @ R )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ M4 @ ( refine2021053540t_unit @ R @ M3 ) )
% 0.16/1.26 = ( ord_le1051254044t_unit @ ( refine341651653t_unit @ R @ M4 ) @ M3 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_283_conc__abs__swap,axiom,
% 0.16/1.26 ! [R: set_Pr451126599t_unit,M4: refine787176636t_unit,M3: refine787176636t_unit] :
% 0.16/1.26 ( ( single330234563t_unit @ R )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ M4 @ ( refine944483349t_unit @ R @ M3 ) )
% 0.16/1.26 = ( ord_le1051254044t_unit @ ( refine838861686t_unit @ R @ M4 ) @ M3 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_284_pw__flat__ge__iff,axiom,
% 0.16/1.26 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.16/1.26 ( ( partia906949161nres_a @ top_to231829469nres_a @ S @ S2 )
% 0.16/1.26 = ( ( refine412683989fail_a @ S )
% 0.16/1.26 => ( ( refine412683989fail_a @ S2 )
% 0.16/1.26 & ! [X3: a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ S @ X3 )
% 0.16/1.26 = ( refine1001002027nres_a @ S2 @ X3 ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_285_pw__flat__ge__iff,axiom,
% 0.16/1.26 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.16/1.26 ( ( partia1658438072t_unit @ top_to177290092t_unit @ S @ S2 )
% 0.16/1.26 = ( ( refine579265252t_unit @ S )
% 0.16/1.26 => ( ( refine579265252t_unit @ S2 )
% 0.16/1.26 & ! [X3: product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ S @ X3 )
% 0.16/1.26 = ( refine558004794t_unit @ S2 @ X3 ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_286_GreatestI2__order,axiom,
% 0.16/1.26 ! [P: refine424419629nres_a > $o,X: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 0.16/1.26 ( ( P @ X )
% 0.16/1.26 => ( ! [Y3: refine424419629nres_a] :
% 0.16/1.26 ( ( P @ Y3 )
% 0.16/1.26 => ( ord_le519537037nres_a @ Y3 @ X ) )
% 0.16/1.26 => ( ! [X2: refine424419629nres_a] :
% 0.16/1.26 ( ( P @ X2 )
% 0.16/1.26 => ( ! [Y5: refine424419629nres_a] :
% 0.16/1.26 ( ( P @ Y5 )
% 0.16/1.26 => ( ord_le519537037nres_a @ Y5 @ X2 ) )
% 0.16/1.26 => ( Q @ X2 ) ) )
% 0.16/1.26 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_287_GreatestI2__order,axiom,
% 0.16/1.26 ! [P: refine787176636t_unit > $o,X: refine787176636t_unit,Q: refine787176636t_unit > $o] :
% 0.16/1.26 ( ( P @ X )
% 0.16/1.26 => ( ! [Y3: refine787176636t_unit] :
% 0.16/1.26 ( ( P @ Y3 )
% 0.16/1.26 => ( ord_le1051254044t_unit @ Y3 @ X ) )
% 0.16/1.26 => ( ! [X2: refine787176636t_unit] :
% 0.16/1.26 ( ( P @ X2 )
% 0.16/1.26 => ( ! [Y5: refine787176636t_unit] :
% 0.16/1.26 ( ( P @ Y5 )
% 0.16/1.26 => ( ord_le1051254044t_unit @ Y5 @ X2 ) )
% 0.16/1.26 => ( Q @ X2 ) ) )
% 0.16/1.26 => ( Q @ ( order_453013155t_unit @ P ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_288_Greatest__equality,axiom,
% 0.16/1.26 ! [P: refine424419629nres_a > $o,X: refine424419629nres_a] :
% 0.16/1.26 ( ( P @ X )
% 0.16/1.26 => ( ! [Y3: refine424419629nres_a] :
% 0.16/1.26 ( ( P @ Y3 )
% 0.16/1.26 => ( ord_le519537037nres_a @ Y3 @ X ) )
% 0.16/1.26 => ( ( order_1714329108nres_a @ P )
% 0.16/1.26 = X ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_289_Greatest__equality,axiom,
% 0.16/1.26 ! [P: refine787176636t_unit > $o,X: refine787176636t_unit] :
% 0.16/1.26 ( ( P @ X )
% 0.16/1.26 => ( ! [Y3: refine787176636t_unit] :
% 0.16/1.26 ( ( P @ Y3 )
% 0.16/1.26 => ( ord_le1051254044t_unit @ Y3 @ X ) )
% 0.16/1.26 => ( ( order_453013155t_unit @ P )
% 0.16/1.26 = X ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_290_Refine__Misc_Oif__mono,axiom,
% 0.16/1.26 ! [B2: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M22: refine424419629nres_a,M23: refine424419629nres_a] :
% 0.16/1.26 ( ( B2
% 0.16/1.26 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 0.16/1.26 => ( ( ~ B2
% 0.16/1.26 => ( ord_le519537037nres_a @ M22 @ M23 ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ M1 @ M22 ) @ ( if_Ref1724547303nres_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_291_Refine__Misc_Oif__mono,axiom,
% 0.16/1.26 ! [B2: $o,M1: refine787176636t_unit,M12: refine787176636t_unit,M22: refine787176636t_unit,M23: refine787176636t_unit] :
% 0.16/1.26 ( ( B2
% 0.16/1.26 => ( ord_le1051254044t_unit @ M1 @ M12 ) )
% 0.16/1.26 => ( ( ~ B2
% 0.16/1.26 => ( ord_le1051254044t_unit @ M22 @ M23 ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B2 @ M1 @ M22 ) @ ( if_Ref1369692790t_unit @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_292_flat__ord__compat_I1_J,axiom,
% 0.16/1.26 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.16/1.26 ( ( partia906949161nres_a @ bot_bo529555393nres_a @ X @ Y )
% 0.16/1.26 => ( ord_le519537037nres_a @ X @ Y ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_293_flat__ord__compat_I1_J,axiom,
% 0.16/1.26 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.16/1.26 ( ( partia1658438072t_unit @ bot_bo658782032t_unit @ X @ Y )
% 0.16/1.26 => ( ord_le1051254044t_unit @ X @ Y ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_294_flat__ord__compat_I2_J,axiom,
% 0.16/1.26 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.16/1.26 ( ( partia906949161nres_a @ top_to231829469nres_a @ X @ Y )
% 0.16/1.26 => ( ord_le519537037nres_a @ Y @ X ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_295_flat__ord__compat_I2_J,axiom,
% 0.16/1.26 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.16/1.26 ( ( partia1658438072t_unit @ top_to177290092t_unit @ X @ Y )
% 0.16/1.26 => ( ord_le1051254044t_unit @ Y @ X ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_296_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.16/1.26 ! [M: refine787176636t_unit,M2: refine787176636t_unit,F: product_unit > refine424419629nres_a,F2: product_unit > refine424419629nres_a] :
% 0.16/1.26 ( ( partia1658438072t_unit @ top_to177290092t_unit @ M @ M2 )
% 0.16/1.26 => ( ! [X2: product_unit] : ( partia906949161nres_a @ top_to231829469nres_a @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.16/1.26 => ( partia906949161nres_a @ top_to231829469nres_a @ ( refine119808503unit_a @ M @ F ) @ ( refine119808503unit_a @ M2 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_297_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.16/1.26 ! [M: refine424419629nres_a,M2: refine424419629nres_a,F: a > refine424419629nres_a,F2: a > refine424419629nres_a] :
% 0.16/1.26 ( ( partia906949161nres_a @ top_to231829469nres_a @ M @ M2 )
% 0.16/1.26 => ( ! [X2: a] : ( partia906949161nres_a @ top_to231829469nres_a @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.16/1.26 => ( partia906949161nres_a @ top_to231829469nres_a @ ( refine436832838nd_a_a @ M @ F ) @ ( refine436832838nd_a_a @ M2 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_298_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.16/1.26 ! [M: refine424419629nres_a,M2: refine424419629nres_a,F: a > refine787176636t_unit,F2: a > refine787176636t_unit] :
% 0.16/1.26 ( ( partia906949161nres_a @ top_to231829469nres_a @ M @ M2 )
% 0.16/1.26 => ( ! [X2: a] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.16/1.26 => ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine96995669t_unit @ M @ F ) @ ( refine96995669t_unit @ M2 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_299_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.16/1.26 ! [M: refine787176636t_unit,M2: refine787176636t_unit,F: product_unit > refine787176636t_unit,F2: product_unit > refine787176636t_unit] :
% 0.16/1.26 ( ( partia1658438072t_unit @ top_to177290092t_unit @ M @ M2 )
% 0.16/1.26 => ( ! [X2: product_unit] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( F @ X2 ) @ ( F2 @ X2 ) )
% 0.16/1.26 => ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine681446406t_unit @ M @ F ) @ ( refine681446406t_unit @ M2 @ F2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_300_conc__fun__R__mono,axiom,
% 0.16/1.26 ! [R: set_Product_prod_a_a,R2: set_Product_prod_a_a,M: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le1824328871od_a_a @ R @ R2 )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( refine1441824853un_a_a @ R @ M ) @ ( refine1441824853un_a_a @ R2 @ M ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_301_conc__fun__R__mono,axiom,
% 0.16/1.26 ! [R: set_Pr1720557880unit_a,R2: set_Pr1720557880unit_a,M: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le2070001880unit_a @ R @ R2 )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( refine2043866374unit_a @ R @ M ) @ ( refine2043866374unit_a @ R2 @ M ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_302_conc__fun__R__mono,axiom,
% 0.16/1.26 ! [R: set_Pr1628433942t_unit,R2: set_Pr1628433942t_unit,M: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1977877942t_unit @ R @ R2 )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( refine2021053540t_unit @ R @ M ) @ ( refine2021053540t_unit @ R2 @ M ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_303_conc__fun__R__mono,axiom,
% 0.16/1.26 ! [R: set_Pr451126599t_unit,R2: set_Pr451126599t_unit,M: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le2035129575t_unit @ R @ R2 )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( refine944483349t_unit @ R @ M ) @ ( refine944483349t_unit @ R2 @ M ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_304_order__mono__setup_Omono__if,axiom,
% 0.16/1.26 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B2: $o] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ T @ T2 )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ E @ E2 )
% 0.16/1.26 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ T @ E ) @ ( if_Ref1724547303nres_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_305_order__mono__setup_Omono__if,axiom,
% 0.16/1.26 ! [T: refine787176636t_unit,T2: refine787176636t_unit,E: refine787176636t_unit,E2: refine787176636t_unit,B2: $o] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ T @ T2 )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ E @ E2 )
% 0.16/1.26 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B2 @ T @ E ) @ ( if_Ref1369692790t_unit @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_306_ac__galois,axiom,
% 0.16/1.26 ! [R: set_Product_prod_a_a] :
% 0.16/1.26 ( ( single_valued_a_a @ R )
% 0.16/1.26 => ( refine2004812827nres_a @ ( refine1136779702un_a_a @ R ) @ ( refine1441824853un_a_a @ R ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_307_ac__galois,axiom,
% 0.16/1.26 ! [R: set_Pr1720557880unit_a] :
% 0.16/1.26 ( ( single249782708unit_a @ R )
% 0.16/1.26 => ( refine2089046860nres_a @ ( refine364464487unit_a @ R ) @ ( refine2043866374unit_a @ R ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_308_ac__galois,axiom,
% 0.16/1.26 ! [R: set_Pr1628433942t_unit] :
% 0.16/1.26 ( ( single226969874t_unit @ R )
% 0.16/1.26 => ( refine327276970t_unit @ ( refine341651653t_unit @ R ) @ ( refine2021053540t_unit @ R ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_309_ac__galois,axiom,
% 0.16/1.26 ! [R: set_Pr451126599t_unit] :
% 0.16/1.26 ( ( single330234563t_unit @ R )
% 0.16/1.26 => ( refine230495195t_unit @ ( refine838861686t_unit @ R ) @ ( refine944483349t_unit @ R ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_310_abs__fun__simps_I3_J,axiom,
% 0.16/1.26 ! [X5: set_a,R: set_Product_prod_a_a] :
% 0.16/1.26 ( ~ ( ord_less_eq_set_a @ X5 @ ( domain_a_a @ R ) )
% 0.16/1.26 => ( ( refine1136779702un_a_a @ R @ ( refine1198353288_RES_a @ X5 ) )
% 0.16/1.26 = top_to231829469nres_a ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_311_abs__fun__simps_I3_J,axiom,
% 0.16/1.26 ! [X5: set_a,R: set_Pr1628433942t_unit] :
% 0.16/1.26 ( ~ ( ord_less_eq_set_a @ X5 @ ( domain799550107t_unit @ R ) )
% 0.16/1.26 => ( ( refine341651653t_unit @ R @ ( refine1198353288_RES_a @ X5 ) )
% 0.16/1.26 = top_to177290092t_unit ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_312_abs__fun__simps_I3_J,axiom,
% 0.16/1.26 ! [X5: set_Product_unit,R: set_Pr1720557880unit_a] :
% 0.16/1.26 ( ~ ( ord_le1023748749t_unit @ X5 @ ( domain822362941unit_a @ R ) )
% 0.16/1.26 => ( ( refine364464487unit_a @ R @ ( refine1777164439t_unit @ X5 ) )
% 0.16/1.26 = top_to231829469nres_a ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_313_abs__fun__simps_I3_J,axiom,
% 0.16/1.26 ! [X5: set_Product_unit,R: set_Pr451126599t_unit] :
% 0.16/1.26 ( ~ ( ord_le1023748749t_unit @ X5 @ ( domain2090798924t_unit @ R ) )
% 0.16/1.26 => ( ( refine838861686t_unit @ R @ ( refine1777164439t_unit @ X5 ) )
% 0.16/1.26 = top_to177290092t_unit ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_314_inres__simps_I2_J,axiom,
% 0.16/1.26 ! [X5: set_a] :
% 0.16/1.26 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X5 ) )
% 0.16/1.26 = ( ^ [X3: a] : ( member_a @ X3 @ X5 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_315_inres__simps_I2_J,axiom,
% 0.16/1.26 ! [X5: set_Product_unit] :
% 0.16/1.26 ( ( refine558004794t_unit @ ( refine1777164439t_unit @ X5 ) )
% 0.16/1.26 = ( ^ [X3: product_unit] : ( member_Product_unit @ X3 @ X5 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_316_nres__more__simps_I2_J,axiom,
% 0.16/1.26 ! [X5: set_Product_unit] :
% 0.16/1.26 ( ( ( refine1777164439t_unit @ X5 )
% 0.16/1.26 = bot_bo658782032t_unit )
% 0.16/1.26 = ( X5 = bot_bo1087887705t_unit ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_317_nres__more__simps_I2_J,axiom,
% 0.16/1.26 ! [X5: set_a] :
% 0.16/1.26 ( ( ( refine1198353288_RES_a @ X5 )
% 0.16/1.26 = bot_bo529555393nres_a )
% 0.16/1.26 = ( X5 = bot_bot_set_a ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_318_nres__more__simps_I1_J,axiom,
% 0.16/1.26 ! [X5: set_Product_unit] :
% 0.16/1.26 ( ( bot_bo658782032t_unit
% 0.16/1.26 = ( refine1777164439t_unit @ X5 ) )
% 0.16/1.26 = ( X5 = bot_bo1087887705t_unit ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_319_nres__more__simps_I1_J,axiom,
% 0.16/1.26 ! [X5: set_a] :
% 0.16/1.26 ( ( bot_bo529555393nres_a
% 0.16/1.26 = ( refine1198353288_RES_a @ X5 ) )
% 0.16/1.26 = ( X5 = bot_bot_set_a ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_320_nres__order__simps_I21_J,axiom,
% 0.16/1.26 ! [X: product_unit,Y6: set_Product_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X ) @ ( refine1777164439t_unit @ Y6 ) )
% 0.16/1.26 = ( member_Product_unit @ X @ Y6 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_321_nres__order__simps_I21_J,axiom,
% 0.16/1.26 ! [X: a,Y6: set_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1198353288_RES_a @ Y6 ) )
% 0.16/1.26 = ( member_a @ X @ Y6 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_322_galois__connection__def,axiom,
% 0.16/1.26 ( refine2004812827nres_a
% 0.16/1.26 = ( ^ [Alpha: refine424419629nres_a > refine424419629nres_a,Gamma: refine424419629nres_a > refine424419629nres_a] :
% 0.16/1.26 ! [C3: refine424419629nres_a,A3: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ C3 @ ( Gamma @ A3 ) )
% 0.16/1.26 = ( ord_le519537037nres_a @ ( Alpha @ C3 ) @ A3 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_323_galois__connection__def,axiom,
% 0.16/1.26 ( refine327276970t_unit
% 0.16/1.26 = ( ^ [Alpha: refine424419629nres_a > refine787176636t_unit,Gamma: refine787176636t_unit > refine424419629nres_a] :
% 0.16/1.26 ! [C3: refine424419629nres_a,A3: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ C3 @ ( Gamma @ A3 ) )
% 0.16/1.26 = ( ord_le1051254044t_unit @ ( Alpha @ C3 ) @ A3 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_324_galois__connection__def,axiom,
% 0.16/1.26 ( refine2089046860nres_a
% 0.16/1.26 = ( ^ [Alpha: refine787176636t_unit > refine424419629nres_a,Gamma: refine424419629nres_a > refine787176636t_unit] :
% 0.16/1.26 ! [C3: refine787176636t_unit,A3: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ C3 @ ( Gamma @ A3 ) )
% 0.16/1.26 = ( ord_le519537037nres_a @ ( Alpha @ C3 ) @ A3 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_325_galois__connection__def,axiom,
% 0.16/1.26 ( refine230495195t_unit
% 0.16/1.26 = ( ^ [Alpha: refine787176636t_unit > refine787176636t_unit,Gamma: refine787176636t_unit > refine787176636t_unit] :
% 0.16/1.26 ! [C3: refine787176636t_unit,A3: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ C3 @ ( Gamma @ A3 ) )
% 0.16/1.26 = ( ord_le1051254044t_unit @ ( Alpha @ C3 ) @ A3 ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_326_galois__connection_Ointro,axiom,
% 0.16/1.26 ! [Gamma2: refine424419629nres_a > refine424419629nres_a,Alpha2: refine424419629nres_a > refine424419629nres_a] :
% 0.16/1.26 ( ! [C4: refine424419629nres_a,A4: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ C4 @ ( Gamma2 @ A4 ) )
% 0.16/1.26 = ( ord_le519537037nres_a @ ( Alpha2 @ C4 ) @ A4 ) )
% 0.16/1.26 => ( refine2004812827nres_a @ Alpha2 @ Gamma2 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_327_galois__connection_Ointro,axiom,
% 0.16/1.26 ! [Gamma2: refine787176636t_unit > refine424419629nres_a,Alpha2: refine424419629nres_a > refine787176636t_unit] :
% 0.16/1.26 ( ! [C4: refine424419629nres_a,A4: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ C4 @ ( Gamma2 @ A4 ) )
% 0.16/1.26 = ( ord_le1051254044t_unit @ ( Alpha2 @ C4 ) @ A4 ) )
% 0.16/1.26 => ( refine327276970t_unit @ Alpha2 @ Gamma2 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_328_galois__connection_Ointro,axiom,
% 0.16/1.26 ! [Gamma2: refine424419629nres_a > refine787176636t_unit,Alpha2: refine787176636t_unit > refine424419629nres_a] :
% 0.16/1.26 ( ! [C4: refine787176636t_unit,A4: refine424419629nres_a] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ C4 @ ( Gamma2 @ A4 ) )
% 0.16/1.26 = ( ord_le519537037nres_a @ ( Alpha2 @ C4 ) @ A4 ) )
% 0.16/1.26 => ( refine2089046860nres_a @ Alpha2 @ Gamma2 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_329_galois__connection_Ointro,axiom,
% 0.16/1.26 ! [Gamma2: refine787176636t_unit > refine787176636t_unit,Alpha2: refine787176636t_unit > refine787176636t_unit] :
% 0.16/1.26 ( ! [C4: refine787176636t_unit,A4: refine787176636t_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ C4 @ ( Gamma2 @ A4 ) )
% 0.16/1.26 = ( ord_le1051254044t_unit @ ( Alpha2 @ C4 ) @ A4 ) )
% 0.16/1.26 => ( refine230495195t_unit @ Alpha2 @ Gamma2 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_330_galois__connection_Ogalois,axiom,
% 0.16/1.26 ! [Alpha2: refine424419629nres_a > refine424419629nres_a,Gamma2: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.16/1.26 ( ( refine2004812827nres_a @ Alpha2 @ Gamma2 )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ C2 @ ( Gamma2 @ A2 ) )
% 0.16/1.26 = ( ord_le519537037nres_a @ ( Alpha2 @ C2 ) @ A2 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_331_galois__connection_Ogalois,axiom,
% 0.16/1.26 ! [Alpha2: refine424419629nres_a > refine787176636t_unit,Gamma2: refine787176636t_unit > refine424419629nres_a,C2: refine424419629nres_a,A2: refine787176636t_unit] :
% 0.16/1.26 ( ( refine327276970t_unit @ Alpha2 @ Gamma2 )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ C2 @ ( Gamma2 @ A2 ) )
% 0.16/1.26 = ( ord_le1051254044t_unit @ ( Alpha2 @ C2 ) @ A2 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_332_galois__connection_Ogalois,axiom,
% 0.16/1.26 ! [Alpha2: refine787176636t_unit > refine424419629nres_a,Gamma2: refine424419629nres_a > refine787176636t_unit,C2: refine787176636t_unit,A2: refine424419629nres_a] :
% 0.16/1.26 ( ( refine2089046860nres_a @ Alpha2 @ Gamma2 )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ C2 @ ( Gamma2 @ A2 ) )
% 0.16/1.26 = ( ord_le519537037nres_a @ ( Alpha2 @ C2 ) @ A2 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_333_galois__connection_Ogalois,axiom,
% 0.16/1.26 ! [Alpha2: refine787176636t_unit > refine787176636t_unit,Gamma2: refine787176636t_unit > refine787176636t_unit,C2: refine787176636t_unit,A2: refine787176636t_unit] :
% 0.16/1.26 ( ( refine230495195t_unit @ Alpha2 @ Gamma2 )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ C2 @ ( Gamma2 @ A2 ) )
% 0.16/1.26 = ( ord_le1051254044t_unit @ ( Alpha2 @ C2 ) @ A2 ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_334_nres__order__simps_I5_J,axiom,
% 0.16/1.26 ! [X5: set_a,Y6: set_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X5 ) @ ( refine1198353288_RES_a @ Y6 ) )
% 0.16/1.26 = ( ord_less_eq_set_a @ X5 @ Y6 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_335_nres__order__simps_I5_J,axiom,
% 0.16/1.26 ! [X5: set_Product_unit,Y6: set_Product_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ X5 ) @ ( refine1777164439t_unit @ Y6 ) )
% 0.16/1.26 = ( ord_le1023748749t_unit @ X5 @ Y6 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_336_less__eq__nres_Osimps_I2_J,axiom,
% 0.16/1.26 ! [A2: set_a,B2: set_a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A2 ) @ ( refine1198353288_RES_a @ B2 ) )
% 0.16/1.26 = ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_337_less__eq__nres_Osimps_I2_J,axiom,
% 0.16/1.26 ! [A2: set_Product_unit,B2: set_Product_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A2 ) @ ( refine1777164439t_unit @ B2 ) )
% 0.16/1.26 = ( ord_le1023748749t_unit @ A2 @ B2 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_338_bot__nres__def,axiom,
% 0.16/1.26 ( bot_bo658782032t_unit
% 0.16/1.26 = ( refine1777164439t_unit @ bot_bo1087887705t_unit ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_339_bot__nres__def,axiom,
% 0.16/1.26 ( bot_bo529555393nres_a
% 0.16/1.26 = ( refine1198353288_RES_a @ bot_bot_set_a ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_340_SPEC__cons__rule,axiom,
% 0.16/1.26 ! [M3: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ M3 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.16/1.26 => ( ! [X2: a] :
% 0.16/1.26 ( ( Phi @ X2 )
% 0.16/1.26 => ( Psi @ X2 ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ M3 @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_341_SPEC__cons__rule,axiom,
% 0.16/1.26 ! [M3: refine787176636t_unit,Phi: product_unit > $o,Psi: product_unit > $o] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ M3 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) )
% 0.16/1.26 => ( ! [X2: product_unit] :
% 0.16/1.26 ( ( Phi @ X2 )
% 0.16/1.26 => ( Psi @ X2 ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ M3 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Psi ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_342_SPEC__trans,axiom,
% 0.16/1.26 ! [X: refine424419629nres_a,Y: refine424419629nres_a,Postcond: a > $o] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ X @ Y )
% 0.16/1.26 => ( ( ord_le519537037nres_a @ Y @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 0.16/1.26 => ( ord_le519537037nres_a @ X @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_343_SPEC__trans,axiom,
% 0.16/1.26 ! [X: refine787176636t_unit,Y: refine787176636t_unit,Postcond: product_unit > $o] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ X @ Y )
% 0.16/1.26 => ( ( ord_le1051254044t_unit @ Y @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) )
% 0.16/1.26 => ( ord_le1051254044t_unit @ X @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_344_nres__order__simps_I22_J,axiom,
% 0.16/1.26 ! [X5: set_Product_unit,Y: product_unit] :
% 0.16/1.26 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ X5 ) @ ( refine1420258419t_unit @ Y ) )
% 0.16/1.26 = ( ord_le1023748749t_unit @ X5 @ ( insert_Product_unit @ Y @ bot_bo1087887705t_unit ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_345_nres__order__simps_I22_J,axiom,
% 0.16/1.26 ! [X5: set_a,Y: a] :
% 0.16/1.26 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X5 ) @ ( refine2063221604TURN_a @ Y ) )
% 0.16/1.26 = ( ord_less_eq_set_a @ X5 @ ( insert_a @ Y @ bot_bot_set_a ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_346_nres__more__simps_I3_J,axiom,
% 0.16/1.26 ! [X5: set_Product_unit,X: product_unit] :
% 0.16/1.26 ( ( ( refine1777164439t_unit @ X5 )
% 0.16/1.26 = ( refine1420258419t_unit @ X ) )
% 0.16/1.26 = ( X5
% 0.16/1.26 = ( insert_Product_unit @ X @ bot_bo1087887705t_unit ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_347_nres__more__simps_I3_J,axiom,
% 0.16/1.26 ! [X5: set_a,X: a] :
% 0.16/1.26 ( ( ( refine1198353288_RES_a @ X5 )
% 0.16/1.26 = ( refine2063221604TURN_a @ X ) )
% 0.16/1.26 = ( X5
% 0.16/1.26 = ( insert_a @ X @ bot_bot_set_a ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_348_nres__more__simps_I5_J,axiom,
% 0.16/1.26 ! [X: product_unit,X5: set_Product_unit] :
% 0.16/1.26 ( ( ( refine1420258419t_unit @ X )
% 0.16/1.26 = ( refine1777164439t_unit @ X5 ) )
% 0.16/1.26 = ( ( insert_Product_unit @ X @ bot_bo1087887705t_unit )
% 0.16/1.26 = X5 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_349_nres__more__simps_I5_J,axiom,
% 0.16/1.26 ! [X: a,X5: set_a] :
% 0.16/1.26 ( ( ( refine2063221604TURN_a @ X )
% 0.16/1.26 = ( refine1198353288_RES_a @ X5 ) )
% 0.16/1.26 = ( ( insert_a @ X @ bot_bot_set_a )
% 0.16/1.26 = X5 ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_350_RETURN__def,axiom,
% 0.16/1.26 ( refine1420258419t_unit
% 0.16/1.26 = ( ^ [X3: product_unit] : ( refine1777164439t_unit @ ( insert_Product_unit @ X3 @ bot_bo1087887705t_unit ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(fact_351_RETURN__def,axiom,
% 0.16/1.26 ( refine2063221604TURN_a
% 0.16/1.26 = ( ^ [X3: a] : ( refine1198353288_RES_a @ ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.16/1.26 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.16/1.26 ( ( if_Ref1724547303nres_a @ $false @ X @ Y )
% 0.16/1.26 = Y ) ).
% 0.16/1.26
% 0.16/1.26 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.16/1.26 ! [X: refine424419629nres_a,Y: refine424419629nres_a] :
% 0.16/1.26 ( ( if_Ref1724547303nres_a @ $true @ X @ Y )
% 0.16/1.26 = X ) ).
% 0.16/1.26
% 0.16/1.26 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.16/1.26 ! [P: $o] :
% 0.16/1.26 ( ( P = $true )
% 0.16/1.26 | ( P = $false ) ) ).
% 0.16/1.26
% 0.16/1.26 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.16/1.26 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.16/1.26 ( ( if_Ref1369692790t_unit @ $false @ X @ Y )
% 0.16/1.26 = Y ) ).
% 0.16/1.26
% 0.16/1.26 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.16/1.26 ! [X: refine787176636t_unit,Y: refine787176636t_unit] :
% 0.16/1.26 ( ( if_Ref1369692790t_unit @ $true @ X @ Y )
% 0.16/1.26 = X ) ).
% 0.16/1.26
% 0.16/1.26 thf(conj_0,conjecture,
% 0.16/1.26 ( ( refine119808503unit_a @ bot_bo658782032t_unit @ f )
% 0.16/1.26 = bot_bo529555393nres_a ) ).
% 0.16/1.26 ------------------------
% 0.16/1.28 % (9906)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9718 for (2999ds/183Mi)
% 0.16/1.28 % (9909)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9718 for (2999ds/2Mi)
% 0.16/1.28 % (9911)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_9718 for (2999ds/275Mi)
% 0.16/1.28 % (9907)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_9718 for (2999ds/4Mi)
% 0.16/1.28 % (9910)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_9718 for (2999ds/2Mi)
% 0.16/1.29 % (9908)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_9718 for (2999ds/27Mi)
% 0.16/1.29 % (9912)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9718 for (2999ds/18Mi)
% 0.16/1.29 % (9909)Instruction limit reached!
% 0.16/1.29 % (9909)------------------------------
% 0.16/1.29 % (9909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.29 % (9909)Termination reason: Unknown
% 0.16/1.29 % (9909)Termination phase: shuffling
% 0.16/1.29
% 0.16/1.29 % (9909)Memory used [KB]: 1407
% 0.16/1.29 % (9909)Time elapsed: 0.003 s
% 0.16/1.29 % (9909)Instructions burned: 3 (million)
% 0.16/1.29 % (9909)------------------------------
% 0.16/1.29 % (9909)------------------------------
% 0.16/1.29 % (9910)Instruction limit reached!
% 0.16/1.29 % (9910)------------------------------
% 0.16/1.29 % (9910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.29 % (9910)Termination reason: Unknown
% 0.16/1.29 % (9910)Termination phase: shuffling
% 0.16/1.29
% 0.16/1.29 % (9910)Memory used [KB]: 1407
% 0.16/1.29 % (9910)Time elapsed: 0.003 s
% 0.16/1.29 % (9910)Instructions burned: 3 (million)
% 0.16/1.29 % (9910)------------------------------
% 0.16/1.29 % (9910)------------------------------
% 0.16/1.29 % (9907)Instruction limit reached!
% 0.16/1.29 % (9907)------------------------------
% 0.16/1.29 % (9907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.29 % (9907)Termination reason: Unknown
% 0.16/1.29 % (9907)Termination phase: shuffling
% 0.16/1.29
% 0.16/1.29 % (9907)Memory used [KB]: 1535
% 0.16/1.29 % (9907)Time elapsed: 0.004 s
% 0.16/1.29 % (9907)Instructions burned: 5 (million)
% 0.16/1.29 % (9907)------------------------------
% 0.16/1.29 % (9907)------------------------------
% 0.16/1.29 % (9912)Instruction limit reached!
% 0.16/1.29 % (9912)------------------------------
% 0.16/1.29 % (9912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.29 % (9912)Termination reason: Unknown
% 0.16/1.29 % (9912)Termination phase: shuffling
% 0.16/1.29
% 0.16/1.29 % (9912)Memory used [KB]: 1918
% 0.16/1.29 % (9912)Time elapsed: 0.011 s
% 0.16/1.29 % (9912)Instructions burned: 19 (million)
% 0.16/1.29 % (9912)------------------------------
% 0.16/1.29 % (9912)------------------------------
% 2.13/1.30 % (9908)Instruction limit reached!
% 2.13/1.30 % (9908)------------------------------
% 2.13/1.30 % (9908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.30 % (9908)Termination reason: Unknown
% 2.13/1.30 % (9908)Termination phase: shuffling
% 2.13/1.30
% 2.13/1.30 % (9908)Memory used [KB]: 1918
% 2.13/1.30 % (9908)Time elapsed: 0.015 s
% 2.13/1.30 % (9908)Instructions burned: 28 (million)
% 2.13/1.30 % (9908)------------------------------
% 2.13/1.30 % (9908)------------------------------
% 2.13/1.30 % (9913)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9718 for (2999ds/3Mi)
% 2.13/1.30 % (9915)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_9718 for (2999ds/15Mi)
% 2.13/1.30 % (9913)Instruction limit reached!
% 2.13/1.30 % (9913)------------------------------
% 2.13/1.30 % (9913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.30 % (9913)Termination reason: Unknown
% 2.13/1.30 % (9913)Termination phase: shuffling
% 2.13/1.30
% 2.13/1.30 % (9913)Memory used [KB]: 1535
% 2.13/1.30 % (9913)Time elapsed: 0.003 s
% 2.13/1.30 % (9913)Instructions burned: 5 (million)
% 2.13/1.30 % (9913)------------------------------
% 2.13/1.30 % (9913)------------------------------
% 2.13/1.30 % (9914)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_9718 for (2999ds/37Mi)
% 2.13/1.31 % (9915)Instruction limit reached!
% 2.13/1.31 % (9915)------------------------------
% 2.13/1.31 % (9915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.31 % (9915)Termination reason: Unknown
% 2.13/1.31 % (9915)Termination phase: shuffling
% 2.13/1.31
% 2.13/1.31 % (9915)Memory used [KB]: 1791
% 2.13/1.31 % (9915)Time elapsed: 0.007 s
% 2.13/1.31 % (9915)Instructions burned: 16 (million)
% 2.13/1.31 % (9915)------------------------------
% 2.13/1.31 % (9915)------------------------------
% 2.13/1.31 % (9916)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_9718 for (2999ds/3Mi)
% 2.13/1.31 % (9916)Instruction limit reached!
% 2.13/1.31 % (9916)------------------------------
% 2.13/1.31 % (9916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.31 % (9916)Termination reason: Unknown
% 2.13/1.31 % (9916)Termination phase: shuffling
% 2.13/1.31
% 2.13/1.31 % (9916)Memory used [KB]: 1535
% 2.13/1.31 % (9916)Time elapsed: 0.003 s
% 2.13/1.31 % (9916)Instructions burned: 4 (million)
% 2.13/1.31 % (9916)------------------------------
% 2.13/1.31 % (9916)------------------------------
% 2.13/1.31 % (9918)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_9718 for (2999ds/1041Mi)
% 2.13/1.31 % (9919)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9718 for (2999ds/7Mi)
% 2.13/1.31 % (9911)First to succeed.
% 2.13/1.31 % (9914)Instruction limit reached!
% 2.13/1.31 % (9914)------------------------------
% 2.13/1.31 % (9914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.31 % (9914)Termination reason: Unknown
% 2.13/1.31 % (9914)Termination phase: shuffling
% 2.13/1.31
% 2.13/1.31 % (9914)Memory used [KB]: 2174
% 2.13/1.31 % (9914)Time elapsed: 0.012 s
% 2.13/1.31 % (9914)Instructions burned: 38 (million)
% 2.13/1.31 % (9914)------------------------------
% 2.13/1.31 % (9914)------------------------------
% 2.13/1.31 % (9911)Refutation found. Thanks to Tanya!
% 2.13/1.31 % SZS status Theorem for DTF2THF_9718
% 2.13/1.31 % SZS output start Proof for DTF2THF_9718
% 2.13/1.31 thf(type_def_5, type, refine787176636t_unit: $tType).
% 2.13/1.31 thf(type_def_7, type, refine424419629nres_a: $tType).
% 2.13/1.31 thf(type_def_8, type, set_Product_unit: $tType).
% 2.13/1.31 thf(type_def_9, type, set_a: $tType).
% 2.13/1.31 thf(type_def_10, type, set_Pr451126599t_unit: $tType).
% 2.13/1.31 thf(type_def_11, type, set_Pr1720557880unit_a: $tType).
% 2.13/1.31 thf(type_def_12, type, set_Pr1628433942t_unit: $tType).
% 2.13/1.31 thf(type_def_13, type, set_Product_prod_a_a: $tType).
% 2.13/1.31 thf(type_def_14, type, product_unit: $tType).
% 2.13/1.31 thf(type_def_15, type, produc971140967t_unit: $tType).
% 2.13/1.31 thf(type_def_16, type, a: $tType).
% 2.13/1.31 thf(type_def_17, type, produc884009688unit_a: $tType).
% 2.13/1.31 thf(type_def_18, type, produc1767851702t_unit: $tType).
% 2.13/1.31 thf(type_def_19, type, product_prod_a_a: $tType).
% 2.13/1.31 thf(func_def_0, type, set_Pr451126599t_unit: $tType).
% 2.13/1.31 thf(func_def_1, type, refine787176636t_unit: $tType).
% 2.13/1.31 thf(func_def_2, type, produc971140967t_unit: $tType).
% 2.13/1.31 thf(func_def_3, type, set_Pr1628433942t_unit: $tType).
% 2.13/1.31 thf(func_def_4, type, set_Pr1720557880unit_a: $tType).
% 2.13/1.31 thf(func_def_5, type, refine424419629nres_a: $tType).
% 2.13/1.31 thf(func_def_6, type, produc1767851702t_unit: $tType).
% 2.13/1.31 thf(func_def_7, type, produc884009688unit_a: $tType).
% 2.13/1.31 thf(func_def_8, type, set_Product_prod_a_a: $tType).
% 2.13/1.31 thf(func_def_9, type, set_Product_unit: $tType).
% 2.13/1.31 thf(func_def_10, type, product_prod_a_a: $tType).
% 2.13/1.31 thf(func_def_11, type, product_unit: $tType).
% 2.13/1.31 thf(func_def_12, type, set_a: $tType).
% 2.13/1.31 thf(func_def_13, type, a: $tType).
% 2.13/1.31 thf(func_def_14, type, if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit).
% 2.13/1.31 thf(func_def_15, type, if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a).
% 2.13/1.31 thf(func_def_16, type, bot_bo658782032t_unit: refine787176636t_unit).
% 2.13/1.31 thf(func_def_17, type, bot_bo529555393nres_a: refine424419629nres_a).
% 2.13/1.31 thf(func_def_18, type, bot_bo1087887705t_unit: set_Product_unit).
% 2.13/1.31 thf(func_def_19, type, bot_bot_set_a: set_a).
% 2.13/1.31 thf(func_def_20, type, ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o).
% 2.13/1.31 thf(func_def_21, type, ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o).
% 2.13/1.31 thf(func_def_22, type, ord_le2035129575t_unit: set_Pr451126599t_unit > set_Pr451126599t_unit > $o).
% 2.13/1.31 thf(func_def_23, type, ord_le2070001880unit_a: set_Pr1720557880unit_a > set_Pr1720557880unit_a > $o).
% 2.13/1.31 thf(func_def_24, type, ord_le1977877942t_unit: set_Pr1628433942t_unit > set_Pr1628433942t_unit > $o).
% 2.13/1.31 thf(func_def_25, type, ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o).
% 2.13/1.31 thf(func_def_26, type, ord_le1023748749t_unit: set_Product_unit > set_Product_unit > $o).
% 2.13/1.31 thf(func_def_27, type, ord_less_eq_set_a: set_a > set_a > $o).
% 2.13/1.31 thf(func_def_28, type, order_453013155t_unit: (refine787176636t_unit > $o) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_29, type, order_1714329108nres_a: (refine424419629nres_a > $o) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_30, type, top_to177290092t_unit: refine787176636t_unit).
% 2.13/1.31 thf(func_def_31, type, top_to231829469nres_a: refine424419629nres_a).
% 2.13/1.31 thf(func_def_32, type, partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o).
% 2.13/1.31 thf(func_def_33, type, partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o).
% 2.13/1.31 thf(func_def_34, type, produc1076565719t_unit: product_unit > product_unit > produc971140967t_unit).
% 2.13/1.31 thf(func_def_35, type, produc1799512520unit_a: product_unit > a > produc884009688unit_a).
% 2.13/1.31 thf(func_def_36, type, produc1776699686t_unit: a > product_unit > produc1767851702t_unit).
% 2.13/1.31 thf(func_def_37, type, product_Pair_a_a: a > a > product_prod_a_a).
% 2.13/1.31 thf(func_def_38, type, refine1420258419t_unit: product_unit > refine787176636t_unit).
% 2.13/1.31 thf(func_def_39, type, refine2063221604TURN_a: a > refine424419629nres_a).
% 2.13/1.31 thf(func_def_40, type, refine838861686t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit).
% 2.13/1.31 thf(func_def_41, type, refine364464487unit_a: set_Pr1720557880unit_a > refine787176636t_unit > refine424419629nres_a).
% 2.13/1.31 thf(func_def_42, type, refine341651653t_unit: set_Pr1628433942t_unit > refine424419629nres_a > refine787176636t_unit).
% 2.13/1.31 thf(func_def_43, type, refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a).
% 2.13/1.31 thf(func_def_44, type, refine681446406t_unit: refine787176636t_unit > (product_unit > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_45, type, refine119808503unit_a: refine787176636t_unit > (product_unit > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_46, type, refine96995669t_unit: refine424419629nres_a > (a > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_47, type, refine436832838nd_a_a: refine424419629nres_a > (a > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_48, type, refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit).
% 2.13/1.31 thf(func_def_49, type, refine2043866374unit_a: set_Pr1720557880unit_a > refine424419629nres_a > refine787176636t_unit).
% 2.13/1.31 thf(func_def_50, type, refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a).
% 2.13/1.31 thf(func_def_51, type, refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a).
% 2.13/1.31 thf(func_def_52, type, refine558004794t_unit: refine787176636t_unit > product_unit > $o).
% 2.13/1.31 thf(func_def_53, type, refine1001002027nres_a: refine424419629nres_a > a > $o).
% 2.13/1.31 thf(func_def_54, type, refine983493746t_unit: refine787176636t_unit > product_unit > $o).
% 2.13/1.31 thf(func_def_55, type, refine1312857699nres_a: refine424419629nres_a > a > $o).
% 2.13/1.31 thf(func_def_56, type, refine579265252t_unit: refine787176636t_unit > $o).
% 2.13/1.31 thf(func_def_57, type, refine412683989fail_a: refine424419629nres_a > $o).
% 2.13/1.31 thf(func_def_58, type, refine1777164439t_unit: set_Product_unit > refine787176636t_unit).
% 2.13/1.31 thf(func_def_59, type, refine1198353288_RES_a: set_a > refine424419629nres_a).
% 2.13/1.31 thf(func_def_60, type, refine230495195t_unit: (refine787176636t_unit > refine787176636t_unit) > (refine787176636t_unit > refine787176636t_unit) > $o).
% 2.13/1.31 thf(func_def_61, type, refine2089046860nres_a: (refine787176636t_unit > refine424419629nres_a) > (refine424419629nres_a > refine787176636t_unit) > $o).
% 2.13/1.31 thf(func_def_62, type, refine327276970t_unit: (refine424419629nres_a > refine787176636t_unit) > (refine787176636t_unit > refine424419629nres_a) > $o).
% 2.13/1.31 thf(func_def_63, type, refine2004812827nres_a: (refine424419629nres_a > refine424419629nres_a) > (refine424419629nres_a > refine424419629nres_a) > $o).
% 2.13/1.31 thf(func_def_64, type, domain2090798924t_unit: set_Pr451126599t_unit > set_Product_unit).
% 2.13/1.31 thf(func_def_65, type, domain822362941unit_a: set_Pr1720557880unit_a > set_Product_unit).
% 2.13/1.31 thf(func_def_66, type, domain799550107t_unit: set_Pr1628433942t_unit > set_a).
% 2.13/1.31 thf(func_def_67, type, domain_a_a: set_Product_prod_a_a > set_a).
% 2.13/1.31 thf(func_def_68, type, single330234563t_unit: set_Pr451126599t_unit > $o).
% 2.13/1.31 thf(func_def_69, type, single249782708unit_a: set_Pr1720557880unit_a > $o).
% 2.13/1.31 thf(func_def_70, type, single226969874t_unit: set_Pr1628433942t_unit > $o).
% 2.13/1.31 thf(func_def_71, type, single_valued_a_a: set_Product_prod_a_a > $o).
% 2.13/1.31 thf(func_def_72, type, collec797068754t_unit: (produc971140967t_unit > $o) > set_Pr451126599t_unit).
% 2.13/1.31 thf(func_def_73, type, collec535904323unit_a: (produc884009688unit_a > $o) > set_Pr1720557880unit_a).
% 2.13/1.31 thf(func_def_74, type, collec1419746337t_unit: (produc1767851702t_unit > $o) > set_Pr1628433942t_unit).
% 2.13/1.31 thf(func_def_75, type, collec645855634od_a_a: (product_prod_a_a > $o) > set_Product_prod_a_a).
% 2.13/1.31 thf(func_def_76, type, collect_Product_unit: (product_unit > $o) > set_Product_unit).
% 2.13/1.31 thf(func_def_77, type, collect_a: (a > $o) > set_a).
% 2.13/1.31 thf(func_def_78, type, insert_Product_unit: product_unit > set_Product_unit > set_Product_unit).
% 2.13/1.31 thf(func_def_79, type, insert_a: a > set_a > set_a).
% 2.13/1.31 thf(func_def_80, type, member1423014800t_unit: produc971140967t_unit > set_Pr451126599t_unit > $o).
% 2.13/1.31 thf(func_def_81, type, member1211819009unit_a: produc884009688unit_a > set_Pr1720557880unit_a > $o).
% 2.13/1.31 thf(func_def_82, type, member2095661023t_unit: produc1767851702t_unit > set_Pr1628433942t_unit > $o).
% 2.13/1.31 thf(func_def_83, type, member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o).
% 2.13/1.31 thf(func_def_84, type, member_Product_unit: product_unit > set_Product_unit > $o).
% 2.13/1.31 thf(func_def_85, type, member_a: a > set_a > $o).
% 2.13/1.31 thf(func_def_86, type, f: product_unit > refine424419629nres_a).
% 2.13/1.31 thf(func_def_99, type, sK0: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_100, type, sK1: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_101, type, sK2: refine787176636t_unit > refine787176636t_unit > product_unit).
% 2.13/1.31 thf(func_def_102, type, sK3: refine424419629nres_a > (product_unit > refine424419629nres_a) > refine787176636t_unit > product_unit).
% 2.13/1.31 thf(func_def_103, type, sK4: (refine787176636t_unit > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_104, type, sK5: (refine787176636t_unit > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_105, type, sK6: (refine787176636t_unit > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_106, type, sK7: (refine787176636t_unit > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_107, type, sK8: (refine424419629nres_a > refine787176636t_unit) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_108, type, sK9: (refine424419629nres_a > refine787176636t_unit) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_109, type, sK10: refine787176636t_unit > (product_unit > refine424419629nres_a) > product_unit).
% 2.13/1.31 thf(func_def_110, type, sK11: refine787176636t_unit > refine787176636t_unit > product_unit).
% 2.13/1.31 thf(func_def_111, type, sK12: (refine424419629nres_a > refine787176636t_unit) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_112, type, sK13: (refine424419629nres_a > refine787176636t_unit) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_113, type, sK14: (product_unit > refine424419629nres_a) > (product_unit > refine424419629nres_a) > refine787176636t_unit > product_unit).
% 2.13/1.31 thf(func_def_114, type, sK15: refine787176636t_unit > refine424419629nres_a > (product_unit > refine424419629nres_a) > product_unit).
% 2.13/1.31 thf(func_def_115, type, sK16: (refine787176636t_unit > refine424419629nres_a) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_116, type, sK17: (refine787176636t_unit > refine424419629nres_a) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_117, type, sK18: (refine787176636t_unit > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_118, type, sK19: (refine787176636t_unit > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_119, type, sK20: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_120, type, sK21: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_121, type, sK22: (refine787176636t_unit > refine424419629nres_a) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_122, type, sK23: (refine787176636t_unit > refine424419629nres_a) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_123, type, sK24: (refine787176636t_unit > refine424419629nres_a) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_124, type, sK25: (refine787176636t_unit > refine424419629nres_a) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_125, type, sK26: (refine787176636t_unit > refine424419629nres_a) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_126, type, sK27: (refine787176636t_unit > refine424419629nres_a) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_127, type, sK28: (refine424419629nres_a > refine787176636t_unit) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_128, type, sK29: (refine424419629nres_a > refine787176636t_unit) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_129, type, sK30: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_130, type, sK31: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_131, type, sK32: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_132, type, sK33: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_133, type, sK34: refine787176636t_unit > (product_unit > refine424419629nres_a) > (product_unit > refine424419629nres_a) > product_unit).
% 2.13/1.31 thf(func_def_134, type, sK35: (refine787176636t_unit > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_135, type, sK36: (refine787176636t_unit > refine787176636t_unit) > refine787176636t_unit).
% 2.13/1.31 thf(func_def_136, type, sK37: (refine424419629nres_a > refine787176636t_unit) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_137, type, sK38: (refine424419629nres_a > refine787176636t_unit) > refine424419629nres_a).
% 2.13/1.31 thf(func_def_138, type, sK39: refine787176636t_unit > refine787176636t_unit > product_unit).
% 2.13/1.31 thf(func_def_140, type, ph41: !>[X0: $tType]:(X0)).
% 2.13/1.31 thf(f1358,plain,(
% 2.13/1.31 $false),
% 2.13/1.31 inference(subsumption_resolution,[status(thm)],[f1254,f1219])).
% 2.13/1.31 thf(f1219,plain,(
% 2.13/1.31 ( ! [X0 : product_unit > refine424419629nres_a] : ((bot_bo529555393nres_a = (refine119808503unit_a @ bot_bo658782032t_unit @ X0))) )),
% 2.13/1.31 inference(cnf_transformation,[status(thm)],[f4])).
% 2.13/1.31 thf(f4,axiom,(
% 2.13/1.31 ! [X0 : product_unit > refine424419629nres_a] : (bot_bo529555393nres_a = (refine119808503unit_a @ bot_bo658782032t_unit @ X0))),
% 2.13/1.31 file('/export/starexec/sandbox2/tmp/tmp.D2qxee7X2B/DTF2THF_9718.p',fact_3_bind__SUCCEED)).
% 2.13/1.31 thf(f1254,plain,(
% 2.13/1.31 (bot_bo529555393nres_a != (refine119808503unit_a @ bot_bo658782032t_unit @ f))),
% 2.13/1.31 inference(cnf_transformation,[status(thm)],[f951])).
% 2.13/1.31 thf(f951,plain,(
% 2.13/1.31 (bot_bo529555393nres_a != (refine119808503unit_a @ bot_bo658782032t_unit @ f))),
% 2.13/1.31 inference(flattening,[status(thm)],[f359])).
% 2.13/1.31 thf(f359,negated_conjecture,(
% 2.13/1.31 ~(bot_bo529555393nres_a = (refine119808503unit_a @ bot_bo658782032t_unit @ f))),
% 2.13/1.31 inference(negated_conjecture,[status(cth)],[f358])).
% 2.13/1.31 thf(f358,conjecture,(
% 2.13/1.31 (bot_bo529555393nres_a = (refine119808503unit_a @ bot_bo658782032t_unit @ f))),
% 2.13/1.31 file('/export/starexec/sandbox2/tmp/tmp.D2qxee7X2B/DTF2THF_9718.p',conj_0)).
% 2.13/1.31 % SZS output end Proof for DTF2THF_9718
% 2.13/1.31 % (9911)------------------------------
% 2.13/1.31 % (9911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.31 % (9911)Termination reason: Refutation
% 2.13/1.31
% 2.13/1.31 % (9911)Memory used [KB]: 6780
% 2.13/1.31 % (9911)Time elapsed: 0.029 s
% 2.13/1.31 % (9911)Instructions burned: 73 (million)
% 2.13/1.31 % (9911)------------------------------
% 2.13/1.31 % (9911)------------------------------
% 2.13/1.31 % (9904)Success in time 0.052 s
%------------------------------------------------------------------------------