%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP159^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 08:56:01 AM UTC 2026
% Result : Theorem 2.56s 1.68s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 46 ( 6 ~; 0 |; 0 &; 40 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 21 ( 20 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 107 ( 104 usr; 12 con; 0-4 aty)
% Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
refine424419629nres_a: $tType ).
thf(type_def_7,type,
refine432681134nres_b: $tType ).
thf(type_def_8,type,
set_Product_prod_a_a: $tType ).
thf(type_def_9,type,
set_a: $tType ).
thf(type_def_10,type,
set_b: $tType ).
thf(type_def_11,type,
refine787176636t_unit: $tType ).
thf(type_def_12,type,
set_Product_prod_a_b: $tType ).
thf(type_def_13,type,
set_Product_prod_b_a: $tType ).
thf(type_def_14,type,
set_Product_prod_b_b: $tType ).
thf(type_def_15,type,
a: $tType ).
thf(type_def_16,type,
product_prod_a_a: $tType ).
thf(type_def_17,type,
b: $tType ).
thf(type_def_18,type,
product_prod_a_b: $tType ).
thf(type_def_19,type,
product_prod_b_b: $tType ).
thf(type_def_20,type,
product_unit: $tType ).
thf(type_def_21,type,
set_Pr451126599t_unit: $tType ).
thf(type_def_22,type,
set_Pr1720557880unit_a: $tType ).
thf(type_def_23,type,
set_Pr712638521unit_b: $tType ).
thf(type_def_24,type,
set_Pr1628433942t_unit: $tType ).
thf(type_def_25,type,
set_Pr1707992533t_unit: $tType ).
thf(func_def_0,type,
set_Pr451126599t_unit: $tType ).
thf(func_def_1,type,
refine787176636t_unit: $tType ).
thf(func_def_2,type,
set_Pr1707992533t_unit: $tType ).
thf(func_def_3,type,
set_Pr1628433942t_unit: $tType ).
thf(func_def_4,type,
set_Pr712638521unit_b: $tType ).
thf(func_def_5,type,
set_Pr1720557880unit_a: $tType ).
thf(func_def_6,type,
refine432681134nres_b: $tType ).
thf(func_def_7,type,
refine424419629nres_a: $tType ).
thf(func_def_8,type,
set_Product_prod_b_b: $tType ).
thf(func_def_9,type,
set_Product_prod_b_a: $tType ).
thf(func_def_10,type,
set_Product_prod_a_b: $tType ).
thf(func_def_11,type,
set_Product_prod_a_a: $tType ).
thf(func_def_12,type,
product_prod_b_b: $tType ).
thf(func_def_13,type,
product_prod_a_b: $tType ).
thf(func_def_14,type,
product_prod_a_a: $tType ).
thf(func_def_15,type,
product_unit: $tType ).
thf(func_def_16,type,
set_b: $tType ).
thf(func_def_17,type,
set_a: $tType ).
thf(func_def_18,type,
b: $tType ).
thf(func_def_19,type,
a: $tType ).
thf(func_def_20,type,
if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
thf(func_def_21,type,
if_o_R697118589nres_b: $o > ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o > refine432681134nres_b ).
thf(func_def_22,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_23,type,
if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
thf(func_def_24,type,
if_set1550076877od_a_a: $o > set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(func_def_25,type,
if_set_a: $o > set_a > set_a > set_a ).
thf(func_def_26,type,
if_set_b: $o > set_b > set_b > set_b ).
thf(func_def_27,type,
sup_su2034729561nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_28,type,
sup_su2042991066nres_b: refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
thf(func_def_29,type,
ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
thf(func_def_30,type,
ord_le1656162903nres_b: ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o ).
thf(func_def_31,type,
ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
thf(func_def_32,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_33,type,
ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o ).
thf(func_def_34,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_35,type,
ord_le816409512od_a_b: set_Product_prod_a_b > set_Product_prod_a_b > $o ).
thf(func_def_36,type,
ord_le2044239718od_b_a: set_Product_prod_b_a > set_Product_prod_b_a > $o ).
thf(func_def_37,type,
ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).
thf(func_def_38,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_39,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(func_def_40,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(func_def_41,type,
order_1722590613nres_b: ( refine432681134nres_b > $o ) > refine432681134nres_b ).
thf(func_def_42,type,
top_to2046902534nres_a: $o > refine424419629nres_a ).
thf(func_def_43,type,
top_to1038983175nres_b: $o > refine432681134nres_b ).
thf(func_def_44,type,
top_to177290092t_unit: refine787176636t_unit ).
thf(func_def_45,type,
top_to231829469nres_a: refine424419629nres_a ).
thf(func_def_46,type,
top_to240090974nres_b: refine432681134nres_b ).
thf(func_def_47,type,
top_to398455383od_a_a: set_Product_prod_a_a ).
thf(func_def_48,type,
top_top_set_a: set_a ).
thf(func_def_49,type,
top_top_set_b: set_b ).
thf(func_def_50,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(func_def_51,type,
product_Pair_a_b: a > b > product_prod_a_b ).
thf(func_def_52,type,
product_Pair_b_b: b > b > product_prod_b_b ).
thf(func_def_53,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(func_def_54,type,
refine2063221605TURN_b: b > refine432681134nres_b ).
thf(func_def_55,type,
refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_56,type,
refine1136779703un_a_b: set_Product_prod_a_b > refine424419629nres_a > refine432681134nres_b ).
thf(func_def_57,type,
refine1964549109un_b_a: set_Product_prod_b_a > refine432681134nres_b > refine424419629nres_a ).
thf(func_def_58,type,
refine1964549110un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
thf(func_def_59,type,
refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_60,type,
refine119808504unit_b: refine787176636t_unit > ( product_unit > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_61,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_62,type,
refine436832839nd_a_b: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_63,type,
refine1264602245nd_b_a: refine432681134nres_b > ( b > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_64,type,
refine1264602246nd_b_b: refine432681134nres_b > ( b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_65,type,
refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(func_def_66,type,
refine2043866374unit_a: set_Pr1720557880unit_a > refine424419629nres_a > refine787176636t_unit ).
thf(func_def_67,type,
refine2043866375unit_b: set_Pr712638521unit_b > refine432681134nres_b > refine787176636t_unit ).
thf(func_def_68,type,
refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a ).
thf(func_def_69,type,
refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_70,type,
refine1441824854un_a_b: set_Product_prod_a_b > refine432681134nres_b > refine424419629nres_a ).
thf(func_def_71,type,
refine2140306339t_unit: set_Pr1707992533t_unit > refine787176636t_unit > refine432681134nres_b ).
thf(func_def_72,type,
refine122110612un_b_a: set_Product_prod_b_a > refine424419629nres_a > refine432681134nres_b ).
thf(func_def_73,type,
refine122110613un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
thf(func_def_74,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(func_def_75,type,
refine1001002028nres_b: refine432681134nres_b > b > $o ).
thf(func_def_76,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(func_def_77,type,
refine412683990fail_b: refine432681134nres_b > $o ).
thf(func_def_78,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(func_def_79,type,
refine1198353289_RES_b: set_b > refine432681134nres_b ).
thf(func_def_80,type,
id_a: set_Product_prod_a_a ).
thf(func_def_81,type,
id_b: set_Product_prod_b_b ).
thf(func_def_82,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_83,type,
collect_b: ( b > $o ) > set_b ).
thf(func_def_84,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_85,type,
member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).
thf(func_def_86,type,
member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
thf(func_def_87,type,
member_a: a > set_a > $o ).
thf(func_def_88,type,
member_b: b > set_b > $o ).
thf(func_def_89,type,
r: set_Product_prod_a_b ).
thf(func_def_90,type,
x: refine424419629nres_a ).
thf(func_def_103,type,
sK0: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_104,type,
sK1: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_105,type,
sK2: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_106,type,
sK3: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_107,type,
sK4: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_108,type,
sK5: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_109,type,
sK6: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_110,type,
sK7: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_111,type,
sK8: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_112,type,
sK9: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_113,type,
sK10: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_114,type,
sK11: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_115,type,
sK12: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_116,type,
sK13: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_117,type,
sK14: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_118,type,
sK15: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_119,type,
sK16: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_120,type,
sK17: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_121,type,
sK18: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_122,type,
sK19: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_123,type,
sK20: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_124,type,
sK21: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_125,type,
sK22: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_126,type,
sK23: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_127,type,
sK24: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_128,type,
sK25: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_129,type,
sK26: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_130,type,
sK27: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_131,type,
sK28: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_132,type,
sK29: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_133,type,
sK30: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_134,type,
sK31: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_136,type,
ph33:
!>[X0: $tType] : X0 ).
thf(f1301,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1300,f1171]) ).
thf(f1171,plain,
! [X0: refine424419629nres_a] :
( ( ord_le519537037nres_a @ X0 @ top_to231829469nres_a )
= $true ),
inference(cnf_transformation,[status(thm)],[f412]) ).
thf(f412,plain,
! [X0: refine424419629nres_a] :
( ( ord_le519537037nres_a @ X0 @ top_to231829469nres_a )
= $true ),
inference(fool_elimination,[status(thm)],[f411]) ).
thf(f411,plain,
! [X0: refine424419629nres_a] : ( ord_le519537037nres_a @ X0 @ top_to231829469nres_a ),
inference(rectify,[status(thm)],[f60]) ).
thf(f60,axiom,
! [X8: refine424419629nres_a] : ( ord_le519537037nres_a @ X8 @ top_to231829469nres_a ),
file('/export/starexec/sandbox/tmp/tmp.C9Bew6RkOr/DTF2THF_10704.p',fact_59_top__greatest) ).
thf(f1300,plain,
( ( ord_le519537037nres_a @ x @ top_to231829469nres_a )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1244,f1188]) ).
thf(f1188,plain,
! [X0: set_Product_prod_a_b] :
( top_to231829469nres_a
= ( refine1441824854un_a_b @ X0 @ top_to240090974nres_b ) ),
inference(cnf_transformation,[status(thm)],[f1018]) ).
thf(f1018,plain,
! [X0: set_Product_prod_a_b] :
( top_to231829469nres_a
= ( refine1441824854un_a_b @ X0 @ top_to240090974nres_b ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,axiom,
! [X1: set_Product_prod_a_b] :
( top_to231829469nres_a
= ( refine1441824854un_a_b @ X1 @ top_to240090974nres_b ) ),
file('/export/starexec/sandbox/tmp/tmp.C9Bew6RkOr/DTF2THF_10704.p',fact_29_conc__fun__FAIL) ).
thf(f1244,plain,
( ( ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1017]) ).
thf(f1017,plain,
( ( ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ) )
!= $true ),
inference(flattening,[status(thm)],[f883]) ).
thf(f883,plain,
( ( ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f882]) ).
thf(f882,plain,
~ ( ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ) ),
inference(rectify,[status(thm)],[f364]) ).
thf(f364,negated_conjecture,
~ ( ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ) ),
inference(negated_conjecture,[status(cth)],[f363]) ).
thf(f363,conjecture,
ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ),
file('/export/starexec/sandbox/tmp/tmp.C9Bew6RkOr/DTF2THF_10704.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP159^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:28:24 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : ITP159^1 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.45 % Domain : Interactive Theorem Proving
% 0.28/0.45 % Problem : Sledgehammer Refine_Basic problem prob_1005__3594596_1
% 0.28/0.45 % Version : Especial.
% 0.28/0.45 % English :
% 0.28/0.45
% 0.28/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.45 % Source : [Des21]
% 0.28/0.45 % Names : Refine_Basic/prob_1005__3594596_1 [Des21]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.28/0.45 % Syntax : Number of formulae : 454 ( 150 unt; 91 typ; 0 def)
% 0.28/0.45 % Number of atoms : 1010 ( 290 equ; 0 cnn)
% 0.28/0.45 % Maximal formula atoms : 6 ( 2 avg)
% 0.28/0.45 % Number of connectives : 2611 ( 27 ~; 1 |; 33 &;2082 @)
% 0.28/0.45 % ( 0 <=>; 468 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 14 ( 7 avg)
% 0.28/0.45 % Number of types : 21 ( 20 usr)
% 0.28/0.45 % Number of type conns : 354 ( 354 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 74 ( 71 usr; 12 con; 0-4 aty)
% 0.28/0.45 % Number of variables : 995 ( 108 ^; 881 !; 6 ?; 995 :)
% 0.28/0.45 % SPC : TH0_THM_EQU_NAR
% 0.28/0.45
% 0.28/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:37.553
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % Could-be-implicit typings (20)
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
% 0.28/0.45 set_Pr451126599t_unit: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.28/0.45 refine787176636t_unit: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Ounit_J_J,type,
% 0.28/0.45 set_Pr1707992533t_unit: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Ounit_J_J,type,
% 0.28/0.45 set_Pr1628433942t_unit: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mtf__b_J_J,type,
% 0.28/0.45 set_Pr712638521unit_b: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mtf__a_J_J,type,
% 0.28/0.45 set_Pr1720557880unit_a: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 0.28/0.45 refine432681134nres_b: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.28/0.45 refine424419629nres_a: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.28/0.45 set_Product_prod_b_b: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
% 0.28/0.45 set_Product_prod_b_a: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
% 0.28/0.45 set_Product_prod_a_b: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.28/0.45 set_Product_prod_a_a: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 0.28/0.45 product_prod_b_b: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
% 0.28/0.45 product_prod_a_b: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.28/0.45 product_prod_a_a: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Product____Type__Ounit,type,
% 0.28/0.45 product_unit: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_Itf__b_J,type,
% 0.28/0.45 set_b: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.28/0.45 set_a: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_tf__b,type,
% 0.28/0.45 b: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_tf__a,type,
% 0.28/0.45 a: $tType ).
% 0.28/0.45
% 0.28/0.45 % Explicit typings (71)
% 0.28/0.45 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.28/0.45 if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 0.28/0.45 if_o_R697118589nres_b: $o > ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.28/0.45 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 0.28/0.45 if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.28/0.45 if_set1550076877od_a_a: $o > set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 0.28/0.45 if_set_a: $o > set_a > set_a > set_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_If_001t__Set__Oset_Itf__b_J,type,
% 0.28/0.45 if_set_b: $o > set_b > set_b > set_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.28/0.45 sup_su2034729561nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 0.28/0.45 sup_su2042991066nres_b: refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.28/0.45 ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 0.28/0.45 ord_le1656162903nres_b: ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.28/0.45 ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.28/0.45 ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 0.28/0.45 ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.28/0.45 ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
% 0.28/0.45 ord_le816409512od_a_b: set_Product_prod_a_b > set_Product_prod_a_b > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
% 0.28/0.45 ord_le2044239718od_b_a: set_Product_prod_b_a > set_Product_prod_b_a > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.28/0.45 ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.28/0.45 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__b_J,type,
% 0.28/0.45 ord_less_eq_set_b: set_b > set_b > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.28/0.45 order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 0.28/0.45 order_1722590613nres_b: ( refine432681134nres_b > $o ) > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.28/0.45 top_to2046902534nres_a: $o > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 0.28/0.45 top_to1038983175nres_b: $o > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.28/0.45 top_to177290092t_unit: refine787176636t_unit ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.28/0.45 top_to231829469nres_a: refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 0.28/0.45 top_to240090974nres_b: refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.28/0.45 top_to398455383od_a_a: set_Product_prod_a_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
% 0.28/0.45 top_top_set_a: set_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__b_J,type,
% 0.28/0.45 top_top_set_b: set_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Product__Type_OPair_001tf__a_001tf__a,type,
% 0.28/0.45 product_Pair_a_a: a > a > product_prod_a_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Product__Type_OPair_001tf__a_001tf__b,type,
% 0.28/0.45 product_Pair_a_b: a > b > product_prod_a_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Product__Type_OPair_001tf__b_001tf__b,type,
% 0.28/0.45 product_Pair_b_b: b > b > product_prod_b_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__a,type,
% 0.28/0.45 refine2063221604TURN_a: a > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__b,type,
% 0.28/0.45 refine2063221605TURN_b: b > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__a_001tf__a,type,
% 0.28/0.45 refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__a_001tf__b,type,
% 0.28/0.45 refine1136779703un_a_b: set_Product_prod_a_b > refine424419629nres_a > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__b_001tf__a,type,
% 0.28/0.45 refine1964549109un_b_a: set_Product_prod_b_a > refine432681134nres_b > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__b_001tf__b,type,
% 0.28/0.45 refine1964549110un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001t__Product____Type__Ounit_001tf__a,type,
% 0.28/0.45 refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001t__Product____Type__Ounit_001tf__b,type,
% 0.28/0.45 refine119808504unit_b: refine787176636t_unit > ( product_unit > refine432681134nres_b ) > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001tf__a,type,
% 0.28/0.45 refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001tf__b,type,
% 0.28/0.45 refine436832839nd_a_b: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__b_001tf__a,type,
% 0.28/0.45 refine1264602245nd_b_a: refine432681134nres_b > ( b > refine424419629nres_a ) > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__b_001tf__b,type,
% 0.28/0.45 refine1264602246nd_b_b: refine432681134nres_b > ( b > refine432681134nres_b ) > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 0.28/0.45 refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001t__Product____Type__Ounit_001tf__a,type,
% 0.28/0.45 refine2043866374unit_a: set_Pr1720557880unit_a > refine424419629nres_a > refine787176636t_unit ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001t__Product____Type__Ounit_001tf__b,type,
% 0.28/0.45 refine2043866375unit_b: set_Pr712638521unit_b > refine432681134nres_b > refine787176636t_unit ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__a_001t__Product____Type__Ounit,type,
% 0.28/0.45 refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__a_001tf__a,type,
% 0.28/0.45 refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__a_001tf__b,type,
% 0.28/0.45 refine1441824854un_a_b: set_Product_prod_a_b > refine432681134nres_b > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__b_001t__Product____Type__Ounit,type,
% 0.28/0.45 refine2140306339t_unit: set_Pr1707992533t_unit > refine787176636t_unit > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__b_001tf__a,type,
% 0.28/0.45 refine122110612un_b_a: set_Product_prod_b_a > refine424419629nres_a > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__b_001tf__b,type,
% 0.28/0.45 refine122110613un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__a,type,
% 0.28/0.45 refine1001002027nres_a: refine424419629nres_a > a > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__b,type,
% 0.28/0.45 refine1001002028nres_b: refine432681134nres_b > b > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__a,type,
% 0.28/0.45 refine412683989fail_a: refine424419629nres_a > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__b,type,
% 0.28/0.45 refine412683990fail_b: refine432681134nres_b > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__a,type,
% 0.28/0.45 refine1198353288_RES_a: set_a > refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__b,type,
% 0.28/0.45 refine1198353289_RES_b: set_b > refine432681134nres_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Relation_OId_001tf__a,type,
% 0.28/0.45 id_a: set_Product_prod_a_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Relation_OId_001tf__b,type,
% 0.28/0.45 id_b: set_Product_prod_b_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.28/0.45 collect_a: ( a > $o ) > set_a ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_001tf__b,type,
% 0.28/0.45 collect_b: ( b > $o ) > set_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.28/0.45 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
% 0.28/0.45 member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 0.28/0.45 member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_001tf__a,type,
% 0.28/0.45 member_a: a > set_a > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_001tf__b,type,
% 0.28/0.45 member_b: b > set_b > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_R,type,
% 0.28/0.45 r: set_Product_prod_a_b ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_X,type,
% 0.28/0.45 x: refine424419629nres_a ).
% 0.28/0.45
% 0.28/0.45 % Relevant facts (347)
% 0.28/0.45 thf(fact_0_nres__order__simps_I4_J,axiom,
% 0.28/0.45 ! [M: refine787176636t_unit] :
% 0.28/0.45 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ M )
% 0.28/0.45 = ( M = top_to177290092t_unit ) ) ).
% 0.28/0.45
% 0.28/0.45 % nres_order_simps(4)
% 0.28/0.45 thf(fact_1_nres__order__simps_I4_J,axiom,
% 0.28/0.45 ! [M: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ M )
% 0.28/0.45 = ( M = top_to240090974nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % nres_order_simps(4)
% 0.28/0.45 thf(fact_2_nres__order__simps_I4_J,axiom,
% 0.28/0.45 ! [M: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M )
% 0.28/0.45 = ( M = top_to231829469nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % nres_order_simps(4)
% 0.28/0.45 thf(fact_3_conc__fun__fail__iff_I2_J,axiom,
% 0.28/0.45 ! [R: set_Pr1707992533t_unit,S: refine787176636t_unit] :
% 0.28/0.45 ( ( top_to240090974nres_b
% 0.28/0.45 = ( refine2140306339t_unit @ R @ S ) )
% 0.28/0.45 = ( S = top_to177290092t_unit ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(2)
% 0.28/0.45 thf(fact_4_conc__fun__fail__iff_I2_J,axiom,
% 0.28/0.45 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 0.28/0.45 ( ( top_to231829469nres_a
% 0.28/0.45 = ( refine2021053540t_unit @ R @ S ) )
% 0.28/0.45 = ( S = top_to177290092t_unit ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(2)
% 0.28/0.45 thf(fact_5_conc__fun__fail__iff_I2_J,axiom,
% 0.28/0.45 ! [R: set_Pr712638521unit_b,S: refine432681134nres_b] :
% 0.28/0.45 ( ( top_to177290092t_unit
% 0.28/0.45 = ( refine2043866375unit_b @ R @ S ) )
% 0.28/0.45 = ( S = top_to240090974nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(2)
% 0.28/0.45 thf(fact_6_conc__fun__fail__iff_I2_J,axiom,
% 0.28/0.45 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 0.28/0.45 ( ( top_to177290092t_unit
% 0.28/0.45 = ( refine2043866374unit_a @ R @ S ) )
% 0.28/0.45 = ( S = top_to231829469nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(2)
% 0.28/0.45 thf(fact_7_conc__fun__fail__iff_I2_J,axiom,
% 0.28/0.45 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.28/0.45 ( ( top_to177290092t_unit
% 0.28/0.45 = ( refine944483349t_unit @ R @ S ) )
% 0.28/0.45 = ( S = top_to177290092t_unit ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(2)
% 0.28/0.45 thf(fact_8_conc__fun__fail__iff_I2_J,axiom,
% 0.28/0.45 ! [R: set_Product_prod_b_a,S: refine424419629nres_a] :
% 0.28/0.45 ( ( top_to240090974nres_b
% 0.28/0.45 = ( refine122110612un_b_a @ R @ S ) )
% 0.28/0.45 = ( S = top_to231829469nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(2)
% 0.28/0.45 thf(fact_9_conc__fun__fail__iff_I2_J,axiom,
% 0.28/0.45 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 0.28/0.45 ( ( top_to231829469nres_a
% 0.28/0.45 = ( refine1441824853un_a_a @ R @ S ) )
% 0.28/0.45 = ( S = top_to231829469nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(2)
% 0.28/0.45 thf(fact_10_conc__fun__fail__iff_I2_J,axiom,
% 0.28/0.45 ! [R: set_Product_prod_b_b,S: refine432681134nres_b] :
% 0.28/0.45 ( ( top_to240090974nres_b
% 0.28/0.45 = ( refine122110613un_b_b @ R @ S ) )
% 0.28/0.45 = ( S = top_to240090974nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(2)
% 0.28/0.45 thf(fact_11_conc__fun__fail__iff_I2_J,axiom,
% 0.28/0.45 ! [R: set_Product_prod_a_b,S: refine432681134nres_b] :
% 0.28/0.45 ( ( top_to231829469nres_a
% 0.28/0.45 = ( refine1441824854un_a_b @ R @ S ) )
% 0.28/0.45 = ( S = top_to240090974nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(2)
% 0.28/0.45 thf(fact_12_conc__fun__fail__iff_I1_J,axiom,
% 0.28/0.45 ! [R: set_Pr1707992533t_unit,S: refine787176636t_unit] :
% 0.28/0.45 ( ( ( refine2140306339t_unit @ R @ S )
% 0.28/0.45 = top_to240090974nres_b )
% 0.28/0.45 = ( S = top_to177290092t_unit ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(1)
% 0.28/0.45 thf(fact_13_conc__fun__fail__iff_I1_J,axiom,
% 0.28/0.45 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 0.28/0.45 ( ( ( refine2021053540t_unit @ R @ S )
% 0.28/0.45 = top_to231829469nres_a )
% 0.28/0.45 = ( S = top_to177290092t_unit ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(1)
% 0.28/0.45 thf(fact_14_conc__fun__fail__iff_I1_J,axiom,
% 0.28/0.45 ! [R: set_Pr712638521unit_b,S: refine432681134nres_b] :
% 0.28/0.45 ( ( ( refine2043866375unit_b @ R @ S )
% 0.28/0.45 = top_to177290092t_unit )
% 0.28/0.45 = ( S = top_to240090974nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(1)
% 0.28/0.45 thf(fact_15_conc__fun__fail__iff_I1_J,axiom,
% 0.28/0.45 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 0.28/0.45 ( ( ( refine2043866374unit_a @ R @ S )
% 0.28/0.45 = top_to177290092t_unit )
% 0.28/0.45 = ( S = top_to231829469nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(1)
% 0.28/0.45 thf(fact_16_conc__fun__fail__iff_I1_J,axiom,
% 0.28/0.45 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.28/0.45 ( ( ( refine944483349t_unit @ R @ S )
% 0.28/0.45 = top_to177290092t_unit )
% 0.28/0.45 = ( S = top_to177290092t_unit ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(1)
% 0.28/0.45 thf(fact_17_conc__fun__fail__iff_I1_J,axiom,
% 0.28/0.45 ! [R: set_Product_prod_b_a,S: refine424419629nres_a] :
% 0.28/0.45 ( ( ( refine122110612un_b_a @ R @ S )
% 0.28/0.45 = top_to240090974nres_b )
% 0.28/0.45 = ( S = top_to231829469nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(1)
% 0.28/0.45 thf(fact_18_conc__fun__fail__iff_I1_J,axiom,
% 0.28/0.45 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 0.28/0.45 ( ( ( refine1441824853un_a_a @ R @ S )
% 0.28/0.45 = top_to231829469nres_a )
% 0.28/0.45 = ( S = top_to231829469nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(1)
% 0.28/0.45 thf(fact_19_conc__fun__fail__iff_I1_J,axiom,
% 0.28/0.45 ! [R: set_Product_prod_b_b,S: refine432681134nres_b] :
% 0.28/0.45 ( ( ( refine122110613un_b_b @ R @ S )
% 0.28/0.45 = top_to240090974nres_b )
% 0.28/0.45 = ( S = top_to240090974nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(1)
% 0.28/0.45 thf(fact_20_conc__fun__fail__iff_I1_J,axiom,
% 0.28/0.45 ! [R: set_Product_prod_a_b,S: refine432681134nres_b] :
% 0.28/0.45 ( ( ( refine1441824854un_a_b @ R @ S )
% 0.28/0.45 = top_to231829469nres_a )
% 0.28/0.45 = ( S = top_to240090974nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_fail_iff(1)
% 0.28/0.45 thf(fact_21_conc__fun__FAIL,axiom,
% 0.28/0.45 ! [R: set_Pr712638521unit_b] :
% 0.28/0.45 ( ( refine2043866375unit_b @ R @ top_to240090974nres_b )
% 0.28/0.45 = top_to177290092t_unit ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_FAIL
% 0.28/0.45 thf(fact_22_conc__fun__FAIL,axiom,
% 0.28/0.45 ! [R: set_Pr1720557880unit_a] :
% 0.28/0.45 ( ( refine2043866374unit_a @ R @ top_to231829469nres_a )
% 0.28/0.45 = top_to177290092t_unit ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_FAIL
% 0.28/0.45 thf(fact_23_conc__fun__FAIL,axiom,
% 0.28/0.45 ! [R: set_Pr1707992533t_unit] :
% 0.28/0.45 ( ( refine2140306339t_unit @ R @ top_to177290092t_unit )
% 0.28/0.45 = top_to240090974nres_b ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_FAIL
% 0.28/0.45 thf(fact_24_conc__fun__FAIL,axiom,
% 0.28/0.45 ! [R: set_Pr1628433942t_unit] :
% 0.28/0.45 ( ( refine2021053540t_unit @ R @ top_to177290092t_unit )
% 0.28/0.45 = top_to231829469nres_a ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_FAIL
% 0.28/0.45 thf(fact_25_conc__fun__FAIL,axiom,
% 0.28/0.45 ! [R: set_Pr451126599t_unit] :
% 0.28/0.45 ( ( refine944483349t_unit @ R @ top_to177290092t_unit )
% 0.28/0.45 = top_to177290092t_unit ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_FAIL
% 0.28/0.45 thf(fact_26_conc__fun__FAIL,axiom,
% 0.28/0.45 ! [R: set_Product_prod_b_a] :
% 0.28/0.45 ( ( refine122110612un_b_a @ R @ top_to231829469nres_a )
% 0.28/0.45 = top_to240090974nres_b ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_FAIL
% 0.28/0.45 thf(fact_27_conc__fun__FAIL,axiom,
% 0.28/0.45 ! [R: set_Product_prod_a_a] :
% 0.28/0.45 ( ( refine1441824853un_a_a @ R @ top_to231829469nres_a )
% 0.28/0.45 = top_to231829469nres_a ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_FAIL
% 0.28/0.45 thf(fact_28_conc__fun__FAIL,axiom,
% 0.28/0.45 ! [R: set_Product_prod_b_b] :
% 0.28/0.45 ( ( refine122110613un_b_b @ R @ top_to240090974nres_b )
% 0.28/0.45 = top_to240090974nres_b ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_FAIL
% 0.28/0.45 thf(fact_29_conc__fun__FAIL,axiom,
% 0.28/0.45 ! [R: set_Product_prod_a_b] :
% 0.28/0.45 ( ( refine1441824854un_a_b @ R @ top_to240090974nres_b )
% 0.28/0.45 = top_to231829469nres_a ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_FAIL
% 0.28/0.45 thf(fact_30_nres__order__simps_I3_J,axiom,
% 0.28/0.45 ! [M: refine787176636t_unit] : ( ord_le1051254044t_unit @ M @ top_to177290092t_unit ) ).
% 0.28/0.45
% 0.28/0.45 % nres_order_simps(3)
% 0.28/0.45 thf(fact_31_nres__order__simps_I3_J,axiom,
% 0.28/0.45 ! [M: refine432681134nres_b] : ( ord_le527798542nres_b @ M @ top_to240090974nres_b ) ).
% 0.28/0.45
% 0.28/0.45 % nres_order_simps(3)
% 0.28/0.45 thf(fact_32_nres__order__simps_I3_J,axiom,
% 0.28/0.45 ! [M: refine424419629nres_a] : ( ord_le519537037nres_a @ M @ top_to231829469nres_a ) ).
% 0.28/0.45
% 0.28/0.45 % nres_order_simps(3)
% 0.28/0.45 thf(fact_33_conc__trans__additional_I1_J,axiom,
% 0.28/0.45 ! [A: refine432681134nres_b,R: set_Product_prod_b_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ R @ B ) )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ B @ C )
% 0.28/0.45 => ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ R @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans_additional(1)
% 0.28/0.45 thf(fact_34_conc__trans__additional_I1_J,axiom,
% 0.28/0.45 ! [A: refine432681134nres_b,R: set_Product_prod_b_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ B ) )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ B @ C )
% 0.28/0.45 => ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans_additional(1)
% 0.28/0.45 thf(fact_35_conc__trans__additional_I1_J,axiom,
% 0.28/0.45 ! [A: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ B ) )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ B @ C )
% 0.28/0.45 => ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans_additional(1)
% 0.28/0.45 thf(fact_36_conc__trans__additional_I1_J,axiom,
% 0.28/0.45 ! [A: refine424419629nres_a,R: set_Product_prod_a_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ B ) )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ B @ C )
% 0.28/0.45 => ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans_additional(1)
% 0.28/0.45 thf(fact_37_conc__trans,axiom,
% 0.28/0.45 ! [C: refine424419629nres_a,R: set_Product_prod_a_b,B: refine432681134nres_b,R2: set_Product_prod_b_a,A: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ R @ B ) )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ B @ ( refine122110612un_b_a @ R2 @ A ) )
% 0.28/0.45 => ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ R @ ( refine122110612un_b_a @ R2 @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans
% 0.28/0.45 thf(fact_38_conc__trans,axiom,
% 0.28/0.45 ! [C: refine432681134nres_b,R: set_Product_prod_b_b,B: refine432681134nres_b,R2: set_Product_prod_b_a,A: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ R @ B ) )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ B @ ( refine122110612un_b_a @ R2 @ A ) )
% 0.28/0.45 => ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ R @ ( refine122110612un_b_a @ R2 @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans
% 0.28/0.45 thf(fact_39_conc__trans,axiom,
% 0.28/0.45 ! [C: refine432681134nres_b,R: set_Product_prod_b_a,B: refine424419629nres_a,R2: set_Product_prod_a_b,A: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ R @ B ) )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ B @ ( refine1441824854un_a_b @ R2 @ A ) )
% 0.28/0.45 => ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ R @ ( refine1441824854un_a_b @ R2 @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans
% 0.28/0.45 thf(fact_40_conc__trans,axiom,
% 0.28/0.45 ! [C: refine432681134nres_b,R: set_Product_prod_b_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ R @ B ) )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R2 @ A ) )
% 0.28/0.45 => ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ R @ ( refine1441824853un_a_a @ R2 @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans
% 0.28/0.45 thf(fact_41_conc__trans,axiom,
% 0.28/0.45 ! [C: refine424419629nres_a,R: set_Product_prod_a_b,B: refine432681134nres_b,R2: set_Product_prod_b_b,A: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ R @ B ) )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ R2 @ A ) )
% 0.28/0.45 => ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ R @ ( refine122110613un_b_b @ R2 @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans
% 0.28/0.45 thf(fact_42_conc__trans,axiom,
% 0.28/0.45 ! [C: refine432681134nres_b,R: set_Product_prod_b_b,B: refine432681134nres_b,R2: set_Product_prod_b_b,A: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ R @ B ) )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ R2 @ A ) )
% 0.28/0.45 => ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ R @ ( refine122110613un_b_b @ R2 @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans
% 0.28/0.45 thf(fact_43_conc__trans,axiom,
% 0.28/0.45 ! [C: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ B ) )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R2 @ A ) )
% 0.28/0.45 => ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ ( refine1441824853un_a_a @ R2 @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans
% 0.28/0.45 thf(fact_44_conc__trans,axiom,
% 0.28/0.45 ! [C: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,R2: set_Product_prod_a_b,A: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ B ) )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ B @ ( refine1441824854un_a_b @ R2 @ A ) )
% 0.28/0.45 => ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ ( refine1441824854un_a_b @ R2 @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_trans
% 0.28/0.45 thf(fact_45_order__mono__setup_Orefl,axiom,
% 0.28/0.45 ! [X: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ X @ X ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.refl
% 0.28/0.45 thf(fact_46_order__mono__setup_Orefl,axiom,
% 0.28/0.45 ! [X: set_b] : ( ord_less_eq_set_b @ X @ X ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.refl
% 0.28/0.45 thf(fact_47_order__mono__setup_Orefl,axiom,
% 0.28/0.45 ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.refl
% 0.28/0.45 thf(fact_48_order__mono__setup_Orefl,axiom,
% 0.28/0.45 ! [X: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ X @ X ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.refl
% 0.28/0.45 thf(fact_49_order__mono__setup_Orefl,axiom,
% 0.28/0.45 ! [X: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ X @ X ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.refl
% 0.28/0.45 thf(fact_50_order__mono__setup_Orefl,axiom,
% 0.28/0.45 ! [X: refine432681134nres_b] : ( ord_le527798542nres_b @ X @ X ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.refl
% 0.28/0.45 thf(fact_51_order__mono__setup_Orefl,axiom,
% 0.28/0.45 ! [X: refine424419629nres_a] : ( ord_le519537037nres_a @ X @ X ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.refl
% 0.28/0.45 thf(fact_52_top__greatest,axiom,
% 0.28/0.45 ! [A2: refine787176636t_unit] : ( ord_le1051254044t_unit @ A2 @ top_to177290092t_unit ) ).
% 0.28/0.45
% 0.28/0.45 % top_greatest
% 0.28/0.45 thf(fact_53_top__greatest,axiom,
% 0.28/0.45 ! [A2: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A2 @ top_to398455383od_a_a ) ).
% 0.28/0.45
% 0.28/0.45 % top_greatest
% 0.28/0.45 thf(fact_54_top__greatest,axiom,
% 0.28/0.45 ! [A2: set_b] : ( ord_less_eq_set_b @ A2 @ top_top_set_b ) ).
% 0.28/0.45
% 0.28/0.45 % top_greatest
% 0.28/0.45 thf(fact_55_top__greatest,axiom,
% 0.28/0.45 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ top_top_set_a ) ).
% 0.28/0.45
% 0.28/0.45 % top_greatest
% 0.28/0.45 thf(fact_56_top__greatest,axiom,
% 0.28/0.45 ! [A2: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A2 @ top_to1038983175nres_b ) ).
% 0.28/0.45
% 0.28/0.45 % top_greatest
% 0.28/0.45 thf(fact_57_top__greatest,axiom,
% 0.28/0.45 ! [A2: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A2 @ top_to2046902534nres_a ) ).
% 0.28/0.45
% 0.28/0.45 % top_greatest
% 0.28/0.45 thf(fact_58_top__greatest,axiom,
% 0.28/0.45 ! [A2: refine432681134nres_b] : ( ord_le527798542nres_b @ A2 @ top_to240090974nres_b ) ).
% 0.28/0.45
% 0.28/0.45 % top_greatest
% 0.28/0.45 thf(fact_59_top__greatest,axiom,
% 0.28/0.45 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ top_to231829469nres_a ) ).
% 0.28/0.45
% 0.28/0.45 % top_greatest
% 0.28/0.45 thf(fact_60_meta__le__everything__if__top,axiom,
% 0.28/0.45 ! [M2: refine787176636t_unit,X: refine787176636t_unit] :
% 0.28/0.45 ( ( M2 = top_to177290092t_unit )
% 0.28/0.45 => ( ord_le1051254044t_unit @ X @ M2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % meta_le_everything_if_top
% 0.28/0.45 thf(fact_61_meta__le__everything__if__top,axiom,
% 0.28/0.45 ! [M2: set_Product_prod_a_a,X: set_Product_prod_a_a] :
% 0.28/0.45 ( ( M2 = top_to398455383od_a_a )
% 0.28/0.45 => ( ord_le1824328871od_a_a @ X @ M2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % meta_le_everything_if_top
% 0.28/0.45 thf(fact_62_meta__le__everything__if__top,axiom,
% 0.28/0.45 ! [M2: set_b,X: set_b] :
% 0.28/0.45 ( ( M2 = top_top_set_b )
% 0.28/0.45 => ( ord_less_eq_set_b @ X @ M2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % meta_le_everything_if_top
% 0.28/0.45 thf(fact_63_meta__le__everything__if__top,axiom,
% 0.28/0.45 ! [M2: set_a,X: set_a] :
% 0.28/0.45 ( ( M2 = top_top_set_a )
% 0.28/0.45 => ( ord_less_eq_set_a @ X @ M2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % meta_le_everything_if_top
% 0.28/0.45 thf(fact_64_meta__le__everything__if__top,axiom,
% 0.28/0.45 ! [M2: $o > refine432681134nres_b,X: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( M2 = top_to1038983175nres_b )
% 0.28/0.45 => ( ord_le1656162903nres_b @ X @ M2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % meta_le_everything_if_top
% 0.28/0.45 thf(fact_65_meta__le__everything__if__top,axiom,
% 0.28/0.45 ! [M2: $o > refine424419629nres_a,X: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( M2 = top_to2046902534nres_a )
% 0.28/0.45 => ( ord_le516598614nres_a @ X @ M2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % meta_le_everything_if_top
% 0.28/0.45 thf(fact_66_meta__le__everything__if__top,axiom,
% 0.28/0.45 ! [M2: refine424419629nres_a,X: refine424419629nres_a] :
% 0.28/0.45 ( ( M2 = top_to231829469nres_a )
% 0.28/0.45 => ( ord_le519537037nres_a @ X @ M2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % meta_le_everything_if_top
% 0.28/0.45 thf(fact_67_meta__le__everything__if__top,axiom,
% 0.28/0.45 ! [M2: refine432681134nres_b,X: refine432681134nres_b] :
% 0.28/0.45 ( ( M2 = top_to240090974nres_b )
% 0.28/0.45 => ( ord_le527798542nres_b @ X @ M2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % meta_le_everything_if_top
% 0.28/0.45 thf(fact_68_top_Oextremum__unique,axiom,
% 0.28/0.45 ! [A2: refine787176636t_unit] :
% 0.28/0.45 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A2 )
% 0.28/0.45 = ( A2 = top_to177290092t_unit ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_unique
% 0.28/0.45 thf(fact_69_top_Oextremum__unique,axiom,
% 0.28/0.45 ! [A2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ top_to398455383od_a_a @ A2 )
% 0.28/0.45 = ( A2 = top_to398455383od_a_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_unique
% 0.28/0.45 thf(fact_70_top_Oextremum__unique,axiom,
% 0.28/0.45 ! [A2: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ top_top_set_b @ A2 )
% 0.28/0.45 = ( A2 = top_top_set_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_unique
% 0.28/0.45 thf(fact_71_top_Oextremum__unique,axiom,
% 0.28/0.45 ! [A2: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ top_top_set_a @ A2 )
% 0.28/0.45 = ( A2 = top_top_set_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_unique
% 0.28/0.45 thf(fact_72_top_Oextremum__unique,axiom,
% 0.28/0.45 ! [A2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ top_to1038983175nres_b @ A2 )
% 0.28/0.45 = ( A2 = top_to1038983175nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_unique
% 0.28/0.45 thf(fact_73_top_Oextremum__unique,axiom,
% 0.28/0.45 ! [A2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ top_to2046902534nres_a @ A2 )
% 0.28/0.45 = ( A2 = top_to2046902534nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_unique
% 0.28/0.45 thf(fact_74_top_Oextremum__unique,axiom,
% 0.28/0.45 ! [A2: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A2 )
% 0.28/0.45 = ( A2 = top_to231829469nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_unique
% 0.28/0.45 thf(fact_75_top_Oextremum__unique,axiom,
% 0.28/0.45 ! [A2: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A2 )
% 0.28/0.45 = ( A2 = top_to240090974nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_unique
% 0.28/0.45 thf(fact_76_top_Oextremum__uniqueI,axiom,
% 0.28/0.45 ! [A2: refine787176636t_unit] :
% 0.28/0.45 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A2 )
% 0.28/0.45 => ( A2 = top_to177290092t_unit ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_uniqueI
% 0.28/0.45 thf(fact_77_top_Oextremum__uniqueI,axiom,
% 0.28/0.45 ! [A2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ top_to398455383od_a_a @ A2 )
% 0.28/0.45 => ( A2 = top_to398455383od_a_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_uniqueI
% 0.28/0.45 thf(fact_78_top_Oextremum__uniqueI,axiom,
% 0.28/0.45 ! [A2: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ top_top_set_b @ A2 )
% 0.28/0.45 => ( A2 = top_top_set_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_uniqueI
% 0.28/0.45 thf(fact_79_top_Oextremum__uniqueI,axiom,
% 0.28/0.45 ! [A2: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ top_top_set_a @ A2 )
% 0.28/0.45 => ( A2 = top_top_set_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_uniqueI
% 0.28/0.45 thf(fact_80_top_Oextremum__uniqueI,axiom,
% 0.28/0.45 ! [A2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ top_to1038983175nres_b @ A2 )
% 0.28/0.45 => ( A2 = top_to1038983175nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_uniqueI
% 0.28/0.45 thf(fact_81_top_Oextremum__uniqueI,axiom,
% 0.28/0.45 ! [A2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ top_to2046902534nres_a @ A2 )
% 0.28/0.45 => ( A2 = top_to2046902534nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_uniqueI
% 0.28/0.45 thf(fact_82_top_Oextremum__uniqueI,axiom,
% 0.28/0.45 ! [A2: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A2 )
% 0.28/0.45 => ( A2 = top_to231829469nres_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_uniqueI
% 0.28/0.45 thf(fact_83_top_Oextremum__uniqueI,axiom,
% 0.28/0.45 ! [A2: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A2 )
% 0.28/0.45 => ( A2 = top_to240090974nres_b ) ) ).
% 0.28/0.45
% 0.28/0.45 % top.extremum_uniqueI
% 0.28/0.45 thf(fact_84_le__funD,axiom,
% 0.28/0.45 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X: $o] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ F @ G )
% 0.28/0.45 => ( ord_le527798542nres_b @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_funD
% 0.28/0.45 thf(fact_85_le__funD,axiom,
% 0.28/0.45 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X: $o] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ F @ G )
% 0.28/0.45 => ( ord_le519537037nres_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_funD
% 0.28/0.45 thf(fact_86_le__funE,axiom,
% 0.28/0.45 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X: $o] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ F @ G )
% 0.28/0.45 => ( ord_le527798542nres_b @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_funE
% 0.28/0.45 thf(fact_87_le__funE,axiom,
% 0.28/0.45 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X: $o] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ F @ G )
% 0.28/0.45 => ( ord_le519537037nres_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_funE
% 0.28/0.45 thf(fact_88_le__funI,axiom,
% 0.28/0.45 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a] :
% 0.28/0.45 ( ! [X2: $o] : ( ord_le519537037nres_a @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.28/0.45 => ( ord_le516598614nres_a @ F @ G ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_funI
% 0.28/0.45 thf(fact_89_le__funI,axiom,
% 0.28/0.45 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b] :
% 0.28/0.45 ( ! [X2: $o] : ( ord_le527798542nres_b @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.28/0.45 => ( ord_le1656162903nres_b @ F @ G ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_funI
% 0.28/0.45 thf(fact_90_Refine__Misc_Oif__mono,axiom,
% 0.28/0.45 ! [B2: $o,M1: set_Product_prod_a_a,M12: set_Product_prod_a_a,M22: set_Product_prod_a_a,M23: set_Product_prod_a_a] :
% 0.28/0.45 ( ( B2
% 0.28/0.45 => ( ord_le1824328871od_a_a @ M1 @ M12 ) )
% 0.28/0.45 => ( ( ~ B2
% 0.28/0.45 => ( ord_le1824328871od_a_a @ M22 @ M23 ) )
% 0.28/0.45 => ( ord_le1824328871od_a_a @ ( if_set1550076877od_a_a @ B2 @ M1 @ M22 ) @ ( if_set1550076877od_a_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Refine_Misc.if_mono
% 0.28/0.45 thf(fact_91_Refine__Misc_Oif__mono,axiom,
% 0.28/0.45 ! [B2: $o,M1: set_b,M12: set_b,M22: set_b,M23: set_b] :
% 0.28/0.45 ( ( B2
% 0.28/0.45 => ( ord_less_eq_set_b @ M1 @ M12 ) )
% 0.28/0.45 => ( ( ~ B2
% 0.28/0.45 => ( ord_less_eq_set_b @ M22 @ M23 ) )
% 0.28/0.45 => ( ord_less_eq_set_b @ ( if_set_b @ B2 @ M1 @ M22 ) @ ( if_set_b @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Refine_Misc.if_mono
% 0.28/0.45 thf(fact_92_Refine__Misc_Oif__mono,axiom,
% 0.28/0.45 ! [B2: $o,M1: set_a,M12: set_a,M22: set_a,M23: set_a] :
% 0.28/0.45 ( ( B2
% 0.28/0.45 => ( ord_less_eq_set_a @ M1 @ M12 ) )
% 0.28/0.45 => ( ( ~ B2
% 0.28/0.45 => ( ord_less_eq_set_a @ M22 @ M23 ) )
% 0.28/0.45 => ( ord_less_eq_set_a @ ( if_set_a @ B2 @ M1 @ M22 ) @ ( if_set_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Refine_Misc.if_mono
% 0.28/0.45 thf(fact_93_Refine__Misc_Oif__mono,axiom,
% 0.28/0.45 ! [B2: $o,M1: $o > refine432681134nres_b,M12: $o > refine432681134nres_b,M22: $o > refine432681134nres_b,M23: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( B2
% 0.28/0.45 => ( ord_le1656162903nres_b @ M1 @ M12 ) )
% 0.28/0.45 => ( ( ~ B2
% 0.28/0.45 => ( ord_le1656162903nres_b @ M22 @ M23 ) )
% 0.28/0.45 => ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ B2 @ M1 @ M22 ) @ ( if_o_R697118589nres_b @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Refine_Misc.if_mono
% 0.28/0.45 thf(fact_94_Refine__Misc_Oif__mono,axiom,
% 0.28/0.45 ! [B2: $o,M1: $o > refine424419629nres_a,M12: $o > refine424419629nres_a,M22: $o > refine424419629nres_a,M23: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( B2
% 0.28/0.45 => ( ord_le516598614nres_a @ M1 @ M12 ) )
% 0.28/0.45 => ( ( ~ B2
% 0.28/0.45 => ( ord_le516598614nres_a @ M22 @ M23 ) )
% 0.28/0.45 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B2 @ M1 @ M22 ) @ ( if_o_R1705037948nres_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Refine_Misc.if_mono
% 0.28/0.45 thf(fact_95_Refine__Misc_Oif__mono,axiom,
% 0.28/0.45 ! [B2: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M22: refine424419629nres_a,M23: refine424419629nres_a] :
% 0.28/0.45 ( ( B2
% 0.28/0.45 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 0.28/0.45 => ( ( ~ B2
% 0.28/0.45 => ( ord_le519537037nres_a @ M22 @ M23 ) )
% 0.28/0.45 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ M1 @ M22 ) @ ( if_Ref1724547303nres_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Refine_Misc.if_mono
% 0.28/0.45 thf(fact_96_Refine__Misc_Oif__mono,axiom,
% 0.28/0.45 ! [B2: $o,M1: refine432681134nres_b,M12: refine432681134nres_b,M22: refine432681134nres_b,M23: refine432681134nres_b] :
% 0.28/0.45 ( ( B2
% 0.28/0.45 => ( ord_le527798542nres_b @ M1 @ M12 ) )
% 0.28/0.45 => ( ( ~ B2
% 0.28/0.45 => ( ord_le527798542nres_b @ M22 @ M23 ) )
% 0.28/0.45 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B2 @ M1 @ M22 ) @ ( if_Ref1732808808nres_b @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Refine_Misc.if_mono
% 0.28/0.45 thf(fact_97_le__fun__def,axiom,
% 0.28/0.45 ( ord_le1656162903nres_b
% 0.28/0.45 = ( ^ [F2: $o > refine432681134nres_b,G2: $o > refine432681134nres_b] :
% 0.28/0.45 ! [X3: $o] : ( ord_le527798542nres_b @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_fun_def
% 0.28/0.45 thf(fact_98_le__fun__def,axiom,
% 0.28/0.45 ( ord_le516598614nres_a
% 0.28/0.45 = ( ^ [F2: $o > refine424419629nres_a,G2: $o > refine424419629nres_a] :
% 0.28/0.45 ! [X3: $o] : ( ord_le519537037nres_a @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % le_fun_def
% 0.28/0.45 thf(fact_99_conc__fun__R__mono,axiom,
% 0.28/0.45 ! [R: set_Product_prod_b_a,R2: set_Product_prod_b_a,M: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le2044239718od_b_a @ R @ R2 )
% 0.28/0.45 => ( ord_le527798542nres_b @ ( refine122110612un_b_a @ R @ M ) @ ( refine122110612un_b_a @ R2 @ M ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_R_mono
% 0.28/0.45 thf(fact_100_conc__fun__R__mono,axiom,
% 0.28/0.45 ! [R: set_Product_prod_a_b,R2: set_Product_prod_a_b,M: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le816409512od_a_b @ R @ R2 )
% 0.28/0.45 => ( ord_le519537037nres_a @ ( refine1441824854un_a_b @ R @ M ) @ ( refine1441824854un_a_b @ R2 @ M ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_R_mono
% 0.28/0.45 thf(fact_101_conc__fun__R__mono,axiom,
% 0.28/0.45 ! [R: set_Product_prod_b_b,R2: set_Product_prod_b_b,M: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1036320359od_b_b @ R @ R2 )
% 0.28/0.45 => ( ord_le527798542nres_b @ ( refine122110613un_b_b @ R @ M ) @ ( refine122110613un_b_b @ R2 @ M ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_R_mono
% 0.28/0.45 thf(fact_102_conc__fun__R__mono,axiom,
% 0.28/0.45 ! [R: set_Product_prod_a_a,R2: set_Product_prod_a_a,M: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ R @ R2 )
% 0.28/0.45 => ( ord_le519537037nres_a @ ( refine1441824853un_a_a @ R @ M ) @ ( refine1441824853un_a_a @ R2 @ M ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % conc_fun_R_mono
% 0.28/0.45 thf(fact_103_order__mono__setup_Omono__if,axiom,
% 0.28/0.45 ! [T: set_Product_prod_a_a,T2: set_Product_prod_a_a,E: set_Product_prod_a_a,E2: set_Product_prod_a_a,B2: $o] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ T @ T2 )
% 0.28/0.45 => ( ( ord_le1824328871od_a_a @ E @ E2 )
% 0.28/0.45 => ( ord_le1824328871od_a_a @ ( if_set1550076877od_a_a @ B2 @ T @ E ) @ ( if_set1550076877od_a_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.mono_if
% 0.28/0.45 thf(fact_104_order__mono__setup_Omono__if,axiom,
% 0.28/0.45 ! [T: set_b,T2: set_b,E: set_b,E2: set_b,B2: $o] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ T @ T2 )
% 0.28/0.45 => ( ( ord_less_eq_set_b @ E @ E2 )
% 0.28/0.45 => ( ord_less_eq_set_b @ ( if_set_b @ B2 @ T @ E ) @ ( if_set_b @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.mono_if
% 0.28/0.45 thf(fact_105_order__mono__setup_Omono__if,axiom,
% 0.28/0.45 ! [T: set_a,T2: set_a,E: set_a,E2: set_a,B2: $o] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ T @ T2 )
% 0.28/0.45 => ( ( ord_less_eq_set_a @ E @ E2 )
% 0.28/0.45 => ( ord_less_eq_set_a @ ( if_set_a @ B2 @ T @ E ) @ ( if_set_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.mono_if
% 0.28/0.45 thf(fact_106_order__mono__setup_Omono__if,axiom,
% 0.28/0.45 ! [T: $o > refine432681134nres_b,T2: $o > refine432681134nres_b,E: $o > refine432681134nres_b,E2: $o > refine432681134nres_b,B2: $o] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ T @ T2 )
% 0.28/0.45 => ( ( ord_le1656162903nres_b @ E @ E2 )
% 0.28/0.45 => ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ B2 @ T @ E ) @ ( if_o_R697118589nres_b @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.mono_if
% 0.28/0.45 thf(fact_107_order__mono__setup_Omono__if,axiom,
% 0.28/0.45 ! [T: $o > refine424419629nres_a,T2: $o > refine424419629nres_a,E: $o > refine424419629nres_a,E2: $o > refine424419629nres_a,B2: $o] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ T @ T2 )
% 0.28/0.45 => ( ( ord_le516598614nres_a @ E @ E2 )
% 0.28/0.45 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B2 @ T @ E ) @ ( if_o_R1705037948nres_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.mono_if
% 0.28/0.45 thf(fact_108_order__mono__setup_Omono__if,axiom,
% 0.28/0.45 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B2: $o] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ T @ T2 )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ E @ E2 )
% 0.28/0.45 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ T @ E ) @ ( if_Ref1724547303nres_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.mono_if
% 0.28/0.45 thf(fact_109_order__mono__setup_Omono__if,axiom,
% 0.28/0.45 ! [T: refine432681134nres_b,T2: refine432681134nres_b,E: refine432681134nres_b,E2: refine432681134nres_b,B2: $o] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ T @ T2 )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ E @ E2 )
% 0.28/0.45 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B2 @ T @ E ) @ ( if_Ref1732808808nres_b @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_mono_setup.mono_if
% 0.28/0.45 thf(fact_110_dual__order_Oantisym,axiom,
% 0.28/0.45 ! [B2: set_Product_prod_a_a,A2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.antisym
% 0.28/0.45 thf(fact_111_dual__order_Oantisym,axiom,
% 0.28/0.45 ! [B2: set_b,A2: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_less_eq_set_b @ A2 @ B2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.antisym
% 0.28/0.45 thf(fact_112_dual__order_Oantisym,axiom,
% 0.28/0.45 ! [B2: set_a,A2: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.antisym
% 0.28/0.45 thf(fact_113_dual__order_Oantisym,axiom,
% 0.28/0.45 ! [B2: $o > refine432681134nres_b,A2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le1656162903nres_b @ A2 @ B2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.antisym
% 0.28/0.45 thf(fact_114_dual__order_Oantisym,axiom,
% 0.28/0.45 ! [B2: $o > refine424419629nres_a,A2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le516598614nres_a @ A2 @ B2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.antisym
% 0.28/0.45 thf(fact_115_dual__order_Oantisym,axiom,
% 0.28/0.45 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.antisym
% 0.28/0.45 thf(fact_116_dual__order_Oantisym,axiom,
% 0.28/0.45 ! [B2: refine432681134nres_b,A2: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.antisym
% 0.28/0.45 thf(fact_117_dual__order_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: set_Product_prod_a_a,B3: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ B3 @ A3 )
% 0.28/0.45 & ( ord_le1824328871od_a_a @ A3 @ B3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.eq_iff
% 0.28/0.45 thf(fact_118_dual__order_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: set_b,Z: set_b] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: set_b,B3: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ B3 @ A3 )
% 0.28/0.45 & ( ord_less_eq_set_b @ A3 @ B3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.eq_iff
% 0.28/0.45 thf(fact_119_dual__order_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: set_a,B3: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 0.28/0.45 & ( ord_less_eq_set_a @ A3 @ B3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.eq_iff
% 0.28/0.45 thf(fact_120_dual__order_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: $o > refine432681134nres_b,Z: $o > refine432681134nres_b] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: $o > refine432681134nres_b,B3: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ B3 @ A3 )
% 0.28/0.45 & ( ord_le1656162903nres_b @ A3 @ B3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.eq_iff
% 0.28/0.45 thf(fact_121_dual__order_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: $o > refine424419629nres_a,B3: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ B3 @ A3 )
% 0.28/0.45 & ( ord_le516598614nres_a @ A3 @ B3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.eq_iff
% 0.28/0.45 thf(fact_122_dual__order_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: refine424419629nres_a,Z: refine424419629nres_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ B3 @ A3 )
% 0.28/0.45 & ( ord_le519537037nres_a @ A3 @ B3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.eq_iff
% 0.28/0.45 thf(fact_123_dual__order_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: refine432681134nres_b,Z: refine432681134nres_b] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: refine432681134nres_b,B3: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ B3 @ A3 )
% 0.28/0.45 & ( ord_le527798542nres_b @ A3 @ B3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.eq_iff
% 0.28/0.45 thf(fact_124_dual__order_Otrans,axiom,
% 0.28/0.45 ! [B2: set_Product_prod_a_a,A2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le1824328871od_a_a @ C2 @ B2 )
% 0.28/0.45 => ( ord_le1824328871od_a_a @ C2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.trans
% 0.28/0.45 thf(fact_125_dual__order_Otrans,axiom,
% 0.28/0.45 ! [B2: set_b,A2: set_b,C2: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_less_eq_set_b @ C2 @ B2 )
% 0.28/0.45 => ( ord_less_eq_set_b @ C2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.trans
% 0.28/0.45 thf(fact_126_dual__order_Otrans,axiom,
% 0.28/0.45 ! [B2: set_a,A2: set_a,C2: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_less_eq_set_a @ C2 @ B2 )
% 0.28/0.45 => ( ord_less_eq_set_a @ C2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.trans
% 0.28/0.45 thf(fact_127_dual__order_Otrans,axiom,
% 0.28/0.45 ! [B2: $o > refine432681134nres_b,A2: $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le1656162903nres_b @ C2 @ B2 )
% 0.28/0.45 => ( ord_le1656162903nres_b @ C2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.trans
% 0.28/0.45 thf(fact_128_dual__order_Otrans,axiom,
% 0.28/0.45 ! [B2: $o > refine424419629nres_a,A2: $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le516598614nres_a @ C2 @ B2 )
% 0.28/0.45 => ( ord_le516598614nres_a @ C2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.trans
% 0.28/0.45 thf(fact_129_dual__order_Otrans,axiom,
% 0.28/0.45 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ C2 @ B2 )
% 0.28/0.45 => ( ord_le519537037nres_a @ C2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.trans
% 0.28/0.45 thf(fact_130_dual__order_Otrans,axiom,
% 0.28/0.45 ! [B2: refine432681134nres_b,A2: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ B2 @ A2 )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ C2 @ B2 )
% 0.28/0.45 => ( ord_le527798542nres_b @ C2 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.trans
% 0.28/0.45 thf(fact_131_dual__order_Orefl,axiom,
% 0.28/0.45 ! [A2: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A2 @ A2 ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.refl
% 0.28/0.45 thf(fact_132_dual__order_Orefl,axiom,
% 0.28/0.45 ! [A2: set_b] : ( ord_less_eq_set_b @ A2 @ A2 ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.refl
% 0.28/0.45 thf(fact_133_dual__order_Orefl,axiom,
% 0.28/0.45 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.refl
% 0.28/0.45 thf(fact_134_dual__order_Orefl,axiom,
% 0.28/0.45 ! [A2: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A2 @ A2 ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.refl
% 0.28/0.45 thf(fact_135_dual__order_Orefl,axiom,
% 0.28/0.45 ! [A2: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A2 @ A2 ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.refl
% 0.28/0.45 thf(fact_136_dual__order_Orefl,axiom,
% 0.28/0.45 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ A2 ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.refl
% 0.28/0.45 thf(fact_137_dual__order_Orefl,axiom,
% 0.28/0.45 ! [A2: refine432681134nres_b] : ( ord_le527798542nres_b @ A2 @ A2 ) ).
% 0.28/0.45
% 0.28/0.45 % dual_order.refl
% 0.28/0.45 thf(fact_138_order__trans,axiom,
% 0.28/0.45 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a,Z2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le1824328871od_a_a @ Y2 @ Z2 )
% 0.28/0.45 => ( ord_le1824328871od_a_a @ X @ Z2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_trans
% 0.28/0.45 thf(fact_139_order__trans,axiom,
% 0.28/0.45 ! [X: set_b,Y2: set_b,Z2: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ X @ Y2 )
% 0.28/0.45 => ( ( ord_less_eq_set_b @ Y2 @ Z2 )
% 0.28/0.45 => ( ord_less_eq_set_b @ X @ Z2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_trans
% 0.28/0.45 thf(fact_140_order__trans,axiom,
% 0.28/0.45 ! [X: set_a,Y2: set_a,Z2: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ X @ Y2 )
% 0.28/0.45 => ( ( ord_less_eq_set_a @ Y2 @ Z2 )
% 0.28/0.45 => ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_trans
% 0.28/0.45 thf(fact_141_order__trans,axiom,
% 0.28/0.45 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b,Z2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le1656162903nres_b @ Y2 @ Z2 )
% 0.28/0.45 => ( ord_le1656162903nres_b @ X @ Z2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_trans
% 0.28/0.45 thf(fact_142_order__trans,axiom,
% 0.28/0.45 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a,Z2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le516598614nres_a @ Y2 @ Z2 )
% 0.28/0.45 => ( ord_le516598614nres_a @ X @ Z2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_trans
% 0.28/0.45 thf(fact_143_order__trans,axiom,
% 0.28/0.45 ! [X: refine424419629nres_a,Y2: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ Y2 @ Z2 )
% 0.28/0.45 => ( ord_le519537037nres_a @ X @ Z2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_trans
% 0.28/0.45 thf(fact_144_order__trans,axiom,
% 0.28/0.45 ! [X: refine432681134nres_b,Y2: refine432681134nres_b,Z2: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ Y2 @ Z2 )
% 0.28/0.45 => ( ord_le527798542nres_b @ X @ Z2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_trans
% 0.28/0.45 thf(fact_145_order__class_Oorder_Oantisym,axiom,
% 0.28/0.45 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le1824328871od_a_a @ B2 @ A2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.antisym
% 0.28/0.45 thf(fact_146_order__class_Oorder_Oantisym,axiom,
% 0.28/0.45 ! [A2: set_b,B2: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_eq_set_b @ B2 @ A2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.antisym
% 0.28/0.45 thf(fact_147_order__class_Oorder_Oantisym,axiom,
% 0.28/0.45 ! [A2: set_a,B2: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.antisym
% 0.28/0.45 thf(fact_148_order__class_Oorder_Oantisym,axiom,
% 0.28/0.45 ! [A2: $o > refine432681134nres_b,B2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le1656162903nres_b @ B2 @ A2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.antisym
% 0.28/0.45 thf(fact_149_order__class_Oorder_Oantisym,axiom,
% 0.28/0.45 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le516598614nres_a @ B2 @ A2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.antisym
% 0.28/0.45 thf(fact_150_order__class_Oorder_Oantisym,axiom,
% 0.28/0.45 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.antisym
% 0.28/0.45 thf(fact_151_order__class_Oorder_Oantisym,axiom,
% 0.28/0.45 ! [A2: refine432681134nres_b,B2: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ B2 @ A2 )
% 0.28/0.45 => ( A2 = B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.antisym
% 0.28/0.45 thf(fact_152_ord__le__eq__trans,axiom,
% 0.28/0.45 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 0.28/0.45 => ( ( B2 = C2 )
% 0.28/0.45 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_le_eq_trans
% 0.28/0.45 thf(fact_153_ord__le__eq__trans,axiom,
% 0.28/0.45 ! [A2: set_b,B2: set_b,C2: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ A2 @ B2 )
% 0.28/0.45 => ( ( B2 = C2 )
% 0.28/0.45 => ( ord_less_eq_set_b @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_le_eq_trans
% 0.28/0.45 thf(fact_154_ord__le__eq__trans,axiom,
% 0.28/0.45 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.28/0.45 => ( ( B2 = C2 )
% 0.28/0.45 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_le_eq_trans
% 0.28/0.45 thf(fact_155_ord__le__eq__trans,axiom,
% 0.28/0.45 ! [A2: $o > refine432681134nres_b,B2: $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ A2 @ B2 )
% 0.28/0.45 => ( ( B2 = C2 )
% 0.28/0.45 => ( ord_le1656162903nres_b @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_le_eq_trans
% 0.28/0.45 thf(fact_156_ord__le__eq__trans,axiom,
% 0.28/0.45 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 0.28/0.45 => ( ( B2 = C2 )
% 0.28/0.45 => ( ord_le516598614nres_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_le_eq_trans
% 0.28/0.45 thf(fact_157_ord__le__eq__trans,axiom,
% 0.28/0.45 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.28/0.45 => ( ( B2 = C2 )
% 0.28/0.45 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_le_eq_trans
% 0.28/0.45 thf(fact_158_ord__le__eq__trans,axiom,
% 0.28/0.45 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.28/0.45 => ( ( B2 = C2 )
% 0.28/0.45 => ( ord_le527798542nres_b @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_le_eq_trans
% 0.28/0.45 thf(fact_159_ord__eq__le__trans,axiom,
% 0.28/0.45 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 => ( ( ord_le1824328871od_a_a @ B2 @ C2 )
% 0.28/0.45 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_le_trans
% 0.28/0.45 thf(fact_160_ord__eq__le__trans,axiom,
% 0.28/0.45 ! [A2: set_b,B2: set_b,C2: set_b] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 => ( ( ord_less_eq_set_b @ B2 @ C2 )
% 0.28/0.45 => ( ord_less_eq_set_b @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_le_trans
% 0.28/0.45 thf(fact_161_ord__eq__le__trans,axiom,
% 0.28/0.45 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.28/0.45 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_le_trans
% 0.28/0.45 thf(fact_162_ord__eq__le__trans,axiom,
% 0.28/0.45 ! [A2: $o > refine432681134nres_b,B2: $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 => ( ( ord_le1656162903nres_b @ B2 @ C2 )
% 0.28/0.45 => ( ord_le1656162903nres_b @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_le_trans
% 0.28/0.45 thf(fact_163_ord__eq__le__trans,axiom,
% 0.28/0.45 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 => ( ( ord_le516598614nres_a @ B2 @ C2 )
% 0.28/0.45 => ( ord_le516598614nres_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_le_trans
% 0.28/0.45 thf(fact_164_ord__eq__le__trans,axiom,
% 0.28/0.45 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.28/0.45 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_le_trans
% 0.28/0.45 thf(fact_165_ord__eq__le__trans,axiom,
% 0.28/0.45 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.45 ( ( A2 = B2 )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 0.28/0.45 => ( ord_le527798542nres_b @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ord_eq_le_trans
% 0.28/0.45 thf(fact_166_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: set_Product_prod_a_a,B3: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ A3 @ B3 )
% 0.28/0.45 & ( ord_le1824328871od_a_a @ B3 @ A3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.eq_iff
% 0.28/0.45 thf(fact_167_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: set_b,Z: set_b] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: set_b,B3: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ A3 @ B3 )
% 0.28/0.45 & ( ord_less_eq_set_b @ B3 @ A3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.eq_iff
% 0.28/0.45 thf(fact_168_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: set_a,B3: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.28/0.45 & ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.eq_iff
% 0.28/0.45 thf(fact_169_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: $o > refine432681134nres_b,Z: $o > refine432681134nres_b] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: $o > refine432681134nres_b,B3: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ A3 @ B3 )
% 0.28/0.45 & ( ord_le1656162903nres_b @ B3 @ A3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.eq_iff
% 0.28/0.45 thf(fact_170_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: $o > refine424419629nres_a,B3: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ A3 @ B3 )
% 0.28/0.45 & ( ord_le516598614nres_a @ B3 @ A3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.eq_iff
% 0.28/0.45 thf(fact_171_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: refine424419629nres_a,Z: refine424419629nres_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 0.28/0.45 & ( ord_le519537037nres_a @ B3 @ A3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.eq_iff
% 0.28/0.45 thf(fact_172_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: refine432681134nres_b,Z: refine432681134nres_b] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [A3: refine432681134nres_b,B3: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ A3 @ B3 )
% 0.28/0.45 & ( ord_le527798542nres_b @ B3 @ A3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order_class.order.eq_iff
% 0.28/0.45 thf(fact_173_antisym__conv,axiom,
% 0.28/0.45 ! [Y2: set_Product_prod_a_a,X: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ Y2 @ X )
% 0.28/0.45 => ( ( ord_le1824328871od_a_a @ X @ Y2 )
% 0.28/0.45 = ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv
% 0.28/0.45 thf(fact_174_antisym__conv,axiom,
% 0.28/0.45 ! [Y2: set_b,X: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ Y2 @ X )
% 0.28/0.45 => ( ( ord_less_eq_set_b @ X @ Y2 )
% 0.28/0.45 = ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv
% 0.28/0.45 thf(fact_175_antisym__conv,axiom,
% 0.28/0.45 ! [Y2: set_a,X: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ Y2 @ X )
% 0.28/0.45 => ( ( ord_less_eq_set_a @ X @ Y2 )
% 0.28/0.45 = ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv
% 0.28/0.45 thf(fact_176_antisym__conv,axiom,
% 0.28/0.45 ! [Y2: $o > refine432681134nres_b,X: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ Y2 @ X )
% 0.28/0.45 => ( ( ord_le1656162903nres_b @ X @ Y2 )
% 0.28/0.45 = ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv
% 0.28/0.45 thf(fact_177_antisym__conv,axiom,
% 0.28/0.45 ! [Y2: $o > refine424419629nres_a,X: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ Y2 @ X )
% 0.28/0.45 => ( ( ord_le516598614nres_a @ X @ Y2 )
% 0.28/0.45 = ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv
% 0.28/0.45 thf(fact_178_antisym__conv,axiom,
% 0.28/0.45 ! [Y2: refine424419629nres_a,X: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ Y2 @ X )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ X @ Y2 )
% 0.28/0.45 = ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv
% 0.28/0.45 thf(fact_179_antisym__conv,axiom,
% 0.28/0.45 ! [Y2: refine432681134nres_b,X: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ Y2 @ X )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ X @ Y2 )
% 0.28/0.45 = ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym_conv
% 0.28/0.45 thf(fact_180_order_Otrans,axiom,
% 0.28/0.45 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le1824328871od_a_a @ B2 @ C2 )
% 0.28/0.45 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.trans
% 0.28/0.45 thf(fact_181_order_Otrans,axiom,
% 0.28/0.45 ! [A2: set_b,B2: set_b,C2: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_eq_set_b @ B2 @ C2 )
% 0.28/0.45 => ( ord_less_eq_set_b @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.trans
% 0.28/0.45 thf(fact_182_order_Otrans,axiom,
% 0.28/0.45 ! [A2: set_a,B2: set_a,C2: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 0.28/0.45 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.trans
% 0.28/0.45 thf(fact_183_order_Otrans,axiom,
% 0.28/0.45 ! [A2: $o > refine432681134nres_b,B2: $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le1656162903nres_b @ B2 @ C2 )
% 0.28/0.45 => ( ord_le1656162903nres_b @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.trans
% 0.28/0.45 thf(fact_184_order_Otrans,axiom,
% 0.28/0.45 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le516598614nres_a @ B2 @ C2 )
% 0.28/0.45 => ( ord_le516598614nres_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.trans
% 0.28/0.45 thf(fact_185_order_Otrans,axiom,
% 0.28/0.45 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.28/0.45 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.trans
% 0.28/0.45 thf(fact_186_order_Otrans,axiom,
% 0.28/0.45 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 0.28/0.45 => ( ord_le527798542nres_b @ A2 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % order.trans
% 0.28/0.45 thf(fact_187_eq__refl,axiom,
% 0.28/0.45 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( X = Y2 )
% 0.28/0.45 => ( ord_le1824328871od_a_a @ X @ Y2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_refl
% 0.28/0.45 thf(fact_188_eq__refl,axiom,
% 0.28/0.45 ! [X: set_b,Y2: set_b] :
% 0.28/0.45 ( ( X = Y2 )
% 0.28/0.45 => ( ord_less_eq_set_b @ X @ Y2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_refl
% 0.28/0.45 thf(fact_189_eq__refl,axiom,
% 0.28/0.45 ! [X: set_a,Y2: set_a] :
% 0.28/0.45 ( ( X = Y2 )
% 0.28/0.45 => ( ord_less_eq_set_a @ X @ Y2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_refl
% 0.28/0.45 thf(fact_190_eq__refl,axiom,
% 0.28/0.45 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( X = Y2 )
% 0.28/0.45 => ( ord_le1656162903nres_b @ X @ Y2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_refl
% 0.28/0.45 thf(fact_191_eq__refl,axiom,
% 0.28/0.45 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( X = Y2 )
% 0.28/0.45 => ( ord_le516598614nres_a @ X @ Y2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_refl
% 0.28/0.45 thf(fact_192_eq__refl,axiom,
% 0.28/0.45 ! [X: refine424419629nres_a,Y2: refine424419629nres_a] :
% 0.28/0.45 ( ( X = Y2 )
% 0.28/0.45 => ( ord_le519537037nres_a @ X @ Y2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_refl
% 0.28/0.45 thf(fact_193_eq__refl,axiom,
% 0.28/0.45 ! [X: refine432681134nres_b,Y2: refine432681134nres_b] :
% 0.28/0.45 ( ( X = Y2 )
% 0.28/0.45 => ( ord_le527798542nres_b @ X @ Y2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_refl
% 0.28/0.45 thf(fact_194_antisym,axiom,
% 0.28/0.45 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le1824328871od_a_a @ Y2 @ X )
% 0.28/0.45 => ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym
% 0.28/0.45 thf(fact_195_antisym,axiom,
% 0.28/0.45 ! [X: set_b,Y2: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ X @ Y2 )
% 0.28/0.45 => ( ( ord_less_eq_set_b @ Y2 @ X )
% 0.28/0.45 => ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym
% 0.28/0.45 thf(fact_196_antisym,axiom,
% 0.28/0.45 ! [X: set_a,Y2: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ X @ Y2 )
% 0.28/0.45 => ( ( ord_less_eq_set_a @ Y2 @ X )
% 0.28/0.45 => ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym
% 0.28/0.45 thf(fact_197_antisym,axiom,
% 0.28/0.45 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le1656162903nres_b @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le1656162903nres_b @ Y2 @ X )
% 0.28/0.45 => ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym
% 0.28/0.45 thf(fact_198_antisym,axiom,
% 0.28/0.45 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le516598614nres_a @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le516598614nres_a @ Y2 @ X )
% 0.28/0.45 => ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym
% 0.28/0.45 thf(fact_199_antisym,axiom,
% 0.28/0.45 ! [X: refine424419629nres_a,Y2: refine424419629nres_a] :
% 0.28/0.45 ( ( ord_le519537037nres_a @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le519537037nres_a @ Y2 @ X )
% 0.28/0.45 => ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym
% 0.28/0.45 thf(fact_200_antisym,axiom,
% 0.28/0.45 ! [X: refine432681134nres_b,Y2: refine432681134nres_b] :
% 0.28/0.45 ( ( ord_le527798542nres_b @ X @ Y2 )
% 0.28/0.45 => ( ( ord_le527798542nres_b @ Y2 @ X )
% 0.28/0.45 => ( X = Y2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % antisym
% 0.28/0.45 thf(fact_201_eq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [X3: set_Product_prod_a_a,Y3: set_Product_prod_a_a] :
% 0.28/0.45 ( ( ord_le1824328871od_a_a @ X3 @ Y3 )
% 0.28/0.45 & ( ord_le1824328871od_a_a @ Y3 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_iff
% 0.28/0.45 thf(fact_202_eq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: set_b,Z: set_b] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [X3: set_b,Y3: set_b] :
% 0.28/0.45 ( ( ord_less_eq_set_b @ X3 @ Y3 )
% 0.28/0.45 & ( ord_less_eq_set_b @ Y3 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_iff
% 0.28/0.45 thf(fact_203_eq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 0.28/0.45 = ( ^ [X3: set_a,Y3: set_a] :
% 0.28/0.45 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.28/0.45 & ( ord_less_eq_set_a @ Y3 @ X3 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % eq_iff
% 0.28/0.45 thf(fact_204_eq__iff,axiom,
% 0.28/0.45 ( ( ^ [Y: $o > refine432681134nres_b,Z: $o > refine432681134nres_b] : ( Y = Z ) )
% 0.28/0.46 = ( ^ [X3: $o > refine432681134nres_b,Y3: $o > refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le1656162903nres_b @ X3 @ Y3 )
% 0.28/0.46 & ( ord_le1656162903nres_b @ Y3 @ X3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_iff
% 0.28/0.46 thf(fact_205_eq__iff,axiom,
% 0.28/0.46 ( ( ^ [Y: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y = Z ) )
% 0.28/0.46 = ( ^ [X3: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le516598614nres_a @ X3 @ Y3 )
% 0.28/0.46 & ( ord_le516598614nres_a @ Y3 @ X3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_iff
% 0.28/0.46 thf(fact_206_eq__iff,axiom,
% 0.28/0.46 ( ( ^ [Y: refine424419629nres_a,Z: refine424419629nres_a] : ( Y = Z ) )
% 0.28/0.46 = ( ^ [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 0.28/0.46 & ( ord_le519537037nres_a @ Y3 @ X3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_iff
% 0.28/0.46 thf(fact_207_eq__iff,axiom,
% 0.28/0.46 ( ( ^ [Y: refine432681134nres_b,Z: refine432681134nres_b] : ( Y = Z ) )
% 0.28/0.46 = ( ^ [X3: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X3 @ Y3 )
% 0.28/0.46 & ( ord_le527798542nres_b @ Y3 @ X3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_iff
% 0.28/0.46 thf(fact_208_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,F: ( $o > refine424419629nres_a ) > set_b,C2: set_b] :
% 0.28/0.46 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C2 )
% 0.28/0.46 => ( ! [X2: $o > refine424419629nres_a,Y4: $o > refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le516598614nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_less_eq_set_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_less_eq_set_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_209_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,F: ( $o > refine424419629nres_a ) > set_a,C2: set_a] :
% 0.28/0.46 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C2 )
% 0.28/0.46 => ( ! [X2: $o > refine424419629nres_a,Y4: $o > refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le516598614nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_210_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,F: ( $o > refine424419629nres_a ) > $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C2 )
% 0.28/0.46 => ( ! [X2: $o > refine424419629nres_a,Y4: $o > refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le516598614nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le1656162903nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le1656162903nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_211_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,F: ( $o > refine424419629nres_a ) > $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C2 )
% 0.28/0.46 => ( ! [X2: $o > refine424419629nres_a,Y4: $o > refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le516598614nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le516598614nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le516598614nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_212_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C2 )
% 0.28/0.46 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_213_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C2 )
% 0.28/0.46 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_214_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C2 )
% 0.28/0.46 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_215_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C2 )
% 0.28/0.46 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_216_ord__eq__le__subst,axiom,
% 0.28/0.46 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.28/0.46 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_subst
% 0.28/0.46 thf(fact_217_ord__eq__le__subst,axiom,
% 0.28/0.46 ! [A2: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.28/0.46 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_subst
% 0.28/0.46 thf(fact_218_ord__eq__le__subst,axiom,
% 0.28/0.46 ! [A2: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 0.28/0.46 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_subst
% 0.28/0.46 thf(fact_219_ord__eq__le__subst,axiom,
% 0.28/0.46 ! [A2: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 0.28/0.46 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_subst
% 0.28/0.46 thf(fact_220_order__subst2,axiom,
% 0.28/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 0.28/0.46 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst2
% 0.28/0.46 thf(fact_221_order__subst2,axiom,
% 0.28/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ ( F @ B2 ) @ C2 )
% 0.28/0.46 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst2
% 0.28/0.46 thf(fact_222_order__subst2,axiom,
% 0.28/0.46 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 0.28/0.46 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst2
% 0.28/0.46 thf(fact_223_order__subst2,axiom,
% 0.28/0.46 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ ( F @ B2 ) @ C2 )
% 0.28/0.46 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst2
% 0.28/0.46 thf(fact_224_order__subst1,axiom,
% 0.28/0.46 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.28/0.46 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst1
% 0.28/0.46 thf(fact_225_order__subst1,axiom,
% 0.28/0.46 ! [A2: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 0.28/0.46 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst1
% 0.28/0.46 thf(fact_226_order__subst1,axiom,
% 0.28/0.46 ! [A2: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A2 @ ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.28/0.46 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst1
% 0.28/0.46 thf(fact_227_order__subst1,axiom,
% 0.28/0.46 ! [A2: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A2 @ ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 0.28/0.46 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst1
% 0.28/0.46 thf(fact_228_Greatest__equality,axiom,
% 0.28/0.46 ! [P: refine424419629nres_a > $o,X: refine424419629nres_a] :
% 0.28/0.46 ( ( P @ X )
% 0.28/0.46 => ( ! [Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( P @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ Y4 @ X ) )
% 0.28/0.46 => ( ( order_1714329108nres_a @ P )
% 0.28/0.46 = X ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Greatest_equality
% 0.28/0.46 thf(fact_229_Greatest__equality,axiom,
% 0.28/0.46 ! [P: refine432681134nres_b > $o,X: refine432681134nres_b] :
% 0.28/0.46 ( ( P @ X )
% 0.28/0.46 => ( ! [Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( P @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ Y4 @ X ) )
% 0.28/0.46 => ( ( order_1722590613nres_b @ P )
% 0.28/0.46 = X ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Greatest_equality
% 0.28/0.46 thf(fact_230_GreatestI2__order,axiom,
% 0.28/0.46 ! [P: refine424419629nres_a > $o,X: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 0.28/0.46 ( ( P @ X )
% 0.28/0.46 => ( ! [Y4: refine424419629nres_a] :
% 0.28/0.46 ( ( P @ Y4 )
% 0.28/0.46 => ( ord_le519537037nres_a @ Y4 @ X ) )
% 0.28/0.46 => ( ! [X2: refine424419629nres_a] :
% 0.28/0.46 ( ( P @ X2 )
% 0.28/0.46 => ( ! [Y5: refine424419629nres_a] :
% 0.28/0.46 ( ( P @ Y5 )
% 0.28/0.46 => ( ord_le519537037nres_a @ Y5 @ X2 ) )
% 0.28/0.46 => ( Q @ X2 ) ) )
% 0.28/0.46 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % GreatestI2_order
% 0.28/0.46 thf(fact_231_GreatestI2__order,axiom,
% 0.28/0.46 ! [P: refine432681134nres_b > $o,X: refine432681134nres_b,Q: refine432681134nres_b > $o] :
% 0.28/0.46 ( ( P @ X )
% 0.28/0.46 => ( ! [Y4: refine432681134nres_b] :
% 0.28/0.46 ( ( P @ Y4 )
% 0.28/0.46 => ( ord_le527798542nres_b @ Y4 @ X ) )
% 0.28/0.46 => ( ! [X2: refine432681134nres_b] :
% 0.28/0.46 ( ( P @ X2 )
% 0.28/0.46 => ( ! [Y5: refine432681134nres_b] :
% 0.28/0.46 ( ( P @ Y5 )
% 0.28/0.46 => ( ord_le527798542nres_b @ Y5 @ X2 ) )
% 0.28/0.46 => ( Q @ X2 ) ) )
% 0.28/0.46 => ( Q @ ( order_1722590613nres_b @ P ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % GreatestI2_order
% 0.28/0.46 thf(fact_232_le__rel__bool__arg__iff,axiom,
% 0.28/0.46 ( ord_le516598614nres_a
% 0.28/0.46 = ( ^ [X4: $o > refine424419629nres_a,Y6: $o > refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.28/0.46 & ( ord_le519537037nres_a @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_rel_bool_arg_iff
% 0.28/0.46 thf(fact_233_le__rel__bool__arg__iff,axiom,
% 0.28/0.46 ( ord_le1656162903nres_b
% 0.28/0.46 = ( ^ [X4: $o > refine432681134nres_b,Y6: $o > refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.28/0.46 & ( ord_le527798542nres_b @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_rel_bool_arg_iff
% 0.28/0.46 thf(fact_234_ord__eq__le__eq__trans,axiom,
% 0.28/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a,D: refine424419629nres_a] :
% 0.28/0.46 ( ( A2 = B2 )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 0.28/0.46 => ( ( C2 = D )
% 0.28/0.46 => ( ord_le519537037nres_a @ A2 @ D ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_eq_trans
% 0.28/0.46 thf(fact_235_ord__eq__le__eq__trans,axiom,
% 0.28/0.46 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b,D: refine432681134nres_b] :
% 0.28/0.46 ( ( A2 = B2 )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 0.28/0.46 => ( ( C2 = D )
% 0.28/0.46 => ( ord_le527798542nres_b @ A2 @ D ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_eq_trans
% 0.28/0.46 thf(fact_236_Id__refine,axiom,
% 0.28/0.46 ! [S: refine432681134nres_b] : ( ord_le527798542nres_b @ S @ ( refine122110613un_b_b @ id_b @ S ) ) ).
% 0.28/0.46
% 0.28/0.46 % Id_refine
% 0.28/0.46 thf(fact_237_Id__refine,axiom,
% 0.28/0.46 ! [S: refine424419629nres_a] : ( ord_le519537037nres_a @ S @ ( refine1441824853un_a_a @ id_a @ S ) ) ).
% 0.28/0.46
% 0.28/0.46 % Id_refine
% 0.28/0.46 thf(fact_238_conc__trans__additional_I2_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ R @ C ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(2)
% 0.28/0.46 thf(fact_239_conc__trans__additional_I2_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B @ ( refine1441824854un_a_b @ R @ C ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(2)
% 0.28/0.46 thf(fact_240_conc__trans__additional_I2_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R @ C ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(2)
% 0.28/0.46 thf(fact_241_conc__trans__additional_I3_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,R: set_Product_prod_b_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ R @ B ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ R @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(3)
% 0.28/0.46 thf(fact_242_conc__trans__additional_I3_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,R: set_Product_prod_a_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ B ) )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(3)
% 0.28/0.46 thf(fact_243_conc__trans__additional_I3_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,R: set_Product_prod_b_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ B ) )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(3)
% 0.28/0.46 thf(fact_244_conc__trans__additional_I3_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ B ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(3)
% 0.28/0.46 thf(fact_245_conc__trans__additional_I6_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A @ B )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(6)
% 0.28/0.46 thf(fact_246_conc__trans__additional_I6_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ B )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(6)
% 0.28/0.46 thf(fact_247_conc__trans__additional_I5_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B @ C )
% 0.28/0.46 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(5)
% 0.28/0.46 thf(fact_248_conc__trans__additional_I5_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B @ C )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(5)
% 0.28/0.46 thf(fact_249_conc__trans__additional_I4_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(4)
% 0.28/0.46 thf(fact_250_conc__trans__additional_I4_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % conc_trans_additional(4)
% 0.28/0.46 thf(fact_251_Id__SPEC__refine,axiom,
% 0.28/0.46 ! [S: refine432681134nres_b,Phi: b > $o] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ S @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ S @ ( refine122110613un_b_b @ id_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Id_SPEC_refine
% 0.28/0.46 thf(fact_252_Id__SPEC__refine,axiom,
% 0.28/0.46 ! [S: refine424419629nres_a,Phi: a > $o] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ S @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ S @ ( refine1441824853un_a_a @ id_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Id_SPEC_refine
% 0.28/0.46 thf(fact_253_abs__trans__additional_I2_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ B ) @ C )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ A ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(2)
% 0.28/0.46 thf(fact_254_abs__trans__additional_I2_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ B ) @ C )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ A ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(2)
% 0.28/0.46 thf(fact_255_abs__trans__additional_I2_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ B ) @ C )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ A ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(2)
% 0.28/0.46 thf(fact_256_abs__trans__additional_I2_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ B ) @ C )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ A ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(2)
% 0.28/0.46 thf(fact_257_abs__trans__additional_I4_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ B ) @ C )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(4)
% 0.28/0.46 thf(fact_258_abs__trans__additional_I4_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ B ) @ C )
% 0.28/0.46 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(4)
% 0.28/0.46 thf(fact_259_abs__trans__additional_I5_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ B @ C )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(5)
% 0.28/0.46 thf(fact_260_abs__trans__additional_I5_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ B @ C )
% 0.28/0.46 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(5)
% 0.28/0.46 thf(fact_261_abs__trans__additional_I6_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ B )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ B ) @ C )
% 0.28/0.46 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(6)
% 0.28/0.46 thf(fact_262_abs__trans__additional_I6_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A @ B )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ B ) @ C )
% 0.28/0.46 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(6)
% 0.28/0.46 thf(fact_263_abs__fun__simps_I1_J,axiom,
% 0.28/0.46 ! [R: set_Product_prod_b_b] :
% 0.28/0.46 ( ( refine1964549110un_b_b @ R @ top_to240090974nres_b )
% 0.28/0.46 = top_to240090974nres_b ) ).
% 0.28/0.46
% 0.28/0.46 % abs_fun_simps(1)
% 0.28/0.46 thf(fact_264_abs__fun__simps_I1_J,axiom,
% 0.28/0.46 ! [R: set_Product_prod_b_a] :
% 0.28/0.46 ( ( refine1964549109un_b_a @ R @ top_to240090974nres_b )
% 0.28/0.46 = top_to231829469nres_a ) ).
% 0.28/0.46
% 0.28/0.46 % abs_fun_simps(1)
% 0.28/0.46 thf(fact_265_abs__fun__simps_I1_J,axiom,
% 0.28/0.46 ! [R: set_Product_prod_a_b] :
% 0.28/0.46 ( ( refine1136779703un_a_b @ R @ top_to231829469nres_a )
% 0.28/0.46 = top_to240090974nres_b ) ).
% 0.28/0.46
% 0.28/0.46 % abs_fun_simps(1)
% 0.28/0.46 thf(fact_266_abs__fun__simps_I1_J,axiom,
% 0.28/0.46 ! [R: set_Product_prod_a_a] :
% 0.28/0.46 ( ( refine1136779702un_a_a @ R @ top_to231829469nres_a )
% 0.28/0.46 = top_to231829469nres_a ) ).
% 0.28/0.46
% 0.28/0.46 % abs_fun_simps(1)
% 0.28/0.46 thf(fact_267_if__rule,axiom,
% 0.28/0.46 ! [B2: $o,S1: refine424419629nres_a,Phi: a > $o,S2: refine424419629nres_a] :
% 0.28/0.46 ( ( B2
% 0.28/0.46 => ( ord_le519537037nres_a @ S1 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.28/0.46 => ( ( ~ B2
% 0.28/0.46 => ( ord_le519537037nres_a @ S2 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ S1 @ S2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % if_rule
% 0.28/0.46 thf(fact_268_if__rule,axiom,
% 0.28/0.46 ! [B2: $o,S1: refine432681134nres_b,Phi: b > $o,S2: refine432681134nres_b] :
% 0.28/0.46 ( ( B2
% 0.28/0.46 => ( ord_le527798542nres_b @ S1 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.28/0.46 => ( ( ~ B2
% 0.28/0.46 => ( ord_le527798542nres_b @ S2 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B2 @ S1 @ S2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % if_rule
% 0.28/0.46 thf(fact_269_RES__rule,axiom,
% 0.28/0.46 ! [S: set_a,Phi: a > $o] :
% 0.28/0.46 ( ! [X2: a] :
% 0.28/0.46 ( ( member_a @ X2 @ S )
% 0.28/0.46 => ( Phi @ X2 ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RES_rule
% 0.28/0.46 thf(fact_270_RES__rule,axiom,
% 0.28/0.46 ! [S: set_b,Phi: b > $o] :
% 0.28/0.46 ( ! [X2: b] :
% 0.28/0.46 ( ( member_b @ X2 @ S )
% 0.28/0.46 => ( Phi @ X2 ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RES_rule
% 0.28/0.46 thf(fact_271_SPEC__rule,axiom,
% 0.28/0.46 ! [Phi: a > $o,Phi2: a > $o] :
% 0.28/0.46 ( ! [X2: a] :
% 0.28/0.46 ( ( Phi @ X2 )
% 0.28/0.46 => ( Phi2 @ X2 ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % SPEC_rule
% 0.28/0.46 thf(fact_272_SPEC__rule,axiom,
% 0.28/0.46 ! [Phi: b > $o,Phi2: b > $o] :
% 0.28/0.46 ( ! [X2: b] :
% 0.28/0.46 ( ( Phi @ X2 )
% 0.28/0.46 => ( Phi2 @ X2 ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % SPEC_rule
% 0.28/0.46 thf(fact_273_SPEC__trans,axiom,
% 0.28/0.46 ! [X: refine424419629nres_a,Y2: refine424419629nres_a,Postcond: a > $o] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ X @ Y2 )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ Y2 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ X @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % SPEC_trans
% 0.28/0.46 thf(fact_274_SPEC__trans,axiom,
% 0.28/0.46 ! [X: refine432681134nres_b,Y2: refine432681134nres_b,Postcond: b > $o] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ X @ Y2 )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ Y2 @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ X @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % SPEC_trans
% 0.28/0.46 thf(fact_275_SPEC__cons__rule,axiom,
% 0.28/0.46 ! [M2: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ M2 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.28/0.46 => ( ! [X2: a] :
% 0.28/0.46 ( ( Phi @ X2 )
% 0.28/0.46 => ( Psi @ X2 ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ M2 @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % SPEC_cons_rule
% 0.28/0.46 thf(fact_276_SPEC__cons__rule,axiom,
% 0.28/0.46 ! [M2: refine432681134nres_b,Phi: b > $o,Psi: b > $o] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ M2 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) )
% 0.28/0.46 => ( ! [X2: b] :
% 0.28/0.46 ( ( Phi @ X2 )
% 0.28/0.46 => ( Psi @ X2 ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ M2 @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % SPEC_cons_rule
% 0.28/0.46 thf(fact_277_nres__inequalities_I1_J,axiom,
% 0.28/0.46 ! [X5: set_b] :
% 0.28/0.46 ( top_to240090974nres_b
% 0.28/0.46 != ( refine1198353289_RES_b @ X5 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_inequalities(1)
% 0.28/0.46 thf(fact_278_nres__inequalities_I1_J,axiom,
% 0.28/0.46 ! [X5: set_a] :
% 0.28/0.46 ( top_to231829469nres_a
% 0.28/0.46 != ( refine1198353288_RES_a @ X5 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_inequalities(1)
% 0.28/0.46 thf(fact_279_nres__cases,axiom,
% 0.28/0.46 ! [M: refine432681134nres_b] :
% 0.28/0.46 ( ( M != top_to240090974nres_b )
% 0.28/0.46 => ~ ! [X6: set_b] :
% 0.28/0.46 ( M
% 0.28/0.46 != ( refine1198353289_RES_b @ X6 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_cases
% 0.28/0.46 thf(fact_280_nres__cases,axiom,
% 0.28/0.46 ! [M: refine424419629nres_a] :
% 0.28/0.46 ( ( M != top_to231829469nres_a )
% 0.28/0.46 => ~ ! [X6: set_a] :
% 0.28/0.46 ( M
% 0.28/0.46 != ( refine1198353288_RES_a @ X6 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_cases
% 0.28/0.46 thf(fact_281_abs__trans__additional_I1_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ B )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ B ) @ C )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ A ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(1)
% 0.28/0.46 thf(fact_282_abs__trans__additional_I1_J,axiom,
% 0.28/0.46 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ A @ B )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ B ) @ C )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ A ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(1)
% 0.28/0.46 thf(fact_283_abs__trans__additional_I1_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_a,C: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A @ B )
% 0.28/0.46 => ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ B ) @ C )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ A ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(1)
% 0.28/0.46 thf(fact_284_abs__trans__additional_I1_J,axiom,
% 0.28/0.46 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_b,C: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ A @ B )
% 0.28/0.46 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ B ) @ C )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ A ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % abs_trans_additional(1)
% 0.28/0.46 thf(fact_285_nres__order__simps_I5_J,axiom,
% 0.28/0.46 ! [X5: set_a,Y7: set_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X5 ) @ ( refine1198353288_RES_a @ Y7 ) )
% 0.28/0.46 = ( ord_less_eq_set_a @ X5 @ Y7 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_order_simps(5)
% 0.28/0.46 thf(fact_286_nres__order__simps_I5_J,axiom,
% 0.28/0.46 ! [X5: set_b,Y7: set_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ X5 ) @ ( refine1198353289_RES_b @ Y7 ) )
% 0.28/0.46 = ( ord_less_eq_set_b @ X5 @ Y7 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_order_simps(5)
% 0.28/0.46 thf(fact_287_less__eq__nres_Osimps_I2_J,axiom,
% 0.28/0.46 ! [A2: set_a,B2: set_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A2 ) @ ( refine1198353288_RES_a @ B2 ) )
% 0.28/0.46 = ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % less_eq_nres.simps(2)
% 0.28/0.46 thf(fact_288_less__eq__nres_Osimps_I2_J,axiom,
% 0.28/0.46 ! [A2: set_b,B2: set_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A2 ) @ ( refine1198353289_RES_b @ B2 ) )
% 0.28/0.46 = ( ord_less_eq_set_b @ A2 @ B2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % less_eq_nres.simps(2)
% 0.28/0.46 thf(fact_289_nres__order__simps_I21_J,axiom,
% 0.28/0.46 ! [X: a,Y7: set_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1198353288_RES_a @ Y7 ) )
% 0.28/0.46 = ( member_a @ X @ Y7 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_order_simps(21)
% 0.28/0.46 thf(fact_290_nres__order__simps_I21_J,axiom,
% 0.28/0.46 ! [X: b,Y7: set_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine1198353289_RES_b @ Y7 ) )
% 0.28/0.46 = ( member_b @ X @ Y7 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_order_simps(21)
% 0.28/0.46 thf(fact_291_nres__order__simps_I20_J,axiom,
% 0.28/0.46 ! [X: a,Y2: a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine2063221604TURN_a @ Y2 ) )
% 0.28/0.46 = ( X = Y2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_order_simps(20)
% 0.28/0.46 thf(fact_292_nres__order__simps_I20_J,axiom,
% 0.28/0.46 ! [X: b,Y2: b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine2063221605TURN_b @ Y2 ) )
% 0.28/0.46 = ( X = Y2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_order_simps(20)
% 0.28/0.46 thf(fact_293_nres__inequalities_I3_J,axiom,
% 0.28/0.46 ! [X: b] :
% 0.28/0.46 ( top_to240090974nres_b
% 0.28/0.46 != ( refine2063221605TURN_b @ X ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_inequalities(3)
% 0.28/0.46 thf(fact_294_nres__inequalities_I3_J,axiom,
% 0.28/0.46 ! [X: a] :
% 0.28/0.46 ( top_to231829469nres_a
% 0.28/0.46 != ( refine2063221604TURN_a @ X ) ) ).
% 0.28/0.46
% 0.28/0.46 % nres_inequalities(3)
% 0.28/0.46 thf(fact_295_RETURN__to__SPEC__rule,axiom,
% 0.28/0.46 ! [M2: refine424419629nres_a,V: a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ M2
% 0.28/0.46 @ ( refine1198353288_RES_a
% 0.28/0.46 @ ( collect_a
% 0.28/0.46 @ ( ^ [Y: a,Z: a] : ( Y = Z )
% 0.28/0.46 @ V ) ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ M2 @ ( refine2063221604TURN_a @ V ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_to_SPEC_rule
% 0.28/0.46 thf(fact_296_RETURN__to__SPEC__rule,axiom,
% 0.28/0.46 ! [M2: refine432681134nres_b,V: b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ M2
% 0.28/0.46 @ ( refine1198353289_RES_b
% 0.28/0.46 @ ( collect_b
% 0.28/0.46 @ ( ^ [Y: b,Z: b] : ( Y = Z )
% 0.28/0.46 @ V ) ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ M2 @ ( refine2063221605TURN_b @ V ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_to_SPEC_rule
% 0.28/0.46 thf(fact_297_RETURN__rule,axiom,
% 0.28/0.46 ! [Phi: a > $o,X: a] :
% 0.28/0.46 ( ( Phi @ X )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_rule
% 0.28/0.46 thf(fact_298_RETURN__rule,axiom,
% 0.28/0.46 ! [Phi: b > $o,X: b] :
% 0.28/0.46 ( ( Phi @ X )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_rule
% 0.28/0.46 thf(fact_299_RETURN__SPEC__refine,axiom,
% 0.28/0.46 ! [X: a,R: set_Product_prod_a_b,Phi: b > $o] :
% 0.28/0.46 ( ? [X7: b] :
% 0.28/0.46 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X @ X7 ) @ R )
% 0.28/0.46 & ( Phi @ X7 ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_SPEC_refine
% 0.28/0.46 thf(fact_300_RETURN__SPEC__refine,axiom,
% 0.28/0.46 ! [X: b,R: set_Product_prod_b_b,Phi: b > $o] :
% 0.28/0.46 ( ? [X7: b] :
% 0.28/0.46 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ X7 ) @ R )
% 0.28/0.46 & ( Phi @ X7 ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_SPEC_refine
% 0.28/0.46 thf(fact_301_RETURN__SPEC__refine,axiom,
% 0.28/0.46 ! [X: a,R: set_Product_prod_a_a,Phi: a > $o] :
% 0.28/0.46 ( ? [X7: a] :
% 0.28/0.46 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ X7 ) @ R )
% 0.28/0.46 & ( Phi @ X7 ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_SPEC_refine
% 0.28/0.46 thf(fact_302_nofail__simps_I1_J,axiom,
% 0.28/0.46 ~ ( refine412683990fail_b @ top_to240090974nres_b ) ).
% 0.28/0.46
% 0.28/0.46 % nofail_simps(1)
% 0.28/0.46 thf(fact_303_nofail__simps_I1_J,axiom,
% 0.28/0.46 ~ ( refine412683989fail_a @ top_to231829469nres_a ) ).
% 0.28/0.46
% 0.28/0.46 % nofail_simps(1)
% 0.28/0.46 thf(fact_304_pw__conc__nofail,axiom,
% 0.28/0.46 ! [R: set_Product_prod_a_b,S: refine432681134nres_b] :
% 0.28/0.46 ( ( refine412683989fail_a @ ( refine1441824854un_a_b @ R @ S ) )
% 0.28/0.46 = ( refine412683990fail_b @ S ) ) ).
% 0.28/0.46
% 0.28/0.46 % pw_conc_nofail
% 0.28/0.46 thf(fact_305_pw__conc__nofail,axiom,
% 0.28/0.46 ! [R: set_Product_prod_b_b,S: refine432681134nres_b] :
% 0.28/0.46 ( ( refine412683990fail_b @ ( refine122110613un_b_b @ R @ S ) )
% 0.28/0.46 = ( refine412683990fail_b @ S ) ) ).
% 0.28/0.46
% 0.28/0.46 % pw_conc_nofail
% 0.28/0.46 thf(fact_306_pw__conc__nofail,axiom,
% 0.28/0.46 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 0.28/0.46 ( ( refine412683989fail_a @ ( refine1441824853un_a_a @ R @ S ) )
% 0.28/0.46 = ( refine412683989fail_a @ S ) ) ).
% 0.28/0.46
% 0.28/0.46 % pw_conc_nofail
% 0.28/0.46 thf(fact_307_intro__nofail_I2_J,axiom,
% 0.28/0.46 ! [S: refine432681134nres_b] :
% 0.28/0.46 ( ( top_to240090974nres_b != S )
% 0.28/0.46 = ( refine412683990fail_b @ S ) ) ).
% 0.28/0.46
% 0.28/0.46 % intro_nofail(2)
% 0.28/0.46 thf(fact_308_intro__nofail_I2_J,axiom,
% 0.28/0.46 ! [S: refine424419629nres_a] :
% 0.28/0.46 ( ( top_to231829469nres_a != S )
% 0.28/0.46 = ( refine412683989fail_a @ S ) ) ).
% 0.28/0.46
% 0.28/0.46 % intro_nofail(2)
% 0.28/0.46 thf(fact_309_nofail__def,axiom,
% 0.28/0.46 ( refine412683990fail_b
% 0.28/0.46 = ( ^ [S3: refine432681134nres_b] : ( S3 != top_to240090974nres_b ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % nofail_def
% 0.28/0.46 thf(fact_310_nofail__def,axiom,
% 0.28/0.46 ( refine412683989fail_a
% 0.28/0.46 = ( ^ [S3: refine424419629nres_a] : ( S3 != top_to231829469nres_a ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % nofail_def
% 0.28/0.46 thf(fact_311_not__nofail__iff,axiom,
% 0.28/0.46 ! [S: refine432681134nres_b] :
% 0.28/0.46 ( ( ~ ( refine412683990fail_b @ S ) )
% 0.28/0.46 = ( S = top_to240090974nres_b ) ) ).
% 0.28/0.46
% 0.28/0.46 % not_nofail_iff
% 0.28/0.46 thf(fact_312_not__nofail__iff,axiom,
% 0.28/0.46 ! [S: refine424419629nres_a] :
% 0.28/0.46 ( ( ~ ( refine412683989fail_a @ S ) )
% 0.28/0.46 = ( S = top_to231829469nres_a ) ) ).
% 0.28/0.46
% 0.28/0.46 % not_nofail_iff
% 0.28/0.46 thf(fact_313_pwD1,axiom,
% 0.28/0.46 ! [S: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ S @ S4 )
% 0.28/0.46 => ( ( refine412683989fail_a @ S4 )
% 0.28/0.46 => ( refine412683989fail_a @ S ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pwD1
% 0.28/0.46 thf(fact_314_pwD1,axiom,
% 0.28/0.46 ! [S: refine432681134nres_b,S4: refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ S @ S4 )
% 0.28/0.46 => ( ( refine412683990fail_b @ S4 )
% 0.28/0.46 => ( refine412683990fail_b @ S ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pwD1
% 0.28/0.46 thf(fact_315_le__nofailI,axiom,
% 0.28/0.46 ! [M3: refine424419629nres_a,M: refine424419629nres_a] :
% 0.28/0.46 ( ( ( refine412683989fail_a @ M3 )
% 0.28/0.46 => ( ord_le519537037nres_a @ M @ M3 ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ M @ M3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_nofailI
% 0.28/0.46 thf(fact_316_le__nofailI,axiom,
% 0.28/0.46 ! [M3: refine432681134nres_b,M: refine432681134nres_b] :
% 0.28/0.46 ( ( ( refine412683990fail_b @ M3 )
% 0.28/0.46 => ( ord_le527798542nres_b @ M @ M3 ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ M @ M3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_nofailI
% 0.28/0.46 thf(fact_317_RES__refine,axiom,
% 0.28/0.46 ! [S: set_a,S4: set_b,R: set_Product_prod_a_b] :
% 0.28/0.46 ( ! [S5: a] :
% 0.28/0.46 ( ( member_a @ S5 @ S )
% 0.28/0.46 => ? [X8: b] :
% 0.28/0.46 ( ( member_b @ X8 @ S4 )
% 0.28/0.46 & ( member458171089od_a_b @ ( product_Pair_a_b @ S5 @ X8 ) @ R ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ S4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RES_refine
% 0.28/0.46 thf(fact_318_RES__refine,axiom,
% 0.28/0.46 ! [S: set_b,S4: set_b,R: set_Product_prod_b_b] :
% 0.28/0.46 ( ! [S5: b] :
% 0.28/0.46 ( ( member_b @ S5 @ S )
% 0.28/0.46 => ? [X8: b] :
% 0.28/0.46 ( ( member_b @ X8 @ S4 )
% 0.28/0.46 & ( member1285940496od_b_b @ ( product_Pair_b_b @ S5 @ X8 ) @ R ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ S4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RES_refine
% 0.28/0.46 thf(fact_319_RES__refine,axiom,
% 0.28/0.46 ! [S: set_a,S4: set_a,R: set_Product_prod_a_a] :
% 0.28/0.46 ( ! [S5: a] :
% 0.28/0.46 ( ( member_a @ S5 @ S )
% 0.28/0.46 => ? [X8: a] :
% 0.28/0.46 ( ( member_a @ X8 @ S4 )
% 0.28/0.46 & ( member449909584od_a_a @ ( product_Pair_a_a @ S5 @ X8 ) @ R ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ S4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RES_refine
% 0.28/0.46 thf(fact_320_RETURN__refine,axiom,
% 0.28/0.46 ! [X: a,X9: b,R: set_Product_prod_a_b] :
% 0.28/0.46 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X @ X9 ) @ R )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1441824854un_a_b @ R @ ( refine2063221605TURN_b @ X9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_refine
% 0.28/0.46 thf(fact_321_RETURN__refine,axiom,
% 0.28/0.46 ! [X: b,X9: b,R: set_Product_prod_b_b] :
% 0.28/0.46 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ X9 ) @ R )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine122110613un_b_b @ R @ ( refine2063221605TURN_b @ X9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_refine
% 0.28/0.46 thf(fact_322_RETURN__refine,axiom,
% 0.28/0.46 ! [X: a,X9: a,R: set_Product_prod_a_a] :
% 0.28/0.46 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ X9 ) @ R )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1441824853un_a_a @ R @ ( refine2063221604TURN_a @ X9 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % RETURN_refine
% 0.28/0.46 thf(fact_323_inres__simps_I1_J,axiom,
% 0.28/0.46 ( ( refine1001002028nres_b @ top_to240090974nres_b )
% 0.28/0.46 = ( ^ [Uu: b] : $true ) ) ).
% 0.28/0.46
% 0.28/0.46 % inres_simps(1)
% 0.28/0.46 thf(fact_324_inres__simps_I1_J,axiom,
% 0.28/0.46 ( ( refine1001002027nres_a @ top_to231829469nres_a )
% 0.28/0.46 = ( ^ [Uu: a] : $true ) ) ).
% 0.28/0.46
% 0.28/0.46 % inres_simps(1)
% 0.28/0.46 thf(fact_325_pwD2,axiom,
% 0.28/0.46 ! [S: refine424419629nres_a,S4: refine424419629nres_a,X: a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ S @ S4 )
% 0.28/0.46 => ( ( refine1001002027nres_a @ S @ X )
% 0.28/0.46 => ( refine1001002027nres_a @ S4 @ X ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pwD2
% 0.28/0.46 thf(fact_326_pwD2,axiom,
% 0.28/0.46 ! [S: refine432681134nres_b,S4: refine432681134nres_b,X: b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ S @ S4 )
% 0.28/0.46 => ( ( refine1001002028nres_b @ S @ X )
% 0.28/0.46 => ( refine1001002028nres_b @ S4 @ X ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pwD2
% 0.28/0.46 thf(fact_327_pw__leI,axiom,
% 0.28/0.46 ! [S4: refine424419629nres_a,S: refine424419629nres_a] :
% 0.28/0.46 ( ( ( refine412683989fail_a @ S4 )
% 0.28/0.46 => ( ( refine412683989fail_a @ S )
% 0.28/0.46 & ! [X2: a] :
% 0.28/0.46 ( ( refine1001002027nres_a @ S @ X2 )
% 0.28/0.46 => ( refine1001002027nres_a @ S4 @ X2 ) ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ S @ S4 ) ) ).
% 0.28/0.46
% 0.28/0.46 % pw_leI
% 0.28/0.46 thf(fact_328_pw__leI,axiom,
% 0.28/0.46 ! [S4: refine432681134nres_b,S: refine432681134nres_b] :
% 0.28/0.46 ( ( ( refine412683990fail_b @ S4 )
% 0.28/0.46 => ( ( refine412683990fail_b @ S )
% 0.28/0.46 & ! [X2: b] :
% 0.28/0.46 ( ( refine1001002028nres_b @ S @ X2 )
% 0.28/0.46 => ( refine1001002028nres_b @ S4 @ X2 ) ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ S @ S4 ) ) ).
% 0.28/0.46
% 0.28/0.46 % pw_leI
% 0.28/0.46 thf(fact_329_pw__leI_H,axiom,
% 0.28/0.46 ! [S4: refine424419629nres_a,S: refine424419629nres_a] :
% 0.28/0.46 ( ( ( refine412683989fail_a @ S4 )
% 0.28/0.46 => ( refine412683989fail_a @ S ) )
% 0.28/0.46 => ( ! [X2: a] :
% 0.28/0.46 ( ( refine412683989fail_a @ S4 )
% 0.28/0.46 => ( ( refine1001002027nres_a @ S @ X2 )
% 0.28/0.46 => ( refine1001002027nres_a @ S4 @ X2 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ S @ S4 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pw_leI'
% 0.28/0.46 thf(fact_330_pw__leI_H,axiom,
% 0.28/0.46 ! [S4: refine432681134nres_b,S: refine432681134nres_b] :
% 0.28/0.46 ( ( ( refine412683990fail_b @ S4 )
% 0.28/0.46 => ( refine412683990fail_b @ S ) )
% 0.28/0.46 => ( ! [X2: b] :
% 0.28/0.46 ( ( refine412683990fail_b @ S4 )
% 0.28/0.46 => ( ( refine1001002028nres_b @ S @ X2 )
% 0.28/0.46 => ( refine1001002028nres_b @ S4 @ X2 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ S @ S4 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pw_leI'
% 0.28/0.46 thf(fact_331_pw__le__iff,axiom,
% 0.28/0.46 ( ord_le519537037nres_a
% 0.28/0.46 = ( ^ [S3: refine424419629nres_a,S6: refine424419629nres_a] :
% 0.28/0.46 ( ( refine412683989fail_a @ S6 )
% 0.28/0.46 => ( ( refine412683989fail_a @ S3 )
% 0.28/0.46 & ! [X3: a] :
% 0.28/0.46 ( ( refine1001002027nres_a @ S3 @ X3 )
% 0.28/0.46 => ( refine1001002027nres_a @ S6 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pw_le_iff
% 0.28/0.46 thf(fact_332_pw__le__iff,axiom,
% 0.28/0.46 ( ord_le527798542nres_b
% 0.28/0.46 = ( ^ [S3: refine432681134nres_b,S6: refine432681134nres_b] :
% 0.28/0.46 ( ( refine412683990fail_b @ S6 )
% 0.28/0.46 => ( ( refine412683990fail_b @ S3 )
% 0.28/0.46 & ! [X3: b] :
% 0.28/0.46 ( ( refine1001002028nres_b @ S3 @ X3 )
% 0.28/0.46 => ( refine1001002028nres_b @ S6 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pw_le_iff
% 0.28/0.46 thf(fact_333_inres__def,axiom,
% 0.28/0.46 ( refine1001002027nres_a
% 0.28/0.46 = ( ^ [S3: refine424419629nres_a,X3: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ S3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inres_def
% 0.28/0.46 thf(fact_334_inres__def,axiom,
% 0.28/0.46 ( refine1001002028nres_b
% 0.28/0.46 = ( ^ [S3: refine432681134nres_b,X3: b] : ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ S3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inres_def
% 0.28/0.46 thf(fact_335_bind__FAIL,axiom,
% 0.28/0.46 ! [F: b > refine432681134nres_b] :
% 0.28/0.46 ( ( refine1264602246nd_b_b @ top_to240090974nres_b @ F )
% 0.28/0.46 = top_to240090974nres_b ) ).
% 0.28/0.46
% 0.28/0.46 % bind_FAIL
% 0.28/0.46 thf(fact_336_bind__FAIL,axiom,
% 0.28/0.46 ! [F: b > refine424419629nres_a] :
% 0.28/0.46 ( ( refine1264602245nd_b_a @ top_to240090974nres_b @ F )
% 0.28/0.46 = top_to231829469nres_a ) ).
% 0.28/0.46
% 0.28/0.46 % bind_FAIL
% 0.28/0.46 thf(fact_337_bind__FAIL,axiom,
% 0.28/0.46 ! [F: a > refine432681134nres_b] :
% 0.28/0.46 ( ( refine436832839nd_a_b @ top_to231829469nres_a @ F )
% 0.28/0.46 = top_to240090974nres_b ) ).
% 0.28/0.46
% 0.28/0.46 % bind_FAIL
% 0.28/0.46 thf(fact_338_bind__FAIL,axiom,
% 0.28/0.46 ! [F: a > refine424419629nres_a] :
% 0.28/0.46 ( ( refine436832838nd_a_a @ top_to231829469nres_a @ F )
% 0.28/0.46 = top_to231829469nres_a ) ).
% 0.28/0.46
% 0.28/0.46 % bind_FAIL
% 0.28/0.46 thf(fact_339_ibind__strict_I2_J,axiom,
% 0.28/0.46 ! [F: product_unit > refine432681134nres_b] :
% 0.28/0.46 ( ( refine119808504unit_b @ top_to177290092t_unit @ F )
% 0.28/0.46 = top_to240090974nres_b ) ).
% 0.28/0.46
% 0.28/0.46 % ibind_strict(2)
% 0.28/0.46 thf(fact_340_ibind__strict_I2_J,axiom,
% 0.28/0.46 ! [F: product_unit > refine424419629nres_a] :
% 0.28/0.46 ( ( refine119808503unit_a @ top_to177290092t_unit @ F )
% 0.28/0.46 = top_to231829469nres_a ) ).
% 0.28/0.46
% 0.28/0.46 % ibind_strict(2)
% 0.28/0.46 thf(fact_341_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.28/0.46 ! [M: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine424419629nres_a,F3: a > refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ M @ M3 )
% 0.28/0.46 => ( ! [X2: a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F3 @ X2 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ ( refine436832838nd_a_a @ M3 @ F3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.28/0.46 thf(fact_342_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.28/0.46 ! [M: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine432681134nres_b,F3: a > refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ M @ M3 )
% 0.28/0.46 => ( ! [X2: a] :
% 0.28/0.46 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F3 @ X2 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F ) @ ( refine436832839nd_a_b @ M3 @ F3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.28/0.46 thf(fact_343_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.28/0.46 ! [M: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine424419629nres_a,F3: b > refine424419629nres_a] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ M @ M3 )
% 0.28/0.46 => ( ! [X2: b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X2 ) @ M )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F3 @ X2 ) ) )
% 0.28/0.46 => ( ord_le519537037nres_a @ ( refine1264602245nd_b_a @ M @ F ) @ ( refine1264602245nd_b_a @ M3 @ F3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.28/0.46 thf(fact_344_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.28/0.46 ! [M: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine432681134nres_b,F3: b > refine432681134nres_b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ M @ M3 )
% 0.28/0.46 => ( ! [X2: b] :
% 0.28/0.46 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X2 ) @ M )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F3 @ X2 ) ) )
% 0.28/0.46 => ( ord_le527798542nres_b @ ( refine1264602246nd_b_b @ M @ F ) @ ( refine1264602246nd_b_b @ M3 @ F3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.28/0.46 thf(fact_345_sup__top__left,axiom,
% 0.28/0.46 ! [X: refine432681134nres_b] :
% 0.28/0.46 ( ( sup_su2042991066nres_b @ top_to240090974nres_b @ X )
% 0.28/0.46 = top_to240090974nres_b ) ).
% 0.28/0.46
% 0.28/0.46 % sup_top_left
% 0.28/0.46 thf(fact_346_sup__top__left,axiom,
% 0.28/0.46 ! [X: refine424419629nres_a] :
% 0.28/0.46 ( ( sup_su2034729561nres_a @ top_to231829469nres_a @ X )
% 0.28/0.46 = top_to231829469nres_a ) ).
% 0.28/0.46
% 0.28/0.46 % sup_top_left
% 0.28/0.46
% 0.28/0.46 % Helper facts (15)
% 0.28/0.46 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.28/0.46 ! [X: set_a,Y2: set_a] :
% 0.28/0.46 ( ( if_set_a @ $false @ X @ Y2 )
% 0.28/0.46 = Y2 ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.28/0.46 ! [X: set_a,Y2: set_a] :
% 0.28/0.46 ( ( if_set_a @ $true @ X @ Y2 )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_2_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 0.28/0.46 ! [X: set_b,Y2: set_b] :
% 0.28/0.46 ( ( if_set_b @ $false @ X @ Y2 )
% 0.28/0.46 = Y2 ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_1_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 0.28/0.46 ! [X: set_b,Y2: set_b] :
% 0.28/0.46 ( ( if_set_b @ $true @ X @ Y2 )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 0.28/0.46 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 0.28/0.46 ( ( if_set1550076877od_a_a @ $false @ X @ Y2 )
% 0.28/0.46 = Y2 ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 0.28/0.46 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 0.28/0.46 ( ( if_set1550076877od_a_a @ $true @ X @ Y2 )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.28/0.46 ! [X: refine424419629nres_a,Y2: refine424419629nres_a] :
% 0.28/0.46 ( ( if_Ref1724547303nres_a @ $false @ X @ Y2 )
% 0.28/0.46 = Y2 ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.28/0.46 ! [X: refine424419629nres_a,Y2: refine424419629nres_a] :
% 0.28/0.46 ( ( if_Ref1724547303nres_a @ $true @ X @ Y2 )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 0.28/0.46 ! [X: refine432681134nres_b,Y2: refine432681134nres_b] :
% 0.28/0.46 ( ( if_Ref1732808808nres_b @ $false @ X @ Y2 )
% 0.28/0.46 = Y2 ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 0.28/0.46 ! [X: refine432681134nres_b,Y2: refine432681134nres_b] :
% 0.28/0.46 ( ( if_Ref1732808808nres_b @ $true @ X @ Y2 )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 0.28/0.46 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a] :
% 0.28/0.46 ( ( if_o_R1705037948nres_a @ $false @ X @ Y2 )
% 0.28/0.46 = Y2 ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 0.28/0.46 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a] :
% 0.28/0.46 ( ( if_o_R1705037948nres_a @ $true @ X @ Y2 )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_3_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 0.28/0.46 ! [P: $o] :
% 0.28/0.46 ( ( P = $true )
% 0.28/0.46 | ( P = $false ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 0.28/0.46 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b] :
% 0.28/0.46 ( ( if_o_R697118589nres_b @ $false @ X @ Y2 )
% 0.28/0.46 = Y2 ) ).
% 0.28/0.46
% 0.28/0.46 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 0.28/0.46 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b] :
% 0.28/0.46 ( ( if_o_R697118589nres_b @ $true @ X @ Y2 )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 % Conjectures (1)
% 0.28/0.46 thf(conj_0,conjecture,
% 0.28/0.46 ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 2.37/1.57 ---- Embedded in THF ---
% 2.37/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.37/1.57 %%% Generated on Tue Feb 24 08:28:25 EST 2026
% 2.37/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.37/1.57 %%% Logic specification used:
% 2.37/1.57 %%% thf(spec, logic, $$dhol).
% 2.37/1.57
% 2.37/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.C9Bew6RkOr/DTF2DTF10704.p
% See solution above
% 2.37/1.57 ------------------------
% 2.56/1.60 ---- Cleaned THF ---
% 2.56/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
% 2.56/1.60 set_Pr451126599t_unit: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 2.56/1.60 refine787176636t_unit: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Ounit_J_J,type,
% 2.56/1.60 set_Pr1707992533t_unit: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Ounit_J_J,type,
% 2.56/1.60 set_Pr1628433942t_unit: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mtf__b_J_J,type,
% 2.56/1.60 set_Pr712638521unit_b: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mtf__a_J_J,type,
% 2.56/1.60 set_Pr1720557880unit_a: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 2.56/1.60 refine432681134nres_b: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 2.56/1.60 refine424419629nres_a: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 2.56/1.60 set_Product_prod_b_b: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
% 2.56/1.60 set_Product_prod_b_a: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
% 2.56/1.60 set_Product_prod_a_b: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 2.56/1.60 set_Product_prod_a_a: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 2.56/1.60 product_prod_b_b: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
% 2.56/1.60 product_prod_a_b: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 2.56/1.60 product_prod_a_a: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Product____Type__Ounit,type,
% 2.56/1.60 product_unit: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_Itf__b_J,type,
% 2.56/1.60 set_b: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.56/1.60 set_a: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_tf__b,type,
% 2.56/1.60 b: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(ty_n_tf__a,type,
% 2.56/1.60 a: $tType ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 2.56/1.60 if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 2.56/1.60 if_o_R697118589nres_b: $o > ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 2.56/1.60 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 2.56/1.60 if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 2.56/1.60 if_set1550076877od_a_a: $o > set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 2.56/1.60 if_set_a: $o > set_a > set_a > set_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_If_001t__Set__Oset_Itf__b_J,type,
% 2.56/1.60 if_set_b: $o > set_b > set_b > set_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Lattices_Osup__class_Osup_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 2.56/1.60 sup_su2034729561nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Lattices_Osup__class_Osup_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 2.56/1.60 sup_su2042991066nres_b: refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 2.56/1.60 ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 2.56/1.60 ord_le1656162903nres_b: ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 2.56/1.60 ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 2.56/1.60 ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 2.56/1.60 ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 2.56/1.60 ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
% 2.56/1.60 ord_le816409512od_a_b: set_Product_prod_a_b > set_Product_prod_a_b > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
% 2.56/1.60 ord_le2044239718od_b_a: set_Product_prod_b_a > set_Product_prod_b_a > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 2.56/1.60 ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 2.56/1.60 ord_less_eq_set_a: set_a > set_a > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__b_J,type,
% 2.56/1.60 ord_less_eq_set_b: set_b > set_b > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 2.56/1.60 order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 2.56/1.60 order_1722590613nres_b: ( refine432681134nres_b > $o ) > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 2.56/1.60 top_to2046902534nres_a: $o > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 2.56/1.60 top_to1038983175nres_b: $o > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 2.56/1.60 top_to177290092t_unit: refine787176636t_unit ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 2.56/1.60 top_to231829469nres_a: refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 2.56/1.60 top_to240090974nres_b: refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 2.56/1.60 top_to398455383od_a_a: set_Product_prod_a_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
% 2.56/1.60 top_top_set_a: set_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__b_J,type,
% 2.56/1.60 top_top_set_b: set_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Product__Type_OPair_001tf__a_001tf__a,type,
% 2.56/1.60 product_Pair_a_a: a > a > product_prod_a_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Product__Type_OPair_001tf__a_001tf__b,type,
% 2.56/1.60 product_Pair_a_b: a > b > product_prod_a_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Product__Type_OPair_001tf__b_001tf__b,type,
% 2.56/1.60 product_Pair_b_b: b > b > product_prod_b_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__a,type,
% 2.56/1.60 refine2063221604TURN_a: a > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__b,type,
% 2.56/1.60 refine2063221605TURN_b: b > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__a_001tf__a,type,
% 2.56/1.60 refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__a_001tf__b,type,
% 2.56/1.60 refine1136779703un_a_b: set_Product_prod_a_b > refine424419629nres_a > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__b_001tf__a,type,
% 2.56/1.60 refine1964549109un_b_a: set_Product_prod_b_a > refine432681134nres_b > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oabs__fun_001tf__b_001tf__b,type,
% 2.56/1.60 refine1964549110un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001t__Product____Type__Ounit_001tf__a,type,
% 2.56/1.60 refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001t__Product____Type__Ounit_001tf__b,type,
% 2.56/1.60 refine119808504unit_b: refine787176636t_unit > ( product_unit > refine432681134nres_b ) > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001tf__a,type,
% 2.56/1.60 refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001tf__b,type,
% 2.56/1.60 refine436832839nd_a_b: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__b_001tf__a,type,
% 2.56/1.60 refine1264602245nd_b_a: refine432681134nres_b > ( b > refine424419629nres_a ) > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__b_001tf__b,type,
% 2.56/1.60 refine1264602246nd_b_b: refine432681134nres_b > ( b > refine432681134nres_b ) > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 2.56/1.60 refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001t__Product____Type__Ounit_001tf__a,type,
% 2.56/1.60 refine2043866374unit_a: set_Pr1720557880unit_a > refine424419629nres_a > refine787176636t_unit ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001t__Product____Type__Ounit_001tf__b,type,
% 2.56/1.60 refine2043866375unit_b: set_Pr712638521unit_b > refine432681134nres_b > refine787176636t_unit ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__a_001t__Product____Type__Ounit,type,
% 2.56/1.60 refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__a_001tf__a,type,
% 2.56/1.60 refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__a_001tf__b,type,
% 2.56/1.60 refine1441824854un_a_b: set_Product_prod_a_b > refine432681134nres_b > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__b_001t__Product____Type__Ounit,type,
% 2.56/1.60 refine2140306339t_unit: set_Pr1707992533t_unit > refine787176636t_unit > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__b_001tf__a,type,
% 2.56/1.60 refine122110612un_b_a: set_Product_prod_b_a > refine424419629nres_a > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oconc__fun_001tf__b_001tf__b,type,
% 2.56/1.60 refine122110613un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__a,type,
% 2.56/1.60 refine1001002027nres_a: refine424419629nres_a > a > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__b,type,
% 2.56/1.60 refine1001002028nres_b: refine432681134nres_b > b > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__a,type,
% 2.56/1.60 refine412683989fail_a: refine424419629nres_a > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__b,type,
% 2.56/1.60 refine412683990fail_b: refine432681134nres_b > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__a,type,
% 2.56/1.60 refine1198353288_RES_a: set_a > refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__b,type,
% 2.56/1.60 refine1198353289_RES_b: set_b > refine432681134nres_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Relation_OId_001tf__a,type,
% 2.56/1.60 id_a: set_Product_prod_a_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Relation_OId_001tf__b,type,
% 2.56/1.60 id_b: set_Product_prod_b_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.56/1.60 collect_a: ( a > $o ) > set_a ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_Set_OCollect_001tf__b,type,
% 2.56/1.60 collect_b: ( b > $o ) > set_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 2.56/1.60 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
% 2.56/1.60 member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 2.56/1.60 member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_member_001tf__a,type,
% 2.56/1.60 member_a: a > set_a > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_c_member_001tf__b,type,
% 2.56/1.60 member_b: b > set_b > $o ).
% 2.56/1.60
% 2.56/1.60 thf(sy_v_R,type,
% 2.56/1.60 r: set_Product_prod_a_b ).
% 2.56/1.60
% 2.56/1.60 thf(sy_v_X,type,
% 2.56/1.60 x: refine424419629nres_a ).
% 2.56/1.60
% 2.56/1.60 thf(fact_0_nres__order__simps_I4_J,axiom,
% 2.56/1.60 ! [M: refine787176636t_unit] :
% 2.56/1.60 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ M )
% 2.56/1.60 = ( M = top_to177290092t_unit ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_1_nres__order__simps_I4_J,axiom,
% 2.56/1.60 ! [M: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ M )
% 2.56/1.60 = ( M = top_to240090974nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_2_nres__order__simps_I4_J,axiom,
% 2.56/1.60 ! [M: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M )
% 2.56/1.60 = ( M = top_to231829469nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_3_conc__fun__fail__iff_I2_J,axiom,
% 2.56/1.60 ! [R: set_Pr1707992533t_unit,S: refine787176636t_unit] :
% 2.56/1.60 ( ( top_to240090974nres_b
% 2.56/1.60 = ( refine2140306339t_unit @ R @ S ) )
% 2.56/1.60 = ( S = top_to177290092t_unit ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_4_conc__fun__fail__iff_I2_J,axiom,
% 2.56/1.60 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 2.56/1.60 ( ( top_to231829469nres_a
% 2.56/1.60 = ( refine2021053540t_unit @ R @ S ) )
% 2.56/1.60 = ( S = top_to177290092t_unit ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_5_conc__fun__fail__iff_I2_J,axiom,
% 2.56/1.60 ! [R: set_Pr712638521unit_b,S: refine432681134nres_b] :
% 2.56/1.60 ( ( top_to177290092t_unit
% 2.56/1.60 = ( refine2043866375unit_b @ R @ S ) )
% 2.56/1.60 = ( S = top_to240090974nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_6_conc__fun__fail__iff_I2_J,axiom,
% 2.56/1.60 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 2.56/1.60 ( ( top_to177290092t_unit
% 2.56/1.60 = ( refine2043866374unit_a @ R @ S ) )
% 2.56/1.60 = ( S = top_to231829469nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_7_conc__fun__fail__iff_I2_J,axiom,
% 2.56/1.60 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 2.56/1.60 ( ( top_to177290092t_unit
% 2.56/1.60 = ( refine944483349t_unit @ R @ S ) )
% 2.56/1.60 = ( S = top_to177290092t_unit ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_8_conc__fun__fail__iff_I2_J,axiom,
% 2.56/1.60 ! [R: set_Product_prod_b_a,S: refine424419629nres_a] :
% 2.56/1.60 ( ( top_to240090974nres_b
% 2.56/1.60 = ( refine122110612un_b_a @ R @ S ) )
% 2.56/1.60 = ( S = top_to231829469nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_9_conc__fun__fail__iff_I2_J,axiom,
% 2.56/1.60 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 2.56/1.60 ( ( top_to231829469nres_a
% 2.56/1.60 = ( refine1441824853un_a_a @ R @ S ) )
% 2.56/1.60 = ( S = top_to231829469nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_10_conc__fun__fail__iff_I2_J,axiom,
% 2.56/1.60 ! [R: set_Product_prod_b_b,S: refine432681134nres_b] :
% 2.56/1.60 ( ( top_to240090974nres_b
% 2.56/1.60 = ( refine122110613un_b_b @ R @ S ) )
% 2.56/1.60 = ( S = top_to240090974nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_11_conc__fun__fail__iff_I2_J,axiom,
% 2.56/1.60 ! [R: set_Product_prod_a_b,S: refine432681134nres_b] :
% 2.56/1.60 ( ( top_to231829469nres_a
% 2.56/1.60 = ( refine1441824854un_a_b @ R @ S ) )
% 2.56/1.60 = ( S = top_to240090974nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_12_conc__fun__fail__iff_I1_J,axiom,
% 2.56/1.60 ! [R: set_Pr1707992533t_unit,S: refine787176636t_unit] :
% 2.56/1.60 ( ( ( refine2140306339t_unit @ R @ S )
% 2.56/1.60 = top_to240090974nres_b )
% 2.56/1.60 = ( S = top_to177290092t_unit ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_13_conc__fun__fail__iff_I1_J,axiom,
% 2.56/1.60 ! [R: set_Pr1628433942t_unit,S: refine787176636t_unit] :
% 2.56/1.60 ( ( ( refine2021053540t_unit @ R @ S )
% 2.56/1.60 = top_to231829469nres_a )
% 2.56/1.60 = ( S = top_to177290092t_unit ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_14_conc__fun__fail__iff_I1_J,axiom,
% 2.56/1.60 ! [R: set_Pr712638521unit_b,S: refine432681134nres_b] :
% 2.56/1.60 ( ( ( refine2043866375unit_b @ R @ S )
% 2.56/1.60 = top_to177290092t_unit )
% 2.56/1.60 = ( S = top_to240090974nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_15_conc__fun__fail__iff_I1_J,axiom,
% 2.56/1.60 ! [R: set_Pr1720557880unit_a,S: refine424419629nres_a] :
% 2.56/1.60 ( ( ( refine2043866374unit_a @ R @ S )
% 2.56/1.60 = top_to177290092t_unit )
% 2.56/1.60 = ( S = top_to231829469nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_16_conc__fun__fail__iff_I1_J,axiom,
% 2.56/1.60 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 2.56/1.60 ( ( ( refine944483349t_unit @ R @ S )
% 2.56/1.60 = top_to177290092t_unit )
% 2.56/1.60 = ( S = top_to177290092t_unit ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_17_conc__fun__fail__iff_I1_J,axiom,
% 2.56/1.60 ! [R: set_Product_prod_b_a,S: refine424419629nres_a] :
% 2.56/1.60 ( ( ( refine122110612un_b_a @ R @ S )
% 2.56/1.60 = top_to240090974nres_b )
% 2.56/1.60 = ( S = top_to231829469nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_18_conc__fun__fail__iff_I1_J,axiom,
% 2.56/1.60 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 2.56/1.60 ( ( ( refine1441824853un_a_a @ R @ S )
% 2.56/1.60 = top_to231829469nres_a )
% 2.56/1.60 = ( S = top_to231829469nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_19_conc__fun__fail__iff_I1_J,axiom,
% 2.56/1.60 ! [R: set_Product_prod_b_b,S: refine432681134nres_b] :
% 2.56/1.60 ( ( ( refine122110613un_b_b @ R @ S )
% 2.56/1.60 = top_to240090974nres_b )
% 2.56/1.60 = ( S = top_to240090974nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_20_conc__fun__fail__iff_I1_J,axiom,
% 2.56/1.60 ! [R: set_Product_prod_a_b,S: refine432681134nres_b] :
% 2.56/1.60 ( ( ( refine1441824854un_a_b @ R @ S )
% 2.56/1.60 = top_to231829469nres_a )
% 2.56/1.60 = ( S = top_to240090974nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_21_conc__fun__FAIL,axiom,
% 2.56/1.60 ! [R: set_Pr712638521unit_b] :
% 2.56/1.60 ( ( refine2043866375unit_b @ R @ top_to240090974nres_b )
% 2.56/1.60 = top_to177290092t_unit ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_22_conc__fun__FAIL,axiom,
% 2.56/1.60 ! [R: set_Pr1720557880unit_a] :
% 2.56/1.60 ( ( refine2043866374unit_a @ R @ top_to231829469nres_a )
% 2.56/1.60 = top_to177290092t_unit ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_23_conc__fun__FAIL,axiom,
% 2.56/1.60 ! [R: set_Pr1707992533t_unit] :
% 2.56/1.60 ( ( refine2140306339t_unit @ R @ top_to177290092t_unit )
% 2.56/1.60 = top_to240090974nres_b ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_24_conc__fun__FAIL,axiom,
% 2.56/1.60 ! [R: set_Pr1628433942t_unit] :
% 2.56/1.60 ( ( refine2021053540t_unit @ R @ top_to177290092t_unit )
% 2.56/1.60 = top_to231829469nres_a ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_25_conc__fun__FAIL,axiom,
% 2.56/1.60 ! [R: set_Pr451126599t_unit] :
% 2.56/1.60 ( ( refine944483349t_unit @ R @ top_to177290092t_unit )
% 2.56/1.60 = top_to177290092t_unit ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_26_conc__fun__FAIL,axiom,
% 2.56/1.60 ! [R: set_Product_prod_b_a] :
% 2.56/1.60 ( ( refine122110612un_b_a @ R @ top_to231829469nres_a )
% 2.56/1.60 = top_to240090974nres_b ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_27_conc__fun__FAIL,axiom,
% 2.56/1.60 ! [R: set_Product_prod_a_a] :
% 2.56/1.60 ( ( refine1441824853un_a_a @ R @ top_to231829469nres_a )
% 2.56/1.60 = top_to231829469nres_a ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_28_conc__fun__FAIL,axiom,
% 2.56/1.60 ! [R: set_Product_prod_b_b] :
% 2.56/1.60 ( ( refine122110613un_b_b @ R @ top_to240090974nres_b )
% 2.56/1.60 = top_to240090974nres_b ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_29_conc__fun__FAIL,axiom,
% 2.56/1.60 ! [R: set_Product_prod_a_b] :
% 2.56/1.60 ( ( refine1441824854un_a_b @ R @ top_to240090974nres_b )
% 2.56/1.60 = top_to231829469nres_a ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_30_nres__order__simps_I3_J,axiom,
% 2.56/1.60 ! [M: refine787176636t_unit] : ( ord_le1051254044t_unit @ M @ top_to177290092t_unit ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_31_nres__order__simps_I3_J,axiom,
% 2.56/1.60 ! [M: refine432681134nres_b] : ( ord_le527798542nres_b @ M @ top_to240090974nres_b ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_32_nres__order__simps_I3_J,axiom,
% 2.56/1.60 ! [M: refine424419629nres_a] : ( ord_le519537037nres_a @ M @ top_to231829469nres_a ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_33_conc__trans__additional_I1_J,axiom,
% 2.56/1.60 ! [A: refine432681134nres_b,R: set_Product_prod_b_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ R @ B ) )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B @ C )
% 2.56/1.60 => ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ R @ C ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_34_conc__trans__additional_I1_J,axiom,
% 2.56/1.60 ! [A: refine432681134nres_b,R: set_Product_prod_b_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ B ) )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B @ C )
% 2.56/1.60 => ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ C ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_35_conc__trans__additional_I1_J,axiom,
% 2.56/1.60 ! [A: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ B ) )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B @ C )
% 2.56/1.60 => ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ C ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_36_conc__trans__additional_I1_J,axiom,
% 2.56/1.60 ! [A: refine424419629nres_a,R: set_Product_prod_a_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ B ) )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B @ C )
% 2.56/1.60 => ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ C ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_37_conc__trans,axiom,
% 2.56/1.60 ! [C: refine424419629nres_a,R: set_Product_prod_a_b,B: refine432681134nres_b,R2: set_Product_prod_b_a,A: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ R @ B ) )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B @ ( refine122110612un_b_a @ R2 @ A ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ R @ ( refine122110612un_b_a @ R2 @ A ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_38_conc__trans,axiom,
% 2.56/1.60 ! [C: refine432681134nres_b,R: set_Product_prod_b_b,B: refine432681134nres_b,R2: set_Product_prod_b_a,A: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ R @ B ) )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B @ ( refine122110612un_b_a @ R2 @ A ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ R @ ( refine122110612un_b_a @ R2 @ A ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_39_conc__trans,axiom,
% 2.56/1.60 ! [C: refine432681134nres_b,R: set_Product_prod_b_a,B: refine424419629nres_a,R2: set_Product_prod_a_b,A: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ R @ B ) )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B @ ( refine1441824854un_a_b @ R2 @ A ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ R @ ( refine1441824854un_a_b @ R2 @ A ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_40_conc__trans,axiom,
% 2.56/1.60 ! [C: refine432681134nres_b,R: set_Product_prod_b_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ R @ B ) )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R2 @ A ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ C @ ( refine122110612un_b_a @ R @ ( refine1441824853un_a_a @ R2 @ A ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_41_conc__trans,axiom,
% 2.56/1.60 ! [C: refine424419629nres_a,R: set_Product_prod_a_b,B: refine432681134nres_b,R2: set_Product_prod_b_b,A: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ R @ B ) )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ R2 @ A ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ C @ ( refine1441824854un_a_b @ R @ ( refine122110613un_b_b @ R2 @ A ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_42_conc__trans,axiom,
% 2.56/1.60 ! [C: refine432681134nres_b,R: set_Product_prod_b_b,B: refine432681134nres_b,R2: set_Product_prod_b_b,A: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ R @ B ) )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ R2 @ A ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ C @ ( refine122110613un_b_b @ R @ ( refine122110613un_b_b @ R2 @ A ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_43_conc__trans,axiom,
% 2.56/1.60 ! [C: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,R2: set_Product_prod_a_a,A: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ B ) )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R2 @ A ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ ( refine1441824853un_a_a @ R2 @ A ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_44_conc__trans,axiom,
% 2.56/1.60 ! [C: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,R2: set_Product_prod_a_b,A: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ B ) )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B @ ( refine1441824854un_a_b @ R2 @ A ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ C @ ( refine1441824853un_a_a @ R @ ( refine1441824854un_a_b @ R2 @ A ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_45_order__mono__setup_Orefl,axiom,
% 2.56/1.60 ! [X: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ X @ X ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_46_order__mono__setup_Orefl,axiom,
% 2.56/1.60 ! [X: set_b] : ( ord_less_eq_set_b @ X @ X ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_47_order__mono__setup_Orefl,axiom,
% 2.56/1.60 ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_48_order__mono__setup_Orefl,axiom,
% 2.56/1.60 ! [X: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ X @ X ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_49_order__mono__setup_Orefl,axiom,
% 2.56/1.60 ! [X: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ X @ X ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_50_order__mono__setup_Orefl,axiom,
% 2.56/1.60 ! [X: refine432681134nres_b] : ( ord_le527798542nres_b @ X @ X ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_51_order__mono__setup_Orefl,axiom,
% 2.56/1.60 ! [X: refine424419629nres_a] : ( ord_le519537037nres_a @ X @ X ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_52_top__greatest,axiom,
% 2.56/1.60 ! [A2: refine787176636t_unit] : ( ord_le1051254044t_unit @ A2 @ top_to177290092t_unit ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_53_top__greatest,axiom,
% 2.56/1.60 ! [A2: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A2 @ top_to398455383od_a_a ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_54_top__greatest,axiom,
% 2.56/1.60 ! [A2: set_b] : ( ord_less_eq_set_b @ A2 @ top_top_set_b ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_55_top__greatest,axiom,
% 2.56/1.60 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ top_top_set_a ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_56_top__greatest,axiom,
% 2.56/1.60 ! [A2: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A2 @ top_to1038983175nres_b ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_57_top__greatest,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A2 @ top_to2046902534nres_a ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_58_top__greatest,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b] : ( ord_le527798542nres_b @ A2 @ top_to240090974nres_b ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_59_top__greatest,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ top_to231829469nres_a ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_60_meta__le__everything__if__top,axiom,
% 2.56/1.60 ! [M2: refine787176636t_unit,X: refine787176636t_unit] :
% 2.56/1.60 ( ( M2 = top_to177290092t_unit )
% 2.56/1.60 => ( ord_le1051254044t_unit @ X @ M2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_61_meta__le__everything__if__top,axiom,
% 2.56/1.60 ! [M2: set_Product_prod_a_a,X: set_Product_prod_a_a] :
% 2.56/1.60 ( ( M2 = top_to398455383od_a_a )
% 2.56/1.60 => ( ord_le1824328871od_a_a @ X @ M2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_62_meta__le__everything__if__top,axiom,
% 2.56/1.60 ! [M2: set_b,X: set_b] :
% 2.56/1.60 ( ( M2 = top_top_set_b )
% 2.56/1.60 => ( ord_less_eq_set_b @ X @ M2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_63_meta__le__everything__if__top,axiom,
% 2.56/1.60 ! [M2: set_a,X: set_a] :
% 2.56/1.60 ( ( M2 = top_top_set_a )
% 2.56/1.60 => ( ord_less_eq_set_a @ X @ M2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_64_meta__le__everything__if__top,axiom,
% 2.56/1.60 ! [M2: $o > refine432681134nres_b,X: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( M2 = top_to1038983175nres_b )
% 2.56/1.60 => ( ord_le1656162903nres_b @ X @ M2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_65_meta__le__everything__if__top,axiom,
% 2.56/1.60 ! [M2: $o > refine424419629nres_a,X: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( M2 = top_to2046902534nres_a )
% 2.56/1.60 => ( ord_le516598614nres_a @ X @ M2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_66_meta__le__everything__if__top,axiom,
% 2.56/1.60 ! [M2: refine424419629nres_a,X: refine424419629nres_a] :
% 2.56/1.60 ( ( M2 = top_to231829469nres_a )
% 2.56/1.60 => ( ord_le519537037nres_a @ X @ M2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_67_meta__le__everything__if__top,axiom,
% 2.56/1.60 ! [M2: refine432681134nres_b,X: refine432681134nres_b] :
% 2.56/1.60 ( ( M2 = top_to240090974nres_b )
% 2.56/1.60 => ( ord_le527798542nres_b @ X @ M2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_68_top_Oextremum__unique,axiom,
% 2.56/1.60 ! [A2: refine787176636t_unit] :
% 2.56/1.60 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A2 )
% 2.56/1.60 = ( A2 = top_to177290092t_unit ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_69_top_Oextremum__unique,axiom,
% 2.56/1.60 ! [A2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ top_to398455383od_a_a @ A2 )
% 2.56/1.60 = ( A2 = top_to398455383od_a_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_70_top_Oextremum__unique,axiom,
% 2.56/1.60 ! [A2: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ top_top_set_b @ A2 )
% 2.56/1.60 = ( A2 = top_top_set_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_71_top_Oextremum__unique,axiom,
% 2.56/1.60 ! [A2: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ top_top_set_a @ A2 )
% 2.56/1.60 = ( A2 = top_top_set_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_72_top_Oextremum__unique,axiom,
% 2.56/1.60 ! [A2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ top_to1038983175nres_b @ A2 )
% 2.56/1.60 = ( A2 = top_to1038983175nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_73_top_Oextremum__unique,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ top_to2046902534nres_a @ A2 )
% 2.56/1.60 = ( A2 = top_to2046902534nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_74_top_Oextremum__unique,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A2 )
% 2.56/1.60 = ( A2 = top_to231829469nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_75_top_Oextremum__unique,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A2 )
% 2.56/1.60 = ( A2 = top_to240090974nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_76_top_Oextremum__uniqueI,axiom,
% 2.56/1.60 ! [A2: refine787176636t_unit] :
% 2.56/1.60 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A2 )
% 2.56/1.60 => ( A2 = top_to177290092t_unit ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_77_top_Oextremum__uniqueI,axiom,
% 2.56/1.60 ! [A2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ top_to398455383od_a_a @ A2 )
% 2.56/1.60 => ( A2 = top_to398455383od_a_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_78_top_Oextremum__uniqueI,axiom,
% 2.56/1.60 ! [A2: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ top_top_set_b @ A2 )
% 2.56/1.60 => ( A2 = top_top_set_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_79_top_Oextremum__uniqueI,axiom,
% 2.56/1.60 ! [A2: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ top_top_set_a @ A2 )
% 2.56/1.60 => ( A2 = top_top_set_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_80_top_Oextremum__uniqueI,axiom,
% 2.56/1.60 ! [A2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ top_to1038983175nres_b @ A2 )
% 2.56/1.60 => ( A2 = top_to1038983175nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_81_top_Oextremum__uniqueI,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ top_to2046902534nres_a @ A2 )
% 2.56/1.60 => ( A2 = top_to2046902534nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_82_top_Oextremum__uniqueI,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A2 )
% 2.56/1.60 => ( A2 = top_to231829469nres_a ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_83_top_Oextremum__uniqueI,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A2 )
% 2.56/1.60 => ( A2 = top_to240090974nres_b ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_84_le__funD,axiom,
% 2.56/1.60 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X: $o] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ F @ G )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_85_le__funD,axiom,
% 2.56/1.60 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X: $o] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ F @ G )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_86_le__funE,axiom,
% 2.56/1.60 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X: $o] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ F @ G )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_87_le__funE,axiom,
% 2.56/1.60 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X: $o] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ F @ G )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_88_le__funI,axiom,
% 2.56/1.60 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a] :
% 2.56/1.60 ( ! [X2: $o] : ( ord_le519537037nres_a @ ( F @ X2 ) @ ( G @ X2 ) )
% 2.56/1.60 => ( ord_le516598614nres_a @ F @ G ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_89_le__funI,axiom,
% 2.56/1.60 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b] :
% 2.56/1.60 ( ! [X2: $o] : ( ord_le527798542nres_b @ ( F @ X2 ) @ ( G @ X2 ) )
% 2.56/1.60 => ( ord_le1656162903nres_b @ F @ G ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_90_Refine__Misc_Oif__mono,axiom,
% 2.56/1.60 ! [B2: $o,M1: set_Product_prod_a_a,M12: set_Product_prod_a_a,M22: set_Product_prod_a_a,M23: set_Product_prod_a_a] :
% 2.56/1.60 ( ( B2
% 2.56/1.60 => ( ord_le1824328871od_a_a @ M1 @ M12 ) )
% 2.56/1.60 => ( ( ~ B2
% 2.56/1.60 => ( ord_le1824328871od_a_a @ M22 @ M23 ) )
% 2.56/1.60 => ( ord_le1824328871od_a_a @ ( if_set1550076877od_a_a @ B2 @ M1 @ M22 ) @ ( if_set1550076877od_a_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_91_Refine__Misc_Oif__mono,axiom,
% 2.56/1.60 ! [B2: $o,M1: set_b,M12: set_b,M22: set_b,M23: set_b] :
% 2.56/1.60 ( ( B2
% 2.56/1.60 => ( ord_less_eq_set_b @ M1 @ M12 ) )
% 2.56/1.60 => ( ( ~ B2
% 2.56/1.60 => ( ord_less_eq_set_b @ M22 @ M23 ) )
% 2.56/1.60 => ( ord_less_eq_set_b @ ( if_set_b @ B2 @ M1 @ M22 ) @ ( if_set_b @ B2 @ M12 @ M23 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_92_Refine__Misc_Oif__mono,axiom,
% 2.56/1.60 ! [B2: $o,M1: set_a,M12: set_a,M22: set_a,M23: set_a] :
% 2.56/1.60 ( ( B2
% 2.56/1.60 => ( ord_less_eq_set_a @ M1 @ M12 ) )
% 2.56/1.60 => ( ( ~ B2
% 2.56/1.60 => ( ord_less_eq_set_a @ M22 @ M23 ) )
% 2.56/1.60 => ( ord_less_eq_set_a @ ( if_set_a @ B2 @ M1 @ M22 ) @ ( if_set_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_93_Refine__Misc_Oif__mono,axiom,
% 2.56/1.60 ! [B2: $o,M1: $o > refine432681134nres_b,M12: $o > refine432681134nres_b,M22: $o > refine432681134nres_b,M23: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( B2
% 2.56/1.60 => ( ord_le1656162903nres_b @ M1 @ M12 ) )
% 2.56/1.60 => ( ( ~ B2
% 2.56/1.60 => ( ord_le1656162903nres_b @ M22 @ M23 ) )
% 2.56/1.60 => ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ B2 @ M1 @ M22 ) @ ( if_o_R697118589nres_b @ B2 @ M12 @ M23 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_94_Refine__Misc_Oif__mono,axiom,
% 2.56/1.60 ! [B2: $o,M1: $o > refine424419629nres_a,M12: $o > refine424419629nres_a,M22: $o > refine424419629nres_a,M23: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( B2
% 2.56/1.60 => ( ord_le516598614nres_a @ M1 @ M12 ) )
% 2.56/1.60 => ( ( ~ B2
% 2.56/1.60 => ( ord_le516598614nres_a @ M22 @ M23 ) )
% 2.56/1.60 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B2 @ M1 @ M22 ) @ ( if_o_R1705037948nres_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_95_Refine__Misc_Oif__mono,axiom,
% 2.56/1.60 ! [B2: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M22: refine424419629nres_a,M23: refine424419629nres_a] :
% 2.56/1.60 ( ( B2
% 2.56/1.60 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 2.56/1.60 => ( ( ~ B2
% 2.56/1.60 => ( ord_le519537037nres_a @ M22 @ M23 ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ M1 @ M22 ) @ ( if_Ref1724547303nres_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_96_Refine__Misc_Oif__mono,axiom,
% 2.56/1.60 ! [B2: $o,M1: refine432681134nres_b,M12: refine432681134nres_b,M22: refine432681134nres_b,M23: refine432681134nres_b] :
% 2.56/1.60 ( ( B2
% 2.56/1.60 => ( ord_le527798542nres_b @ M1 @ M12 ) )
% 2.56/1.60 => ( ( ~ B2
% 2.56/1.60 => ( ord_le527798542nres_b @ M22 @ M23 ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B2 @ M1 @ M22 ) @ ( if_Ref1732808808nres_b @ B2 @ M12 @ M23 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_97_le__fun__def,axiom,
% 2.56/1.60 ( ord_le1656162903nres_b
% 2.56/1.60 = ( ^ [F2: $o > refine432681134nres_b,G2: $o > refine432681134nres_b] :
% 2.56/1.60 ! [X3: $o] : ( ord_le527798542nres_b @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_98_le__fun__def,axiom,
% 2.56/1.60 ( ord_le516598614nres_a
% 2.56/1.60 = ( ^ [F2: $o > refine424419629nres_a,G2: $o > refine424419629nres_a] :
% 2.56/1.60 ! [X3: $o] : ( ord_le519537037nres_a @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_99_conc__fun__R__mono,axiom,
% 2.56/1.60 ! [R: set_Product_prod_b_a,R2: set_Product_prod_b_a,M: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le2044239718od_b_a @ R @ R2 )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( refine122110612un_b_a @ R @ M ) @ ( refine122110612un_b_a @ R2 @ M ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_100_conc__fun__R__mono,axiom,
% 2.56/1.60 ! [R: set_Product_prod_a_b,R2: set_Product_prod_a_b,M: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le816409512od_a_b @ R @ R2 )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( refine1441824854un_a_b @ R @ M ) @ ( refine1441824854un_a_b @ R2 @ M ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_101_conc__fun__R__mono,axiom,
% 2.56/1.60 ! [R: set_Product_prod_b_b,R2: set_Product_prod_b_b,M: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1036320359od_b_b @ R @ R2 )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( refine122110613un_b_b @ R @ M ) @ ( refine122110613un_b_b @ R2 @ M ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_102_conc__fun__R__mono,axiom,
% 2.56/1.60 ! [R: set_Product_prod_a_a,R2: set_Product_prod_a_a,M: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ R @ R2 )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( refine1441824853un_a_a @ R @ M ) @ ( refine1441824853un_a_a @ R2 @ M ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_103_order__mono__setup_Omono__if,axiom,
% 2.56/1.60 ! [T: set_Product_prod_a_a,T2: set_Product_prod_a_a,E: set_Product_prod_a_a,E2: set_Product_prod_a_a,B2: $o] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ T @ T2 )
% 2.56/1.60 => ( ( ord_le1824328871od_a_a @ E @ E2 )
% 2.56/1.60 => ( ord_le1824328871od_a_a @ ( if_set1550076877od_a_a @ B2 @ T @ E ) @ ( if_set1550076877od_a_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_104_order__mono__setup_Omono__if,axiom,
% 2.56/1.60 ! [T: set_b,T2: set_b,E: set_b,E2: set_b,B2: $o] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ T @ T2 )
% 2.56/1.60 => ( ( ord_less_eq_set_b @ E @ E2 )
% 2.56/1.60 => ( ord_less_eq_set_b @ ( if_set_b @ B2 @ T @ E ) @ ( if_set_b @ B2 @ T2 @ E2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_105_order__mono__setup_Omono__if,axiom,
% 2.56/1.60 ! [T: set_a,T2: set_a,E: set_a,E2: set_a,B2: $o] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ T @ T2 )
% 2.56/1.60 => ( ( ord_less_eq_set_a @ E @ E2 )
% 2.56/1.60 => ( ord_less_eq_set_a @ ( if_set_a @ B2 @ T @ E ) @ ( if_set_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_106_order__mono__setup_Omono__if,axiom,
% 2.56/1.60 ! [T: $o > refine432681134nres_b,T2: $o > refine432681134nres_b,E: $o > refine432681134nres_b,E2: $o > refine432681134nres_b,B2: $o] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ T @ T2 )
% 2.56/1.60 => ( ( ord_le1656162903nres_b @ E @ E2 )
% 2.56/1.60 => ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ B2 @ T @ E ) @ ( if_o_R697118589nres_b @ B2 @ T2 @ E2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_107_order__mono__setup_Omono__if,axiom,
% 2.56/1.60 ! [T: $o > refine424419629nres_a,T2: $o > refine424419629nres_a,E: $o > refine424419629nres_a,E2: $o > refine424419629nres_a,B2: $o] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ T @ T2 )
% 2.56/1.60 => ( ( ord_le516598614nres_a @ E @ E2 )
% 2.56/1.60 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B2 @ T @ E ) @ ( if_o_R1705037948nres_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_108_order__mono__setup_Omono__if,axiom,
% 2.56/1.60 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B2: $o] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ T @ T2 )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ E @ E2 )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ T @ E ) @ ( if_Ref1724547303nres_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_109_order__mono__setup_Omono__if,axiom,
% 2.56/1.60 ! [T: refine432681134nres_b,T2: refine432681134nres_b,E: refine432681134nres_b,E2: refine432681134nres_b,B2: $o] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ T @ T2 )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ E @ E2 )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B2 @ T @ E ) @ ( if_Ref1732808808nres_b @ B2 @ T2 @ E2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_110_dual__order_Oantisym,axiom,
% 2.56/1.60 ! [B2: set_Product_prod_a_a,A2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_111_dual__order_Oantisym,axiom,
% 2.56/1.60 ! [B2: set_b,A2: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_less_eq_set_b @ A2 @ B2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_112_dual__order_Oantisym,axiom,
% 2.56/1.60 ! [B2: set_a,A2: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_113_dual__order_Oantisym,axiom,
% 2.56/1.60 ! [B2: $o > refine432681134nres_b,A2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le1656162903nres_b @ A2 @ B2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_114_dual__order_Oantisym,axiom,
% 2.56/1.60 ! [B2: $o > refine424419629nres_a,A2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le516598614nres_a @ A2 @ B2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_115_dual__order_Oantisym,axiom,
% 2.56/1.60 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ A2 @ B2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_116_dual__order_Oantisym,axiom,
% 2.56/1.60 ! [B2: refine432681134nres_b,A2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ A2 @ B2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_117_dual__order_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: set_Product_prod_a_a,B3: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ B3 @ A3 )
% 2.56/1.60 & ( ord_le1824328871od_a_a @ A3 @ B3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_118_dual__order_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: set_b,Z: set_b] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: set_b,B3: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ B3 @ A3 )
% 2.56/1.60 & ( ord_less_eq_set_b @ A3 @ B3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_119_dual__order_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: set_a,B3: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 2.56/1.60 & ( ord_less_eq_set_a @ A3 @ B3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_120_dual__order_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: $o > refine432681134nres_b,Z: $o > refine432681134nres_b] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: $o > refine432681134nres_b,B3: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ B3 @ A3 )
% 2.56/1.60 & ( ord_le1656162903nres_b @ A3 @ B3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_121_dual__order_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: $o > refine424419629nres_a,B3: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ B3 @ A3 )
% 2.56/1.60 & ( ord_le516598614nres_a @ A3 @ B3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_122_dual__order_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: refine424419629nres_a,Z: refine424419629nres_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ B3 @ A3 )
% 2.56/1.60 & ( ord_le519537037nres_a @ A3 @ B3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_123_dual__order_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: refine432681134nres_b,Z: refine432681134nres_b] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: refine432681134nres_b,B3: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ B3 @ A3 )
% 2.56/1.60 & ( ord_le527798542nres_b @ A3 @ B3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_124_dual__order_Otrans,axiom,
% 2.56/1.60 ! [B2: set_Product_prod_a_a,A2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le1824328871od_a_a @ C2 @ B2 )
% 2.56/1.60 => ( ord_le1824328871od_a_a @ C2 @ A2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_125_dual__order_Otrans,axiom,
% 2.56/1.60 ! [B2: set_b,A2: set_b,C2: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_less_eq_set_b @ C2 @ B2 )
% 2.56/1.60 => ( ord_less_eq_set_b @ C2 @ A2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_126_dual__order_Otrans,axiom,
% 2.56/1.60 ! [B2: set_a,A2: set_a,C2: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_less_eq_set_a @ C2 @ B2 )
% 2.56/1.60 => ( ord_less_eq_set_a @ C2 @ A2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_127_dual__order_Otrans,axiom,
% 2.56/1.60 ! [B2: $o > refine432681134nres_b,A2: $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le1656162903nres_b @ C2 @ B2 )
% 2.56/1.60 => ( ord_le1656162903nres_b @ C2 @ A2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_128_dual__order_Otrans,axiom,
% 2.56/1.60 ! [B2: $o > refine424419629nres_a,A2: $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le516598614nres_a @ C2 @ B2 )
% 2.56/1.60 => ( ord_le516598614nres_a @ C2 @ A2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_129_dual__order_Otrans,axiom,
% 2.56/1.60 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ C2 @ B2 )
% 2.56/1.60 => ( ord_le519537037nres_a @ C2 @ A2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_130_dual__order_Otrans,axiom,
% 2.56/1.60 ! [B2: refine432681134nres_b,A2: refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ B2 @ A2 )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ C2 @ B2 )
% 2.56/1.60 => ( ord_le527798542nres_b @ C2 @ A2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_131_dual__order_Orefl,axiom,
% 2.56/1.60 ! [A2: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A2 @ A2 ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_132_dual__order_Orefl,axiom,
% 2.56/1.60 ! [A2: set_b] : ( ord_less_eq_set_b @ A2 @ A2 ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_133_dual__order_Orefl,axiom,
% 2.56/1.60 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_134_dual__order_Orefl,axiom,
% 2.56/1.60 ! [A2: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ A2 @ A2 ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_135_dual__order_Orefl,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A2 @ A2 ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_136_dual__order_Orefl,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ A2 ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_137_dual__order_Orefl,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b] : ( ord_le527798542nres_b @ A2 @ A2 ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_138_order__trans,axiom,
% 2.56/1.60 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a,Z2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le1824328871od_a_a @ Y2 @ Z2 )
% 2.56/1.60 => ( ord_le1824328871od_a_a @ X @ Z2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_139_order__trans,axiom,
% 2.56/1.60 ! [X: set_b,Y2: set_b,Z2: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ X @ Y2 )
% 2.56/1.60 => ( ( ord_less_eq_set_b @ Y2 @ Z2 )
% 2.56/1.60 => ( ord_less_eq_set_b @ X @ Z2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_140_order__trans,axiom,
% 2.56/1.60 ! [X: set_a,Y2: set_a,Z2: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ X @ Y2 )
% 2.56/1.60 => ( ( ord_less_eq_set_a @ Y2 @ Z2 )
% 2.56/1.60 => ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_141_order__trans,axiom,
% 2.56/1.60 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b,Z2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le1656162903nres_b @ Y2 @ Z2 )
% 2.56/1.60 => ( ord_le1656162903nres_b @ X @ Z2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_142_order__trans,axiom,
% 2.56/1.60 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a,Z2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le516598614nres_a @ Y2 @ Z2 )
% 2.56/1.60 => ( ord_le516598614nres_a @ X @ Z2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_143_order__trans,axiom,
% 2.56/1.60 ! [X: refine424419629nres_a,Y2: refine424419629nres_a,Z2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ Y2 @ Z2 )
% 2.56/1.60 => ( ord_le519537037nres_a @ X @ Z2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_144_order__trans,axiom,
% 2.56/1.60 ! [X: refine432681134nres_b,Y2: refine432681134nres_b,Z2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ Y2 @ Z2 )
% 2.56/1.60 => ( ord_le527798542nres_b @ X @ Z2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_145_order__class_Oorder_Oantisym,axiom,
% 2.56/1.60 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le1824328871od_a_a @ B2 @ A2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_146_order__class_Oorder_Oantisym,axiom,
% 2.56/1.60 ! [A2: set_b,B2: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_less_eq_set_b @ B2 @ A2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_147_order__class_Oorder_Oantisym,axiom,
% 2.56/1.60 ! [A2: set_a,B2: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_less_eq_set_a @ B2 @ A2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_148_order__class_Oorder_Oantisym,axiom,
% 2.56/1.60 ! [A2: $o > refine432681134nres_b,B2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le1656162903nres_b @ B2 @ A2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_149_order__class_Oorder_Oantisym,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le516598614nres_a @ B2 @ A2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_150_order__class_Oorder_Oantisym,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B2 @ A2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_151_order__class_Oorder_Oantisym,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b,B2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B2 @ A2 )
% 2.56/1.60 => ( A2 = B2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_152_ord__le__eq__trans,axiom,
% 2.56/1.60 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 2.56/1.60 => ( ( B2 = C2 )
% 2.56/1.60 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_153_ord__le__eq__trans,axiom,
% 2.56/1.60 ! [A2: set_b,B2: set_b,C2: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ A2 @ B2 )
% 2.56/1.60 => ( ( B2 = C2 )
% 2.56/1.60 => ( ord_less_eq_set_b @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_154_ord__le__eq__trans,axiom,
% 2.56/1.60 ! [A2: set_a,B2: set_a,C2: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.56/1.60 => ( ( B2 = C2 )
% 2.56/1.60 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_155_ord__le__eq__trans,axiom,
% 2.56/1.60 ! [A2: $o > refine432681134nres_b,B2: $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ A2 @ B2 )
% 2.56/1.60 => ( ( B2 = C2 )
% 2.56/1.60 => ( ord_le1656162903nres_b @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_156_ord__le__eq__trans,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( B2 = C2 )
% 2.56/1.60 => ( ord_le516598614nres_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_157_ord__le__eq__trans,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( B2 = C2 )
% 2.56/1.60 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_158_ord__le__eq__trans,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 2.56/1.60 => ( ( B2 = C2 )
% 2.56/1.60 => ( ord_le527798542nres_b @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_159_ord__eq__le__trans,axiom,
% 2.56/1.60 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( A2 = B2 )
% 2.56/1.60 => ( ( ord_le1824328871od_a_a @ B2 @ C2 )
% 2.56/1.60 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_160_ord__eq__le__trans,axiom,
% 2.56/1.60 ! [A2: set_b,B2: set_b,C2: set_b] :
% 2.56/1.60 ( ( A2 = B2 )
% 2.56/1.60 => ( ( ord_less_eq_set_b @ B2 @ C2 )
% 2.56/1.60 => ( ord_less_eq_set_b @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_161_ord__eq__le__trans,axiom,
% 2.56/1.60 ! [A2: set_a,B2: set_a,C2: set_a] :
% 2.56/1.60 ( ( A2 = B2 )
% 2.56/1.60 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 2.56/1.60 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_162_ord__eq__le__trans,axiom,
% 2.56/1.60 ! [A2: $o > refine432681134nres_b,B2: $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( A2 = B2 )
% 2.56/1.60 => ( ( ord_le1656162903nres_b @ B2 @ C2 )
% 2.56/1.60 => ( ord_le1656162903nres_b @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_163_ord__eq__le__trans,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( A2 = B2 )
% 2.56/1.60 => ( ( ord_le516598614nres_a @ B2 @ C2 )
% 2.56/1.60 => ( ord_le516598614nres_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_164_ord__eq__le__trans,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.60 ( ( A2 = B2 )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 2.56/1.60 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_165_ord__eq__le__trans,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.60 ( ( A2 = B2 )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 2.56/1.60 => ( ord_le527798542nres_b @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_166_order__class_Oorder_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: set_Product_prod_a_a,B3: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ A3 @ B3 )
% 2.56/1.60 & ( ord_le1824328871od_a_a @ B3 @ A3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_167_order__class_Oorder_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: set_b,Z: set_b] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: set_b,B3: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ A3 @ B3 )
% 2.56/1.60 & ( ord_less_eq_set_b @ B3 @ A3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_168_order__class_Oorder_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: set_a,B3: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 2.56/1.60 & ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_169_order__class_Oorder_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: $o > refine432681134nres_b,Z: $o > refine432681134nres_b] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: $o > refine432681134nres_b,B3: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ A3 @ B3 )
% 2.56/1.60 & ( ord_le1656162903nres_b @ B3 @ A3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_170_order__class_Oorder_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: $o > refine424419629nres_a,B3: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ A3 @ B3 )
% 2.56/1.60 & ( ord_le516598614nres_a @ B3 @ A3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_171_order__class_Oorder_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: refine424419629nres_a,Z: refine424419629nres_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 2.56/1.60 & ( ord_le519537037nres_a @ B3 @ A3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_172_order__class_Oorder_Oeq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: refine432681134nres_b,Z: refine432681134nres_b] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [A3: refine432681134nres_b,B3: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ A3 @ B3 )
% 2.56/1.60 & ( ord_le527798542nres_b @ B3 @ A3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_173_antisym__conv,axiom,
% 2.56/1.60 ! [Y2: set_Product_prod_a_a,X: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ Y2 @ X )
% 2.56/1.60 => ( ( ord_le1824328871od_a_a @ X @ Y2 )
% 2.56/1.60 = ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_174_antisym__conv,axiom,
% 2.56/1.60 ! [Y2: set_b,X: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ Y2 @ X )
% 2.56/1.60 => ( ( ord_less_eq_set_b @ X @ Y2 )
% 2.56/1.60 = ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_175_antisym__conv,axiom,
% 2.56/1.60 ! [Y2: set_a,X: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ Y2 @ X )
% 2.56/1.60 => ( ( ord_less_eq_set_a @ X @ Y2 )
% 2.56/1.60 = ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_176_antisym__conv,axiom,
% 2.56/1.60 ! [Y2: $o > refine432681134nres_b,X: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ Y2 @ X )
% 2.56/1.60 => ( ( ord_le1656162903nres_b @ X @ Y2 )
% 2.56/1.60 = ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_177_antisym__conv,axiom,
% 2.56/1.60 ! [Y2: $o > refine424419629nres_a,X: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ Y2 @ X )
% 2.56/1.60 => ( ( ord_le516598614nres_a @ X @ Y2 )
% 2.56/1.60 = ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_178_antisym__conv,axiom,
% 2.56/1.60 ! [Y2: refine424419629nres_a,X: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ Y2 @ X )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ X @ Y2 )
% 2.56/1.60 = ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_179_antisym__conv,axiom,
% 2.56/1.60 ! [Y2: refine432681134nres_b,X: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ Y2 @ X )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ X @ Y2 )
% 2.56/1.60 = ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_180_order_Otrans,axiom,
% 2.56/1.60 ! [A2: set_Product_prod_a_a,B2: set_Product_prod_a_a,C2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le1824328871od_a_a @ B2 @ C2 )
% 2.56/1.60 => ( ord_le1824328871od_a_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_181_order_Otrans,axiom,
% 2.56/1.60 ! [A2: set_b,B2: set_b,C2: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_less_eq_set_b @ B2 @ C2 )
% 2.56/1.60 => ( ord_less_eq_set_b @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_182_order_Otrans,axiom,
% 2.56/1.60 ! [A2: set_a,B2: set_a,C2: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_less_eq_set_a @ B2 @ C2 )
% 2.56/1.60 => ( ord_less_eq_set_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_183_order_Otrans,axiom,
% 2.56/1.60 ! [A2: $o > refine432681134nres_b,B2: $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le1656162903nres_b @ B2 @ C2 )
% 2.56/1.60 => ( ord_le1656162903nres_b @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_184_order_Otrans,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le516598614nres_a @ B2 @ C2 )
% 2.56/1.60 => ( ord_le516598614nres_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_185_order_Otrans,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 2.56/1.60 => ( ord_le519537037nres_a @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_186_order_Otrans,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 2.56/1.60 => ( ord_le527798542nres_b @ A2 @ C2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_187_eq__refl,axiom,
% 2.56/1.60 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( X = Y2 )
% 2.56/1.60 => ( ord_le1824328871od_a_a @ X @ Y2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_188_eq__refl,axiom,
% 2.56/1.60 ! [X: set_b,Y2: set_b] :
% 2.56/1.60 ( ( X = Y2 )
% 2.56/1.60 => ( ord_less_eq_set_b @ X @ Y2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_189_eq__refl,axiom,
% 2.56/1.60 ! [X: set_a,Y2: set_a] :
% 2.56/1.60 ( ( X = Y2 )
% 2.56/1.60 => ( ord_less_eq_set_a @ X @ Y2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_190_eq__refl,axiom,
% 2.56/1.60 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( X = Y2 )
% 2.56/1.60 => ( ord_le1656162903nres_b @ X @ Y2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_191_eq__refl,axiom,
% 2.56/1.60 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( X = Y2 )
% 2.56/1.60 => ( ord_le516598614nres_a @ X @ Y2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_192_eq__refl,axiom,
% 2.56/1.60 ! [X: refine424419629nres_a,Y2: refine424419629nres_a] :
% 2.56/1.60 ( ( X = Y2 )
% 2.56/1.60 => ( ord_le519537037nres_a @ X @ Y2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_193_eq__refl,axiom,
% 2.56/1.60 ! [X: refine432681134nres_b,Y2: refine432681134nres_b] :
% 2.56/1.60 ( ( X = Y2 )
% 2.56/1.60 => ( ord_le527798542nres_b @ X @ Y2 ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_194_antisym,axiom,
% 2.56/1.60 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le1824328871od_a_a @ Y2 @ X )
% 2.56/1.60 => ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_195_antisym,axiom,
% 2.56/1.60 ! [X: set_b,Y2: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ X @ Y2 )
% 2.56/1.60 => ( ( ord_less_eq_set_b @ Y2 @ X )
% 2.56/1.60 => ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_196_antisym,axiom,
% 2.56/1.60 ! [X: set_a,Y2: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ X @ Y2 )
% 2.56/1.60 => ( ( ord_less_eq_set_a @ Y2 @ X )
% 2.56/1.60 => ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_197_antisym,axiom,
% 2.56/1.60 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le1656162903nres_b @ Y2 @ X )
% 2.56/1.60 => ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_198_antisym,axiom,
% 2.56/1.60 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le516598614nres_a @ Y2 @ X )
% 2.56/1.60 => ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_199_antisym,axiom,
% 2.56/1.60 ! [X: refine424419629nres_a,Y2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ Y2 @ X )
% 2.56/1.60 => ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_200_antisym,axiom,
% 2.56/1.60 ! [X: refine432681134nres_b,Y2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ X @ Y2 )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ Y2 @ X )
% 2.56/1.60 => ( X = Y2 ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_201_eq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: set_Product_prod_a_a,Z: set_Product_prod_a_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [X3: set_Product_prod_a_a,Y3: set_Product_prod_a_a] :
% 2.56/1.60 ( ( ord_le1824328871od_a_a @ X3 @ Y3 )
% 2.56/1.60 & ( ord_le1824328871od_a_a @ Y3 @ X3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_202_eq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: set_b,Z: set_b] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [X3: set_b,Y3: set_b] :
% 2.56/1.60 ( ( ord_less_eq_set_b @ X3 @ Y3 )
% 2.56/1.60 & ( ord_less_eq_set_b @ Y3 @ X3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_203_eq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: set_a,Z: set_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [X3: set_a,Y3: set_a] :
% 2.56/1.60 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 2.56/1.60 & ( ord_less_eq_set_a @ Y3 @ X3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_204_eq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: $o > refine432681134nres_b,Z: $o > refine432681134nres_b] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [X3: $o > refine432681134nres_b,Y3: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le1656162903nres_b @ X3 @ Y3 )
% 2.56/1.60 & ( ord_le1656162903nres_b @ Y3 @ X3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_205_eq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [X3: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ X3 @ Y3 )
% 2.56/1.60 & ( ord_le516598614nres_a @ Y3 @ X3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_206_eq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: refine424419629nres_a,Z: refine424419629nres_a] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 2.56/1.60 & ( ord_le519537037nres_a @ Y3 @ X3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_207_eq__iff,axiom,
% 2.56/1.60 ( ( ^ [Y: refine432681134nres_b,Z: refine432681134nres_b] : ( Y = Z ) )
% 2.56/1.60 = ( ^ [X3: refine432681134nres_b,Y3: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ X3 @ Y3 )
% 2.56/1.60 & ( ord_le527798542nres_b @ Y3 @ X3 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_208_ord__le__eq__subst,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,F: ( $o > refine424419629nres_a ) > set_b,C2: set_b] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ( F @ B2 )
% 2.56/1.60 = C2 )
% 2.56/1.60 => ( ! [X2: $o > refine424419629nres_a,Y4: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_less_eq_set_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_less_eq_set_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_209_ord__le__eq__subst,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,F: ( $o > refine424419629nres_a ) > set_a,C2: set_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ( F @ B2 )
% 2.56/1.60 = C2 )
% 2.56/1.60 => ( ! [X2: $o > refine424419629nres_a,Y4: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_210_ord__le__eq__subst,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,F: ( $o > refine424419629nres_a ) > $o > refine432681134nres_b,C2: $o > refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ( F @ B2 )
% 2.56/1.60 = C2 )
% 2.56/1.60 => ( ! [X2: $o > refine424419629nres_a,Y4: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le1656162903nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le1656162903nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_211_ord__le__eq__subst,axiom,
% 2.56/1.60 ! [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a,F: ( $o > refine424419629nres_a ) > $o > refine424419629nres_a,C2: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ( F @ B2 )
% 2.56/1.60 = C2 )
% 2.56/1.60 => ( ! [X2: $o > refine424419629nres_a,Y4: $o > refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le516598614nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le516598614nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le516598614nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_212_ord__le__eq__subst,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ( F @ B2 )
% 2.56/1.60 = C2 )
% 2.56/1.60 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_213_ord__le__eq__subst,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ( F @ B2 )
% 2.56/1.60 = C2 )
% 2.56/1.60 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_214_ord__le__eq__subst,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 2.56/1.60 => ( ( ( F @ B2 )
% 2.56/1.60 = C2 )
% 2.56/1.60 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_215_ord__le__eq__subst,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 2.56/1.60 => ( ( ( F @ B2 )
% 2.56/1.60 = C2 )
% 2.56/1.60 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_216_ord__eq__le__subst,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.60 ( ( A2
% 2.56/1.60 = ( F @ B2 ) )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 2.56/1.60 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_217_ord__eq__le__subst,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.60 ( ( A2
% 2.56/1.60 = ( F @ B2 ) )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 2.56/1.60 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_218_ord__eq__le__subst,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.60 ( ( A2
% 2.56/1.60 = ( F @ B2 ) )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 2.56/1.60 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_219_ord__eq__le__subst,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.60 ( ( A2
% 2.56/1.60 = ( F @ B2 ) )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 2.56/1.60 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_220_order__subst2,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 2.56/1.60 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_221_order__subst2,axiom,
% 2.56/1.60 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 2.56/1.60 => ( ( ord_le527798542nres_b @ ( F @ B2 ) @ C2 )
% 2.56/1.60 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 2.56/1.60 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.60 => ( ord_le527798542nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.60
% 2.56/1.60 thf(fact_222_order__subst2,axiom,
% 2.56/1.60 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C2 )
% 2.56/1.61 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_223_order__subst2,axiom,
% 2.56/1.61 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ ( F @ B2 ) @ C2 )
% 2.56/1.61 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_224_order__subst1,axiom,
% 2.56/1.61 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 2.56/1.61 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_225_order__subst1,axiom,
% 2.56/1.61 ! [A2: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 2.56/1.61 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_226_order__subst1,axiom,
% 2.56/1.61 ! [A2: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B2: refine424419629nres_a,C2: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A2 @ ( F @ B2 ) )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 2.56/1.61 => ( ! [X2: refine424419629nres_a,Y4: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ X2 @ Y4 )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_227_order__subst1,axiom,
% 2.56/1.61 ! [A2: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A2 @ ( F @ B2 ) )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 2.56/1.61 => ( ! [X2: refine432681134nres_b,Y4: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ X2 @ Y4 )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_228_Greatest__equality,axiom,
% 2.56/1.61 ! [P: refine424419629nres_a > $o,X: refine424419629nres_a] :
% 2.56/1.61 ( ( P @ X )
% 2.56/1.61 => ( ! [Y4: refine424419629nres_a] :
% 2.56/1.61 ( ( P @ Y4 )
% 2.56/1.61 => ( ord_le519537037nres_a @ Y4 @ X ) )
% 2.56/1.61 => ( ( order_1714329108nres_a @ P )
% 2.56/1.61 = X ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_229_Greatest__equality,axiom,
% 2.56/1.61 ! [P: refine432681134nres_b > $o,X: refine432681134nres_b] :
% 2.56/1.61 ( ( P @ X )
% 2.56/1.61 => ( ! [Y4: refine432681134nres_b] :
% 2.56/1.61 ( ( P @ Y4 )
% 2.56/1.61 => ( ord_le527798542nres_b @ Y4 @ X ) )
% 2.56/1.61 => ( ( order_1722590613nres_b @ P )
% 2.56/1.61 = X ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_230_GreatestI2__order,axiom,
% 2.56/1.61 ! [P: refine424419629nres_a > $o,X: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 2.56/1.61 ( ( P @ X )
% 2.56/1.61 => ( ! [Y4: refine424419629nres_a] :
% 2.56/1.61 ( ( P @ Y4 )
% 2.56/1.61 => ( ord_le519537037nres_a @ Y4 @ X ) )
% 2.56/1.61 => ( ! [X2: refine424419629nres_a] :
% 2.56/1.61 ( ( P @ X2 )
% 2.56/1.61 => ( ! [Y5: refine424419629nres_a] :
% 2.56/1.61 ( ( P @ Y5 )
% 2.56/1.61 => ( ord_le519537037nres_a @ Y5 @ X2 ) )
% 2.56/1.61 => ( Q @ X2 ) ) )
% 2.56/1.61 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_231_GreatestI2__order,axiom,
% 2.56/1.61 ! [P: refine432681134nres_b > $o,X: refine432681134nres_b,Q: refine432681134nres_b > $o] :
% 2.56/1.61 ( ( P @ X )
% 2.56/1.61 => ( ! [Y4: refine432681134nres_b] :
% 2.56/1.61 ( ( P @ Y4 )
% 2.56/1.61 => ( ord_le527798542nres_b @ Y4 @ X ) )
% 2.56/1.61 => ( ! [X2: refine432681134nres_b] :
% 2.56/1.61 ( ( P @ X2 )
% 2.56/1.61 => ( ! [Y5: refine432681134nres_b] :
% 2.56/1.61 ( ( P @ Y5 )
% 2.56/1.61 => ( ord_le527798542nres_b @ Y5 @ X2 ) )
% 2.56/1.61 => ( Q @ X2 ) ) )
% 2.56/1.61 => ( Q @ ( order_1722590613nres_b @ P ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_232_le__rel__bool__arg__iff,axiom,
% 2.56/1.61 ( ord_le516598614nres_a
% 2.56/1.61 = ( ^ [X4: $o > refine424419629nres_a,Y6: $o > refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 2.56/1.61 & ( ord_le519537037nres_a @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_233_le__rel__bool__arg__iff,axiom,
% 2.56/1.61 ( ord_le1656162903nres_b
% 2.56/1.61 = ( ^ [X4: $o > refine432681134nres_b,Y6: $o > refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 2.56/1.61 & ( ord_le527798542nres_b @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_234_ord__eq__le__eq__trans,axiom,
% 2.56/1.61 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C2: refine424419629nres_a,D: refine424419629nres_a] :
% 2.56/1.61 ( ( A2 = B2 )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B2 @ C2 )
% 2.56/1.61 => ( ( C2 = D )
% 2.56/1.61 => ( ord_le519537037nres_a @ A2 @ D ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_235_ord__eq__le__eq__trans,axiom,
% 2.56/1.61 ! [A2: refine432681134nres_b,B2: refine432681134nres_b,C2: refine432681134nres_b,D: refine432681134nres_b] :
% 2.56/1.61 ( ( A2 = B2 )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B2 @ C2 )
% 2.56/1.61 => ( ( C2 = D )
% 2.56/1.61 => ( ord_le527798542nres_b @ A2 @ D ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_236_Id__refine,axiom,
% 2.56/1.61 ! [S: refine432681134nres_b] : ( ord_le527798542nres_b @ S @ ( refine122110613un_b_b @ id_b @ S ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_237_Id__refine,axiom,
% 2.56/1.61 ! [S: refine424419629nres_a] : ( ord_le519537037nres_a @ S @ ( refine1441824853un_a_a @ id_a @ S ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_238_conc__trans__additional_I2_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ R @ C ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ C ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_239_conc__trans__additional_I2_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B @ ( refine1441824854un_a_b @ R @ C ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ C ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_240_conc__trans__additional_I2_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ R @ C ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ C ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_241_conc__trans__additional_I3_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,R: set_Product_prod_b_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ R @ B ) )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ A @ ( refine122110612un_b_a @ R @ C ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_242_conc__trans__additional_I3_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,R: set_Product_prod_a_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ B ) )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ ( refine1441824854un_a_b @ R @ C ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_243_conc__trans__additional_I3_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,R: set_Product_prod_b_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ B ) )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ R @ C ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_244_conc__trans__additional_I3_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,R: set_Product_prod_a_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ B ) )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ R @ C ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_245_conc__trans__additional_I6_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A @ B )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_246_conc__trans__additional_I6_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ B )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_247_conc__trans__additional_I5_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B @ C )
% 2.56/1.61 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_248_conc__trans__additional_I5_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B @ C )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_249_conc__trans__additional_I4_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A @ ( refine122110613un_b_b @ id_b @ B ) )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B @ ( refine122110613un_b_b @ id_b @ C ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_250_conc__trans__additional_I4_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ ( refine1441824853un_a_a @ id_a @ B ) )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B @ ( refine1441824853un_a_a @ id_a @ C ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_251_Id__SPEC__refine,axiom,
% 2.56/1.61 ! [S: refine432681134nres_b,Phi: b > $o] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ S @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ S @ ( refine122110613un_b_b @ id_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_252_Id__SPEC__refine,axiom,
% 2.56/1.61 ! [S: refine424419629nres_a,Phi: a > $o] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ S @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ S @ ( refine1441824853un_a_a @ id_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_253_abs__trans__additional_I2_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ B ) @ C )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ A ) @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_254_abs__trans__additional_I2_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ B ) @ C )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ A ) @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_255_abs__trans__additional_I2_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ B ) @ C )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ A ) @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_256_abs__trans__additional_I2_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ B ) @ C )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ A ) @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_257_abs__trans__additional_I4_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ B ) @ C )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_258_abs__trans__additional_I4_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ B ) @ C )
% 2.56/1.61 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_259_abs__trans__additional_I5_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ A ) @ B )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ B @ C )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_260_abs__trans__additional_I5_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ A ) @ B )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ B @ C )
% 2.56/1.61 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_261_abs__trans__additional_I6_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ B )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ id_a @ B ) @ C )
% 2.56/1.61 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_262_abs__trans__additional_I6_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A @ B )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ id_b @ B ) @ C )
% 2.56/1.61 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_263_abs__fun__simps_I1_J,axiom,
% 2.56/1.61 ! [R: set_Product_prod_b_b] :
% 2.56/1.61 ( ( refine1964549110un_b_b @ R @ top_to240090974nres_b )
% 2.56/1.61 = top_to240090974nres_b ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_264_abs__fun__simps_I1_J,axiom,
% 2.56/1.61 ! [R: set_Product_prod_b_a] :
% 2.56/1.61 ( ( refine1964549109un_b_a @ R @ top_to240090974nres_b )
% 2.56/1.61 = top_to231829469nres_a ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_265_abs__fun__simps_I1_J,axiom,
% 2.56/1.61 ! [R: set_Product_prod_a_b] :
% 2.56/1.61 ( ( refine1136779703un_a_b @ R @ top_to231829469nres_a )
% 2.56/1.61 = top_to240090974nres_b ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_266_abs__fun__simps_I1_J,axiom,
% 2.56/1.61 ! [R: set_Product_prod_a_a] :
% 2.56/1.61 ( ( refine1136779702un_a_a @ R @ top_to231829469nres_a )
% 2.56/1.61 = top_to231829469nres_a ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_267_if__rule,axiom,
% 2.56/1.61 ! [B2: $o,S1: refine424419629nres_a,Phi: a > $o,S2: refine424419629nres_a] :
% 2.56/1.61 ( ( B2
% 2.56/1.61 => ( ord_le519537037nres_a @ S1 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 2.56/1.61 => ( ( ~ B2
% 2.56/1.61 => ( ord_le519537037nres_a @ S2 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ S1 @ S2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_268_if__rule,axiom,
% 2.56/1.61 ! [B2: $o,S1: refine432681134nres_b,Phi: b > $o,S2: refine432681134nres_b] :
% 2.56/1.61 ( ( B2
% 2.56/1.61 => ( ord_le527798542nres_b @ S1 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 2.56/1.61 => ( ( ~ B2
% 2.56/1.61 => ( ord_le527798542nres_b @ S2 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B2 @ S1 @ S2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_269_RES__rule,axiom,
% 2.56/1.61 ! [S: set_a,Phi: a > $o] :
% 2.56/1.61 ( ! [X2: a] :
% 2.56/1.61 ( ( member_a @ X2 @ S )
% 2.56/1.61 => ( Phi @ X2 ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_270_RES__rule,axiom,
% 2.56/1.61 ! [S: set_b,Phi: b > $o] :
% 2.56/1.61 ( ! [X2: b] :
% 2.56/1.61 ( ( member_b @ X2 @ S )
% 2.56/1.61 => ( Phi @ X2 ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_271_SPEC__rule,axiom,
% 2.56/1.61 ! [Phi: a > $o,Phi2: a > $o] :
% 2.56/1.61 ( ! [X2: a] :
% 2.56/1.61 ( ( Phi @ X2 )
% 2.56/1.61 => ( Phi2 @ X2 ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi2 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_272_SPEC__rule,axiom,
% 2.56/1.61 ! [Phi: b > $o,Phi2: b > $o] :
% 2.56/1.61 ( ! [X2: b] :
% 2.56/1.61 ( ( Phi @ X2 )
% 2.56/1.61 => ( Phi2 @ X2 ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi2 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_273_SPEC__trans,axiom,
% 2.56/1.61 ! [X: refine424419629nres_a,Y2: refine424419629nres_a,Postcond: a > $o] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ X @ Y2 )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ Y2 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ X @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_274_SPEC__trans,axiom,
% 2.56/1.61 ! [X: refine432681134nres_b,Y2: refine432681134nres_b,Postcond: b > $o] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ X @ Y2 )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ Y2 @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ X @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_275_SPEC__cons__rule,axiom,
% 2.56/1.61 ! [M2: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ M2 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 2.56/1.61 => ( ! [X2: a] :
% 2.56/1.61 ( ( Phi @ X2 )
% 2.56/1.61 => ( Psi @ X2 ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ M2 @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_276_SPEC__cons__rule,axiom,
% 2.56/1.61 ! [M2: refine432681134nres_b,Phi: b > $o,Psi: b > $o] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ M2 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) )
% 2.56/1.61 => ( ! [X2: b] :
% 2.56/1.61 ( ( Phi @ X2 )
% 2.56/1.61 => ( Psi @ X2 ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ M2 @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_277_nres__inequalities_I1_J,axiom,
% 2.56/1.61 ! [X5: set_b] :
% 2.56/1.61 ( top_to240090974nres_b
% 2.56/1.61 != ( refine1198353289_RES_b @ X5 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_278_nres__inequalities_I1_J,axiom,
% 2.56/1.61 ! [X5: set_a] :
% 2.56/1.61 ( top_to231829469nres_a
% 2.56/1.61 != ( refine1198353288_RES_a @ X5 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_279_nres__cases,axiom,
% 2.56/1.61 ! [M: refine432681134nres_b] :
% 2.56/1.61 ( ( M != top_to240090974nres_b )
% 2.56/1.61 => ~ ! [X6: set_b] :
% 2.56/1.61 ( M
% 2.56/1.61 != ( refine1198353289_RES_b @ X6 ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_280_nres__cases,axiom,
% 2.56/1.61 ! [M: refine424419629nres_a] :
% 2.56/1.61 ( ( M != top_to231829469nres_a )
% 2.56/1.61 => ~ ! [X6: set_a] :
% 2.56/1.61 ( M
% 2.56/1.61 != ( refine1198353288_RES_a @ X6 ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_281_abs__trans__additional_I1_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ B )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ B ) @ C )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ A ) @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_282_abs__trans__additional_I1_J,axiom,
% 2.56/1.61 ! [A: refine424419629nres_a,B: refine424419629nres_a,R: set_Product_prod_a_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ A @ B )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ B ) @ C )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ A ) @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_283_abs__trans__additional_I1_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_a,C: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A @ B )
% 2.56/1.61 => ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ B ) @ C )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ A ) @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_284_abs__trans__additional_I1_J,axiom,
% 2.56/1.61 ! [A: refine432681134nres_b,B: refine432681134nres_b,R: set_Product_prod_b_b,C: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ A @ B )
% 2.56/1.61 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ B ) @ C )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ A ) @ C ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_285_nres__order__simps_I5_J,axiom,
% 2.56/1.61 ! [X5: set_a,Y7: set_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X5 ) @ ( refine1198353288_RES_a @ Y7 ) )
% 2.56/1.61 = ( ord_less_eq_set_a @ X5 @ Y7 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_286_nres__order__simps_I5_J,axiom,
% 2.56/1.61 ! [X5: set_b,Y7: set_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ X5 ) @ ( refine1198353289_RES_b @ Y7 ) )
% 2.56/1.61 = ( ord_less_eq_set_b @ X5 @ Y7 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_287_less__eq__nres_Osimps_I2_J,axiom,
% 2.56/1.61 ! [A2: set_a,B2: set_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A2 ) @ ( refine1198353288_RES_a @ B2 ) )
% 2.56/1.61 = ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_288_less__eq__nres_Osimps_I2_J,axiom,
% 2.56/1.61 ! [A2: set_b,B2: set_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A2 ) @ ( refine1198353289_RES_b @ B2 ) )
% 2.56/1.61 = ( ord_less_eq_set_b @ A2 @ B2 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_289_nres__order__simps_I21_J,axiom,
% 2.56/1.61 ! [X: a,Y7: set_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1198353288_RES_a @ Y7 ) )
% 2.56/1.61 = ( member_a @ X @ Y7 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_290_nres__order__simps_I21_J,axiom,
% 2.56/1.61 ! [X: b,Y7: set_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine1198353289_RES_b @ Y7 ) )
% 2.56/1.61 = ( member_b @ X @ Y7 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_291_nres__order__simps_I20_J,axiom,
% 2.56/1.61 ! [X: a,Y2: a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine2063221604TURN_a @ Y2 ) )
% 2.56/1.61 = ( X = Y2 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_292_nres__order__simps_I20_J,axiom,
% 2.56/1.61 ! [X: b,Y2: b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine2063221605TURN_b @ Y2 ) )
% 2.56/1.61 = ( X = Y2 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_293_nres__inequalities_I3_J,axiom,
% 2.56/1.61 ! [X: b] :
% 2.56/1.61 ( top_to240090974nres_b
% 2.56/1.61 != ( refine2063221605TURN_b @ X ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_294_nres__inequalities_I3_J,axiom,
% 2.56/1.61 ! [X: a] :
% 2.56/1.61 ( top_to231829469nres_a
% 2.56/1.61 != ( refine2063221604TURN_a @ X ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_295_RETURN__to__SPEC__rule,axiom,
% 2.56/1.61 ! [M2: refine424419629nres_a,V: a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ M2
% 2.56/1.61 @ ( refine1198353288_RES_a
% 2.56/1.61 @ ( collect_a
% 2.56/1.61 @ ( ^ [Y: a,Z: a] : ( Y = Z )
% 2.56/1.61 @ V ) ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ M2 @ ( refine2063221604TURN_a @ V ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_296_RETURN__to__SPEC__rule,axiom,
% 2.56/1.61 ! [M2: refine432681134nres_b,V: b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ M2
% 2.56/1.61 @ ( refine1198353289_RES_b
% 2.56/1.61 @ ( collect_b
% 2.56/1.61 @ ( ^ [Y: b,Z: b] : ( Y = Z )
% 2.56/1.61 @ V ) ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ M2 @ ( refine2063221605TURN_b @ V ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_297_RETURN__rule,axiom,
% 2.56/1.61 ! [Phi: a > $o,X: a] :
% 2.56/1.61 ( ( Phi @ X )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_298_RETURN__rule,axiom,
% 2.56/1.61 ! [Phi: b > $o,X: b] :
% 2.56/1.61 ( ( Phi @ X )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_299_RETURN__SPEC__refine,axiom,
% 2.56/1.61 ! [X: a,R: set_Product_prod_a_b,Phi: b > $o] :
% 2.56/1.61 ( ? [X7: b] :
% 2.56/1.61 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X @ X7 ) @ R )
% 2.56/1.61 & ( Phi @ X7 ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_300_RETURN__SPEC__refine,axiom,
% 2.56/1.61 ! [X: b,R: set_Product_prod_b_b,Phi: b > $o] :
% 2.56/1.61 ( ? [X7: b] :
% 2.56/1.61 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ X7 ) @ R )
% 2.56/1.61 & ( Phi @ X7 ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_301_RETURN__SPEC__refine,axiom,
% 2.56/1.61 ! [X: a,R: set_Product_prod_a_a,Phi: a > $o] :
% 2.56/1.61 ( ? [X7: a] :
% 2.56/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ X7 ) @ R )
% 2.56/1.61 & ( Phi @ X7 ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_302_nofail__simps_I1_J,axiom,
% 2.56/1.61 ~ ( refine412683990fail_b @ top_to240090974nres_b ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_303_nofail__simps_I1_J,axiom,
% 2.56/1.61 ~ ( refine412683989fail_a @ top_to231829469nres_a ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_304_pw__conc__nofail,axiom,
% 2.56/1.61 ! [R: set_Product_prod_a_b,S: refine432681134nres_b] :
% 2.56/1.61 ( ( refine412683989fail_a @ ( refine1441824854un_a_b @ R @ S ) )
% 2.56/1.61 = ( refine412683990fail_b @ S ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_305_pw__conc__nofail,axiom,
% 2.56/1.61 ! [R: set_Product_prod_b_b,S: refine432681134nres_b] :
% 2.56/1.61 ( ( refine412683990fail_b @ ( refine122110613un_b_b @ R @ S ) )
% 2.56/1.61 = ( refine412683990fail_b @ S ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_306_pw__conc__nofail,axiom,
% 2.56/1.61 ! [R: set_Product_prod_a_a,S: refine424419629nres_a] :
% 2.56/1.61 ( ( refine412683989fail_a @ ( refine1441824853un_a_a @ R @ S ) )
% 2.56/1.61 = ( refine412683989fail_a @ S ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_307_intro__nofail_I2_J,axiom,
% 2.56/1.61 ! [S: refine432681134nres_b] :
% 2.56/1.61 ( ( top_to240090974nres_b != S )
% 2.56/1.61 = ( refine412683990fail_b @ S ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_308_intro__nofail_I2_J,axiom,
% 2.56/1.61 ! [S: refine424419629nres_a] :
% 2.56/1.61 ( ( top_to231829469nres_a != S )
% 2.56/1.61 = ( refine412683989fail_a @ S ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_309_nofail__def,axiom,
% 2.56/1.61 ( refine412683990fail_b
% 2.56/1.61 = ( ^ [S3: refine432681134nres_b] : ( S3 != top_to240090974nres_b ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_310_nofail__def,axiom,
% 2.56/1.61 ( refine412683989fail_a
% 2.56/1.61 = ( ^ [S3: refine424419629nres_a] : ( S3 != top_to231829469nres_a ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_311_not__nofail__iff,axiom,
% 2.56/1.61 ! [S: refine432681134nres_b] :
% 2.56/1.61 ( ( ~ ( refine412683990fail_b @ S ) )
% 2.56/1.61 = ( S = top_to240090974nres_b ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_312_not__nofail__iff,axiom,
% 2.56/1.61 ! [S: refine424419629nres_a] :
% 2.56/1.61 ( ( ~ ( refine412683989fail_a @ S ) )
% 2.56/1.61 = ( S = top_to231829469nres_a ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_313_pwD1,axiom,
% 2.56/1.61 ! [S: refine424419629nres_a,S4: refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ S @ S4 )
% 2.56/1.61 => ( ( refine412683989fail_a @ S4 )
% 2.56/1.61 => ( refine412683989fail_a @ S ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_314_pwD1,axiom,
% 2.56/1.61 ! [S: refine432681134nres_b,S4: refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ S @ S4 )
% 2.56/1.61 => ( ( refine412683990fail_b @ S4 )
% 2.56/1.61 => ( refine412683990fail_b @ S ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_315_le__nofailI,axiom,
% 2.56/1.61 ! [M3: refine424419629nres_a,M: refine424419629nres_a] :
% 2.56/1.61 ( ( ( refine412683989fail_a @ M3 )
% 2.56/1.61 => ( ord_le519537037nres_a @ M @ M3 ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ M @ M3 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_316_le__nofailI,axiom,
% 2.56/1.61 ! [M3: refine432681134nres_b,M: refine432681134nres_b] :
% 2.56/1.61 ( ( ( refine412683990fail_b @ M3 )
% 2.56/1.61 => ( ord_le527798542nres_b @ M @ M3 ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ M @ M3 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_317_RES__refine,axiom,
% 2.56/1.61 ! [S: set_a,S4: set_b,R: set_Product_prod_a_b] :
% 2.56/1.61 ( ! [S5: a] :
% 2.56/1.61 ( ( member_a @ S5 @ S )
% 2.56/1.61 => ? [X8: b] :
% 2.56/1.61 ( ( member_b @ X8 @ S4 )
% 2.56/1.61 & ( member458171089od_a_b @ ( product_Pair_a_b @ S5 @ X8 ) @ R ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ S4 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_318_RES__refine,axiom,
% 2.56/1.61 ! [S: set_b,S4: set_b,R: set_Product_prod_b_b] :
% 2.56/1.61 ( ! [S5: b] :
% 2.56/1.61 ( ( member_b @ S5 @ S )
% 2.56/1.61 => ? [X8: b] :
% 2.56/1.61 ( ( member_b @ X8 @ S4 )
% 2.56/1.61 & ( member1285940496od_b_b @ ( product_Pair_b_b @ S5 @ X8 ) @ R ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ S4 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_319_RES__refine,axiom,
% 2.56/1.61 ! [S: set_a,S4: set_a,R: set_Product_prod_a_a] :
% 2.56/1.61 ( ! [S5: a] :
% 2.56/1.61 ( ( member_a @ S5 @ S )
% 2.56/1.61 => ? [X8: a] :
% 2.56/1.61 ( ( member_a @ X8 @ S4 )
% 2.56/1.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ S5 @ X8 ) @ R ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ S4 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_320_RETURN__refine,axiom,
% 2.56/1.61 ! [X: a,X9: b,R: set_Product_prod_a_b] :
% 2.56/1.61 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X @ X9 ) @ R )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1441824854un_a_b @ R @ ( refine2063221605TURN_b @ X9 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_321_RETURN__refine,axiom,
% 2.56/1.61 ! [X: b,X9: b,R: set_Product_prod_b_b] :
% 2.56/1.61 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ X9 ) @ R )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X ) @ ( refine122110613un_b_b @ R @ ( refine2063221605TURN_b @ X9 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_322_RETURN__refine,axiom,
% 2.56/1.61 ! [X: a,X9: a,R: set_Product_prod_a_a] :
% 2.56/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ X9 ) @ R )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X ) @ ( refine1441824853un_a_a @ R @ ( refine2063221604TURN_a @ X9 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_323_inres__simps_I1_J,axiom,
% 2.56/1.61 ( ( refine1001002028nres_b @ top_to240090974nres_b )
% 2.56/1.61 = ( ^ [Uu: b] : $true ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_324_inres__simps_I1_J,axiom,
% 2.56/1.61 ( ( refine1001002027nres_a @ top_to231829469nres_a )
% 2.56/1.61 = ( ^ [Uu: a] : $true ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_325_pwD2,axiom,
% 2.56/1.61 ! [S: refine424419629nres_a,S4: refine424419629nres_a,X: a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ S @ S4 )
% 2.56/1.61 => ( ( refine1001002027nres_a @ S @ X )
% 2.56/1.61 => ( refine1001002027nres_a @ S4 @ X ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_326_pwD2,axiom,
% 2.56/1.61 ! [S: refine432681134nres_b,S4: refine432681134nres_b,X: b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ S @ S4 )
% 2.56/1.61 => ( ( refine1001002028nres_b @ S @ X )
% 2.56/1.61 => ( refine1001002028nres_b @ S4 @ X ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_327_pw__leI,axiom,
% 2.56/1.61 ! [S4: refine424419629nres_a,S: refine424419629nres_a] :
% 2.56/1.61 ( ( ( refine412683989fail_a @ S4 )
% 2.56/1.61 => ( ( refine412683989fail_a @ S )
% 2.56/1.61 & ! [X2: a] :
% 2.56/1.61 ( ( refine1001002027nres_a @ S @ X2 )
% 2.56/1.61 => ( refine1001002027nres_a @ S4 @ X2 ) ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ S @ S4 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_328_pw__leI,axiom,
% 2.56/1.61 ! [S4: refine432681134nres_b,S: refine432681134nres_b] :
% 2.56/1.61 ( ( ( refine412683990fail_b @ S4 )
% 2.56/1.61 => ( ( refine412683990fail_b @ S )
% 2.56/1.61 & ! [X2: b] :
% 2.56/1.61 ( ( refine1001002028nres_b @ S @ X2 )
% 2.56/1.61 => ( refine1001002028nres_b @ S4 @ X2 ) ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ S @ S4 ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_329_pw__leI_H,axiom,
% 2.56/1.61 ! [S4: refine424419629nres_a,S: refine424419629nres_a] :
% 2.56/1.61 ( ( ( refine412683989fail_a @ S4 )
% 2.56/1.61 => ( refine412683989fail_a @ S ) )
% 2.56/1.61 => ( ! [X2: a] :
% 2.56/1.61 ( ( refine412683989fail_a @ S4 )
% 2.56/1.61 => ( ( refine1001002027nres_a @ S @ X2 )
% 2.56/1.61 => ( refine1001002027nres_a @ S4 @ X2 ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ S @ S4 ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_330_pw__leI_H,axiom,
% 2.56/1.61 ! [S4: refine432681134nres_b,S: refine432681134nres_b] :
% 2.56/1.61 ( ( ( refine412683990fail_b @ S4 )
% 2.56/1.61 => ( refine412683990fail_b @ S ) )
% 2.56/1.61 => ( ! [X2: b] :
% 2.56/1.61 ( ( refine412683990fail_b @ S4 )
% 2.56/1.61 => ( ( refine1001002028nres_b @ S @ X2 )
% 2.56/1.61 => ( refine1001002028nres_b @ S4 @ X2 ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ S @ S4 ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_331_pw__le__iff,axiom,
% 2.56/1.61 ( ord_le519537037nres_a
% 2.56/1.61 = ( ^ [S3: refine424419629nres_a,S6: refine424419629nres_a] :
% 2.56/1.61 ( ( refine412683989fail_a @ S6 )
% 2.56/1.61 => ( ( refine412683989fail_a @ S3 )
% 2.56/1.61 & ! [X3: a] :
% 2.56/1.61 ( ( refine1001002027nres_a @ S3 @ X3 )
% 2.56/1.61 => ( refine1001002027nres_a @ S6 @ X3 ) ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_332_pw__le__iff,axiom,
% 2.56/1.61 ( ord_le527798542nres_b
% 2.56/1.61 = ( ^ [S3: refine432681134nres_b,S6: refine432681134nres_b] :
% 2.56/1.61 ( ( refine412683990fail_b @ S6 )
% 2.56/1.61 => ( ( refine412683990fail_b @ S3 )
% 2.56/1.61 & ! [X3: b] :
% 2.56/1.61 ( ( refine1001002028nres_b @ S3 @ X3 )
% 2.56/1.61 => ( refine1001002028nres_b @ S6 @ X3 ) ) ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_333_inres__def,axiom,
% 2.56/1.61 ( refine1001002027nres_a
% 2.56/1.61 = ( ^ [S3: refine424419629nres_a,X3: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ S3 ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_334_inres__def,axiom,
% 2.56/1.61 ( refine1001002028nres_b
% 2.56/1.61 = ( ^ [S3: refine432681134nres_b,X3: b] : ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ S3 ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_335_bind__FAIL,axiom,
% 2.56/1.61 ! [F: b > refine432681134nres_b] :
% 2.56/1.61 ( ( refine1264602246nd_b_b @ top_to240090974nres_b @ F )
% 2.56/1.61 = top_to240090974nres_b ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_336_bind__FAIL,axiom,
% 2.56/1.61 ! [F: b > refine424419629nres_a] :
% 2.56/1.61 ( ( refine1264602245nd_b_a @ top_to240090974nres_b @ F )
% 2.56/1.61 = top_to231829469nres_a ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_337_bind__FAIL,axiom,
% 2.56/1.61 ! [F: a > refine432681134nres_b] :
% 2.56/1.61 ( ( refine436832839nd_a_b @ top_to231829469nres_a @ F )
% 2.56/1.61 = top_to240090974nres_b ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_338_bind__FAIL,axiom,
% 2.56/1.61 ! [F: a > refine424419629nres_a] :
% 2.56/1.61 ( ( refine436832838nd_a_a @ top_to231829469nres_a @ F )
% 2.56/1.61 = top_to231829469nres_a ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_339_ibind__strict_I2_J,axiom,
% 2.56/1.61 ! [F: product_unit > refine432681134nres_b] :
% 2.56/1.61 ( ( refine119808504unit_b @ top_to177290092t_unit @ F )
% 2.56/1.61 = top_to240090974nres_b ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_340_ibind__strict_I2_J,axiom,
% 2.56/1.61 ! [F: product_unit > refine424419629nres_a] :
% 2.56/1.61 ( ( refine119808503unit_a @ top_to177290092t_unit @ F )
% 2.56/1.61 = top_to231829469nres_a ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_341_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 2.56/1.61 ! [M: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine424419629nres_a,F3: a > refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ M @ M3 )
% 2.56/1.61 => ( ! [X2: a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F3 @ X2 ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ ( refine436832838nd_a_a @ M3 @ F3 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_342_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 2.56/1.61 ! [M: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine432681134nres_b,F3: a > refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ M @ M3 )
% 2.56/1.61 => ( ! [X2: a] :
% 2.56/1.61 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X2 ) @ M )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F3 @ X2 ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F ) @ ( refine436832839nd_a_b @ M3 @ F3 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_343_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 2.56/1.61 ! [M: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine424419629nres_a,F3: b > refine424419629nres_a] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ M @ M3 )
% 2.56/1.61 => ( ! [X2: b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X2 ) @ M )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( F @ X2 ) @ ( F3 @ X2 ) ) )
% 2.56/1.61 => ( ord_le519537037nres_a @ ( refine1264602245nd_b_a @ M @ F ) @ ( refine1264602245nd_b_a @ M3 @ F3 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_344_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 2.56/1.61 ! [M: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine432681134nres_b,F3: b > refine432681134nres_b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ M @ M3 )
% 2.56/1.61 => ( ! [X2: b] :
% 2.56/1.61 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X2 ) @ M )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( F @ X2 ) @ ( F3 @ X2 ) ) )
% 2.56/1.61 => ( ord_le527798542nres_b @ ( refine1264602246nd_b_b @ M @ F ) @ ( refine1264602246nd_b_b @ M3 @ F3 ) ) ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_345_sup__top__left,axiom,
% 2.56/1.61 ! [X: refine432681134nres_b] :
% 2.56/1.61 ( ( sup_su2042991066nres_b @ top_to240090974nres_b @ X )
% 2.56/1.61 = top_to240090974nres_b ) ).
% 2.56/1.61
% 2.56/1.61 thf(fact_346_sup__top__left,axiom,
% 2.56/1.61 ! [X: refine424419629nres_a] :
% 2.56/1.61 ( ( sup_su2034729561nres_a @ top_to231829469nres_a @ X )
% 2.56/1.61 = top_to231829469nres_a ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 2.56/1.61 ! [X: set_a,Y2: set_a] :
% 2.56/1.61 ( ( if_set_a @ $false @ X @ Y2 )
% 2.56/1.61 = Y2 ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 2.56/1.61 ! [X: set_a,Y2: set_a] :
% 2.56/1.61 ( ( if_set_a @ $true @ X @ Y2 )
% 2.56/1.61 = X ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_2_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 2.56/1.61 ! [X: set_b,Y2: set_b] :
% 2.56/1.61 ( ( if_set_b @ $false @ X @ Y2 )
% 2.56/1.61 = Y2 ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_1_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 2.56/1.61 ! [X: set_b,Y2: set_b] :
% 2.56/1.61 ( ( if_set_b @ $true @ X @ Y2 )
% 2.56/1.61 = X ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 2.56/1.61 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 2.56/1.61 ( ( if_set1550076877od_a_a @ $false @ X @ Y2 )
% 2.56/1.61 = Y2 ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 2.56/1.61 ! [X: set_Product_prod_a_a,Y2: set_Product_prod_a_a] :
% 2.56/1.61 ( ( if_set1550076877od_a_a @ $true @ X @ Y2 )
% 2.56/1.61 = X ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 2.56/1.61 ! [X: refine424419629nres_a,Y2: refine424419629nres_a] :
% 2.56/1.61 ( ( if_Ref1724547303nres_a @ $false @ X @ Y2 )
% 2.56/1.61 = Y2 ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 2.56/1.61 ! [X: refine424419629nres_a,Y2: refine424419629nres_a] :
% 2.56/1.61 ( ( if_Ref1724547303nres_a @ $true @ X @ Y2 )
% 2.56/1.61 = X ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 2.56/1.61 ! [X: refine432681134nres_b,Y2: refine432681134nres_b] :
% 2.56/1.61 ( ( if_Ref1732808808nres_b @ $false @ X @ Y2 )
% 2.56/1.61 = Y2 ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 2.56/1.61 ! [X: refine432681134nres_b,Y2: refine432681134nres_b] :
% 2.56/1.61 ( ( if_Ref1732808808nres_b @ $true @ X @ Y2 )
% 2.56/1.61 = X ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 2.56/1.61 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a] :
% 2.56/1.61 ( ( if_o_R1705037948nres_a @ $false @ X @ Y2 )
% 2.56/1.61 = Y2 ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 2.56/1.61 ! [X: $o > refine424419629nres_a,Y2: $o > refine424419629nres_a] :
% 2.56/1.61 ( ( if_o_R1705037948nres_a @ $true @ X @ Y2 )
% 2.56/1.61 = X ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_3_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 2.56/1.61 ! [P: $o] :
% 2.56/1.61 ( ( P = $true )
% 2.56/1.61 | ( P = $false ) ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 2.56/1.61 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b] :
% 2.56/1.61 ( ( if_o_R697118589nres_b @ $false @ X @ Y2 )
% 2.56/1.61 = Y2 ) ).
% 2.56/1.61
% 2.56/1.61 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 2.56/1.61 ! [X: $o > refine432681134nres_b,Y2: $o > refine432681134nres_b] :
% 2.56/1.61 ( ( if_o_R697118589nres_b @ $true @ X @ Y2 )
% 2.56/1.61 = X ) ).
% 2.56/1.61
% 2.56/1.61 thf(conj_0,conjecture,
% 2.56/1.61 ord_le519537037nres_a @ x @ ( refine1441824854un_a_b @ r @ top_to240090974nres_b ) ).
% 2.56/1.61 ------------------------
% 2.56/1.64 % (10810)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10704 for (2999ds/183Mi)
% 2.56/1.64 % (10814)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_10704 for (2999ds/2Mi)
% 2.56/1.64 % (10814)Instruction limit reached!
% 2.56/1.64 % (10814)------------------------------
% 2.56/1.64 % (10814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.64 % (10814)Termination reason: Unknown
% 2.56/1.64 % (10814)Termination phase: shuffling
% 2.56/1.64
% 2.56/1.64 % (10814)Memory used [KB]: 1535
% 2.56/1.64 % (10814)Time elapsed: 0.002 s
% 2.56/1.64 % (10814)Instructions burned: 2 (million)
% 2.56/1.64 % (10814)------------------------------
% 2.56/1.64 % (10814)------------------------------
% 2.56/1.65 % (10815)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_10704 for (2999ds/275Mi)
% 2.56/1.65 % (10811)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_10704 for (2999ds/4Mi)
% 2.56/1.65 % (10812)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_10704 for (2999ds/27Mi)
% 2.56/1.65 % (10813)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10704 for (2999ds/2Mi)
% 2.56/1.65 % (10811)Instruction limit reached!
% 2.56/1.65 % (10811)------------------------------
% 2.56/1.65 % (10811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.65 % (10811)Termination reason: Unknown
% 2.56/1.65 % (10811)Termination phase: shuffling
% 2.56/1.65
% 2.56/1.65 % (10811)Memory used [KB]: 1535
% 2.56/1.65 % (10811)Time elapsed: 0.004 s
% 2.56/1.65 % (10811)Instructions burned: 4 (million)
% 2.56/1.65 % (10811)------------------------------
% 2.56/1.65 % (10811)------------------------------
% 2.56/1.65 % (10813)Instruction limit reached!
% 2.56/1.65 % (10813)------------------------------
% 2.56/1.65 % (10813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.65 % (10813)Termination reason: Unknown
% 2.56/1.65 % (10813)Termination phase: shuffling
% 2.56/1.65
% 2.56/1.65 % (10813)Memory used [KB]: 1535
% 2.56/1.65 % (10813)Time elapsed: 0.004 s
% 2.56/1.65 % (10813)Instructions burned: 3 (million)
% 2.56/1.65 % (10813)------------------------------
% 2.56/1.65 % (10813)------------------------------
% 2.56/1.65 % (10817)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10704 for (2999ds/3Mi)
% 2.56/1.65 % (10816)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10704 for (2999ds/18Mi)
% 2.56/1.65 % (10817)Instruction limit reached!
% 2.56/1.65 % (10817)------------------------------
% 2.56/1.65 % (10817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.65 % (10817)Termination reason: Unknown
% 2.56/1.65 % (10817)Termination phase: shuffling
% 2.56/1.65
% 2.56/1.65 % (10817)Memory used [KB]: 1535
% 2.56/1.65 % (10817)Time elapsed: 0.002 s
% 2.56/1.65 % (10817)Instructions burned: 3 (million)
% 2.56/1.65 % (10817)------------------------------
% 2.56/1.65 % (10817)------------------------------
% 2.56/1.66 % (10820)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_10704 for (2999ds/3Mi)
% 2.56/1.66 % (10820)Instruction limit reached!
% 2.56/1.66 % (10820)------------------------------
% 2.56/1.66 % (10820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.66 % (10820)Termination reason: Unknown
% 2.56/1.66 % (10820)Termination phase: shuffling
% 2.56/1.66
% 2.56/1.66 % (10820)Memory used [KB]: 1535
% 2.56/1.66 % (10820)Time elapsed: 0.002 s
% 2.56/1.66 % (10820)Instructions burned: 3 (million)
% 2.56/1.66 % (10820)------------------------------
% 2.56/1.66 % (10820)------------------------------
% 2.56/1.66 % (10816)Instruction limit reached!
% 2.56/1.66 % (10816)------------------------------
% 2.56/1.66 % (10816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.66 % (10816)Termination reason: Unknown
% 2.56/1.66 % (10816)Termination phase: shuffling
% 2.56/1.66
% 2.56/1.66 % (10816)Memory used [KB]: 1918
% 2.56/1.66 % (10816)Time elapsed: 0.013 s
% 2.56/1.66 % (10816)Instructions burned: 18 (million)
% 2.56/1.66 % (10816)------------------------------
% 2.56/1.66 % (10816)------------------------------
% 2.56/1.66 % (10818)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_10704 for (2999ds/37Mi)
% 2.56/1.67 % (10812)Instruction limit reached!
% 2.56/1.67 % (10812)------------------------------
% 2.56/1.67 % (10812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.67 % (10812)Termination reason: Unknown
% 2.56/1.67 % (10812)Termination phase: Property scanning
% 2.56/1.67
% 2.56/1.67 % (10812)Memory used [KB]: 2046
% 2.56/1.67 % (10812)Time elapsed: 0.019 s
% 2.56/1.67 % (10812)Instructions burned: 27 (million)
% 2.56/1.67 % (10812)------------------------------
% 2.56/1.67 % (10812)------------------------------
% 2.56/1.67 % (10819)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_10704 for (2999ds/15Mi)
% 2.56/1.67 % (10821)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_10704 for (2999ds/1041Mi)
% 2.56/1.68 % (10815)First to succeed.
% 2.56/1.68 % (10818)Instruction limit reached!
% 2.56/1.68 % (10818)------------------------------
% 2.56/1.68 % (10818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.68 % (10818)Termination reason: Unknown
% 2.56/1.68 % (10818)Termination phase: shuffling
% 2.56/1.68
% 2.56/1.68 % (10818)Memory used [KB]: 2302
% 2.56/1.68 % (10818)Time elapsed: 0.014 s
% 2.56/1.68 % (10818)Instructions burned: 39 (million)
% 2.56/1.68 % (10818)------------------------------
% 2.56/1.68 % (10818)------------------------------
% 2.56/1.68 % (10815)Refutation found. Thanks to Tanya!
% 2.56/1.68 % SZS status Theorem for DTF2THF_10704
% 2.56/1.68 % SZS output start Proof for DTF2THF_10704
% 2.56/1.68 thf(type_def_5, type, refine424419629nres_a: $tType).
% 2.56/1.68 thf(type_def_7, type, refine432681134nres_b: $tType).
% 2.56/1.68 thf(type_def_8, type, set_Product_prod_a_a: $tType).
% 2.56/1.68 thf(type_def_9, type, set_a: $tType).
% 2.56/1.68 thf(type_def_10, type, set_b: $tType).
% 2.56/1.68 thf(type_def_11, type, refine787176636t_unit: $tType).
% 2.56/1.68 thf(type_def_12, type, set_Product_prod_a_b: $tType).
% 2.56/1.68 thf(type_def_13, type, set_Product_prod_b_a: $tType).
% 2.56/1.68 thf(type_def_14, type, set_Product_prod_b_b: $tType).
% 2.56/1.68 thf(type_def_15, type, a: $tType).
% 2.56/1.68 thf(type_def_16, type, product_prod_a_a: $tType).
% 2.56/1.68 thf(type_def_17, type, b: $tType).
% 2.56/1.68 thf(type_def_18, type, product_prod_a_b: $tType).
% 2.56/1.68 thf(type_def_19, type, product_prod_b_b: $tType).
% 2.56/1.68 thf(type_def_20, type, product_unit: $tType).
% 2.56/1.68 thf(type_def_21, type, set_Pr451126599t_unit: $tType).
% 2.56/1.68 thf(type_def_22, type, set_Pr1720557880unit_a: $tType).
% 2.56/1.68 thf(type_def_23, type, set_Pr712638521unit_b: $tType).
% 2.56/1.68 thf(type_def_24, type, set_Pr1628433942t_unit: $tType).
% 2.56/1.68 thf(type_def_25, type, set_Pr1707992533t_unit: $tType).
% 2.56/1.68 thf(func_def_0, type, set_Pr451126599t_unit: $tType).
% 2.56/1.68 thf(func_def_1, type, refine787176636t_unit: $tType).
% 2.56/1.68 thf(func_def_2, type, set_Pr1707992533t_unit: $tType).
% 2.56/1.68 thf(func_def_3, type, set_Pr1628433942t_unit: $tType).
% 2.56/1.68 thf(func_def_4, type, set_Pr712638521unit_b: $tType).
% 2.56/1.68 thf(func_def_5, type, set_Pr1720557880unit_a: $tType).
% 2.56/1.68 thf(func_def_6, type, refine432681134nres_b: $tType).
% 2.56/1.68 thf(func_def_7, type, refine424419629nres_a: $tType).
% 2.56/1.68 thf(func_def_8, type, set_Product_prod_b_b: $tType).
% 2.56/1.68 thf(func_def_9, type, set_Product_prod_b_a: $tType).
% 2.56/1.68 thf(func_def_10, type, set_Product_prod_a_b: $tType).
% 2.56/1.68 thf(func_def_11, type, set_Product_prod_a_a: $tType).
% 2.56/1.68 thf(func_def_12, type, product_prod_b_b: $tType).
% 2.56/1.68 thf(func_def_13, type, product_prod_a_b: $tType).
% 2.56/1.68 thf(func_def_14, type, product_prod_a_a: $tType).
% 2.56/1.68 thf(func_def_15, type, product_unit: $tType).
% 2.56/1.68 thf(func_def_16, type, set_b: $tType).
% 2.56/1.68 thf(func_def_17, type, set_a: $tType).
% 2.56/1.68 thf(func_def_18, type, b: $tType).
% 2.56/1.68 thf(func_def_19, type, a: $tType).
% 2.56/1.68 thf(func_def_20, type, if_o_R1705037948nres_a: $o > ($o > refine424419629nres_a) > ($o > refine424419629nres_a) > $o > refine424419629nres_a).
% 2.56/1.68 thf(func_def_21, type, if_o_R697118589nres_b: $o > ($o > refine432681134nres_b) > ($o > refine432681134nres_b) > $o > refine432681134nres_b).
% 2.56/1.68 thf(func_def_22, type, if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a).
% 2.56/1.68 thf(func_def_23, type, if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b).
% 2.56/1.68 thf(func_def_24, type, if_set1550076877od_a_a: $o > set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a).
% 2.56/1.68 thf(func_def_25, type, if_set_a: $o > set_a > set_a > set_a).
% 2.56/1.68 thf(func_def_26, type, if_set_b: $o > set_b > set_b > set_b).
% 2.56/1.68 thf(func_def_27, type, sup_su2034729561nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a).
% 2.56/1.68 thf(func_def_28, type, sup_su2042991066nres_b: refine432681134nres_b > refine432681134nres_b > refine432681134nres_b).
% 2.56/1.68 thf(func_def_29, type, ord_le516598614nres_a: ($o > refine424419629nres_a) > ($o > refine424419629nres_a) > $o).
% 2.56/1.68 thf(func_def_30, type, ord_le1656162903nres_b: ($o > refine432681134nres_b) > ($o > refine432681134nres_b) > $o).
% 2.56/1.68 thf(func_def_31, type, ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o).
% 2.56/1.68 thf(func_def_32, type, ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o).
% 2.56/1.68 thf(func_def_33, type, ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o).
% 2.56/1.68 thf(func_def_34, type, ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o).
% 2.56/1.68 thf(func_def_35, type, ord_le816409512od_a_b: set_Product_prod_a_b > set_Product_prod_a_b > $o).
% 2.56/1.68 thf(func_def_36, type, ord_le2044239718od_b_a: set_Product_prod_b_a > set_Product_prod_b_a > $o).
% 2.56/1.68 thf(func_def_37, type, ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o).
% 2.56/1.68 thf(func_def_38, type, ord_less_eq_set_a: set_a > set_a > $o).
% 2.56/1.68 thf(func_def_39, type, ord_less_eq_set_b: set_b > set_b > $o).
% 2.56/1.68 thf(func_def_40, type, order_1714329108nres_a: (refine424419629nres_a > $o) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_41, type, order_1722590613nres_b: (refine432681134nres_b > $o) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_42, type, top_to2046902534nres_a: $o > refine424419629nres_a).
% 2.56/1.68 thf(func_def_43, type, top_to1038983175nres_b: $o > refine432681134nres_b).
% 2.56/1.68 thf(func_def_44, type, top_to177290092t_unit: refine787176636t_unit).
% 2.56/1.68 thf(func_def_45, type, top_to231829469nres_a: refine424419629nres_a).
% 2.56/1.68 thf(func_def_46, type, top_to240090974nres_b: refine432681134nres_b).
% 2.56/1.68 thf(func_def_47, type, top_to398455383od_a_a: set_Product_prod_a_a).
% 2.56/1.68 thf(func_def_48, type, top_top_set_a: set_a).
% 2.56/1.68 thf(func_def_49, type, top_top_set_b: set_b).
% 2.56/1.68 thf(func_def_50, type, product_Pair_a_a: a > a > product_prod_a_a).
% 2.56/1.68 thf(func_def_51, type, product_Pair_a_b: a > b > product_prod_a_b).
% 2.56/1.68 thf(func_def_52, type, product_Pair_b_b: b > b > product_prod_b_b).
% 2.56/1.68 thf(func_def_53, type, refine2063221604TURN_a: a > refine424419629nres_a).
% 2.56/1.68 thf(func_def_54, type, refine2063221605TURN_b: b > refine432681134nres_b).
% 2.56/1.68 thf(func_def_55, type, refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a).
% 2.56/1.68 thf(func_def_56, type, refine1136779703un_a_b: set_Product_prod_a_b > refine424419629nres_a > refine432681134nres_b).
% 2.56/1.68 thf(func_def_57, type, refine1964549109un_b_a: set_Product_prod_b_a > refine432681134nres_b > refine424419629nres_a).
% 2.56/1.68 thf(func_def_58, type, refine1964549110un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b).
% 2.56/1.68 thf(func_def_59, type, refine119808503unit_a: refine787176636t_unit > (product_unit > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_60, type, refine119808504unit_b: refine787176636t_unit > (product_unit > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_61, type, refine436832838nd_a_a: refine424419629nres_a > (a > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_62, type, refine436832839nd_a_b: refine424419629nres_a > (a > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_63, type, refine1264602245nd_b_a: refine432681134nres_b > (b > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_64, type, refine1264602246nd_b_b: refine432681134nres_b > (b > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_65, type, refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit).
% 2.56/1.68 thf(func_def_66, type, refine2043866374unit_a: set_Pr1720557880unit_a > refine424419629nres_a > refine787176636t_unit).
% 2.56/1.68 thf(func_def_67, type, refine2043866375unit_b: set_Pr712638521unit_b > refine432681134nres_b > refine787176636t_unit).
% 2.56/1.68 thf(func_def_68, type, refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a).
% 2.56/1.68 thf(func_def_69, type, refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a).
% 2.56/1.68 thf(func_def_70, type, refine1441824854un_a_b: set_Product_prod_a_b > refine432681134nres_b > refine424419629nres_a).
% 2.56/1.68 thf(func_def_71, type, refine2140306339t_unit: set_Pr1707992533t_unit > refine787176636t_unit > refine432681134nres_b).
% 2.56/1.68 thf(func_def_72, type, refine122110612un_b_a: set_Product_prod_b_a > refine424419629nres_a > refine432681134nres_b).
% 2.56/1.68 thf(func_def_73, type, refine122110613un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b).
% 2.56/1.68 thf(func_def_74, type, refine1001002027nres_a: refine424419629nres_a > a > $o).
% 2.56/1.68 thf(func_def_75, type, refine1001002028nres_b: refine432681134nres_b > b > $o).
% 2.56/1.68 thf(func_def_76, type, refine412683989fail_a: refine424419629nres_a > $o).
% 2.56/1.68 thf(func_def_77, type, refine412683990fail_b: refine432681134nres_b > $o).
% 2.56/1.68 thf(func_def_78, type, refine1198353288_RES_a: set_a > refine424419629nres_a).
% 2.56/1.68 thf(func_def_79, type, refine1198353289_RES_b: set_b > refine432681134nres_b).
% 2.56/1.68 thf(func_def_80, type, id_a: set_Product_prod_a_a).
% 2.56/1.68 thf(func_def_81, type, id_b: set_Product_prod_b_b).
% 2.56/1.68 thf(func_def_82, type, collect_a: (a > $o) > set_a).
% 2.56/1.68 thf(func_def_83, type, collect_b: (b > $o) > set_b).
% 2.56/1.68 thf(func_def_84, type, member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o).
% 2.56/1.68 thf(func_def_85, type, member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o).
% 2.56/1.68 thf(func_def_86, type, member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o).
% 2.56/1.68 thf(func_def_87, type, member_a: a > set_a > $o).
% 2.56/1.68 thf(func_def_88, type, member_b: b > set_b > $o).
% 2.56/1.68 thf(func_def_89, type, r: set_Product_prod_a_b).
% 2.56/1.68 thf(func_def_90, type, x: refine424419629nres_a).
% 2.56/1.68 thf(func_def_103, type, sK0: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_104, type, sK1: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_105, type, sK2: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_106, type, sK3: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_107, type, sK4: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_108, type, sK5: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_109, type, sK6: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_110, type, sK7: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_111, type, sK8: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_112, type, sK9: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_113, type, sK10: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_114, type, sK11: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_115, type, sK12: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_116, type, sK13: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_117, type, sK14: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_118, type, sK15: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_119, type, sK16: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_120, type, sK17: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_121, type, sK18: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_122, type, sK19: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_123, type, sK20: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_124, type, sK21: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_125, type, sK22: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_126, type, sK23: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_127, type, sK24: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_128, type, sK25: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_129, type, sK26: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_130, type, sK27: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_131, type, sK28: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_132, type, sK29: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 2.56/1.68 thf(func_def_133, type, sK30: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_134, type, sK31: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 2.56/1.68 thf(func_def_136, type, ph33: !>[X0: $tType]:(X0)).
% 2.56/1.68 thf(f1301,plain,(
% 2.56/1.68 $false),
% 2.56/1.68 inference(subsumption_resolution,[status(thm)],[f1300,f1171])).
% 2.56/1.68 thf(f1171,plain,(
% 2.56/1.68 ( ! [X0 : refine424419629nres_a] : (((ord_le519537037nres_a @ X0 @ top_to231829469nres_a) = $true)) )),
% 2.56/1.68 inference(cnf_transformation,[status(thm)],[f412])).
% 2.56/1.68 thf(f412,plain,(
% 2.56/1.68 ! [X0 : refine424419629nres_a] : ((ord_le519537037nres_a @ X0 @ top_to231829469nres_a) = $true)),
% 2.56/1.68 inference(fool_elimination,[status(thm)],[f411])).
% 2.56/1.68 thf(f411,plain,(
% 2.56/1.68 ! [X0 : refine424419629nres_a] : (ord_le519537037nres_a @ X0 @ top_to231829469nres_a)),
% 2.56/1.68 inference(rectify,[status(thm)],[f60])).
% 2.56/1.68 thf(f60,axiom,(
% 2.56/1.68 ! [X8 : refine424419629nres_a] : (ord_le519537037nres_a @ X8 @ top_to231829469nres_a)),
% 2.56/1.68 file('/export/starexec/sandbox/tmp/tmp.C9Bew6RkOr/DTF2THF_10704.p',fact_59_top__greatest)).
% 2.56/1.68 thf(f1300,plain,(
% 2.56/1.68 ((ord_le519537037nres_a @ x @ top_to231829469nres_a) != $true)),
% 2.56/1.68 inference(forward_demodulation,[status(thm)],[f1244,f1188])).
% 2.56/1.68 thf(f1188,plain,(
% 2.56/1.68 ( ! [X0 : set_Product_prod_a_b] : ((top_to231829469nres_a = (refine1441824854un_a_b @ X0 @ top_to240090974nres_b))) )),
% 2.56/1.68 inference(cnf_transformation,[status(thm)],[f1018])).
% 2.56/1.68 thf(f1018,plain,(
% 2.56/1.68 ! [X0 : set_Product_prod_a_b] : (top_to231829469nres_a = (refine1441824854un_a_b @ X0 @ top_to240090974nres_b))),
% 2.56/1.68 inference(rectify,[status(thm)],[f30])).
% 2.56/1.68 thf(f30,axiom,(
% 2.56/1.68 ! [X1 : set_Product_prod_a_b] : (top_to231829469nres_a = (refine1441824854un_a_b @ X1 @ top_to240090974nres_b))),
% 2.56/1.68 file('/export/starexec/sandbox/tmp/tmp.C9Bew6RkOr/DTF2THF_10704.p',fact_29_conc__fun__FAIL)).
% 2.56/1.68 thf(f1244,plain,(
% 2.56/1.68 ((ord_le519537037nres_a @ x @ (refine1441824854un_a_b @ r @ top_to240090974nres_b)) != $true)),
% 2.56/1.68 inference(cnf_transformation,[status(thm)],[f1017])).
% 2.56/1.68 thf(f1017,plain,(
% 2.56/1.68 ((ord_le519537037nres_a @ x @ (refine1441824854un_a_b @ r @ top_to240090974nres_b)) != $true)),
% 2.56/1.68 inference(flattening,[status(thm)],[f883])).
% 2.56/1.68 thf(f883,plain,(
% 2.56/1.68 ~((ord_le519537037nres_a @ x @ (refine1441824854un_a_b @ r @ top_to240090974nres_b)) = $true)),
% 2.56/1.68 inference(fool_elimination,[status(thm)],[f882])).
% 2.56/1.68 thf(f882,plain,(
% 2.56/1.68 ~(ord_le519537037nres_a @ x @ (refine1441824854un_a_b @ r @ top_to240090974nres_b))),
% 2.56/1.68 inference(rectify,[status(thm)],[f364])).
% 2.56/1.68 thf(f364,negated_conjecture,(
% 2.56/1.68 ~(ord_le519537037nres_a @ x @ (refine1441824854un_a_b @ r @ top_to240090974nres_b))),
% 2.56/1.68 inference(negated_conjecture,[status(cth)],[f363])).
% 2.56/1.68 thf(f363,conjecture,(
% 2.56/1.68 (ord_le519537037nres_a @ x @ (refine1441824854un_a_b @ r @ top_to240090974nres_b))),
% 2.56/1.68 file('/export/starexec/sandbox/tmp/tmp.C9Bew6RkOr/DTF2THF_10704.p',conj_0)).
% 2.56/1.68 % SZS output end Proof for DTF2THF_10704
% 2.56/1.68 % (10815)------------------------------
% 2.56/1.68 % (10815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.68 % (10815)Termination reason: Refutation
% 2.56/1.68
% 2.56/1.68 % (10815)Memory used [KB]: 6780
% 2.56/1.68 % (10815)Time elapsed: 0.033 s
% 2.56/1.68 % (10815)Instructions burned: 62 (million)
% 2.56/1.68 % (10815)------------------------------
% 2.56/1.68 % (10815)------------------------------
% 2.56/1.68 % (10809)Success in time 0.059 s
%------------------------------------------------------------------------------