%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP165^1 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:04 AM UTC 2026
% Result : Theorem 4.18s 2.29s
% Output : Refutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 12 unt; 0 typ; 5 def)
% Number of atoms : 276 ( 59 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 271 ( 44 ~; 57 |; 0 &; 158 @)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 82 usr; 21 con; 0-4 aty)
% Number of variables : 27 ( 5 ^; 22 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_a: $tType ).
thf(type_def_7,type,
refine424419629nres_a: $tType ).
thf(type_def_8,type,
refine787176636t_unit: $tType ).
thf(type_def_9,type,
a: $tType ).
thf(type_def_10,type,
set_Product_unit: $tType ).
thf(type_def_11,type,
product_unit: $tType ).
thf(func_def_0,type,
refine787176636t_unit: $tType ).
thf(func_def_1,type,
refine424419629nres_a: $tType ).
thf(func_def_2,type,
set_Product_unit: $tType ).
thf(func_def_3,type,
product_unit: $tType ).
thf(func_def_4,type,
set_a: $tType ).
thf(func_def_5,type,
a: $tType ).
thf(func_def_6,type,
uminus_uminus_set_a: set_a > set_a ).
thf(func_def_7,type,
if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
thf(func_def_8,type,
if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(func_def_9,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_10,type,
if_set_a: $o > set_a > set_a > set_a ).
thf(func_def_11,type,
bot_bot_a_o: a > $o ).
thf(func_def_12,type,
bot_bo658782032t_unit: refine787176636t_unit ).
thf(func_def_13,type,
bot_bo529555393nres_a: refine424419629nres_a ).
thf(func_def_14,type,
bot_bo1087887705t_unit: set_Product_unit ).
thf(func_def_15,type,
bot_bot_set_a: set_a ).
thf(func_def_16,type,
ord_le1960259811nres_a: ( $o > $o > refine424419629nres_a ) > ( $o > $o > refine424419629nres_a ) > $o ).
thf(func_def_17,type,
ord_le1633311077t_unit: ( $o > refine787176636t_unit ) > ( $o > refine787176636t_unit ) > $o ).
thf(func_def_18,type,
ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
thf(func_def_19,type,
ord_less_eq_o_set_a: ( $o > set_a ) > ( $o > set_a ) > $o ).
thf(func_def_20,type,
ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
thf(func_def_21,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_22,type,
ord_le1023748749t_unit: set_Product_unit > set_Product_unit > $o ).
thf(func_def_23,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_24,type,
order_245837199nres_a: ( ( $o > refine424419629nres_a ) > $o ) > $o > refine424419629nres_a ).
thf(func_def_25,type,
order_453013155t_unit: ( refine787176636t_unit > $o ) > refine787176636t_unit ).
thf(func_def_26,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(func_def_27,type,
order_Greatest_set_a: ( set_a > $o ) > set_a ).
thf(func_def_28,type,
top_to177290092t_unit: refine787176636t_unit ).
thf(func_def_29,type,
top_to231829469nres_a: refine424419629nres_a ).
thf(func_def_30,type,
top_top_set_a: set_a ).
thf(func_def_31,type,
partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o ).
thf(func_def_32,type,
partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_33,type,
refine23983189ASSUME: $o > refine787176636t_unit ).
thf(func_def_34,type,
refine1420258419t_unit: product_unit > refine787176636t_unit ).
thf(func_def_35,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(func_def_36,type,
refine681446406t_unit: refine787176636t_unit > ( product_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_37,type,
refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_38,type,
refine96995669t_unit: refine424419629nres_a > ( a > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_39,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_40,type,
refine558004794t_unit: refine787176636t_unit > product_unit > $o ).
thf(func_def_41,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(func_def_42,type,
refine983493746t_unit: refine787176636t_unit > product_unit > $o ).
thf(func_def_43,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(func_def_44,type,
refine579265252t_unit: refine787176636t_unit > $o ).
thf(func_def_45,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(func_def_46,type,
refine464223677AILi_a: refine424419629nres_a ).
thf(func_def_47,type,
refine1777164439t_unit: set_Product_unit > refine787176636t_unit ).
thf(func_def_48,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(func_def_49,type,
refine1208325748t_unit: refine787176636t_unit > set_Product_unit ).
thf(func_def_50,type,
refine1822134885_RES_a: refine424419629nres_a > set_a ).
thf(func_def_51,type,
refine459374679t_unit: ( refine787176636t_unit > refine787176636t_unit ) > $o ).
thf(func_def_52,type,
collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).
thf(func_def_53,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_54,type,
insert_a: a > set_a > set_a ).
thf(func_def_55,type,
is_singleton_a: set_a > $o ).
thf(func_def_56,type,
member_Product_unit: product_unit > set_Product_unit > $o ).
thf(func_def_57,type,
member_a: a > set_a > $o ).
thf(func_def_58,type,
s1: refine424419629nres_a ).
thf(func_def_59,type,
s2: refine424419629nres_a ).
thf(func_def_60,type,
phi: a > $o ).
thf(func_def_75,type,
sK0: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_76,type,
sK1: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_77,type,
sK2: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_78,type,
sK3: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_79,type,
sK4: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_80,type,
sK5: set_a > ( a > $o ) > a ).
thf(func_def_81,type,
sK6: set_a > ( a > $o ) > a ).
thf(func_def_82,type,
sK7: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_83,type,
sK8: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_84,type,
sK9: ( a > $o ) > a ).
thf(func_def_85,type,
sK10: ( a > $o ) > a ).
thf(func_def_86,type,
sK11: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_87,type,
sK12: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_88,type,
sK13: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_89,type,
sK14: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_90,type,
sK15: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_91,type,
sK16: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_93,type,
ph18:
!>[X0: $tType] : X0 ).
thf(func_def_94,type,
sK19: a ).
thf(func_def_95,type,
sK20: a ).
thf(func_def_96,type,
sK21: a ).
thf(f1446,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1193,f1200,f1381,f1390,f1397,f1445]) ).
thf(f1445,plain,
( spl17_1
| spl17_8
| spl17_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f1444]) ).
thf(f1444,plain,
( $false
| spl17_1
| spl17_8
| spl17_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1443]) ).
thf(f1443,plain,
( ( $true = $false )
| spl17_1
| spl17_8
| spl17_11 ),
inference(backward_demodulation,[status(thm)],[f1441,f1442]) ).
thf(f1442,plain,
( ( ( phi @ sK21 )
= $false )
| spl17_8
| spl17_11 ),
inference(subsumption_resolution,[status(thm)],[f1440,f1292]) ).
thf(f1292,plain,
( ( b != $false )
| spl17_11 ),
inference(avatar_component_clause,[status(thm)],[f1291]) ).
thf(f1291,definition,
( spl17_11
<=> ( b = $false ) ),
introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition]) ).
thf(f1440,plain,
( ( ( phi @ sK21 )
= $false )
| ( b = $false )
| spl17_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1438]) ).
thf(f1438,plain,
( ( b
!= ( phi @ sK21 ) )
| spl17_8 ),
inference(beta_eta_normalization,[status(thm)],[f1437]) ).
thf(f1437,plain,
( ( ( phi @ sK21 )
!= ( ^ [Y0: a] : b
@ sK21 ) )
| spl17_8 ),
inference(negative_extensionality,[status(thm)],[f1253]) ).
thf(f1253,plain,
( ( phi
!= ( ^ [Y0: a] : b ) )
| spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f1251]) ).
thf(f1251,definition,
( spl17_8
<=> ( phi
= ( ^ [Y0: a] : b ) ) ),
introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition]) ).
thf(f1441,plain,
( ( $true
= ( phi @ sK21 ) )
| spl17_1
| spl17_8 ),
inference(subsumption_resolution,[status(thm)],[f1439,f1188]) ).
thf(f1188,plain,
( ( b != $true )
| spl17_1 ),
inference(avatar_component_clause,[status(thm)],[f1186]) ).
thf(f1186,definition,
( spl17_1
<=> ( b = $true ) ),
introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition]) ).
thf(f1439,plain,
( ( b = $true )
| ( $true
= ( phi @ sK21 ) )
| spl17_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1438]) ).
thf(f1397,plain,
( ~ spl17_1
| ~ spl17_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f1396]) ).
thf(f1396,plain,
( $false
| ~ spl17_1
| ~ spl17_2 ),
inference(subsumption_resolution,[status(thm)],[f1395,f1192]) ).
thf(f1192,plain,
( ( ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true )
| ~ spl17_2 ),
inference(avatar_component_clause,[status(thm)],[f1190]) ).
thf(f1190,definition,
( spl17_2
<=> ( ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition]) ).
thf(f1395,plain,
( ( ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
!= $true )
| ~ spl17_1 ),
inference(forward_demodulation,[status(thm)],[f1394,f1149]) ).
thf(f1149,plain,
! [X0: refine424419629nres_a,X1: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ X1 @ X0 )
= X1 ),
inference(cnf_transformation,[status(thm)],[f456]) ).
thf(f456,plain,
! [X0: refine424419629nres_a,X1: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ X1 @ X0 )
= X1 ),
inference(fool_elimination,[status(thm)],[f455]) ).
thf(f455,plain,
! [X0: refine424419629nres_a,X1: refine424419629nres_a] :
( X1
= ( if_Ref1724547303nres_a @ $true @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f354]) ).
thf(f354,axiom,
! [X9: refine424419629nres_a,X8: refine424419629nres_a] :
( X8
= ( if_Ref1724547303nres_a @ $true @ X8 @ X9 ) ),
file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(f1394,plain,
( ( ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ $true @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
!= $true )
| ~ spl17_1 ),
inference(forward_demodulation,[status(thm)],[f1112,f1187]) ).
thf(f1187,plain,
( ( b = $true )
| ~ spl17_1 ),
inference(avatar_component_clause,[status(thm)],[f1186]) ).
thf(f1112,plain,
( ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1009]) ).
thf(f1009,plain,
( ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
!= $true ),
inference(flattening,[status(thm)],[f468]) ).
thf(f468,plain,
( ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f467]) ).
thf(f467,plain,
~ ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ),
inference(rectify,[status(thm)],[f363]) ).
thf(f363,negated_conjecture,
~ ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ),
inference(negated_conjecture,[status(cth)],[f362]) ).
thf(f362,conjecture,
ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ),
file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',conj_2) ).
thf(f1390,plain,
( ~ spl17_3
| ~ spl17_11 ),
inference(avatar_split_clause,[status(thm)],[f1387,f1291,f1197]) ).
thf(f1197,definition,
( spl17_3
<=> ( ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition]) ).
thf(f1387,plain,
( ( ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
!= $true )
| ~ spl17_11 ),
inference(forward_demodulation,[status(thm)],[f1385,f1147]) ).
thf(f1147,plain,
! [X0: refine424419629nres_a,X1: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ X1 @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f625]) ).
thf(f625,plain,
! [X0: refine424419629nres_a,X1: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ X1 @ X0 )
= X0 ),
inference(fool_elimination,[status(thm)],[f624]) ).
thf(f624,plain,
! [X0: refine424419629nres_a,X1: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ X1 @ X0 )
= X0 ),
inference(rectify,[status(thm)],[f353]) ).
thf(f353,axiom,
! [X9: refine424419629nres_a,X8: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ X8 @ X9 )
= X9 ),
file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(f1385,plain,
( ( ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ $false @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
!= $true )
| ~ spl17_11 ),
inference(backward_demodulation,[status(thm)],[f1112,f1293]) ).
thf(f1293,plain,
( ( b = $false )
| ~ spl17_11 ),
inference(avatar_component_clause,[status(thm)],[f1291]) ).
thf(f1381,plain,
( spl17_1
| ~ spl17_8
| spl17_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f1380]) ).
thf(f1380,plain,
( $false
| spl17_1
| ~ spl17_8
| spl17_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1379]) ).
thf(f1379,plain,
( ( $true = $false )
| spl17_1
| ~ spl17_8
| spl17_11 ),
inference(forward_demodulation,[status(thm)],[f1378,f1375]) ).
thf(f1375,plain,
( ! [X1: a] :
( ( phi @ X1 )
= $false )
| spl17_1
| ~ spl17_8 ),
inference(subsumption_resolution,[status(thm)],[f1373,f1188]) ).
thf(f1373,plain,
( ! [X1: a] :
( ( ( phi @ X1 )
= $false )
| ( b = $true ) )
| ~ spl17_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1372]) ).
thf(f1372,plain,
( ! [X1: a] :
( b
= ( phi @ X1 ) )
| ~ spl17_8 ),
inference(beta_eta_normalization,[status(thm)],[f1367]) ).
thf(f1367,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : b
@ X1 )
= ( phi @ X1 ) )
| ~ spl17_8 ),
inference(argument_congruence,[status(thm)],[f1252]) ).
thf(f1252,plain,
( ( phi
= ( ^ [Y0: a] : b ) )
| ~ spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f1251]) ).
thf(f1378,plain,
( ! [X1: a] :
( $true
= ( phi @ X1 ) )
| ~ spl17_8
| spl17_11 ),
inference(subsumption_resolution,[status(thm)],[f1374,f1292]) ).
thf(f1374,plain,
( ! [X1: a] :
( ( b = $false )
| ( $true
= ( phi @ X1 ) ) )
| ~ spl17_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1372]) ).
thf(f1200,plain,
( spl17_3
| spl17_1 ),
inference(avatar_split_clause,[status(thm)],[f1146,f1186,f1197]) ).
thf(f1146,plain,
( ( ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true )
| ( b = $true ) ),
inference(cnf_transformation,[status(thm)],[f1058]) ).
thf(f1058,plain,
( ( b = $true )
| ( ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f1010]) ).
thf(f1010,plain,
( ( b != $true )
=> ( ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true ) ),
inference(flattening,[status(thm)],[f881]) ).
thf(f881,plain,
( ( b != $true )
=> ( ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f880]) ).
thf(f880,plain,
( ~ b
=> ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
inference(rectify,[status(thm)],[f361]) ).
thf(f361,axiom,
( ~ b
=> ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',conj_1) ).
thf(f1193,plain,
( ~ spl17_1
| spl17_2 ),
inference(avatar_split_clause,[status(thm)],[f1119,f1190,f1186]) ).
thf(f1119,plain,
( ( ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true )
| ( b != $true ) ),
inference(cnf_transformation,[status(thm)],[f1032]) ).
thf(f1032,plain,
( ( ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true )
| ( b != $true ) ),
inference(ennf_transformation,[status(thm)],[f544]) ).
thf(f544,plain,
( ( b = $true )
=> ( ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f543]) ).
thf(f543,plain,
( b
=> ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
inference(rectify,[status(thm)],[f360]) ).
thf(f360,axiom,
( b
=> ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP165^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n026.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 08:28:55 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.43 ---- Original DTF file ---
% 0.19/0.43 thf(spec,logic,$$dhol).
% 0.19/0.43 %------------------------------------------------------------------------------
% 0.19/0.43 % File : ITP165^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.43 % Domain : Interactive Theorem Proving
% 0.19/0.43 % Problem : Sledgehammer Refine_Basic problem prob_892__3593680_1
% 0.19/0.43 % Version : Especial.
% 0.19/0.43 % English :
% 0.19/0.43
% 0.19/0.43 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.43 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.43 % Source : [Des21]
% 0.19/0.43 % Names : Refine_Basic/prob_892__3593680_1 [Des21]
% 0.19/0.43
% 0.19/0.43 % Status : Theorem
% 0.19/0.43 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% 0.19/0.43 % Syntax : Number of formulae : 424 ( 168 unt; 62 typ; 0 def)
% 0.19/0.43 % Number of atoms : 1137 ( 342 equ; 0 cnn)
% 0.19/0.43 % Maximal formula atoms : 7 ( 3 avg)
% 0.19/0.43 % Number of connectives : 2725 ( 62 ~; 2 |; 45 &;2081 @)
% 0.19/0.43 % ( 0 <=>; 535 =>; 0 <=; 0 <~>)
% 0.19/0.43 % Maximal formula depth : 14 ( 6 avg)
% 0.19/0.43 % Number of types : 7 ( 6 usr)
% 0.19/0.43 % Number of type conns : 328 ( 328 >; 0 *; 0 +; 0 <<)
% 0.19/0.43 % Number of symbols : 59 ( 56 usr; 13 con; 0-4 aty)
% 0.19/0.43 % Number of variables : 1034 ( 110 ^; 917 !; 7 ?;1034 :)
% 0.19/0.43 % SPC : TH0_THM_EQU_NAR
% 0.19/0.43
% 0.19/0.43 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:27.762
% 0.19/0.43 %------------------------------------------------------------------------------
% 0.19/0.43 % Could-be-implicit typings (6)
% 0.19/0.43 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.19/0.43 refine787176636t_unit: $tType ).
% 0.19/0.43
% 0.19/0.43 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.19/0.43 refine424419629nres_a: $tType ).
% 0.19/0.43
% 0.19/0.43 thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.19/0.43 set_Product_unit: $tType ).
% 0.19/0.43
% 0.19/0.43 thf(ty_n_t__Product____Type__Ounit,type,
% 0.19/0.43 product_unit: $tType ).
% 0.19/0.43
% 0.19/0.43 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.19/0.43 set_a: $tType ).
% 0.19/0.43
% 0.19/0.43 thf(ty_n_tf__a,type,
% 0.19/0.43 a: $tType ).
% 0.19/0.43
% 0.19/0.43 % Explicit typings (56)
% 0.19/0.43 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.43 uminus_uminus_set_a: set_a > set_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.19/0.43 if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.19/0.43 if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.19/0.43 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.43 if_set_a: $o > set_a > set_a > set_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 0.19/0.43 bot_bot_a_o: a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Obot__class_Obot_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.19/0.43 bot_bo658782032t_unit: refine787176636t_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Obot__class_Obot_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.19/0.43 bot_bo529555393nres_a: refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.19/0.43 bot_bo1087887705t_unit: set_Product_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.43 bot_bot_set_a: set_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_J,type,
% 0.19/0.43 ord_le1960259811nres_a: ( $o > $o > refine424419629nres_a ) > ( $o > $o > refine424419629nres_a ) > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_J,type,
% 0.19/0.43 ord_le1633311077t_unit: ( $o > refine787176636t_unit ) > ( $o > refine787176636t_unit ) > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.19/0.43 ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_Itf__a_J_J,type,
% 0.19/0.43 ord_less_eq_o_set_a: ( $o > set_a ) > ( $o > set_a ) > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.19/0.43 ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.19/0.43 ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.19/0.43 ord_le1023748749t_unit: set_Product_unit > set_Product_unit > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.43 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.19/0.43 order_245837199nres_a: ( ( $o > refine424419629nres_a ) > $o ) > $o > refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.19/0.43 order_453013155t_unit: ( refine787176636t_unit > $o ) > refine787176636t_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.19/0.43 order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.43 order_Greatest_set_a: ( set_a > $o ) > set_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.19/0.43 top_to177290092t_unit: refine787176636t_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.19/0.43 top_to231829469nres_a: refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.43 top_top_set_a: set_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Partial__Function_Oflat__ord_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.19/0.43 partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Partial__Function_Oflat__ord_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.19/0.43 partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_OASSUME,type,
% 0.19/0.43 refine23983189ASSUME: $o > refine787176636t_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001t__Product____Type__Ounit,type,
% 0.19/0.43 refine1420258419t_unit: product_unit > refine787176636t_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__a,type,
% 0.19/0.43 refine2063221604TURN_a: a > refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 0.19/0.43 refine681446406t_unit: refine787176636t_unit > ( product_unit > refine787176636t_unit ) > refine787176636t_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001t__Product____Type__Ounit_001tf__a,type,
% 0.19/0.43 refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001t__Product____Type__Ounit,type,
% 0.19/0.43 refine96995669t_unit: refine424419629nres_a > ( a > refine787176636t_unit ) > refine787176636t_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001tf__a,type,
% 0.19/0.43 refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001t__Product____Type__Ounit,type,
% 0.19/0.43 refine558004794t_unit: refine787176636t_unit > product_unit > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__a,type,
% 0.19/0.43 refine1001002027nres_a: refine424419629nres_a > a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onf__inres_001t__Product____Type__Ounit,type,
% 0.19/0.43 refine983493746t_unit: refine787176636t_unit > product_unit > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onf__inres_001tf__a,type,
% 0.19/0.43 refine1312857699nres_a: refine424419629nres_a > a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001t__Product____Type__Ounit,type,
% 0.19/0.43 refine579265252t_unit: refine787176636t_unit > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__a,type,
% 0.19/0.43 refine412683989fail_a: refine424419629nres_a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_OFAILi_001tf__a,type,
% 0.19/0.43 refine464223677AILi_a: refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001t__Product____Type__Ounit,type,
% 0.19/0.43 refine1777164439t_unit: set_Product_unit > refine787176636t_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__a,type,
% 0.19/0.43 refine1198353288_RES_a: set_a > refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001t__Product____Type__Ounit,type,
% 0.19/0.43 refine1208325748t_unit: refine787176636t_unit > set_Product_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001tf__a,type,
% 0.19/0.43 refine1822134885_RES_a: refine424419629nres_a > set_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Refine__Misc_Ostrict_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.19/0.43 refine459374679t_unit: ( refine787176636t_unit > refine787176636t_unit ) > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Set_OCollect_001t__Product____Type__Ounit,type,
% 0.19/0.43 collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.19/0.43 collect_a: ( a > $o ) > set_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.19/0.43 insert_a: a > set_a > set_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_Set_Ois__singleton_001tf__a,type,
% 0.19/0.43 is_singleton_a: set_a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_member_001t__Product____Type__Ounit,type,
% 0.19/0.43 member_Product_unit: product_unit > set_Product_unit > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_c_member_001tf__a,type,
% 0.19/0.43 member_a: a > set_a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_v_S1,type,
% 0.19/0.43 s1: refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_v_S2,type,
% 0.19/0.43 s2: refine424419629nres_a ).
% 0.19/0.43
% 0.19/0.43 thf(sy_v__092_060Phi_062,type,
% 0.19/0.43 phi: a > $o ).
% 0.19/0.43
% 0.19/0.43 thf(sy_v_b,type,
% 0.19/0.43 b: $o ).
% 0.19/0.43
% 0.19/0.43 % Relevant facts (350)
% 0.19/0.43 thf(fact_0_nres__more__simps_I4_J,axiom,
% 0.19/0.43 ! [X: set_Product_unit,Y: set_Product_unit] :
% 0.19/0.43 ( ( ( refine1777164439t_unit @ X )
% 0.19/0.43 = ( refine1777164439t_unit @ Y ) )
% 0.19/0.43 = ( X = Y ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_more_simps(4)
% 0.19/0.43 thf(fact_1_nres__more__simps_I4_J,axiom,
% 0.19/0.43 ! [X: set_a,Y: set_a] :
% 0.19/0.43 ( ( ( refine1198353288_RES_a @ X )
% 0.19/0.43 = ( refine1198353288_RES_a @ Y ) )
% 0.19/0.43 = ( X = Y ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_more_simps(4)
% 0.19/0.43 thf(fact_2_nres_Oinject,axiom,
% 0.19/0.43 ! [X2: set_Product_unit,Y2: set_Product_unit] :
% 0.19/0.43 ( ( ( refine1777164439t_unit @ X2 )
% 0.19/0.43 = ( refine1777164439t_unit @ Y2 ) )
% 0.19/0.43 = ( X2 = Y2 ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres.inject
% 0.19/0.43 thf(fact_3_nres_Oinject,axiom,
% 0.19/0.43 ! [X2: set_a,Y2: set_a] :
% 0.19/0.43 ( ( ( refine1198353288_RES_a @ X2 )
% 0.19/0.43 = ( refine1198353288_RES_a @ Y2 ) )
% 0.19/0.43 = ( X2 = Y2 ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres.inject
% 0.19/0.43 thf(fact_4_RES__rule,axiom,
% 0.19/0.43 ! [S: set_Product_unit,Phi: product_unit > $o] :
% 0.19/0.43 ( ! [X3: product_unit] :
% 0.19/0.43 ( ( member_Product_unit @ X3 @ S )
% 0.19/0.43 => ( Phi @ X3 ) )
% 0.19/0.43 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ S ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % RES_rule
% 0.19/0.43 thf(fact_5_RES__rule,axiom,
% 0.19/0.43 ! [S: set_a,Phi: a > $o] :
% 0.19/0.43 ( ! [X3: a] :
% 0.19/0.43 ( ( member_a @ X3 @ S )
% 0.19/0.43 => ( Phi @ X3 ) )
% 0.19/0.43 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % RES_rule
% 0.19/0.43 thf(fact_6_SPEC__rule,axiom,
% 0.19/0.43 ! [Phi: product_unit > $o,Phi2: product_unit > $o] :
% 0.19/0.43 ( ! [X3: product_unit] :
% 0.19/0.43 ( ( Phi @ X3 )
% 0.19/0.43 => ( Phi2 @ X3 ) )
% 0.19/0.43 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % SPEC_rule
% 0.19/0.43 thf(fact_7_SPEC__rule,axiom,
% 0.19/0.43 ! [Phi: a > $o,Phi2: a > $o] :
% 0.19/0.43 ( ! [X3: a] :
% 0.19/0.43 ( ( Phi @ X3 )
% 0.19/0.43 => ( Phi2 @ X3 ) )
% 0.19/0.43 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % SPEC_rule
% 0.19/0.43 thf(fact_8_SPEC__trans,axiom,
% 0.19/0.43 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit,Postcond: product_unit > $o] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 0.19/0.43 => ( ( ord_le1051254044t_unit @ Y3 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) )
% 0.19/0.43 => ( ord_le1051254044t_unit @ X4 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % SPEC_trans
% 0.19/0.43 thf(fact_9_SPEC__trans,axiom,
% 0.19/0.43 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Postcond: a > $o] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.19/0.43 => ( ( ord_le519537037nres_a @ Y3 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 0.19/0.43 => ( ord_le519537037nres_a @ X4 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % SPEC_trans
% 0.19/0.43 thf(fact_10_SPEC__cons__rule,axiom,
% 0.19/0.43 ! [M: refine787176636t_unit,Phi: product_unit > $o,Psi: product_unit > $o] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) )
% 0.19/0.43 => ( ! [X3: product_unit] :
% 0.19/0.43 ( ( Phi @ X3 )
% 0.19/0.43 => ( Psi @ X3 ) )
% 0.19/0.43 => ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Psi ) ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % SPEC_cons_rule
% 0.19/0.43 thf(fact_11_SPEC__cons__rule,axiom,
% 0.19/0.43 ! [M: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.19/0.43 => ( ! [X3: a] :
% 0.19/0.43 ( ( Phi @ X3 )
% 0.19/0.43 => ( Psi @ X3 ) )
% 0.19/0.43 => ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % SPEC_cons_rule
% 0.19/0.43 thf(fact_12_nf__inres__RES,axiom,
% 0.19/0.43 ! [X: set_Product_unit,X4: product_unit] :
% 0.19/0.43 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ X ) @ X4 )
% 0.19/0.43 = ( member_Product_unit @ X4 @ X ) ) ).
% 0.19/0.43
% 0.19/0.43 % nf_inres_RES
% 0.19/0.43 thf(fact_13_nf__inres__RES,axiom,
% 0.19/0.43 ! [X: set_a,X4: a] :
% 0.19/0.43 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X ) @ X4 )
% 0.19/0.43 = ( member_a @ X4 @ X ) ) ).
% 0.19/0.43
% 0.19/0.43 % nf_inres_RES
% 0.19/0.43 thf(fact_14_nf__inres__SPEC,axiom,
% 0.19/0.43 ! [Phi: product_unit > $o,X4: product_unit] :
% 0.19/0.43 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ X4 )
% 0.19/0.43 = ( Phi @ X4 ) ) ).
% 0.19/0.43
% 0.19/0.43 % nf_inres_SPEC
% 0.19/0.43 thf(fact_15_nf__inres__SPEC,axiom,
% 0.19/0.43 ! [Phi: a > $o,X4: a] :
% 0.19/0.43 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ X4 )
% 0.19/0.43 = ( Phi @ X4 ) ) ).
% 0.19/0.43
% 0.19/0.43 % nf_inres_SPEC
% 0.19/0.43 thf(fact_16_order__mono__setup_Orefl,axiom,
% 0.19/0.43 ! [X4: set_a] : ( ord_less_eq_set_a @ X4 @ X4 ) ).
% 0.19/0.43
% 0.19/0.43 % order_mono_setup.refl
% 0.19/0.43 thf(fact_17_order__mono__setup_Orefl,axiom,
% 0.19/0.43 ! [X4: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ X4 @ X4 ) ).
% 0.19/0.43
% 0.19/0.43 % order_mono_setup.refl
% 0.19/0.43 thf(fact_18_order__mono__setup_Orefl,axiom,
% 0.19/0.43 ! [X4: refine787176636t_unit] : ( ord_le1051254044t_unit @ X4 @ X4 ) ).
% 0.19/0.43
% 0.19/0.43 % order_mono_setup.refl
% 0.19/0.43 thf(fact_19_order__mono__setup_Orefl,axiom,
% 0.19/0.43 ! [X4: refine424419629nres_a] : ( ord_le519537037nres_a @ X4 @ X4 ) ).
% 0.19/0.43
% 0.19/0.43 % order_mono_setup.refl
% 0.19/0.43 thf(fact_20_the__RES_Osimps,axiom,
% 0.19/0.43 ! [X: set_Product_unit] :
% 0.19/0.43 ( ( refine1208325748t_unit @ ( refine1777164439t_unit @ X ) )
% 0.19/0.43 = X ) ).
% 0.19/0.43
% 0.19/0.43 % the_RES.simps
% 0.19/0.43 thf(fact_21_the__RES_Osimps,axiom,
% 0.19/0.43 ! [X: set_a] :
% 0.19/0.43 ( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ X ) )
% 0.19/0.43 = X ) ).
% 0.19/0.43
% 0.19/0.43 % the_RES.simps
% 0.19/0.43 thf(fact_22_nres__order__simps_I21_J,axiom,
% 0.19/0.43 ! [X4: product_unit,Y: set_Product_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X4 ) @ ( refine1777164439t_unit @ Y ) )
% 0.19/0.43 = ( member_Product_unit @ X4 @ Y ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_order_simps(21)
% 0.19/0.43 thf(fact_23_nres__order__simps_I21_J,axiom,
% 0.19/0.43 ! [X4: a,Y: set_a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ Y ) )
% 0.19/0.43 = ( member_a @ X4 @ Y ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_order_simps(21)
% 0.19/0.43 thf(fact_24_le__funD,axiom,
% 0.19/0.43 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 0.19/0.43 ( ( ord_le516598614nres_a @ F @ G )
% 0.19/0.43 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % le_funD
% 0.19/0.43 thf(fact_25_le__funE,axiom,
% 0.19/0.43 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 0.19/0.43 ( ( ord_le516598614nres_a @ F @ G )
% 0.19/0.43 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % le_funE
% 0.19/0.43 thf(fact_26_le__funI,axiom,
% 0.19/0.43 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a] :
% 0.19/0.43 ( ! [X3: $o] : ( ord_le519537037nres_a @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.19/0.43 => ( ord_le516598614nres_a @ F @ G ) ) ).
% 0.19/0.43
% 0.19/0.43 % le_funI
% 0.19/0.43 thf(fact_27_Refine__Misc_Oif__mono,axiom,
% 0.19/0.43 ! [B: $o,M1: set_a,M12: set_a,M2: set_a,M22: set_a] :
% 0.19/0.43 ( ( B
% 0.19/0.43 => ( ord_less_eq_set_a @ M1 @ M12 ) )
% 0.19/0.43 => ( ( ~ B
% 0.19/0.43 => ( ord_less_eq_set_a @ M2 @ M22 ) )
% 0.19/0.43 => ( ord_less_eq_set_a @ ( if_set_a @ B @ M1 @ M2 ) @ ( if_set_a @ B @ M12 @ M22 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % Refine_Misc.if_mono
% 0.19/0.43 thf(fact_28_Refine__Misc_Oif__mono,axiom,
% 0.19/0.43 ! [B: $o,M1: $o > refine424419629nres_a,M12: $o > refine424419629nres_a,M2: $o > refine424419629nres_a,M22: $o > refine424419629nres_a] :
% 0.19/0.43 ( ( B
% 0.19/0.43 => ( ord_le516598614nres_a @ M1 @ M12 ) )
% 0.19/0.43 => ( ( ~ B
% 0.19/0.43 => ( ord_le516598614nres_a @ M2 @ M22 ) )
% 0.19/0.43 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B @ M1 @ M2 ) @ ( if_o_R1705037948nres_a @ B @ M12 @ M22 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % Refine_Misc.if_mono
% 0.19/0.43 thf(fact_29_Refine__Misc_Oif__mono,axiom,
% 0.19/0.43 ! [B: $o,M1: refine787176636t_unit,M12: refine787176636t_unit,M2: refine787176636t_unit,M22: refine787176636t_unit] :
% 0.19/0.43 ( ( B
% 0.19/0.43 => ( ord_le1051254044t_unit @ M1 @ M12 ) )
% 0.19/0.43 => ( ( ~ B
% 0.19/0.43 => ( ord_le1051254044t_unit @ M2 @ M22 ) )
% 0.19/0.43 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ M1 @ M2 ) @ ( if_Ref1369692790t_unit @ B @ M12 @ M22 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % Refine_Misc.if_mono
% 0.19/0.43 thf(fact_30_Refine__Misc_Oif__mono,axiom,
% 0.19/0.43 ! [B: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M2: refine424419629nres_a,M22: refine424419629nres_a] :
% 0.19/0.43 ( ( B
% 0.19/0.43 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 0.19/0.43 => ( ( ~ B
% 0.19/0.43 => ( ord_le519537037nres_a @ M2 @ M22 ) )
% 0.19/0.43 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ M1 @ M2 ) @ ( if_Ref1724547303nres_a @ B @ M12 @ M22 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % Refine_Misc.if_mono
% 0.19/0.43 thf(fact_31_le__fun__def,axiom,
% 0.19/0.43 ( ord_le516598614nres_a
% 0.19/0.43 = ( ^ [F2: $o > refine424419629nres_a,G2: $o > refine424419629nres_a] :
% 0.19/0.43 ! [X5: $o] : ( ord_le519537037nres_a @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % le_fun_def
% 0.19/0.43 thf(fact_32_nres__more__simps_I6_J,axiom,
% 0.19/0.43 ! [X4: a,Y3: a] :
% 0.19/0.43 ( ( ( refine2063221604TURN_a @ X4 )
% 0.19/0.43 = ( refine2063221604TURN_a @ Y3 ) )
% 0.19/0.43 = ( X4 = Y3 ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_more_simps(6)
% 0.19/0.43 thf(fact_33_nres__more__simps_I6_J,axiom,
% 0.19/0.43 ! [X4: product_unit,Y3: product_unit] :
% 0.19/0.43 ( ( ( refine1420258419t_unit @ X4 )
% 0.19/0.43 = ( refine1420258419t_unit @ Y3 ) )
% 0.19/0.43 = ( X4 = Y3 ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_more_simps(6)
% 0.19/0.43 thf(fact_34_nres__order__simps_I20_J,axiom,
% 0.19/0.43 ! [X4: product_unit,Y3: product_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X4 ) @ ( refine1420258419t_unit @ Y3 ) )
% 0.19/0.43 = ( X4 = Y3 ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_order_simps(20)
% 0.19/0.43 thf(fact_35_nres__order__simps_I20_J,axiom,
% 0.19/0.43 ! [X4: a,Y3: a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine2063221604TURN_a @ Y3 ) )
% 0.19/0.43 = ( X4 = Y3 ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_order_simps(20)
% 0.19/0.43 thf(fact_36_less__eq__nres_Osimps_I2_J,axiom,
% 0.19/0.43 ! [A: set_Product_unit,B: set_Product_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1777164439t_unit @ B ) )
% 0.19/0.43 = ( ord_le1023748749t_unit @ A @ B ) ) ).
% 0.19/0.43
% 0.19/0.43 % less_eq_nres.simps(2)
% 0.19/0.43 thf(fact_37_less__eq__nres_Osimps_I2_J,axiom,
% 0.19/0.43 ! [A: set_a,B: set_a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 0.19/0.43 = ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.19/0.43
% 0.19/0.43 % less_eq_nres.simps(2)
% 0.19/0.43 thf(fact_38_nres__order__simps_I5_J,axiom,
% 0.19/0.43 ! [X: set_Product_unit,Y: set_Product_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ X ) @ ( refine1777164439t_unit @ Y ) )
% 0.19/0.43 = ( ord_le1023748749t_unit @ X @ Y ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_order_simps(5)
% 0.19/0.43 thf(fact_39_nres__order__simps_I5_J,axiom,
% 0.19/0.43 ! [X: set_a,Y: set_a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine1198353288_RES_a @ Y ) )
% 0.19/0.43 = ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.19/0.43
% 0.19/0.43 % nres_order_simps(5)
% 0.19/0.43 thf(fact_40_RETURN__to__SPEC__rule,axiom,
% 0.19/0.43 ! [M: refine787176636t_unit,V: product_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ M
% 0.19/0.43 @ ( refine1777164439t_unit
% 0.19/0.43 @ ( collect_Product_unit
% 0.19/0.43 @ ( ^ [Y4: product_unit,Z: product_unit] : ( Y4 = Z )
% 0.19/0.43 @ V ) ) ) )
% 0.19/0.43 => ( ord_le1051254044t_unit @ M @ ( refine1420258419t_unit @ V ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % RETURN_to_SPEC_rule
% 0.19/0.43 thf(fact_41_RETURN__to__SPEC__rule,axiom,
% 0.19/0.43 ! [M: refine424419629nres_a,V: a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ M
% 0.19/0.43 @ ( refine1198353288_RES_a
% 0.19/0.43 @ ( collect_a
% 0.19/0.43 @ ( ^ [Y4: a,Z: a] : ( Y4 = Z )
% 0.19/0.43 @ V ) ) ) )
% 0.19/0.43 => ( ord_le519537037nres_a @ M @ ( refine2063221604TURN_a @ V ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % RETURN_to_SPEC_rule
% 0.19/0.43 thf(fact_42_RETURN__rule,axiom,
% 0.19/0.43 ! [Phi: product_unit > $o,X4: product_unit] :
% 0.19/0.43 ( ( Phi @ X4 )
% 0.19/0.43 => ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X4 ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % RETURN_rule
% 0.19/0.43 thf(fact_43_RETURN__rule,axiom,
% 0.19/0.43 ! [Phi: a > $o,X4: a] :
% 0.19/0.43 ( ( Phi @ X4 )
% 0.19/0.43 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % RETURN_rule
% 0.19/0.43 thf(fact_44_order__mono__setup_Omono__if,axiom,
% 0.19/0.43 ! [T: set_a,T2: set_a,E: set_a,E2: set_a,B: $o] :
% 0.19/0.43 ( ( ord_less_eq_set_a @ T @ T2 )
% 0.19/0.43 => ( ( ord_less_eq_set_a @ E @ E2 )
% 0.19/0.43 => ( ord_less_eq_set_a @ ( if_set_a @ B @ T @ E ) @ ( if_set_a @ B @ T2 @ E2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_mono_setup.mono_if
% 0.19/0.43 thf(fact_45_order__mono__setup_Omono__if,axiom,
% 0.19/0.43 ! [T: $o > refine424419629nres_a,T2: $o > refine424419629nres_a,E: $o > refine424419629nres_a,E2: $o > refine424419629nres_a,B: $o] :
% 0.19/0.43 ( ( ord_le516598614nres_a @ T @ T2 )
% 0.19/0.43 => ( ( ord_le516598614nres_a @ E @ E2 )
% 0.19/0.43 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B @ T @ E ) @ ( if_o_R1705037948nres_a @ B @ T2 @ E2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_mono_setup.mono_if
% 0.19/0.43 thf(fact_46_order__mono__setup_Omono__if,axiom,
% 0.19/0.43 ! [T: refine787176636t_unit,T2: refine787176636t_unit,E: refine787176636t_unit,E2: refine787176636t_unit,B: $o] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ T @ T2 )
% 0.19/0.43 => ( ( ord_le1051254044t_unit @ E @ E2 )
% 0.19/0.43 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ T @ E ) @ ( if_Ref1369692790t_unit @ B @ T2 @ E2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_mono_setup.mono_if
% 0.19/0.43 thf(fact_47_order__mono__setup_Omono__if,axiom,
% 0.19/0.43 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B: $o] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ T @ T2 )
% 0.19/0.43 => ( ( ord_le519537037nres_a @ E @ E2 )
% 0.19/0.43 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ ( if_Ref1724547303nres_a @ B @ T2 @ E2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_mono_setup.mono_if
% 0.19/0.43 thf(fact_48_dual__order_Oantisym,axiom,
% 0.19/0.43 ! [B: set_a,A: set_a] :
% 0.19/0.43 ( ( ord_less_eq_set_a @ B @ A )
% 0.19/0.43 => ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.43 => ( A = B ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.antisym
% 0.19/0.43 thf(fact_49_dual__order_Oantisym,axiom,
% 0.19/0.43 ! [B: $o > refine424419629nres_a,A: $o > refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le516598614nres_a @ B @ A )
% 0.19/0.43 => ( ( ord_le516598614nres_a @ A @ B )
% 0.19/0.43 => ( A = B ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.antisym
% 0.19/0.43 thf(fact_50_dual__order_Oantisym,axiom,
% 0.19/0.43 ! [B: refine787176636t_unit,A: refine787176636t_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ B @ A )
% 0.19/0.43 => ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.43 => ( A = B ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.antisym
% 0.19/0.43 thf(fact_51_dual__order_Oantisym,axiom,
% 0.19/0.43 ! [B: refine424419629nres_a,A: refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ B @ A )
% 0.19/0.43 => ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.43 => ( A = B ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.antisym
% 0.19/0.43 thf(fact_52_dual__order_Oeq__iff,axiom,
% 0.19/0.43 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.19/0.43 = ( ^ [A2: set_a,B2: set_a] :
% 0.19/0.43 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.19/0.43 & ( ord_less_eq_set_a @ A2 @ B2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.eq_iff
% 0.19/0.43 thf(fact_53_dual__order_Oeq__iff,axiom,
% 0.19/0.43 ( ( ^ [Y4: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y4 = Z ) )
% 0.19/0.43 = ( ^ [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le516598614nres_a @ B2 @ A2 )
% 0.19/0.43 & ( ord_le516598614nres_a @ A2 @ B2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.eq_iff
% 0.19/0.43 thf(fact_54_dual__order_Oeq__iff,axiom,
% 0.19/0.43 ( ( ^ [Y4: refine787176636t_unit,Z: refine787176636t_unit] : ( Y4 = Z ) )
% 0.19/0.43 = ( ^ [A2: refine787176636t_unit,B2: refine787176636t_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ B2 @ A2 )
% 0.19/0.43 & ( ord_le1051254044t_unit @ A2 @ B2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.eq_iff
% 0.19/0.43 thf(fact_55_dual__order_Oeq__iff,axiom,
% 0.19/0.43 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 0.19/0.43 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.19/0.43 & ( ord_le519537037nres_a @ A2 @ B2 ) ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.eq_iff
% 0.19/0.43 thf(fact_56_dual__order_Otrans,axiom,
% 0.19/0.43 ! [B: set_a,A: set_a,C: set_a] :
% 0.19/0.43 ( ( ord_less_eq_set_a @ B @ A )
% 0.19/0.43 => ( ( ord_less_eq_set_a @ C @ B )
% 0.19/0.43 => ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.trans
% 0.19/0.43 thf(fact_57_dual__order_Otrans,axiom,
% 0.19/0.43 ! [B: $o > refine424419629nres_a,A: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le516598614nres_a @ B @ A )
% 0.19/0.43 => ( ( ord_le516598614nres_a @ C @ B )
% 0.19/0.43 => ( ord_le516598614nres_a @ C @ A ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.trans
% 0.19/0.43 thf(fact_58_dual__order_Otrans,axiom,
% 0.19/0.43 ! [B: refine787176636t_unit,A: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ B @ A )
% 0.19/0.43 => ( ( ord_le1051254044t_unit @ C @ B )
% 0.19/0.43 => ( ord_le1051254044t_unit @ C @ A ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.trans
% 0.19/0.43 thf(fact_59_dual__order_Otrans,axiom,
% 0.19/0.43 ! [B: refine424419629nres_a,A: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ B @ A )
% 0.19/0.43 => ( ( ord_le519537037nres_a @ C @ B )
% 0.19/0.43 => ( ord_le519537037nres_a @ C @ A ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.trans
% 0.19/0.43 thf(fact_60_dual__order_Orefl,axiom,
% 0.19/0.43 ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.refl
% 0.19/0.43 thf(fact_61_dual__order_Orefl,axiom,
% 0.19/0.43 ! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ A ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.refl
% 0.19/0.43 thf(fact_62_dual__order_Orefl,axiom,
% 0.19/0.43 ! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ A ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.refl
% 0.19/0.43 thf(fact_63_dual__order_Orefl,axiom,
% 0.19/0.43 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ) ).
% 0.19/0.43
% 0.19/0.43 % dual_order.refl
% 0.19/0.43 thf(fact_64_order__trans,axiom,
% 0.19/0.43 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 0.19/0.43 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 0.19/0.43 => ( ( ord_less_eq_set_a @ Y3 @ Z2 )
% 0.19/0.43 => ( ord_less_eq_set_a @ X4 @ Z2 ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_trans
% 0.19/0.43 thf(fact_65_order__trans,axiom,
% 0.19/0.43 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a,Z2: $o > refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le516598614nres_a @ X4 @ Y3 )
% 0.19/0.43 => ( ( ord_le516598614nres_a @ Y3 @ Z2 )
% 0.19/0.43 => ( ord_le516598614nres_a @ X4 @ Z2 ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_trans
% 0.19/0.43 thf(fact_66_order__trans,axiom,
% 0.19/0.43 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit,Z2: refine787176636t_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 0.19/0.43 => ( ( ord_le1051254044t_unit @ Y3 @ Z2 )
% 0.19/0.43 => ( ord_le1051254044t_unit @ X4 @ Z2 ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_trans
% 0.19/0.43 thf(fact_67_order__trans,axiom,
% 0.19/0.43 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.19/0.43 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 0.19/0.43 => ( ord_le519537037nres_a @ X4 @ Z2 ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_trans
% 0.19/0.43 thf(fact_68_order__class_Oorder_Oantisym,axiom,
% 0.19/0.43 ! [A: set_a,B: set_a] :
% 0.19/0.43 ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.43 => ( ( ord_less_eq_set_a @ B @ A )
% 0.19/0.43 => ( A = B ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_class.order.antisym
% 0.19/0.43 thf(fact_69_order__class_Oorder_Oantisym,axiom,
% 0.19/0.43 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le516598614nres_a @ A @ B )
% 0.19/0.43 => ( ( ord_le516598614nres_a @ B @ A )
% 0.19/0.43 => ( A = B ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_class.order.antisym
% 0.19/0.43 thf(fact_70_order__class_Oorder_Oantisym,axiom,
% 0.19/0.43 ! [A: refine787176636t_unit,B: refine787176636t_unit] :
% 0.19/0.43 ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.43 => ( ( ord_le1051254044t_unit @ B @ A )
% 0.19/0.43 => ( A = B ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_class.order.antisym
% 0.19/0.43 thf(fact_71_order__class_Oorder_Oantisym,axiom,
% 0.19/0.43 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.19/0.43 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.43 => ( ( ord_le519537037nres_a @ B @ A )
% 0.19/0.43 => ( A = B ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % order_class.order.antisym
% 0.19/0.43 thf(fact_72_ord__le__eq__trans,axiom,
% 0.19/0.43 ! [A: set_a,B: set_a,C: set_a] :
% 0.19/0.43 ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.43 => ( ( B = C )
% 0.19/0.43 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.19/0.43
% 0.19/0.43 % ord_le_eq_trans
% 0.19/0.43 thf(fact_73_ord__le__eq__trans,axiom,
% 0.19/0.44 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le516598614nres_a @ A @ B )
% 0.19/0.44 => ( ( B = C )
% 0.19/0.44 => ( ord_le516598614nres_a @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_trans
% 0.19/0.44 thf(fact_74_ord__le__eq__trans,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.44 => ( ( B = C )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_trans
% 0.19/0.44 thf(fact_75_ord__le__eq__trans,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( B = C )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_trans
% 0.19/0.44 thf(fact_76_ord__eq__le__trans,axiom,
% 0.19/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.19/0.44 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_trans
% 0.19/0.44 thf(fact_77_ord__eq__le__trans,axiom,
% 0.19/0.44 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( ord_le516598614nres_a @ B @ C )
% 0.19/0.44 => ( ord_le516598614nres_a @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_trans
% 0.19/0.44 thf(fact_78_ord__eq__le__trans,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_trans
% 0.19/0.44 thf(fact_79_ord__eq__le__trans,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_trans
% 0.19/0.44 thf(fact_80_order__class_Oorder_Oeq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [A2: set_a,B2: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.19/0.44 & ( ord_less_eq_set_a @ B2 @ A2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_class.order.eq_iff
% 0.19/0.44 thf(fact_81_order__class_Oorder_Oeq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 0.19/0.44 & ( ord_le516598614nres_a @ B2 @ A2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_class.order.eq_iff
% 0.19/0.44 thf(fact_82_order__class_Oorder_Oeq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: refine787176636t_unit,Z: refine787176636t_unit] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [A2: refine787176636t_unit,B2: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 0.19/0.44 & ( ord_le1051254044t_unit @ B2 @ A2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_class.order.eq_iff
% 0.19/0.44 thf(fact_83_order__class_Oorder_Oeq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.19/0.44 & ( ord_le519537037nres_a @ B2 @ A2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_class.order.eq_iff
% 0.19/0.44 thf(fact_84_antisym__conv,axiom,
% 0.19/0.44 ! [Y3: set_a,X4: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 0.19/0.44 = ( X4 = Y3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % antisym_conv
% 0.19/0.44 thf(fact_85_antisym__conv,axiom,
% 0.19/0.44 ! [Y3: $o > refine424419629nres_a,X4: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le516598614nres_a @ Y3 @ X4 )
% 0.19/0.44 => ( ( ord_le516598614nres_a @ X4 @ Y3 )
% 0.19/0.44 = ( X4 = Y3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % antisym_conv
% 0.19/0.44 thf(fact_86_antisym__conv,axiom,
% 0.19/0.44 ! [Y3: refine787176636t_unit,X4: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ Y3 @ X4 )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 0.19/0.44 = ( X4 = Y3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % antisym_conv
% 0.19/0.44 thf(fact_87_antisym__conv,axiom,
% 0.19/0.44 ! [Y3: refine424419629nres_a,X4: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.19/0.44 = ( X4 = Y3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % antisym_conv
% 0.19/0.44 thf(fact_88_order_Otrans,axiom,
% 0.19/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.19/0.44 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order.trans
% 0.19/0.44 thf(fact_89_order_Otrans,axiom,
% 0.19/0.44 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le516598614nres_a @ A @ B )
% 0.19/0.44 => ( ( ord_le516598614nres_a @ B @ C )
% 0.19/0.44 => ( ord_le516598614nres_a @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order.trans
% 0.19/0.44 thf(fact_90_order_Otrans,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order.trans
% 0.19/0.44 thf(fact_91_order_Otrans,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order.trans
% 0.19/0.44 thf(fact_92_eq__refl,axiom,
% 0.19/0.44 ! [X4: set_a,Y3: set_a] :
% 0.19/0.44 ( ( X4 = Y3 )
% 0.19/0.44 => ( ord_less_eq_set_a @ X4 @ Y3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % eq_refl
% 0.19/0.44 thf(fact_93_eq__refl,axiom,
% 0.19/0.44 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( X4 = Y3 )
% 0.19/0.44 => ( ord_le516598614nres_a @ X4 @ Y3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % eq_refl
% 0.19/0.44 thf(fact_94_eq__refl,axiom,
% 0.19/0.44 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.19/0.44 ( ( X4 = Y3 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ X4 @ Y3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % eq_refl
% 0.19/0.44 thf(fact_95_eq__refl,axiom,
% 0.19/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.19/0.44 ( ( X4 = Y3 )
% 0.19/0.44 => ( ord_le519537037nres_a @ X4 @ Y3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % eq_refl
% 0.19/0.44 thf(fact_96_antisym,axiom,
% 0.19/0.44 ! [X4: set_a,Y3: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 0.19/0.44 => ( X4 = Y3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % antisym
% 0.19/0.44 thf(fact_97_antisym,axiom,
% 0.19/0.44 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le516598614nres_a @ X4 @ Y3 )
% 0.19/0.44 => ( ( ord_le516598614nres_a @ Y3 @ X4 )
% 0.19/0.44 => ( X4 = Y3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % antisym
% 0.19/0.44 thf(fact_98_antisym,axiom,
% 0.19/0.44 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ Y3 @ X4 )
% 0.19/0.44 => ( X4 = Y3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % antisym
% 0.19/0.44 thf(fact_99_antisym,axiom,
% 0.19/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 0.19/0.44 => ( X4 = Y3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % antisym
% 0.19/0.44 thf(fact_100_eq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [X5: set_a,Y5: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.19/0.44 & ( ord_less_eq_set_a @ Y5 @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % eq_iff
% 0.19/0.44 thf(fact_101_eq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [X5: $o > refine424419629nres_a,Y5: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le516598614nres_a @ X5 @ Y5 )
% 0.19/0.44 & ( ord_le516598614nres_a @ Y5 @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % eq_iff
% 0.19/0.44 thf(fact_102_eq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: refine787176636t_unit,Z: refine787176636t_unit] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [X5: refine787176636t_unit,Y5: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X5 @ Y5 )
% 0.19/0.44 & ( ord_le1051254044t_unit @ Y5 @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % eq_iff
% 0.19/0.44 thf(fact_103_eq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.19/0.44 & ( ord_le519537037nres_a @ Y5 @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % eq_iff
% 0.19/0.44 thf(fact_104_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_105_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_106_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_107_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: set_a,B: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_108_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_109_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: set_a,B: set_a,F: set_a > refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_110_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_111_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > set_a,C: set_a] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_112_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_113_ord__le__eq__subst,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( ( F @ B )
% 0.19/0.44 = C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le516598614nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le516598614nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_le_eq_subst
% 0.19/0.44 thf(fact_114_mem__Collect__eq,axiom,
% 0.19/0.44 ! [A: product_unit,P: product_unit > $o] :
% 0.19/0.44 ( ( member_Product_unit @ A @ ( collect_Product_unit @ P ) )
% 0.19/0.44 = ( P @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % mem_Collect_eq
% 0.19/0.44 thf(fact_115_mem__Collect__eq,axiom,
% 0.19/0.44 ! [A: a,P: a > $o] :
% 0.19/0.44 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.19/0.44 = ( P @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % mem_Collect_eq
% 0.19/0.44 thf(fact_116_Collect__mem__eq,axiom,
% 0.19/0.44 ! [A3: set_Product_unit] :
% 0.19/0.44 ( ( collect_Product_unit
% 0.19/0.44 @ ^ [X5: product_unit] : ( member_Product_unit @ X5 @ A3 ) )
% 0.19/0.44 = A3 ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mem_eq
% 0.19/0.44 thf(fact_117_Collect__mem__eq,axiom,
% 0.19/0.44 ! [A3: set_a] :
% 0.19/0.44 ( ( collect_a
% 0.19/0.44 @ ^ [X5: a] : ( member_a @ X5 @ A3 ) )
% 0.19/0.44 = A3 ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mem_eq
% 0.19/0.44 thf(fact_118_Collect__cong,axiom,
% 0.19/0.44 ! [P: product_unit > $o,Q: product_unit > $o] :
% 0.19/0.44 ( ! [X3: product_unit] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 = ( Q @ X3 ) )
% 0.19/0.44 => ( ( collect_Product_unit @ P )
% 0.19/0.44 = ( collect_Product_unit @ Q ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_cong
% 0.19/0.44 thf(fact_119_Collect__cong,axiom,
% 0.19/0.44 ! [P: a > $o,Q: a > $o] :
% 0.19/0.44 ( ! [X3: a] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 = ( Q @ X3 ) )
% 0.19/0.44 => ( ( collect_a @ P )
% 0.19/0.44 = ( collect_a @ Q ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_cong
% 0.19/0.44 thf(fact_120_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_121_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: set_a,F: refine424419629nres_a > set_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_122_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,F: refine424419629nres_a > refine787176636t_unit,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_123_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,F: set_a > refine424419629nres_a,B: set_a,C: set_a] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_124_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_125_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,F: set_a > refine787176636t_unit,B: set_a,C: set_a] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_126_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,F: refine787176636t_unit > refine424419629nres_a,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_127_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: set_a,F: refine787176636t_unit > set_a,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_128_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_129_ord__eq__le__subst,axiom,
% 0.19/0.44 ! [A: $o > refine424419629nres_a,F: refine424419629nres_a > $o > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( A
% 0.19/0.44 = ( F @ B ) )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le516598614nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le516598614nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_subst
% 0.19/0.44 thf(fact_130_order__subst2,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_131_order__subst2,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_132_order__subst2,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_133_order__subst2,axiom,
% 0.19/0.44 ! [A: set_a,B: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_134_order__subst2,axiom,
% 0.19/0.44 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_135_order__subst2,axiom,
% 0.19/0.44 ! [A: set_a,B: set_a,F: set_a > refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_136_order__subst2,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_137_order__subst2,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > set_a,C: set_a] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_138_order__subst2,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ B )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_139_order__subst2,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.19/0.44 => ( ( ord_le516598614nres_a @ ( F @ B ) @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le516598614nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le516598614nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst2
% 0.19/0.44 thf(fact_140_order__subst1,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_141_order__subst1,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,F: set_a > refine424419629nres_a,B: set_a,C: set_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_142_order__subst1,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,F: refine787176636t_unit > refine424419629nres_a,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_143_order__subst1,axiom,
% 0.19/0.44 ! [A: set_a,F: refine424419629nres_a > set_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_144_order__subst1,axiom,
% 0.19/0.44 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_145_order__subst1,axiom,
% 0.19/0.44 ! [A: set_a,F: refine787176636t_unit > set_a,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_146_order__subst1,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,F: refine424419629nres_a > refine787176636t_unit,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_147_order__subst1,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,F: set_a > refine787176636t_unit,B: set_a,C: set_a] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.19/0.44 => ( ! [X3: set_a,Y6: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_148_order__subst1,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_149_order__subst1,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,F: ( $o > refine424419629nres_a ) > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.19/0.44 => ( ( ord_le516598614nres_a @ B @ C )
% 0.19/0.44 => ( ! [X3: $o > refine424419629nres_a,Y6: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le516598614nres_a @ X3 @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % order_subst1
% 0.19/0.44 thf(fact_150_the__RES__inv,axiom,
% 0.19/0.44 ! [M: refine787176636t_unit] :
% 0.19/0.44 ( ( refine579265252t_unit @ M )
% 0.19/0.44 => ( ( refine1777164439t_unit @ ( refine1208325748t_unit @ M ) )
% 0.19/0.44 = M ) ) ).
% 0.19/0.44
% 0.19/0.44 % the_RES_inv
% 0.19/0.44 thf(fact_151_the__RES__inv,axiom,
% 0.19/0.44 ! [M: refine424419629nres_a] :
% 0.19/0.44 ( ( refine412683989fail_a @ M )
% 0.19/0.44 => ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ M ) )
% 0.19/0.44 = M ) ) ).
% 0.19/0.44
% 0.19/0.44 % the_RES_inv
% 0.19/0.44 thf(fact_152_Greatest__equality,axiom,
% 0.19/0.44 ! [P: set_a > $o,X4: set_a] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 => ( ! [Y6: set_a] :
% 0.19/0.44 ( ( P @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ Y6 @ X4 ) )
% 0.19/0.44 => ( ( order_Greatest_set_a @ P )
% 0.19/0.44 = X4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Greatest_equality
% 0.19/0.44 thf(fact_153_Greatest__equality,axiom,
% 0.19/0.44 ! [P: ( $o > refine424419629nres_a ) > $o,X4: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 => ( ! [Y6: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( P @ Y6 )
% 0.19/0.44 => ( ord_le516598614nres_a @ Y6 @ X4 ) )
% 0.19/0.44 => ( ( order_245837199nres_a @ P )
% 0.19/0.44 = X4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Greatest_equality
% 0.19/0.44 thf(fact_154_Greatest__equality,axiom,
% 0.19/0.44 ! [P: refine787176636t_unit > $o,X4: refine787176636t_unit] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 => ( ! [Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( P @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ Y6 @ X4 ) )
% 0.19/0.44 => ( ( order_453013155t_unit @ P )
% 0.19/0.44 = X4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Greatest_equality
% 0.19/0.44 thf(fact_155_Greatest__equality,axiom,
% 0.19/0.44 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 => ( ! [Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( P @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ Y6 @ X4 ) )
% 0.19/0.44 => ( ( order_1714329108nres_a @ P )
% 0.19/0.44 = X4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Greatest_equality
% 0.19/0.44 thf(fact_156_GreatestI2__order,axiom,
% 0.19/0.44 ! [P: set_a > $o,X4: set_a,Q: set_a > $o] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 => ( ! [Y6: set_a] :
% 0.19/0.44 ( ( P @ Y6 )
% 0.19/0.44 => ( ord_less_eq_set_a @ Y6 @ X4 ) )
% 0.19/0.44 => ( ! [X3: set_a] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 => ( ! [Y7: set_a] :
% 0.19/0.44 ( ( P @ Y7 )
% 0.19/0.44 => ( ord_less_eq_set_a @ Y7 @ X3 ) )
% 0.19/0.44 => ( Q @ X3 ) ) )
% 0.19/0.44 => ( Q @ ( order_Greatest_set_a @ P ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % GreatestI2_order
% 0.19/0.44 thf(fact_157_GreatestI2__order,axiom,
% 0.19/0.44 ! [P: ( $o > refine424419629nres_a ) > $o,X4: $o > refine424419629nres_a,Q: ( $o > refine424419629nres_a ) > $o] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 => ( ! [Y6: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( P @ Y6 )
% 0.19/0.44 => ( ord_le516598614nres_a @ Y6 @ X4 ) )
% 0.19/0.44 => ( ! [X3: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 => ( ! [Y7: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( P @ Y7 )
% 0.19/0.44 => ( ord_le516598614nres_a @ Y7 @ X3 ) )
% 0.19/0.44 => ( Q @ X3 ) ) )
% 0.19/0.44 => ( Q @ ( order_245837199nres_a @ P ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % GreatestI2_order
% 0.19/0.44 thf(fact_158_GreatestI2__order,axiom,
% 0.19/0.44 ! [P: refine787176636t_unit > $o,X4: refine787176636t_unit,Q: refine787176636t_unit > $o] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 => ( ! [Y6: refine787176636t_unit] :
% 0.19/0.44 ( ( P @ Y6 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ Y6 @ X4 ) )
% 0.19/0.44 => ( ! [X3: refine787176636t_unit] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 => ( ! [Y7: refine787176636t_unit] :
% 0.19/0.44 ( ( P @ Y7 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ Y7 @ X3 ) )
% 0.19/0.44 => ( Q @ X3 ) ) )
% 0.19/0.44 => ( Q @ ( order_453013155t_unit @ P ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % GreatestI2_order
% 0.19/0.44 thf(fact_159_GreatestI2__order,axiom,
% 0.19/0.44 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 => ( ! [Y6: refine424419629nres_a] :
% 0.19/0.44 ( ( P @ Y6 )
% 0.19/0.44 => ( ord_le519537037nres_a @ Y6 @ X4 ) )
% 0.19/0.44 => ( ! [X3: refine424419629nres_a] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 => ( ! [Y7: refine424419629nres_a] :
% 0.19/0.44 ( ( P @ Y7 )
% 0.19/0.44 => ( ord_le519537037nres_a @ Y7 @ X3 ) )
% 0.19/0.44 => ( Q @ X3 ) ) )
% 0.19/0.44 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % GreatestI2_order
% 0.19/0.44 thf(fact_160_le__rel__bool__arg__iff,axiom,
% 0.19/0.44 ( ord_less_eq_o_set_a
% 0.19/0.44 = ( ^ [X6: $o > set_a,Y8: $o > set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 0.19/0.44 & ( ord_less_eq_set_a @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % le_rel_bool_arg_iff
% 0.19/0.44 thf(fact_161_le__rel__bool__arg__iff,axiom,
% 0.19/0.44 ( ord_le1960259811nres_a
% 0.19/0.44 = ( ^ [X6: $o > $o > refine424419629nres_a,Y8: $o > $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le516598614nres_a @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 0.19/0.44 & ( ord_le516598614nres_a @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % le_rel_bool_arg_iff
% 0.19/0.44 thf(fact_162_le__rel__bool__arg__iff,axiom,
% 0.19/0.44 ( ord_le1633311077t_unit
% 0.19/0.44 = ( ^ [X6: $o > refine787176636t_unit,Y8: $o > refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 0.19/0.44 & ( ord_le1051254044t_unit @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % le_rel_bool_arg_iff
% 0.19/0.44 thf(fact_163_le__rel__bool__arg__iff,axiom,
% 0.19/0.44 ( ord_le516598614nres_a
% 0.19/0.44 = ( ^ [X6: $o > refine424419629nres_a,Y8: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 0.19/0.44 & ( ord_le519537037nres_a @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % le_rel_bool_arg_iff
% 0.19/0.44 thf(fact_164_ord__eq__le__eq__trans,axiom,
% 0.19/0.44 ! [A: set_a,B: set_a,C: set_a,D: set_a] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.19/0.44 => ( ( C = D )
% 0.19/0.44 => ( ord_less_eq_set_a @ A @ D ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_eq_trans
% 0.19/0.44 thf(fact_165_ord__eq__le__eq__trans,axiom,
% 0.19/0.44 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a,D: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( ord_le516598614nres_a @ B @ C )
% 0.19/0.44 => ( ( C = D )
% 0.19/0.44 => ( ord_le516598614nres_a @ A @ D ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_eq_trans
% 0.19/0.44 thf(fact_166_ord__eq__le__eq__trans,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( ord_le1051254044t_unit @ B @ C )
% 0.19/0.44 => ( ( C = D )
% 0.19/0.44 => ( ord_le1051254044t_unit @ A @ D ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_eq_trans
% 0.19/0.44 thf(fact_167_ord__eq__le__eq__trans,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.19/0.44 => ( ( C = D )
% 0.19/0.44 => ( ord_le519537037nres_a @ A @ D ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ord_eq_le_eq_trans
% 0.19/0.44 thf(fact_168_bind__cong,axiom,
% 0.19/0.44 ! [M: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine424419629nres_a,F3: a > refine424419629nres_a] :
% 0.19/0.44 ( ( M = M3 )
% 0.19/0.44 => ( ! [X3: a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M3 )
% 0.19/0.44 => ( ( F @ X3 )
% 0.19/0.44 = ( F3 @ X3 ) ) )
% 0.19/0.44 => ( ( refine436832838nd_a_a @ M @ F )
% 0.19/0.44 = ( refine436832838nd_a_a @ M3 @ F3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % bind_cong
% 0.19/0.44 thf(fact_169_bind__cong,axiom,
% 0.19/0.44 ! [M: refine787176636t_unit,M3: refine787176636t_unit,F: product_unit > refine787176636t_unit,F3: product_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( M = M3 )
% 0.19/0.44 => ( ! [X3: product_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ M3 )
% 0.19/0.44 => ( ( F @ X3 )
% 0.19/0.44 = ( F3 @ X3 ) ) )
% 0.19/0.44 => ( ( refine681446406t_unit @ M @ F )
% 0.19/0.44 = ( refine681446406t_unit @ M3 @ F3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % bind_cong
% 0.19/0.44 thf(fact_170_bind__cong,axiom,
% 0.19/0.44 ! [M: refine787176636t_unit,M3: refine787176636t_unit,F: product_unit > refine424419629nres_a,F3: product_unit > refine424419629nres_a] :
% 0.19/0.44 ( ( M = M3 )
% 0.19/0.44 => ( ! [X3: product_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ M3 )
% 0.19/0.44 => ( ( F @ X3 )
% 0.19/0.44 = ( F3 @ X3 ) ) )
% 0.19/0.44 => ( ( refine119808503unit_a @ M @ F )
% 0.19/0.44 = ( refine119808503unit_a @ M3 @ F3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % bind_cong
% 0.19/0.44 thf(fact_171_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a,M5: refine424419629nres_a,F: a > refine787176636t_unit,F3: a > refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ M4 @ M5 )
% 0.19/0.44 => ( ! [X3: a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M4 @ F ) @ ( refine96995669t_unit @ M5 @ F3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.19/0.44 thf(fact_172_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.19/0.44 ! [M4: refine787176636t_unit,M5: refine787176636t_unit,F: product_unit > refine787176636t_unit,F3: product_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ M4 @ M5 )
% 0.19/0.44 => ( ! [X3: product_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ M4 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M4 @ F ) @ ( refine681446406t_unit @ M5 @ F3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.19/0.44 thf(fact_173_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.19/0.44 ! [M4: refine787176636t_unit,M5: refine787176636t_unit,F: product_unit > refine424419629nres_a,F3: product_unit > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ M4 @ M5 )
% 0.19/0.44 => ( ! [X3: product_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ M4 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( refine119808503unit_a @ M4 @ F ) @ ( refine119808503unit_a @ M5 @ F3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.19/0.44 thf(fact_174_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a,M5: refine424419629nres_a,F: a > refine424419629nres_a,F3: a > refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ M4 @ M5 )
% 0.19/0.44 => ( ! [X3: a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine436832838nd_a_a @ M5 @ F3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.19/0.44 thf(fact_175_nofail__simps_I2_J,axiom,
% 0.19/0.44 ! [X: set_Product_unit] : ( refine579265252t_unit @ ( refine1777164439t_unit @ X ) ) ).
% 0.19/0.44
% 0.19/0.44 % nofail_simps(2)
% 0.19/0.44 thf(fact_176_nofail__simps_I2_J,axiom,
% 0.19/0.44 ! [X: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X ) ) ).
% 0.19/0.44
% 0.19/0.44 % nofail_simps(2)
% 0.19/0.44 thf(fact_177_nofail__simps_I3_J,axiom,
% 0.19/0.44 ! [X4: a] : ( refine412683989fail_a @ ( refine2063221604TURN_a @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % nofail_simps(3)
% 0.19/0.44 thf(fact_178_nofail__simps_I3_J,axiom,
% 0.19/0.44 ! [X4: product_unit] : ( refine579265252t_unit @ ( refine1420258419t_unit @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % nofail_simps(3)
% 0.19/0.44 thf(fact_179_nres__monad2,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a] :
% 0.19/0.44 ( ( refine436832838nd_a_a @ M4 @ refine2063221604TURN_a )
% 0.19/0.44 = M4 ) ).
% 0.19/0.44
% 0.19/0.44 % nres_monad2
% 0.19/0.44 thf(fact_180_nres__monad2,axiom,
% 0.19/0.44 ! [M4: refine787176636t_unit] :
% 0.19/0.44 ( ( refine681446406t_unit @ M4 @ refine1420258419t_unit )
% 0.19/0.44 = M4 ) ).
% 0.19/0.44
% 0.19/0.44 % nres_monad2
% 0.19/0.44 thf(fact_181_nres__monad1,axiom,
% 0.19/0.44 ! [X4: a,F: a > refine424419629nres_a] :
% 0.19/0.44 ( ( refine436832838nd_a_a @ ( refine2063221604TURN_a @ X4 ) @ F )
% 0.19/0.44 = ( F @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_monad1
% 0.19/0.44 thf(fact_182_nres__monad1,axiom,
% 0.19/0.44 ! [X4: product_unit,F: product_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( refine681446406t_unit @ ( refine1420258419t_unit @ X4 ) @ F )
% 0.19/0.44 = ( F @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_monad1
% 0.19/0.44 thf(fact_183_nres__monad1,axiom,
% 0.19/0.44 ! [X4: product_unit,F: product_unit > refine424419629nres_a] :
% 0.19/0.44 ( ( refine119808503unit_a @ ( refine1420258419t_unit @ X4 ) @ F )
% 0.19/0.44 = ( F @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_monad1
% 0.19/0.44 thf(fact_184_subset__Collect__conv,axiom,
% 0.19/0.44 ! [S: set_Product_unit,P: product_unit > $o] :
% 0.19/0.44 ( ( ord_le1023748749t_unit @ S @ ( collect_Product_unit @ P ) )
% 0.19/0.44 = ( ! [X5: product_unit] :
% 0.19/0.44 ( ( member_Product_unit @ X5 @ S )
% 0.19/0.44 => ( P @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_Collect_conv
% 0.19/0.44 thf(fact_185_subset__Collect__conv,axiom,
% 0.19/0.44 ! [S: set_a,P: a > $o] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ S @ ( collect_a @ P ) )
% 0.19/0.44 = ( ! [X5: a] :
% 0.19/0.44 ( ( member_a @ X5 @ S )
% 0.19/0.44 => ( P @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_Collect_conv
% 0.19/0.44 thf(fact_186_nofail__antimono__fun,axiom,
% 0.19/0.44 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 0.19/0.44 ( ( ord_le516598614nres_a @ F @ G )
% 0.19/0.44 => ( ( refine412683989fail_a @ ( G @ X4 ) )
% 0.19/0.44 => ( refine412683989fail_a @ ( F @ X4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nofail_antimono_fun
% 0.19/0.44 thf(fact_187_nofail__RES__conv,axiom,
% 0.19/0.44 ( refine579265252t_unit
% 0.19/0.44 = ( ^ [M6: refine787176636t_unit] :
% 0.19/0.44 ? [M7: set_Product_unit] :
% 0.19/0.44 ( M6
% 0.19/0.44 = ( refine1777164439t_unit @ M7 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nofail_RES_conv
% 0.19/0.44 thf(fact_188_nofail__RES__conv,axiom,
% 0.19/0.44 ( refine412683989fail_a
% 0.19/0.44 = ( ^ [M6: refine424419629nres_a] :
% 0.19/0.44 ? [M7: set_a] :
% 0.19/0.44 ( M6
% 0.19/0.44 = ( refine1198353288_RES_a @ M7 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nofail_RES_conv
% 0.19/0.44 thf(fact_189_pwD1,axiom,
% 0.19/0.44 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ S @ S2 )
% 0.19/0.44 => ( ( refine412683989fail_a @ S2 )
% 0.19/0.44 => ( refine412683989fail_a @ S ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pwD1
% 0.19/0.44 thf(fact_190_pwD1,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ S @ S2 )
% 0.19/0.44 => ( ( refine579265252t_unit @ S2 )
% 0.19/0.44 => ( refine579265252t_unit @ S ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pwD1
% 0.19/0.44 thf(fact_191_le__nofailI,axiom,
% 0.19/0.44 ! [M5: refine424419629nres_a,M4: refine424419629nres_a] :
% 0.19/0.44 ( ( ( refine412683989fail_a @ M5 )
% 0.19/0.44 => ( ord_le519537037nres_a @ M4 @ M5 ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ M4 @ M5 ) ) ).
% 0.19/0.44
% 0.19/0.44 % le_nofailI
% 0.19/0.44 thf(fact_192_le__nofailI,axiom,
% 0.19/0.44 ! [M5: refine787176636t_unit,M4: refine787176636t_unit] :
% 0.19/0.44 ( ( ( refine579265252t_unit @ M5 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ M4 @ M5 ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ M4 @ M5 ) ) ).
% 0.19/0.44
% 0.19/0.44 % le_nofailI
% 0.19/0.44 thf(fact_193_subsetI,axiom,
% 0.19/0.44 ! [A3: set_Product_unit,B3: set_Product_unit] :
% 0.19/0.44 ( ! [X3: product_unit] :
% 0.19/0.44 ( ( member_Product_unit @ X3 @ A3 )
% 0.19/0.44 => ( member_Product_unit @ X3 @ B3 ) )
% 0.19/0.44 => ( ord_le1023748749t_unit @ A3 @ B3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % subsetI
% 0.19/0.44 thf(fact_194_subsetI,axiom,
% 0.19/0.44 ! [A3: set_a,B3: set_a] :
% 0.19/0.44 ( ! [X3: a] :
% 0.19/0.44 ( ( member_a @ X3 @ A3 )
% 0.19/0.44 => ( member_a @ X3 @ B3 ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % subsetI
% 0.19/0.44 thf(fact_195_subset__antisym,axiom,
% 0.19/0.44 ! [A3: set_a,B3: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B3 @ A3 )
% 0.19/0.44 => ( A3 = B3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_antisym
% 0.19/0.44 thf(fact_196_pw__bind__leI,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit,M4: refine424419629nres_a,F: a > refine787176636t_unit] :
% 0.19/0.44 ( ( ( refine579265252t_unit @ S )
% 0.19/0.44 => ( refine412683989fail_a @ M4 ) )
% 0.19/0.44 => ( ! [X3: a] :
% 0.19/0.44 ( ( refine412683989fail_a @ M4 )
% 0.19/0.44 => ( ( refine1001002027nres_a @ M4 @ X3 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ S ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M4 @ F ) @ S ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_leI
% 0.19/0.44 thf(fact_197_pw__bind__leI,axiom,
% 0.19/0.44 ! [S: refine424419629nres_a,M4: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.19/0.44 ( ( ( refine412683989fail_a @ S )
% 0.19/0.44 => ( refine412683989fail_a @ M4 ) )
% 0.19/0.44 => ( ! [X3: a] :
% 0.19/0.44 ( ( refine412683989fail_a @ M4 )
% 0.19/0.44 => ( ( refine1001002027nres_a @ M4 @ X3 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ S ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ S ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_leI
% 0.19/0.44 thf(fact_198_pw__bind__leI,axiom,
% 0.19/0.44 ! [S: refine424419629nres_a,M4: refine787176636t_unit,F: product_unit > refine424419629nres_a] :
% 0.19/0.44 ( ( ( refine412683989fail_a @ S )
% 0.19/0.44 => ( refine579265252t_unit @ M4 ) )
% 0.19/0.44 => ( ! [X3: product_unit] :
% 0.19/0.44 ( ( refine579265252t_unit @ M4 )
% 0.19/0.44 => ( ( refine558004794t_unit @ M4 @ X3 )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ S ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( refine119808503unit_a @ M4 @ F ) @ S ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_leI
% 0.19/0.44 thf(fact_199_pw__bind__leI,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit,M4: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( ( refine579265252t_unit @ S )
% 0.19/0.44 => ( refine579265252t_unit @ M4 ) )
% 0.19/0.44 => ( ! [X3: product_unit] :
% 0.19/0.44 ( ( refine579265252t_unit @ M4 )
% 0.19/0.44 => ( ( refine558004794t_unit @ M4 @ X3 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ S ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M4 @ F ) @ S ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_leI
% 0.19/0.44 thf(fact_200_pw__bind__le__iff,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a,F: a > refine787176636t_unit,S: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M4 @ F ) @ S )
% 0.19/0.44 = ( ( ( refine579265252t_unit @ S )
% 0.19/0.44 => ( refine412683989fail_a @ M4 ) )
% 0.19/0.44 & ! [X5: a] :
% 0.19/0.44 ( ( ( refine412683989fail_a @ M4 )
% 0.19/0.44 & ( refine1001002027nres_a @ M4 @ X5 ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X5 ) @ S ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_le_iff
% 0.19/0.44 thf(fact_201_pw__bind__le__iff,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a,F: a > refine424419629nres_a,S: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ S )
% 0.19/0.44 = ( ( ( refine412683989fail_a @ S )
% 0.19/0.44 => ( refine412683989fail_a @ M4 ) )
% 0.19/0.44 & ! [X5: a] :
% 0.19/0.44 ( ( ( refine412683989fail_a @ M4 )
% 0.19/0.44 & ( refine1001002027nres_a @ M4 @ X5 ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X5 ) @ S ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_le_iff
% 0.19/0.44 thf(fact_202_pw__bind__le__iff,axiom,
% 0.19/0.44 ! [M4: refine787176636t_unit,F: product_unit > refine424419629nres_a,S: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ ( refine119808503unit_a @ M4 @ F ) @ S )
% 0.19/0.44 = ( ( ( refine412683989fail_a @ S )
% 0.19/0.44 => ( refine579265252t_unit @ M4 ) )
% 0.19/0.44 & ! [X5: product_unit] :
% 0.19/0.44 ( ( ( refine579265252t_unit @ M4 )
% 0.19/0.44 & ( refine558004794t_unit @ M4 @ X5 ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ ( F @ X5 ) @ S ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_le_iff
% 0.19/0.44 thf(fact_203_pw__bind__le__iff,axiom,
% 0.19/0.44 ! [M4: refine787176636t_unit,F: product_unit > refine787176636t_unit,S: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M4 @ F ) @ S )
% 0.19/0.44 = ( ( ( refine579265252t_unit @ S )
% 0.19/0.44 => ( refine579265252t_unit @ M4 ) )
% 0.19/0.44 & ! [X5: product_unit] :
% 0.19/0.44 ( ( ( refine579265252t_unit @ M4 )
% 0.19/0.44 & ( refine558004794t_unit @ M4 @ X5 ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ ( F @ X5 ) @ S ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_le_iff
% 0.19/0.44 thf(fact_204_relprop__triggers_I6_J,axiom,
% 0.19/0.44 ! [R: set_a,R2: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ R @ R2 )
% 0.19/0.44 => ( ord_less_eq_set_a @ R @ R2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % relprop_triggers(6)
% 0.19/0.44 thf(fact_205_in__mono,axiom,
% 0.19/0.44 ! [A3: set_Product_unit,B3: set_Product_unit,X4: product_unit] :
% 0.19/0.44 ( ( ord_le1023748749t_unit @ A3 @ B3 )
% 0.19/0.44 => ( ( member_Product_unit @ X4 @ A3 )
% 0.19/0.44 => ( member_Product_unit @ X4 @ B3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_mono
% 0.19/0.44 thf(fact_206_in__mono,axiom,
% 0.19/0.44 ! [A3: set_a,B3: set_a,X4: a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.19/0.44 => ( ( member_a @ X4 @ A3 )
% 0.19/0.44 => ( member_a @ X4 @ B3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_mono
% 0.19/0.44 thf(fact_207_subsetD,axiom,
% 0.19/0.44 ! [A3: set_Product_unit,B3: set_Product_unit,C: product_unit] :
% 0.19/0.44 ( ( ord_le1023748749t_unit @ A3 @ B3 )
% 0.19/0.44 => ( ( member_Product_unit @ C @ A3 )
% 0.19/0.44 => ( member_Product_unit @ C @ B3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subsetD
% 0.19/0.44 thf(fact_208_subsetD,axiom,
% 0.19/0.44 ! [A3: set_a,B3: set_a,C: a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.19/0.44 => ( ( member_a @ C @ A3 )
% 0.19/0.44 => ( member_a @ C @ B3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subsetD
% 0.19/0.44 thf(fact_209_inres__simps_I2_J,axiom,
% 0.19/0.44 ! [X: set_Product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ ( refine1777164439t_unit @ X ) )
% 0.19/0.44 = ( ^ [X5: product_unit] : ( member_Product_unit @ X5 @ X ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % inres_simps(2)
% 0.19/0.44 thf(fact_210_inres__simps_I2_J,axiom,
% 0.19/0.44 ! [X: set_a] :
% 0.19/0.44 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X ) )
% 0.19/0.44 = ( ^ [X5: a] : ( member_a @ X5 @ X ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % inres_simps(2)
% 0.19/0.44 thf(fact_211_inres__simps_I3_J,axiom,
% 0.19/0.44 ! [X4: a] :
% 0.19/0.44 ( ( refine1001002027nres_a @ ( refine2063221604TURN_a @ X4 ) )
% 0.19/0.44 = ( ^ [Y4: a,Z: a] : ( Y4 = Z )
% 0.19/0.44 @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % inres_simps(3)
% 0.19/0.44 thf(fact_212_inres__simps_I3_J,axiom,
% 0.19/0.44 ! [X4: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ ( refine1420258419t_unit @ X4 ) )
% 0.19/0.44 = ( ^ [Y4: product_unit,Z: product_unit] : ( Y4 = Z )
% 0.19/0.44 @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % inres_simps(3)
% 0.19/0.44 thf(fact_213_pwD2,axiom,
% 0.19/0.44 ! [S: refine424419629nres_a,S2: refine424419629nres_a,X4: a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ S @ S2 )
% 0.19/0.44 => ( ( refine1001002027nres_a @ S @ X4 )
% 0.19/0.44 => ( refine1001002027nres_a @ S2 @ X4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pwD2
% 0.19/0.44 thf(fact_214_pwD2,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit,S2: refine787176636t_unit,X4: product_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ S @ S2 )
% 0.19/0.44 => ( ( refine558004794t_unit @ S @ X4 )
% 0.19/0.44 => ( refine558004794t_unit @ S2 @ X4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pwD2
% 0.19/0.44 thf(fact_215_pw__eqI,axiom,
% 0.19/0.44 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.19/0.44 ( ( ( refine412683989fail_a @ S )
% 0.19/0.44 = ( refine412683989fail_a @ S2 ) )
% 0.19/0.44 => ( ! [X3: a] :
% 0.19/0.44 ( ( refine1001002027nres_a @ S @ X3 )
% 0.19/0.44 = ( refine1001002027nres_a @ S2 @ X3 ) )
% 0.19/0.44 => ( S = S2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_eqI
% 0.19/0.44 thf(fact_216_pw__eqI,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.19/0.44 ( ( ( refine579265252t_unit @ S )
% 0.19/0.44 = ( refine579265252t_unit @ S2 ) )
% 0.19/0.44 => ( ! [X3: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ S @ X3 )
% 0.19/0.44 = ( refine558004794t_unit @ S2 @ X3 ) )
% 0.19/0.44 => ( S = S2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_eqI
% 0.19/0.44 thf(fact_217_pw__eq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.19/0.44 ( ( ( refine412683989fail_a @ S3 )
% 0.19/0.44 = ( refine412683989fail_a @ S4 ) )
% 0.19/0.44 & ! [X5: a] :
% 0.19/0.44 ( ( refine1001002027nres_a @ S3 @ X5 )
% 0.19/0.44 = ( refine1001002027nres_a @ S4 @ X5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_eq_iff
% 0.19/0.44 thf(fact_218_pw__eq__iff,axiom,
% 0.19/0.44 ( ( ^ [Y4: refine787176636t_unit,Z: refine787176636t_unit] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [S3: refine787176636t_unit,S4: refine787176636t_unit] :
% 0.19/0.44 ( ( ( refine579265252t_unit @ S3 )
% 0.19/0.44 = ( refine579265252t_unit @ S4 ) )
% 0.19/0.44 & ! [X5: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ S3 @ X5 )
% 0.19/0.44 = ( refine558004794t_unit @ S4 @ X5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_eq_iff
% 0.19/0.44 thf(fact_219_not__nofail__inres,axiom,
% 0.19/0.44 ! [S: refine424419629nres_a,X4: a] :
% 0.19/0.44 ( ~ ( refine412683989fail_a @ S )
% 0.19/0.44 => ( refine1001002027nres_a @ S @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % not_nofail_inres
% 0.19/0.44 thf(fact_220_not__nofail__inres,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit,X4: product_unit] :
% 0.19/0.44 ( ~ ( refine579265252t_unit @ S )
% 0.19/0.44 => ( refine558004794t_unit @ S @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % not_nofail_inres
% 0.19/0.44 thf(fact_221_pw__le__iff,axiom,
% 0.19/0.44 ( ord_le519537037nres_a
% 0.19/0.44 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.19/0.44 ( ( refine412683989fail_a @ S4 )
% 0.19/0.44 => ( ( refine412683989fail_a @ S3 )
% 0.19/0.44 & ! [X5: a] :
% 0.19/0.44 ( ( refine1001002027nres_a @ S3 @ X5 )
% 0.19/0.44 => ( refine1001002027nres_a @ S4 @ X5 ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_le_iff
% 0.19/0.44 thf(fact_222_pw__le__iff,axiom,
% 0.19/0.44 ( ord_le1051254044t_unit
% 0.19/0.44 = ( ^ [S3: refine787176636t_unit,S4: refine787176636t_unit] :
% 0.19/0.44 ( ( refine579265252t_unit @ S4 )
% 0.19/0.44 => ( ( refine579265252t_unit @ S3 )
% 0.19/0.44 & ! [X5: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ S3 @ X5 )
% 0.19/0.44 => ( refine558004794t_unit @ S4 @ X5 ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_le_iff
% 0.19/0.44 thf(fact_223_pw__leI_H,axiom,
% 0.19/0.44 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 0.19/0.44 ( ( ( refine412683989fail_a @ S2 )
% 0.19/0.44 => ( refine412683989fail_a @ S ) )
% 0.19/0.44 => ( ! [X3: a] :
% 0.19/0.44 ( ( refine412683989fail_a @ S2 )
% 0.19/0.44 => ( ( refine1001002027nres_a @ S @ X3 )
% 0.19/0.44 => ( refine1001002027nres_a @ S2 @ X3 ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ S @ S2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_leI'
% 0.19/0.44 thf(fact_224_pw__leI_H,axiom,
% 0.19/0.44 ! [S2: refine787176636t_unit,S: refine787176636t_unit] :
% 0.19/0.44 ( ( ( refine579265252t_unit @ S2 )
% 0.19/0.44 => ( refine579265252t_unit @ S ) )
% 0.19/0.44 => ( ! [X3: product_unit] :
% 0.19/0.44 ( ( refine579265252t_unit @ S2 )
% 0.19/0.44 => ( ( refine558004794t_unit @ S @ X3 )
% 0.19/0.44 => ( refine558004794t_unit @ S2 @ X3 ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ S @ S2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_leI'
% 0.19/0.44 thf(fact_225_pw__leI,axiom,
% 0.19/0.44 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 0.19/0.44 ( ( ( refine412683989fail_a @ S2 )
% 0.19/0.44 => ( ( refine412683989fail_a @ S )
% 0.19/0.44 & ! [X3: a] :
% 0.19/0.44 ( ( refine1001002027nres_a @ S @ X3 )
% 0.19/0.44 => ( refine1001002027nres_a @ S2 @ X3 ) ) ) )
% 0.19/0.44 => ( ord_le519537037nres_a @ S @ S2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_leI
% 0.19/0.44 thf(fact_226_pw__leI,axiom,
% 0.19/0.44 ! [S2: refine787176636t_unit,S: refine787176636t_unit] :
% 0.19/0.44 ( ( ( refine579265252t_unit @ S2 )
% 0.19/0.44 => ( ( refine579265252t_unit @ S )
% 0.19/0.44 & ! [X3: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ S @ X3 )
% 0.19/0.44 => ( refine558004794t_unit @ S2 @ X3 ) ) ) )
% 0.19/0.44 => ( ord_le1051254044t_unit @ S @ S2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_leI
% 0.19/0.44 thf(fact_227_pw__bind__nofail,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a,F: a > refine787176636t_unit] :
% 0.19/0.44 ( ( refine579265252t_unit @ ( refine96995669t_unit @ M4 @ F ) )
% 0.19/0.44 = ( ( refine412683989fail_a @ M4 )
% 0.19/0.44 & ! [X5: a] :
% 0.19/0.44 ( ( refine1001002027nres_a @ M4 @ X5 )
% 0.19/0.44 => ( refine579265252t_unit @ ( F @ X5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_nofail
% 0.19/0.44 thf(fact_228_pw__bind__nofail,axiom,
% 0.19/0.44 ! [M4: refine787176636t_unit,F: product_unit > refine424419629nres_a] :
% 0.19/0.44 ( ( refine412683989fail_a @ ( refine119808503unit_a @ M4 @ F ) )
% 0.19/0.44 = ( ( refine579265252t_unit @ M4 )
% 0.19/0.44 & ! [X5: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ M4 @ X5 )
% 0.19/0.44 => ( refine412683989fail_a @ ( F @ X5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_nofail
% 0.19/0.44 thf(fact_229_pw__bind__nofail,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.19/0.44 ( ( refine412683989fail_a @ ( refine436832838nd_a_a @ M4 @ F ) )
% 0.19/0.44 = ( ( refine412683989fail_a @ M4 )
% 0.19/0.44 & ! [X5: a] :
% 0.19/0.44 ( ( refine1001002027nres_a @ M4 @ X5 )
% 0.19/0.44 => ( refine412683989fail_a @ ( F @ X5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_nofail
% 0.19/0.44 thf(fact_230_pw__bind__nofail,axiom,
% 0.19/0.44 ! [M4: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( refine579265252t_unit @ ( refine681446406t_unit @ M4 @ F ) )
% 0.19/0.44 = ( ( refine579265252t_unit @ M4 )
% 0.19/0.44 & ! [X5: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ M4 @ X5 )
% 0.19/0.44 => ( refine579265252t_unit @ ( F @ X5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_bind_nofail
% 0.19/0.44 thf(fact_231_inres__def,axiom,
% 0.19/0.44 ( refine1001002027nres_a
% 0.19/0.44 = ( ^ [S3: refine424419629nres_a,X5: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X5 ) @ S3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % inres_def
% 0.19/0.44 thf(fact_232_inres__def,axiom,
% 0.19/0.44 ( refine558004794t_unit
% 0.19/0.44 = ( ^ [S3: refine787176636t_unit,X5: product_unit] : ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X5 ) @ S3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % inres_def
% 0.19/0.44 thf(fact_233_nf__inres__def,axiom,
% 0.19/0.44 ( refine983493746t_unit
% 0.19/0.44 = ( ^ [M6: refine787176636t_unit,X5: product_unit] :
% 0.19/0.44 ( ( refine579265252t_unit @ M6 )
% 0.19/0.44 & ( refine558004794t_unit @ M6 @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nf_inres_def
% 0.19/0.44 thf(fact_234_nf__inres__def,axiom,
% 0.19/0.44 ( refine1312857699nres_a
% 0.19/0.44 = ( ^ [M6: refine424419629nres_a,X5: a] :
% 0.19/0.44 ( ( refine412683989fail_a @ M6 )
% 0.19/0.44 & ( refine1001002027nres_a @ M6 @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nf_inres_def
% 0.19/0.44 thf(fact_235_Collect__mono__iff,axiom,
% 0.19/0.44 ! [P: product_unit > $o,Q: product_unit > $o] :
% 0.19/0.44 ( ( ord_le1023748749t_unit @ ( collect_Product_unit @ P ) @ ( collect_Product_unit @ Q ) )
% 0.19/0.44 = ( ! [X5: product_unit] :
% 0.19/0.44 ( ( P @ X5 )
% 0.19/0.44 => ( Q @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mono_iff
% 0.19/0.44 thf(fact_236_Collect__mono__iff,axiom,
% 0.19/0.44 ! [P: a > $o,Q: a > $o] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.19/0.44 = ( ! [X5: a] :
% 0.19/0.44 ( ( P @ X5 )
% 0.19/0.44 => ( Q @ X5 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mono_iff
% 0.19/0.44 thf(fact_237_set__eq__subset,axiom,
% 0.19/0.44 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.19/0.44 = ( ^ [A4: set_a,B4: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A4 @ B4 )
% 0.19/0.44 & ( ord_less_eq_set_a @ B4 @ A4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % set_eq_subset
% 0.19/0.44 thf(fact_238_subset__trans,axiom,
% 0.19/0.44 ! [A3: set_a,B3: set_a,C2: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.19/0.44 => ( ord_less_eq_set_a @ A3 @ C2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_trans
% 0.19/0.44 thf(fact_239_Collect__mono,axiom,
% 0.19/0.44 ! [P: product_unit > $o,Q: product_unit > $o] :
% 0.19/0.44 ( ! [X3: product_unit] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 => ( Q @ X3 ) )
% 0.19/0.44 => ( ord_le1023748749t_unit @ ( collect_Product_unit @ P ) @ ( collect_Product_unit @ Q ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mono
% 0.19/0.44 thf(fact_240_Collect__mono,axiom,
% 0.19/0.44 ! [P: a > $o,Q: a > $o] :
% 0.19/0.44 ( ! [X3: a] :
% 0.19/0.44 ( ( P @ X3 )
% 0.19/0.44 => ( Q @ X3 ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mono
% 0.19/0.44 thf(fact_241_subset__refl,axiom,
% 0.19/0.44 ! [A3: set_a] : ( ord_less_eq_set_a @ A3 @ A3 ) ).
% 0.19/0.44
% 0.19/0.44 % subset_refl
% 0.19/0.44 thf(fact_242_subset__iff,axiom,
% 0.19/0.44 ( ord_le1023748749t_unit
% 0.19/0.44 = ( ^ [A4: set_Product_unit,B4: set_Product_unit] :
% 0.19/0.44 ! [T3: product_unit] :
% 0.19/0.44 ( ( member_Product_unit @ T3 @ A4 )
% 0.19/0.44 => ( member_Product_unit @ T3 @ B4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_iff
% 0.19/0.44 thf(fact_243_subset__iff,axiom,
% 0.19/0.44 ( ord_less_eq_set_a
% 0.19/0.44 = ( ^ [A4: set_a,B4: set_a] :
% 0.19/0.44 ! [T3: a] :
% 0.19/0.44 ( ( member_a @ T3 @ A4 )
% 0.19/0.44 => ( member_a @ T3 @ B4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_iff
% 0.19/0.44 thf(fact_244_equalityD2,axiom,
% 0.19/0.44 ! [A3: set_a,B3: set_a] :
% 0.19/0.44 ( ( A3 = B3 )
% 0.19/0.44 => ( ord_less_eq_set_a @ B3 @ A3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % equalityD2
% 0.19/0.44 thf(fact_245_equalityD1,axiom,
% 0.19/0.44 ! [A3: set_a,B3: set_a] :
% 0.19/0.44 ( ( A3 = B3 )
% 0.19/0.44 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % equalityD1
% 0.19/0.44 thf(fact_246_subset__eq,axiom,
% 0.19/0.44 ( ord_le1023748749t_unit
% 0.19/0.44 = ( ^ [A4: set_Product_unit,B4: set_Product_unit] :
% 0.19/0.44 ! [X5: product_unit] :
% 0.19/0.44 ( ( member_Product_unit @ X5 @ A4 )
% 0.19/0.44 => ( member_Product_unit @ X5 @ B4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_eq
% 0.19/0.44 thf(fact_247_subset__eq,axiom,
% 0.19/0.44 ( ord_less_eq_set_a
% 0.19/0.44 = ( ^ [A4: set_a,B4: set_a] :
% 0.19/0.44 ! [X5: a] :
% 0.19/0.44 ( ( member_a @ X5 @ A4 )
% 0.19/0.44 => ( member_a @ X5 @ B4 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_eq
% 0.19/0.44 thf(fact_248_less__eq__nres_Oelims_I1_J,axiom,
% 0.19/0.44 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 0.19/0.44 ( ( ( ord_le519537037nres_a @ X4 @ Xa )
% 0.19/0.44 = Y3 )
% 0.19/0.44 => ( ( ( Xa = refine464223677AILi_a )
% 0.19/0.44 => ~ Y3 )
% 0.19/0.44 => ( ! [A5: set_a] :
% 0.19/0.44 ( ( X4
% 0.19/0.44 = ( refine1198353288_RES_a @ A5 ) )
% 0.19/0.44 => ! [B5: set_a] :
% 0.19/0.44 ( ( Xa
% 0.19/0.44 = ( refine1198353288_RES_a @ B5 ) )
% 0.19/0.44 => ( Y3
% 0.19/0.44 = ( ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) )
% 0.19/0.44 => ~ ( ( X4 = refine464223677AILi_a )
% 0.19/0.44 => ( ? [Uv: set_a] :
% 0.19/0.44 ( Xa
% 0.19/0.44 = ( refine1198353288_RES_a @ Uv ) )
% 0.19/0.44 => Y3 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % less_eq_nres.elims(1)
% 0.19/0.44 thf(fact_249_less__eq__nres_Oelims_I2_J,axiom,
% 0.19/0.44 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ X4 @ Xa )
% 0.19/0.44 => ( ( Xa != refine464223677AILi_a )
% 0.19/0.44 => ~ ! [A5: set_a] :
% 0.19/0.44 ( ( X4
% 0.19/0.44 = ( refine1198353288_RES_a @ A5 ) )
% 0.19/0.44 => ! [B5: set_a] :
% 0.19/0.44 ( ( Xa
% 0.19/0.44 = ( refine1198353288_RES_a @ B5 ) )
% 0.19/0.44 => ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % less_eq_nres.elims(2)
% 0.19/0.44 thf(fact_250_less__eq__nres_Oelims_I3_J,axiom,
% 0.19/0.44 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.19/0.44 ( ~ ( ord_le519537037nres_a @ X4 @ Xa )
% 0.19/0.44 => ( ! [A5: set_a] :
% 0.19/0.44 ( ( X4
% 0.19/0.44 = ( refine1198353288_RES_a @ A5 ) )
% 0.19/0.44 => ! [B5: set_a] :
% 0.19/0.44 ( ( Xa
% 0.19/0.44 = ( refine1198353288_RES_a @ B5 ) )
% 0.19/0.44 => ( ord_less_eq_set_a @ A5 @ B5 ) ) )
% 0.19/0.44 => ~ ( ( X4 = refine464223677AILi_a )
% 0.19/0.44 => ! [Uv: set_a] :
% 0.19/0.44 ( Xa
% 0.19/0.44 != ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % less_eq_nres.elims(3)
% 0.19/0.44 thf(fact_251_nres__order__simps_I22_J,axiom,
% 0.19/0.44 ! [X: set_a,Y3: a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine2063221604TURN_a @ Y3 ) )
% 0.19/0.44 = ( ord_less_eq_set_a @ X @ ( insert_a @ Y3 @ bot_bot_set_a ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_order_simps(22)
% 0.19/0.44 thf(fact_252_less__eq__nres_Osimps_I3_J,axiom,
% 0.19/0.44 ! [Uv2: set_a] :
% 0.19/0.44 ~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % less_eq_nres.simps(3)
% 0.19/0.44 thf(fact_253_empty__iff,axiom,
% 0.19/0.44 ! [C: a] :
% 0.19/0.44 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 0.19/0.44
% 0.19/0.44 % empty_iff
% 0.19/0.44 thf(fact_254_all__not__in__conv,axiom,
% 0.19/0.44 ! [A3: set_a] :
% 0.19/0.44 ( ( ! [X5: a] :
% 0.19/0.44 ~ ( member_a @ X5 @ A3 ) )
% 0.19/0.44 = ( A3 = bot_bot_set_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % all_not_in_conv
% 0.19/0.44 thf(fact_255_Collect__empty__eq,axiom,
% 0.19/0.44 ! [P: a > $o] :
% 0.19/0.44 ( ( ( collect_a @ P )
% 0.19/0.44 = bot_bot_set_a )
% 0.19/0.44 = ( ! [X5: a] :
% 0.19/0.44 ~ ( P @ X5 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_empty_eq
% 0.19/0.44 thf(fact_256_empty__Collect__eq,axiom,
% 0.19/0.44 ! [P: a > $o] :
% 0.19/0.44 ( ( bot_bot_set_a
% 0.19/0.44 = ( collect_a @ P ) )
% 0.19/0.44 = ( ! [X5: a] :
% 0.19/0.44 ~ ( P @ X5 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % empty_Collect_eq
% 0.19/0.44 thf(fact_257_insertCI,axiom,
% 0.19/0.44 ! [A: a,B3: set_a,B: a] :
% 0.19/0.44 ( ( ~ ( member_a @ A @ B3 )
% 0.19/0.44 => ( A = B ) )
% 0.19/0.44 => ( member_a @ A @ ( insert_a @ B @ B3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % insertCI
% 0.19/0.44 thf(fact_258_insert__iff,axiom,
% 0.19/0.44 ! [A: a,B: a,A3: set_a] :
% 0.19/0.44 ( ( member_a @ A @ ( insert_a @ B @ A3 ) )
% 0.19/0.44 = ( ( A = B )
% 0.19/0.44 | ( member_a @ A @ A3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % insert_iff
% 0.19/0.44 thf(fact_259_singletonI,axiom,
% 0.19/0.44 ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % singletonI
% 0.19/0.44 thf(fact_260_insert__subset,axiom,
% 0.19/0.44 ! [X4: a,A3: set_a,B3: set_a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ ( insert_a @ X4 @ A3 ) @ B3 )
% 0.19/0.44 = ( ( member_a @ X4 @ B3 )
% 0.19/0.44 & ( ord_less_eq_set_a @ A3 @ B3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % insert_subset
% 0.19/0.44 thf(fact_261_nres__more__simps_I5_J,axiom,
% 0.19/0.44 ! [X4: a,X: set_a] :
% 0.19/0.44 ( ( ( refine2063221604TURN_a @ X4 )
% 0.19/0.44 = ( refine1198353288_RES_a @ X ) )
% 0.19/0.44 = ( ( insert_a @ X4 @ bot_bot_set_a )
% 0.19/0.44 = X ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_more_simps(5)
% 0.19/0.44 thf(fact_262_nres__more__simps_I3_J,axiom,
% 0.19/0.44 ! [X: set_a,X4: a] :
% 0.19/0.44 ( ( ( refine1198353288_RES_a @ X )
% 0.19/0.44 = ( refine2063221604TURN_a @ X4 ) )
% 0.19/0.44 = ( X
% 0.19/0.44 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_more_simps(3)
% 0.19/0.44 thf(fact_263_emptyE,axiom,
% 0.19/0.44 ! [A: a] :
% 0.19/0.44 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 0.19/0.44
% 0.19/0.44 % emptyE
% 0.19/0.44 thf(fact_264_insertE,axiom,
% 0.19/0.44 ! [A: a,B: a,A3: set_a] :
% 0.19/0.44 ( ( member_a @ A @ ( insert_a @ B @ A3 ) )
% 0.19/0.44 => ( ( A != B )
% 0.19/0.44 => ( member_a @ A @ A3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % insertE
% 0.19/0.44 thf(fact_265_equals0D,axiom,
% 0.19/0.44 ! [A3: set_a,A: a] :
% 0.19/0.44 ( ( A3 = bot_bot_set_a )
% 0.19/0.44 => ~ ( member_a @ A @ A3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % equals0D
% 0.19/0.44 thf(fact_266_equals0I,axiom,
% 0.19/0.44 ! [A3: set_a] :
% 0.19/0.44 ( ! [Y6: a] :
% 0.19/0.44 ~ ( member_a @ Y6 @ A3 )
% 0.19/0.44 => ( A3 = bot_bot_set_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % equals0I
% 0.19/0.44 thf(fact_267_insertI1,axiom,
% 0.19/0.44 ! [A: a,B3: set_a] : ( member_a @ A @ ( insert_a @ A @ B3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % insertI1
% 0.19/0.44 thf(fact_268_insertI2,axiom,
% 0.19/0.44 ! [A: a,B3: set_a,B: a] :
% 0.19/0.44 ( ( member_a @ A @ B3 )
% 0.19/0.44 => ( member_a @ A @ ( insert_a @ B @ B3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % insertI2
% 0.19/0.44 thf(fact_269_ex__in__conv,axiom,
% 0.19/0.44 ! [A3: set_a] :
% 0.19/0.44 ( ( ? [X5: a] : ( member_a @ X5 @ A3 ) )
% 0.19/0.44 = ( A3 != bot_bot_set_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % ex_in_conv
% 0.19/0.44 thf(fact_270_Set_Oset__insert,axiom,
% 0.19/0.44 ! [X4: a,A3: set_a] :
% 0.19/0.44 ( ( member_a @ X4 @ A3 )
% 0.19/0.44 => ~ ! [B6: set_a] :
% 0.19/0.44 ( ( A3
% 0.19/0.44 = ( insert_a @ X4 @ B6 ) )
% 0.19/0.44 => ( member_a @ X4 @ B6 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Set.set_insert
% 0.19/0.44 thf(fact_271_singletonD,axiom,
% 0.19/0.44 ! [B: a,A: a] :
% 0.19/0.44 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 0.19/0.44 => ( B = A ) ) ).
% 0.19/0.44
% 0.19/0.44 % singletonD
% 0.19/0.44 thf(fact_272_insert__ident,axiom,
% 0.19/0.44 ! [X4: a,A3: set_a,B3: set_a] :
% 0.19/0.44 ( ~ ( member_a @ X4 @ A3 )
% 0.19/0.44 => ( ~ ( member_a @ X4 @ B3 )
% 0.19/0.44 => ( ( ( insert_a @ X4 @ A3 )
% 0.19/0.44 = ( insert_a @ X4 @ B3 ) )
% 0.19/0.44 = ( A3 = B3 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % insert_ident
% 0.19/0.44 thf(fact_273_insert__absorb,axiom,
% 0.19/0.44 ! [A: a,A3: set_a] :
% 0.19/0.44 ( ( member_a @ A @ A3 )
% 0.19/0.44 => ( ( insert_a @ A @ A3 )
% 0.19/0.44 = A3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % insert_absorb
% 0.19/0.44 thf(fact_274_insert__eq__iff,axiom,
% 0.19/0.44 ! [A: a,A3: set_a,B: a,B3: set_a] :
% 0.19/0.44 ( ~ ( member_a @ A @ A3 )
% 0.19/0.44 => ( ~ ( member_a @ B @ B3 )
% 0.19/0.44 => ( ( ( insert_a @ A @ A3 )
% 0.19/0.44 = ( insert_a @ B @ B3 ) )
% 0.19/0.44 = ( ( ( A = B )
% 0.19/0.44 => ( A3 = B3 ) )
% 0.19/0.44 & ( ( A != B )
% 0.19/0.44 => ? [C3: set_a] :
% 0.19/0.44 ( ( A3
% 0.19/0.44 = ( insert_a @ B @ C3 ) )
% 0.19/0.44 & ~ ( member_a @ B @ C3 )
% 0.19/0.44 & ( B3
% 0.19/0.44 = ( insert_a @ A @ C3 ) )
% 0.19/0.44 & ~ ( member_a @ A @ C3 ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % insert_eq_iff
% 0.19/0.44 thf(fact_275_singleton__iff,axiom,
% 0.19/0.44 ! [B: a,A: a] :
% 0.19/0.44 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 0.19/0.44 = ( B = A ) ) ).
% 0.19/0.44
% 0.19/0.44 % singleton_iff
% 0.19/0.44 thf(fact_276_mk__disjoint__insert,axiom,
% 0.19/0.44 ! [A: a,A3: set_a] :
% 0.19/0.44 ( ( member_a @ A @ A3 )
% 0.19/0.44 => ? [B6: set_a] :
% 0.19/0.44 ( ( A3
% 0.19/0.44 = ( insert_a @ A @ B6 ) )
% 0.19/0.44 & ~ ( member_a @ A @ B6 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % mk_disjoint_insert
% 0.19/0.44 thf(fact_277_set__notEmptyE,axiom,
% 0.19/0.44 ! [S: set_a] :
% 0.19/0.44 ( ( S != bot_bot_set_a )
% 0.19/0.44 => ~ ! [X3: a] :
% 0.19/0.44 ~ ( member_a @ X3 @ S ) ) ).
% 0.19/0.44
% 0.19/0.44 % set_notEmptyE
% 0.19/0.44 thf(fact_278_memb__imp__not__empty,axiom,
% 0.19/0.44 ! [X4: a,S: set_a] :
% 0.19/0.44 ( ( member_a @ X4 @ S )
% 0.19/0.44 => ( S != bot_bot_set_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % memb_imp_not_empty
% 0.19/0.44 thf(fact_279_bot_Oextremum,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ A ) ).
% 0.19/0.44
% 0.19/0.44 % bot.extremum
% 0.19/0.44 thf(fact_280_bot_Oextremum,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ) ).
% 0.19/0.44
% 0.19/0.44 % bot.extremum
% 0.19/0.44 thf(fact_281_bot_Oextremum__unique,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
% 0.19/0.44 = ( A = bot_bo658782032t_unit ) ) ).
% 0.19/0.44
% 0.19/0.44 % bot.extremum_unique
% 0.19/0.44 thf(fact_282_bot_Oextremum__unique,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
% 0.19/0.44 = ( A = bot_bo529555393nres_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % bot.extremum_unique
% 0.19/0.44 thf(fact_283_bot_Oextremum__uniqueI,axiom,
% 0.19/0.44 ! [A: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
% 0.19/0.44 => ( A = bot_bo658782032t_unit ) ) ).
% 0.19/0.44
% 0.19/0.44 % bot.extremum_uniqueI
% 0.19/0.44 thf(fact_284_bot_Oextremum__uniqueI,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
% 0.19/0.44 => ( A = bot_bo529555393nres_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % bot.extremum_uniqueI
% 0.19/0.44 thf(fact_285_subset__insert,axiom,
% 0.19/0.44 ! [X4: a,A3: set_a,B3: set_a] :
% 0.19/0.44 ( ~ ( member_a @ X4 @ A3 )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ A3 @ ( insert_a @ X4 @ B3 ) )
% 0.19/0.44 = ( ord_less_eq_set_a @ A3 @ B3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_insert
% 0.19/0.44 thf(fact_286_RETURN__def,axiom,
% 0.19/0.44 ( refine2063221604TURN_a
% 0.19/0.44 = ( ^ [X5: a] : ( refine1198353288_RES_a @ ( insert_a @ X5 @ bot_bot_set_a ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % RETURN_def
% 0.19/0.44 thf(fact_287_nres_Odistinct_I1_J,axiom,
% 0.19/0.44 ! [X2: set_a] :
% 0.19/0.44 ( refine464223677AILi_a
% 0.19/0.44 != ( refine1198353288_RES_a @ X2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres.distinct(1)
% 0.19/0.44 thf(fact_288_nres_Oinduct,axiom,
% 0.19/0.44 ! [P: refine424419629nres_a > $o,Nres: refine424419629nres_a] :
% 0.19/0.44 ( ( P @ refine464223677AILi_a )
% 0.19/0.44 => ( ! [X3: set_a] : ( P @ ( refine1198353288_RES_a @ X3 ) )
% 0.19/0.44 => ( P @ Nres ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres.induct
% 0.19/0.44 thf(fact_289_nres_Oexhaust,axiom,
% 0.19/0.44 ! [Y3: refine424419629nres_a] :
% 0.19/0.44 ( ( Y3 != refine464223677AILi_a )
% 0.19/0.44 => ~ ! [X22: set_a] :
% 0.19/0.44 ( Y3
% 0.19/0.44 != ( refine1198353288_RES_a @ X22 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres.exhaust
% 0.19/0.44 thf(fact_290_sup__nres_Oinduct,axiom,
% 0.19/0.44 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.19/0.44 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.19/0.44 => ( ! [V2: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V2 ) )
% 0.19/0.44 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.19/0.44 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % sup_nres.induct
% 0.19/0.44 thf(fact_291_less__nres_Oinduct,axiom,
% 0.19/0.44 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.19/0.44 ( ! [X_1: refine424419629nres_a] : ( P @ refine464223677AILi_a @ X_1 )
% 0.19/0.44 => ( ! [Uv: set_a] : ( P @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a )
% 0.19/0.44 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.19/0.44 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % less_nres.induct
% 0.19/0.44 thf(fact_292_less__eq__nres_Oinduct,axiom,
% 0.19/0.44 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.19/0.44 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.19/0.44 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.19/0.44 => ( ! [Uv: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) )
% 0.19/0.44 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % less_eq_nres.induct
% 0.19/0.44 thf(fact_293_less__eq__nres_Osimps_I1_J,axiom,
% 0.19/0.44 ! [Uu2: refine424419629nres_a] : ( ord_le519537037nres_a @ Uu2 @ refine464223677AILi_a ) ).
% 0.19/0.44
% 0.19/0.44 % less_eq_nres.simps(1)
% 0.19/0.44 thf(fact_294_insert__subsetI,axiom,
% 0.19/0.44 ! [X4: a,A3: set_a,X: set_a] :
% 0.19/0.44 ( ( member_a @ X4 @ A3 )
% 0.19/0.44 => ( ( ord_less_eq_set_a @ X @ A3 )
% 0.19/0.44 => ( ord_less_eq_set_a @ ( insert_a @ X4 @ X ) @ A3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % insert_subsetI
% 0.19/0.44 thf(fact_295_subset__emptyI,axiom,
% 0.19/0.44 ! [A3: set_a] :
% 0.19/0.44 ( ! [X3: a] :
% 0.19/0.44 ~ ( member_a @ X3 @ A3 )
% 0.19/0.44 => ( ord_less_eq_set_a @ A3 @ bot_bot_set_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_emptyI
% 0.19/0.44 thf(fact_296_nres__order__simps_I2_J,axiom,
% 0.19/0.44 ! [M4: refine787176636t_unit] :
% 0.19/0.44 ( ( ord_le1051254044t_unit @ M4 @ bot_bo658782032t_unit )
% 0.19/0.44 = ( M4 = bot_bo658782032t_unit ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_order_simps(2)
% 0.19/0.44 thf(fact_297_nres__order__simps_I2_J,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ M4 @ bot_bo529555393nres_a )
% 0.19/0.44 = ( M4 = bot_bo529555393nres_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_order_simps(2)
% 0.19/0.44 thf(fact_298_nofail__simps_I4_J,axiom,
% 0.19/0.44 refine579265252t_unit @ bot_bo658782032t_unit ).
% 0.19/0.44
% 0.19/0.44 % nofail_simps(4)
% 0.19/0.44 thf(fact_299_inres__simps_I4_J,axiom,
% 0.19/0.44 ( ( refine558004794t_unit @ bot_bo658782032t_unit )
% 0.19/0.44 = ( ^ [Uu3: product_unit] : $false ) ) ).
% 0.19/0.44
% 0.19/0.44 % inres_simps(4)
% 0.19/0.44 thf(fact_300_bind__SUCCEED,axiom,
% 0.19/0.44 ! [F: product_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( refine681446406t_unit @ bot_bo658782032t_unit @ F )
% 0.19/0.44 = bot_bo658782032t_unit ) ).
% 0.19/0.44
% 0.19/0.44 % bind_SUCCEED
% 0.19/0.44 thf(fact_301_nres__more__simps_I2_J,axiom,
% 0.19/0.44 ! [X: set_Product_unit] :
% 0.19/0.44 ( ( ( refine1777164439t_unit @ X )
% 0.19/0.44 = bot_bo658782032t_unit )
% 0.19/0.44 = ( X = bot_bo1087887705t_unit ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_more_simps(2)
% 0.19/0.44 thf(fact_302_nres__more__simps_I2_J,axiom,
% 0.19/0.44 ! [X: set_a] :
% 0.19/0.44 ( ( ( refine1198353288_RES_a @ X )
% 0.19/0.44 = bot_bo529555393nres_a )
% 0.19/0.44 = ( X = bot_bot_set_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_more_simps(2)
% 0.19/0.44 thf(fact_303_nres__more__simps_I1_J,axiom,
% 0.19/0.44 ! [X: set_Product_unit] :
% 0.19/0.44 ( ( bot_bo658782032t_unit
% 0.19/0.44 = ( refine1777164439t_unit @ X ) )
% 0.19/0.44 = ( X = bot_bo1087887705t_unit ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_more_simps(1)
% 0.19/0.44 thf(fact_304_nres__more__simps_I1_J,axiom,
% 0.19/0.44 ! [X: set_a] :
% 0.19/0.44 ( ( bot_bo529555393nres_a
% 0.19/0.44 = ( refine1198353288_RES_a @ X ) )
% 0.19/0.44 = ( X = bot_bot_set_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_more_simps(1)
% 0.19/0.44 thf(fact_305_bot__set__def,axiom,
% 0.19/0.44 ( bot_bot_set_a
% 0.19/0.44 = ( collect_a @ bot_bot_a_o ) ) ).
% 0.19/0.44
% 0.19/0.44 % bot_set_def
% 0.19/0.44 thf(fact_306_nres__order__simps_I1_J,axiom,
% 0.19/0.44 ! [M4: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ M4 ) ).
% 0.19/0.44
% 0.19/0.44 % nres_order_simps(1)
% 0.19/0.44 thf(fact_307_nres__order__simps_I1_J,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ M4 ) ).
% 0.19/0.44
% 0.19/0.44 % nres_order_simps(1)
% 0.19/0.44 thf(fact_308_nres__inequalities_I5_J,axiom,
% 0.19/0.44 ! [X4: product_unit] :
% 0.19/0.44 ( bot_bo658782032t_unit
% 0.19/0.44 != ( refine1420258419t_unit @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_inequalities(5)
% 0.19/0.44 thf(fact_309_bot__nres__def,axiom,
% 0.19/0.44 ( bot_bo658782032t_unit
% 0.19/0.44 = ( refine1777164439t_unit @ bot_bo1087887705t_unit ) ) ).
% 0.19/0.44
% 0.19/0.44 % bot_nres_def
% 0.19/0.44 thf(fact_310_bot__nres__def,axiom,
% 0.19/0.44 ( bot_bo529555393nres_a
% 0.19/0.44 = ( refine1198353288_RES_a @ bot_bot_set_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % bot_nres_def
% 0.19/0.44 thf(fact_311_SUCCEED__rule,axiom,
% 0.19/0.44 ! [Phi: product_unit > $o] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % SUCCEED_rule
% 0.19/0.44 thf(fact_312_SUCCEED__rule,axiom,
% 0.19/0.44 ! [Phi: a > $o] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % SUCCEED_rule
% 0.19/0.44 thf(fact_313_is__singletonI_H,axiom,
% 0.19/0.44 ! [A3: set_a] :
% 0.19/0.44 ( ( A3 != bot_bot_set_a )
% 0.19/0.44 => ( ! [X3: a,Y6: a] :
% 0.19/0.44 ( ( member_a @ X3 @ A3 )
% 0.19/0.44 => ( ( member_a @ Y6 @ A3 )
% 0.19/0.44 => ( X3 = Y6 ) ) )
% 0.19/0.44 => ( is_singleton_a @ A3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % is_singletonI'
% 0.19/0.44 thf(fact_314_subset__Compl__singleton,axiom,
% 0.19/0.44 ! [A3: set_a,B: a] :
% 0.19/0.44 ( ( ord_less_eq_set_a @ A3 @ ( uminus_uminus_set_a @ ( insert_a @ B @ bot_bot_set_a ) ) )
% 0.19/0.44 = ( ~ ( member_a @ B @ A3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % subset_Compl_singleton
% 0.19/0.44 thf(fact_315_strictD__simp,axiom,
% 0.19/0.44 ! [F: refine787176636t_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( refine459374679t_unit @ F )
% 0.19/0.44 => ( ( F @ bot_bo658782032t_unit )
% 0.19/0.44 = bot_bo658782032t_unit ) ) ).
% 0.19/0.44
% 0.19/0.44 % strictD_simp
% 0.19/0.44 thf(fact_316_Collect__empty__eq__bot,axiom,
% 0.19/0.44 ! [P: a > $o] :
% 0.19/0.44 ( ( ( collect_a @ P )
% 0.19/0.44 = bot_bot_set_a )
% 0.19/0.44 = ( P = bot_bot_a_o ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_empty_eq_bot
% 0.19/0.44 thf(fact_317_ComplI,axiom,
% 0.19/0.44 ! [C: a,A3: set_a] :
% 0.19/0.44 ( ~ ( member_a @ C @ A3 )
% 0.19/0.44 => ( member_a @ C @ ( uminus_uminus_set_a @ A3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ComplI
% 0.19/0.44 thf(fact_318_Compl__iff,axiom,
% 0.19/0.44 ! [C: a,A3: set_a] :
% 0.19/0.44 ( ( member_a @ C @ ( uminus_uminus_set_a @ A3 ) )
% 0.19/0.44 = ( ~ ( member_a @ C @ A3 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Compl_iff
% 0.19/0.44 thf(fact_319_ibind__strict_I1_J,axiom,
% 0.19/0.44 ! [F: product_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( refine681446406t_unit @ bot_bo658782032t_unit @ F )
% 0.19/0.44 = bot_bo658782032t_unit ) ).
% 0.19/0.44
% 0.19/0.44 % ibind_strict(1)
% 0.19/0.44 thf(fact_320_ComplD,axiom,
% 0.19/0.44 ! [C: a,A3: set_a] :
% 0.19/0.44 ( ( member_a @ C @ ( uminus_uminus_set_a @ A3 ) )
% 0.19/0.44 => ~ ( member_a @ C @ A3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % ComplD
% 0.19/0.44 thf(fact_321_strictD,axiom,
% 0.19/0.44 ! [F: refine787176636t_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( refine459374679t_unit @ F )
% 0.19/0.44 => ( ( F @ bot_bo658782032t_unit )
% 0.19/0.44 = bot_bo658782032t_unit ) ) ).
% 0.19/0.44
% 0.19/0.44 % strictD
% 0.19/0.44 thf(fact_322_strictI,axiom,
% 0.19/0.44 ! [F: refine787176636t_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( ( F @ bot_bo658782032t_unit )
% 0.19/0.44 = bot_bo658782032t_unit )
% 0.19/0.44 => ( refine459374679t_unit @ F ) ) ).
% 0.19/0.44
% 0.19/0.44 % strictI
% 0.19/0.44 thf(fact_323_strict__def,axiom,
% 0.19/0.44 ( refine459374679t_unit
% 0.19/0.44 = ( ^ [F2: refine787176636t_unit > refine787176636t_unit] :
% 0.19/0.44 ( ( F2 @ bot_bo658782032t_unit )
% 0.19/0.44 = bot_bo658782032t_unit ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % strict_def
% 0.19/0.44 thf(fact_324_bot__empty__eq,axiom,
% 0.19/0.44 ( bot_bot_a_o
% 0.19/0.44 = ( ^ [X5: a] : ( member_a @ X5 @ bot_bot_set_a ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % bot_empty_eq
% 0.19/0.44 thf(fact_325_ASSUME__simps_I2_J,axiom,
% 0.19/0.44 ( ( refine23983189ASSUME @ $false )
% 0.19/0.44 = bot_bo658782032t_unit ) ).
% 0.19/0.44
% 0.19/0.44 % ASSUME_simps(2)
% 0.19/0.44 thf(fact_326_pw__flat__le__iff,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.19/0.44 ( ( partia1658438072t_unit @ bot_bo658782032t_unit @ S @ S2 )
% 0.19/0.44 = ( ? [X7: product_unit] : ( refine558004794t_unit @ S @ X7 )
% 0.19/0.44 => ( ( ( refine579265252t_unit @ S )
% 0.19/0.44 = ( refine579265252t_unit @ S2 ) )
% 0.19/0.44 & ! [X5: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ S @ X5 )
% 0.19/0.44 = ( refine558004794t_unit @ S2 @ X5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_flat_le_iff
% 0.19/0.44 thf(fact_327_pw__ASSUME_I2_J,axiom,
% 0.19/0.44 ! [Phi: $o,X4: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ ( refine23983189ASSUME @ Phi ) @ X4 )
% 0.19/0.44 = Phi ) ).
% 0.19/0.44
% 0.19/0.44 % pw_ASSUME(2)
% 0.19/0.44 thf(fact_328_pw__ASSUME_I1_J,axiom,
% 0.19/0.44 ! [Phi: $o] : ( refine579265252t_unit @ ( refine23983189ASSUME @ Phi ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_ASSUME(1)
% 0.19/0.44 thf(fact_329_flat__ord__compat_I1_J,axiom,
% 0.19/0.44 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.19/0.44 ( ( partia1658438072t_unit @ bot_bo658782032t_unit @ X4 @ Y3 )
% 0.19/0.44 => ( ord_le1051254044t_unit @ X4 @ Y3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % flat_ord_compat(1)
% 0.19/0.44 thf(fact_330_flat__ord__compat_I1_J,axiom,
% 0.19/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.19/0.44 ( ( partia906949161nres_a @ bot_bo529555393nres_a @ X4 @ Y3 )
% 0.19/0.44 => ( ord_le519537037nres_a @ X4 @ Y3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % flat_ord_compat(1)
% 0.19/0.44 thf(fact_331_pw__flat__ge__iff,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 0.19/0.44 ( ( partia1658438072t_unit @ top_to177290092t_unit @ S @ S2 )
% 0.19/0.44 = ( ( refine579265252t_unit @ S )
% 0.19/0.44 => ( ( refine579265252t_unit @ S2 )
% 0.19/0.44 & ! [X5: product_unit] :
% 0.19/0.44 ( ( refine558004794t_unit @ S @ X5 )
% 0.19/0.44 = ( refine558004794t_unit @ S2 @ X5 ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % pw_flat_ge_iff
% 0.19/0.44 thf(fact_332_nres__order__simps_I4_J,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M4 )
% 0.19/0.44 = ( M4 = top_to231829469nres_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_order_simps(4)
% 0.19/0.44 thf(fact_333_nofail__simps_I1_J,axiom,
% 0.19/0.44 ~ ( refine579265252t_unit @ top_to177290092t_unit ) ).
% 0.19/0.44
% 0.19/0.44 % nofail_simps(1)
% 0.19/0.44 thf(fact_334_inres__simps_I1_J,axiom,
% 0.19/0.44 ( ( refine558004794t_unit @ top_to177290092t_unit )
% 0.19/0.44 = ( ^ [Uu3: product_unit] : $true ) ) ).
% 0.19/0.44
% 0.19/0.44 % inres_simps(1)
% 0.19/0.44 thf(fact_335_flat__ord__compat_I2_J,axiom,
% 0.19/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.19/0.44 ( ( partia906949161nres_a @ top_to231829469nres_a @ X4 @ Y3 )
% 0.19/0.44 => ( ord_le519537037nres_a @ Y3 @ X4 ) ) ).
% 0.19/0.44
% 0.19/0.44 % flat_ord_compat(2)
% 0.19/0.44 thf(fact_336_top__greatest,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ) ).
% 0.19/0.44
% 0.19/0.44 % top_greatest
% 0.19/0.44 thf(fact_337_top_Oextremum__unique,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 0.19/0.44 = ( A = top_to231829469nres_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % top.extremum_unique
% 0.19/0.44 thf(fact_338_top_Oextremum__uniqueI,axiom,
% 0.19/0.44 ! [A: refine424419629nres_a] :
% 0.19/0.44 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 0.19/0.44 => ( A = top_to231829469nres_a ) ) ).
% 0.19/0.44
% 0.19/0.44 % top.extremum_uniqueI
% 0.19/0.44 thf(fact_339_meta__le__everything__if__top,axiom,
% 0.19/0.44 ! [M: refine424419629nres_a,X4: refine424419629nres_a] :
% 0.19/0.44 ( ( M = top_to231829469nres_a )
% 0.19/0.44 => ( ord_le519537037nres_a @ X4 @ M ) ) ).
% 0.19/0.44
% 0.19/0.44 % meta_le_everything_if_top
% 0.19/0.44 thf(fact_340_not__nofail__iff,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit] :
% 0.19/0.44 ( ( ~ ( refine579265252t_unit @ S ) )
% 0.19/0.44 = ( S = top_to177290092t_unit ) ) ).
% 0.19/0.44
% 0.19/0.44 % not_nofail_iff
% 0.19/0.44 thf(fact_341_nofail__def,axiom,
% 0.19/0.44 ( refine579265252t_unit
% 0.19/0.44 = ( ^ [S3: refine787176636t_unit] : ( S3 != top_to177290092t_unit ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nofail_def
% 0.19/0.44 thf(fact_342_intro__nofail_I2_J,axiom,
% 0.19/0.44 ! [S: refine787176636t_unit] :
% 0.19/0.44 ( ( top_to177290092t_unit != S )
% 0.19/0.44 = ( refine579265252t_unit @ S ) ) ).
% 0.19/0.44
% 0.19/0.44 % intro_nofail(2)
% 0.19/0.44 thf(fact_343_nres__order__simps_I3_J,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a] : ( ord_le519537037nres_a @ M4 @ top_to231829469nres_a ) ).
% 0.19/0.44
% 0.19/0.44 % nres_order_simps(3)
% 0.19/0.44 thf(fact_344_nres__inequalities_I1_J,axiom,
% 0.19/0.44 ! [X: set_a] :
% 0.19/0.44 ( top_to231829469nres_a
% 0.19/0.44 != ( refine1198353288_RES_a @ X ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_inequalities(1)
% 0.19/0.44 thf(fact_345_nres__cases,axiom,
% 0.19/0.44 ! [M4: refine424419629nres_a] :
% 0.19/0.44 ( ( M4 != top_to231829469nres_a )
% 0.19/0.44 => ~ ! [X8: set_a] :
% 0.19/0.44 ( M4
% 0.19/0.44 != ( refine1198353288_RES_a @ X8 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % nres_cases
% 0.19/0.44 thf(fact_346_nres__inequalities_I4_J,axiom,
% 0.19/0.44 bot_bo658782032t_unit != top_to177290092t_unit ).
% 0.19/0.44
% 0.19/0.44 % nres_inequalities(4)
% 0.19/0.44 thf(fact_347_nres__inequalities_I2_J,axiom,
% 0.19/0.44 top_to177290092t_unit != bot_bo658782032t_unit ).
% 0.19/0.44
% 0.19/0.44 % nres_inequalities(2)
% 0.19/0.44 thf(fact_348_UNIV__I,axiom,
% 0.19/0.44 ! [X4: a] : ( member_a @ X4 @ top_top_set_a ) ).
% 0.19/0.44
% 0.19/0.44 % UNIV_I
% 0.19/0.44 thf(fact_349_eq__UNIV__iff,axiom,
% 0.19/0.44 ! [S: set_a] :
% 0.19/0.44 ( ( S = top_top_set_a )
% 0.19/0.44 = ( ! [X5: a] : ( member_a @ X5 @ S ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % eq_UNIV_iff
% 0.19/0.44
% 0.19/0.44 % Helper facts (9)
% 0.19/0.44 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.19/0.44 ! [X4: set_a,Y3: set_a] :
% 0.19/0.44 ( ( if_set_a @ $false @ X4 @ Y3 )
% 0.19/0.44 = Y3 ) ).
% 0.19/0.44
% 0.19/0.44 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.19/0.44 ! [X4: set_a,Y3: set_a] :
% 0.19/0.44 ( ( if_set_a @ $true @ X4 @ Y3 )
% 0.19/0.44 = X4 ) ).
% 0.19/0.44
% 0.19/0.44 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.19/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.19/0.44 ( ( if_Ref1724547303nres_a @ $false @ X4 @ Y3 )
% 0.19/0.44 = Y3 ) ).
% 0.19/0.44
% 0.19/0.44 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.19/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.19/0.44 ( ( if_Ref1724547303nres_a @ $true @ X4 @ Y3 )
% 0.19/0.44 = X4 ) ).
% 0.19/0.44
% 0.19/0.44 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 0.19/0.44 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( if_o_R1705037948nres_a @ $false @ X4 @ Y3 )
% 0.19/0.44 = Y3 ) ).
% 0.19/0.44
% 0.19/0.44 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 0.19/0.44 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 0.19/0.44 ( ( if_o_R1705037948nres_a @ $true @ X4 @ Y3 )
% 0.19/0.44 = X4 ) ).
% 0.19/0.44
% 0.19/0.44 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.19/0.44 ! [P: $o] :
% 0.19/0.44 ( ( P = $true )
% 0.19/0.44 | ( P = $false ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.19/0.44 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.19/0.44 ( ( if_Ref1369692790t_unit @ $false @ X4 @ Y3 )
% 0.19/0.44 = Y3 ) ).
% 0.19/0.44
% 0.19/0.44 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.19/0.44 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.19/0.44 ( ( if_Ref1369692790t_unit @ $true @ X4 @ Y3 )
% 0.19/0.44 = X4 ) ).
% 0.19/0.44
% 0.19/0.44 % Conjectures (3)
% 0.19/0.44 thf(conj_0,hypothesis,
% 0.19/0.44 ( b
% 0.19/0.44 => ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(conj_1,hypothesis,
% 0.19/0.44 ( ~ b
% 0.19/0.44 => ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(conj_2,conjecture,
% 0.19/0.44 ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 3.78/2.02 ---- Embedded in THF ---
% 3.78/2.02 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.78/2.02 %%% Generated on Tue Feb 24 08:28:56 EST 2026
% 3.78/2.02 %%% using '$$dhol' embedding, version 1.3.0.
% 3.78/2.02 %%% Logic specification used:
% 3.78/2.02 %%% thf(spec, logic, $$dhol).
% 3.78/2.02
% 3.78/2.02 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2DTF5795.p
% See solution above
% 3.78/2.02 ------------------------
% 4.12/2.08 ---- Cleaned THF ---
% 4.12/2.08 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 4.12/2.08 refine787176636t_unit: $tType ).
% 4.12/2.08
% 4.12/2.08 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 4.12/2.08 refine424419629nres_a: $tType ).
% 4.12/2.08
% 4.12/2.08 thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 4.12/2.08 set_Product_unit: $tType ).
% 4.12/2.08
% 4.12/2.08 thf(ty_n_t__Product____Type__Ounit,type,
% 4.12/2.08 product_unit: $tType ).
% 4.12/2.08
% 4.12/2.08 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 4.12/2.08 set_a: $tType ).
% 4.12/2.08
% 4.12/2.08 thf(ty_n_tf__a,type,
% 4.12/2.08 a: $tType ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_Itf__a_J,type,
% 4.12/2.08 uminus_uminus_set_a: set_a > set_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 4.12/2.08 if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 4.12/2.08 if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 4.12/2.08 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 4.12/2.08 if_set_a: $o > set_a > set_a > set_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 4.12/2.08 bot_bot_a_o: a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Obot__class_Obot_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 4.12/2.08 bot_bo658782032t_unit: refine787176636t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Obot__class_Obot_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 4.12/2.08 bot_bo529555393nres_a: refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 4.12/2.08 bot_bo1087887705t_unit: set_Product_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 4.12/2.08 bot_bot_set_a: set_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_J,type,
% 4.12/2.08 ord_le1960259811nres_a: ( $o > $o > refine424419629nres_a ) > ( $o > $o > refine424419629nres_a ) > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_J,type,
% 4.12/2.08 ord_le1633311077t_unit: ( $o > refine787176636t_unit ) > ( $o > refine787176636t_unit ) > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 4.12/2.08 ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_Itf__a_J_J,type,
% 4.12/2.08 ord_less_eq_o_set_a: ( $o > set_a ) > ( $o > set_a ) > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 4.12/2.08 ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 4.12/2.08 ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 4.12/2.08 ord_le1023748749t_unit: set_Product_unit > set_Product_unit > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 4.12/2.08 ord_less_eq_set_a: set_a > set_a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 4.12/2.08 order_245837199nres_a: ( ( $o > refine424419629nres_a ) > $o ) > $o > refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 4.12/2.08 order_453013155t_unit: ( refine787176636t_unit > $o ) > refine787176636t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 4.12/2.08 order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_Itf__a_J,type,
% 4.12/2.08 order_Greatest_set_a: ( set_a > $o ) > set_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 4.12/2.08 top_to177290092t_unit: refine787176636t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 4.12/2.08 top_to231829469nres_a: refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
% 4.12/2.08 top_top_set_a: set_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Partial__Function_Oflat__ord_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 4.12/2.08 partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Partial__Function_Oflat__ord_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 4.12/2.08 partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_OASSUME,type,
% 4.12/2.08 refine23983189ASSUME: $o > refine787176636t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001t__Product____Type__Ounit,type,
% 4.12/2.08 refine1420258419t_unit: product_unit > refine787176636t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__a,type,
% 4.12/2.08 refine2063221604TURN_a: a > refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 4.12/2.08 refine681446406t_unit: refine787176636t_unit > ( product_unit > refine787176636t_unit ) > refine787176636t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001t__Product____Type__Ounit_001tf__a,type,
% 4.12/2.08 refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001t__Product____Type__Ounit,type,
% 4.12/2.08 refine96995669t_unit: refine424419629nres_a > ( a > refine787176636t_unit ) > refine787176636t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001tf__a,type,
% 4.12/2.08 refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001t__Product____Type__Ounit,type,
% 4.12/2.08 refine558004794t_unit: refine787176636t_unit > product_unit > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__a,type,
% 4.12/2.08 refine1001002027nres_a: refine424419629nres_a > a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onf__inres_001t__Product____Type__Ounit,type,
% 4.12/2.08 refine983493746t_unit: refine787176636t_unit > product_unit > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onf__inres_001tf__a,type,
% 4.12/2.08 refine1312857699nres_a: refine424419629nres_a > a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001t__Product____Type__Ounit,type,
% 4.12/2.08 refine579265252t_unit: refine787176636t_unit > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__a,type,
% 4.12/2.08 refine412683989fail_a: refine424419629nres_a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_OFAILi_001tf__a,type,
% 4.12/2.08 refine464223677AILi_a: refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001t__Product____Type__Ounit,type,
% 4.12/2.08 refine1777164439t_unit: set_Product_unit > refine787176636t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__a,type,
% 4.12/2.08 refine1198353288_RES_a: set_a > refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001t__Product____Type__Ounit,type,
% 4.12/2.08 refine1208325748t_unit: refine787176636t_unit > set_Product_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001tf__a,type,
% 4.12/2.08 refine1822134885_RES_a: refine424419629nres_a > set_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Refine__Misc_Ostrict_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 4.12/2.08 refine459374679t_unit: ( refine787176636t_unit > refine787176636t_unit ) > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Set_OCollect_001t__Product____Type__Ounit,type,
% 4.12/2.08 collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Set_OCollect_001tf__a,type,
% 4.12/2.08 collect_a: ( a > $o ) > set_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Set_Oinsert_001tf__a,type,
% 4.12/2.08 insert_a: a > set_a > set_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_Set_Ois__singleton_001tf__a,type,
% 4.12/2.08 is_singleton_a: set_a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_member_001t__Product____Type__Ounit,type,
% 4.12/2.08 member_Product_unit: product_unit > set_Product_unit > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_c_member_001tf__a,type,
% 4.12/2.08 member_a: a > set_a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_v_S1,type,
% 4.12/2.08 s1: refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_v_S2,type,
% 4.12/2.08 s2: refine424419629nres_a ).
% 4.12/2.08
% 4.12/2.08 thf(sy_v__092_060Phi_062,type,
% 4.12/2.08 phi: a > $o ).
% 4.12/2.08
% 4.12/2.08 thf(sy_v_b,type,
% 4.12/2.08 b: $o ).
% 4.12/2.08
% 4.12/2.08 thf(fact_0_nres__more__simps_I4_J,axiom,
% 4.12/2.08 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.12/2.08 ( ( ( refine1777164439t_unit @ X )
% 4.12/2.08 = ( refine1777164439t_unit @ Y ) )
% 4.12/2.08 = ( X = Y ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_1_nres__more__simps_I4_J,axiom,
% 4.12/2.08 ! [X: set_a,Y: set_a] :
% 4.12/2.08 ( ( ( refine1198353288_RES_a @ X )
% 4.12/2.08 = ( refine1198353288_RES_a @ Y ) )
% 4.12/2.08 = ( X = Y ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_2_nres_Oinject,axiom,
% 4.12/2.08 ! [X2: set_Product_unit,Y2: set_Product_unit] :
% 4.12/2.08 ( ( ( refine1777164439t_unit @ X2 )
% 4.12/2.08 = ( refine1777164439t_unit @ Y2 ) )
% 4.12/2.08 = ( X2 = Y2 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_3_nres_Oinject,axiom,
% 4.12/2.08 ! [X2: set_a,Y2: set_a] :
% 4.12/2.08 ( ( ( refine1198353288_RES_a @ X2 )
% 4.12/2.08 = ( refine1198353288_RES_a @ Y2 ) )
% 4.12/2.08 = ( X2 = Y2 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_4_RES__rule,axiom,
% 4.12/2.08 ! [S: set_Product_unit,Phi: product_unit > $o] :
% 4.12/2.08 ( ! [X3: product_unit] :
% 4.12/2.08 ( ( member_Product_unit @ X3 @ S )
% 4.12/2.08 => ( Phi @ X3 ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ S ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_5_RES__rule,axiom,
% 4.12/2.08 ! [S: set_a,Phi: a > $o] :
% 4.12/2.08 ( ! [X3: a] :
% 4.12/2.08 ( ( member_a @ X3 @ S )
% 4.12/2.08 => ( Phi @ X3 ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_6_SPEC__rule,axiom,
% 4.12/2.08 ! [Phi: product_unit > $o,Phi2: product_unit > $o] :
% 4.12/2.08 ( ! [X3: product_unit] :
% 4.12/2.08 ( ( Phi @ X3 )
% 4.12/2.08 => ( Phi2 @ X3 ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_7_SPEC__rule,axiom,
% 4.12/2.08 ! [Phi: a > $o,Phi2: a > $o] :
% 4.12/2.08 ( ! [X3: a] :
% 4.12/2.08 ( ( Phi @ X3 )
% 4.12/2.08 => ( Phi2 @ X3 ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_8_SPEC__trans,axiom,
% 4.12/2.08 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit,Postcond: product_unit > $o] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ Y3 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ X4 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_9_SPEC__trans,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Postcond: a > $o] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ Y3 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ X4 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_10_SPEC__cons__rule,axiom,
% 4.12/2.08 ! [M: refine787176636t_unit,Phi: product_unit > $o,Psi: product_unit > $o] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) )
% 4.12/2.08 => ( ! [X3: product_unit] :
% 4.12/2.08 ( ( Phi @ X3 )
% 4.12/2.08 => ( Psi @ X3 ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Psi ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_11_SPEC__cons__rule,axiom,
% 4.12/2.08 ! [M: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 4.12/2.08 => ( ! [X3: a] :
% 4.12/2.08 ( ( Phi @ X3 )
% 4.12/2.08 => ( Psi @ X3 ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_12_nf__inres__RES,axiom,
% 4.12/2.08 ! [X: set_Product_unit,X4: product_unit] :
% 4.12/2.08 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ X ) @ X4 )
% 4.12/2.08 = ( member_Product_unit @ X4 @ X ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_13_nf__inres__RES,axiom,
% 4.12/2.08 ! [X: set_a,X4: a] :
% 4.12/2.08 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X ) @ X4 )
% 4.12/2.08 = ( member_a @ X4 @ X ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_14_nf__inres__SPEC,axiom,
% 4.12/2.08 ! [Phi: product_unit > $o,X4: product_unit] :
% 4.12/2.08 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ X4 )
% 4.12/2.08 = ( Phi @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_15_nf__inres__SPEC,axiom,
% 4.12/2.08 ! [Phi: a > $o,X4: a] :
% 4.12/2.08 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ X4 )
% 4.12/2.08 = ( Phi @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_16_order__mono__setup_Orefl,axiom,
% 4.12/2.08 ! [X4: set_a] : ( ord_less_eq_set_a @ X4 @ X4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_17_order__mono__setup_Orefl,axiom,
% 4.12/2.08 ! [X4: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ X4 @ X4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_18_order__mono__setup_Orefl,axiom,
% 4.12/2.08 ! [X4: refine787176636t_unit] : ( ord_le1051254044t_unit @ X4 @ X4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_19_order__mono__setup_Orefl,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a] : ( ord_le519537037nres_a @ X4 @ X4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_20_the__RES_Osimps,axiom,
% 4.12/2.08 ! [X: set_Product_unit] :
% 4.12/2.08 ( ( refine1208325748t_unit @ ( refine1777164439t_unit @ X ) )
% 4.12/2.08 = X ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_21_the__RES_Osimps,axiom,
% 4.12/2.08 ! [X: set_a] :
% 4.12/2.08 ( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ X ) )
% 4.12/2.08 = X ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_22_nres__order__simps_I21_J,axiom,
% 4.12/2.08 ! [X4: product_unit,Y: set_Product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X4 ) @ ( refine1777164439t_unit @ Y ) )
% 4.12/2.08 = ( member_Product_unit @ X4 @ Y ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_23_nres__order__simps_I21_J,axiom,
% 4.12/2.08 ! [X4: a,Y: set_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ Y ) )
% 4.12/2.08 = ( member_a @ X4 @ Y ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_24_le__funD,axiom,
% 4.12/2.08 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ F @ G )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_25_le__funE,axiom,
% 4.12/2.08 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ F @ G )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_26_le__funI,axiom,
% 4.12/2.08 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a] :
% 4.12/2.08 ( ! [X3: $o] : ( ord_le519537037nres_a @ ( F @ X3 ) @ ( G @ X3 ) )
% 4.12/2.08 => ( ord_le516598614nres_a @ F @ G ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_27_Refine__Misc_Oif__mono,axiom,
% 4.12/2.08 ! [B: $o,M1: set_a,M12: set_a,M2: set_a,M22: set_a] :
% 4.12/2.08 ( ( B
% 4.12/2.08 => ( ord_less_eq_set_a @ M1 @ M12 ) )
% 4.12/2.08 => ( ( ~ B
% 4.12/2.08 => ( ord_less_eq_set_a @ M2 @ M22 ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( if_set_a @ B @ M1 @ M2 ) @ ( if_set_a @ B @ M12 @ M22 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_28_Refine__Misc_Oif__mono,axiom,
% 4.12/2.08 ! [B: $o,M1: $o > refine424419629nres_a,M12: $o > refine424419629nres_a,M2: $o > refine424419629nres_a,M22: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( B
% 4.12/2.08 => ( ord_le516598614nres_a @ M1 @ M12 ) )
% 4.12/2.08 => ( ( ~ B
% 4.12/2.08 => ( ord_le516598614nres_a @ M2 @ M22 ) )
% 4.12/2.08 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B @ M1 @ M2 ) @ ( if_o_R1705037948nres_a @ B @ M12 @ M22 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_29_Refine__Misc_Oif__mono,axiom,
% 4.12/2.08 ! [B: $o,M1: refine787176636t_unit,M12: refine787176636t_unit,M2: refine787176636t_unit,M22: refine787176636t_unit] :
% 4.12/2.08 ( ( B
% 4.12/2.08 => ( ord_le1051254044t_unit @ M1 @ M12 ) )
% 4.12/2.08 => ( ( ~ B
% 4.12/2.08 => ( ord_le1051254044t_unit @ M2 @ M22 ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ M1 @ M2 ) @ ( if_Ref1369692790t_unit @ B @ M12 @ M22 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_30_Refine__Misc_Oif__mono,axiom,
% 4.12/2.08 ! [B: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M2: refine424419629nres_a,M22: refine424419629nres_a] :
% 4.12/2.08 ( ( B
% 4.12/2.08 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 4.12/2.08 => ( ( ~ B
% 4.12/2.08 => ( ord_le519537037nres_a @ M2 @ M22 ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ M1 @ M2 ) @ ( if_Ref1724547303nres_a @ B @ M12 @ M22 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_31_le__fun__def,axiom,
% 4.12/2.08 ( ord_le516598614nres_a
% 4.12/2.08 = ( ^ [F2: $o > refine424419629nres_a,G2: $o > refine424419629nres_a] :
% 4.12/2.08 ! [X5: $o] : ( ord_le519537037nres_a @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_32_nres__more__simps_I6_J,axiom,
% 4.12/2.08 ! [X4: a,Y3: a] :
% 4.12/2.08 ( ( ( refine2063221604TURN_a @ X4 )
% 4.12/2.08 = ( refine2063221604TURN_a @ Y3 ) )
% 4.12/2.08 = ( X4 = Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_33_nres__more__simps_I6_J,axiom,
% 4.12/2.08 ! [X4: product_unit,Y3: product_unit] :
% 4.12/2.08 ( ( ( refine1420258419t_unit @ X4 )
% 4.12/2.08 = ( refine1420258419t_unit @ Y3 ) )
% 4.12/2.08 = ( X4 = Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_34_nres__order__simps_I20_J,axiom,
% 4.12/2.08 ! [X4: product_unit,Y3: product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X4 ) @ ( refine1420258419t_unit @ Y3 ) )
% 4.12/2.08 = ( X4 = Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_35_nres__order__simps_I20_J,axiom,
% 4.12/2.08 ! [X4: a,Y3: a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine2063221604TURN_a @ Y3 ) )
% 4.12/2.08 = ( X4 = Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_36_less__eq__nres_Osimps_I2_J,axiom,
% 4.12/2.08 ! [A: set_Product_unit,B: set_Product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ A ) @ ( refine1777164439t_unit @ B ) )
% 4.12/2.08 = ( ord_le1023748749t_unit @ A @ B ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_37_less__eq__nres_Osimps_I2_J,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 4.12/2.08 = ( ord_less_eq_set_a @ A @ B ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_38_nres__order__simps_I5_J,axiom,
% 4.12/2.08 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ X ) @ ( refine1777164439t_unit @ Y ) )
% 4.12/2.08 = ( ord_le1023748749t_unit @ X @ Y ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_39_nres__order__simps_I5_J,axiom,
% 4.12/2.08 ! [X: set_a,Y: set_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine1198353288_RES_a @ Y ) )
% 4.12/2.08 = ( ord_less_eq_set_a @ X @ Y ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_40_RETURN__to__SPEC__rule,axiom,
% 4.12/2.08 ! [M: refine787176636t_unit,V: product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ M
% 4.12/2.08 @ ( refine1777164439t_unit
% 4.12/2.08 @ ( collect_Product_unit
% 4.12/2.08 @ ( ^ [Y4: product_unit,Z: product_unit] : ( Y4 = Z )
% 4.12/2.08 @ V ) ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ M @ ( refine1420258419t_unit @ V ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_41_RETURN__to__SPEC__rule,axiom,
% 4.12/2.08 ! [M: refine424419629nres_a,V: a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ M
% 4.12/2.08 @ ( refine1198353288_RES_a
% 4.12/2.08 @ ( collect_a
% 4.12/2.08 @ ( ^ [Y4: a,Z: a] : ( Y4 = Z )
% 4.12/2.08 @ V ) ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ M @ ( refine2063221604TURN_a @ V ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_42_RETURN__rule,axiom,
% 4.12/2.08 ! [Phi: product_unit > $o,X4: product_unit] :
% 4.12/2.08 ( ( Phi @ X4 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X4 ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_43_RETURN__rule,axiom,
% 4.12/2.08 ! [Phi: a > $o,X4: a] :
% 4.12/2.08 ( ( Phi @ X4 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_44_order__mono__setup_Omono__if,axiom,
% 4.12/2.08 ! [T: set_a,T2: set_a,E: set_a,E2: set_a,B: $o] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ T @ T2 )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ E @ E2 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( if_set_a @ B @ T @ E ) @ ( if_set_a @ B @ T2 @ E2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_45_order__mono__setup_Omono__if,axiom,
% 4.12/2.08 ! [T: $o > refine424419629nres_a,T2: $o > refine424419629nres_a,E: $o > refine424419629nres_a,E2: $o > refine424419629nres_a,B: $o] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ T @ T2 )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ E @ E2 )
% 4.12/2.08 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B @ T @ E ) @ ( if_o_R1705037948nres_a @ B @ T2 @ E2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_46_order__mono__setup_Omono__if,axiom,
% 4.12/2.08 ! [T: refine787176636t_unit,T2: refine787176636t_unit,E: refine787176636t_unit,E2: refine787176636t_unit,B: $o] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ T @ T2 )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ E @ E2 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ T @ E ) @ ( if_Ref1369692790t_unit @ B @ T2 @ E2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_47_order__mono__setup_Omono__if,axiom,
% 4.12/2.08 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B: $o] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ T @ T2 )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ E @ E2 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ ( if_Ref1724547303nres_a @ B @ T2 @ E2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_48_dual__order_Oantisym,axiom,
% 4.12/2.08 ! [B: set_a,A: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ B @ A )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( A = B ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_49_dual__order_Oantisym,axiom,
% 4.12/2.08 ! [B: $o > refine424419629nres_a,A: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ B @ A )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ A @ B )
% 4.12/2.08 => ( A = B ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_50_dual__order_Oantisym,axiom,
% 4.12/2.08 ! [B: refine787176636t_unit,A: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ B @ A )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( A = B ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_51_dual__order_Oantisym,axiom,
% 4.12/2.08 ! [B: refine424419629nres_a,A: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ B @ A )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( A = B ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_52_dual__order_Oeq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [A2: set_a,B2: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 4.12/2.08 & ( ord_less_eq_set_a @ A2 @ B2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_53_dual__order_Oeq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ B2 @ A2 )
% 4.12/2.08 & ( ord_le516598614nres_a @ A2 @ B2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_54_dual__order_Oeq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: refine787176636t_unit,Z: refine787176636t_unit] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [A2: refine787176636t_unit,B2: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ B2 @ A2 )
% 4.12/2.08 & ( ord_le1051254044t_unit @ A2 @ B2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_55_dual__order_Oeq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 4.12/2.08 & ( ord_le519537037nres_a @ A2 @ B2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_56_dual__order_Otrans,axiom,
% 4.12/2.08 ! [B: set_a,A: set_a,C: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ B @ A )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ C @ B )
% 4.12/2.08 => ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_57_dual__order_Otrans,axiom,
% 4.12/2.08 ! [B: $o > refine424419629nres_a,A: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ B @ A )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ C @ B )
% 4.12/2.08 => ( ord_le516598614nres_a @ C @ A ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_58_dual__order_Otrans,axiom,
% 4.12/2.08 ! [B: refine787176636t_unit,A: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ B @ A )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ C @ B )
% 4.12/2.08 => ( ord_le1051254044t_unit @ C @ A ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_59_dual__order_Otrans,axiom,
% 4.12/2.08 ! [B: refine424419629nres_a,A: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ B @ A )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ C @ B )
% 4.12/2.08 => ( ord_le519537037nres_a @ C @ A ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_60_dual__order_Orefl,axiom,
% 4.12/2.08 ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_61_dual__order_Orefl,axiom,
% 4.12/2.08 ! [A: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ A @ A ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_62_dual__order_Orefl,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ A ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_63_dual__order_Orefl,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_64_order__trans,axiom,
% 4.12/2.08 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ Y3 @ Z2 )
% 4.12/2.08 => ( ord_less_eq_set_a @ X4 @ Z2 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_65_order__trans,axiom,
% 4.12/2.08 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a,Z2: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ Y3 @ Z2 )
% 4.12/2.08 => ( ord_le516598614nres_a @ X4 @ Z2 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_66_order__trans,axiom,
% 4.12/2.08 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit,Z2: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ Y3 @ Z2 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ X4 @ Z2 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_67_order__trans,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 4.12/2.08 => ( ord_le519537037nres_a @ X4 @ Z2 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_68_order__class_Oorder_Oantisym,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ A )
% 4.12/2.08 => ( A = B ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_69_order__class_Oorder_Oantisym,axiom,
% 4.12/2.08 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ A @ B )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ B @ A )
% 4.12/2.08 => ( A = B ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_70_order__class_Oorder_Oantisym,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ A )
% 4.12/2.08 => ( A = B ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_71_order__class_Oorder_Oantisym,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ A )
% 4.12/2.08 => ( A = B ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_72_ord__le__eq__trans,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,C: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( ( B = C )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_73_ord__le__eq__trans,axiom,
% 4.12/2.08 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ A @ B )
% 4.12/2.08 => ( ( B = C )
% 4.12/2.08 => ( ord_le516598614nres_a @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_74_ord__le__eq__trans,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( ( B = C )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_75_ord__le__eq__trans,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( B = C )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_76_ord__eq__le__trans,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,C: set_a] :
% 4.12/2.08 ( ( A = B )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ C )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_77_ord__eq__le__trans,axiom,
% 4.12/2.08 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( A = B )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ B @ C )
% 4.12/2.08 => ( ord_le516598614nres_a @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_78_ord__eq__le__trans,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( A = B )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ C )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_79_ord__eq__le__trans,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( A = B )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_80_order__class_Oorder_Oeq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [A2: set_a,B2: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 4.12/2.08 & ( ord_less_eq_set_a @ B2 @ A2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_81_order__class_Oorder_Oeq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [A2: $o > refine424419629nres_a,B2: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ A2 @ B2 )
% 4.12/2.08 & ( ord_le516598614nres_a @ B2 @ A2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_82_order__class_Oorder_Oeq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: refine787176636t_unit,Z: refine787176636t_unit] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [A2: refine787176636t_unit,B2: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A2 @ B2 )
% 4.12/2.08 & ( ord_le1051254044t_unit @ B2 @ A2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_83_order__class_Oorder_Oeq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 4.12/2.08 & ( ord_le519537037nres_a @ B2 @ A2 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_84_antisym__conv,axiom,
% 4.12/2.08 ! [Y3: set_a,X4: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 4.12/2.08 = ( X4 = Y3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_85_antisym__conv,axiom,
% 4.12/2.08 ! [Y3: $o > refine424419629nres_a,X4: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ Y3 @ X4 )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ X4 @ Y3 )
% 4.12/2.08 = ( X4 = Y3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_86_antisym__conv,axiom,
% 4.12/2.08 ! [Y3: refine787176636t_unit,X4: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ Y3 @ X4 )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 4.12/2.08 = ( X4 = Y3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_87_antisym__conv,axiom,
% 4.12/2.08 ! [Y3: refine424419629nres_a,X4: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 4.12/2.08 = ( X4 = Y3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_88_order_Otrans,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,C: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ C )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_89_order_Otrans,axiom,
% 4.12/2.08 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ A @ B )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ B @ C )
% 4.12/2.08 => ( ord_le516598614nres_a @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_90_order_Otrans,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ C )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_91_order_Otrans,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_92_eq__refl,axiom,
% 4.12/2.08 ! [X4: set_a,Y3: set_a] :
% 4.12/2.08 ( ( X4 = Y3 )
% 4.12/2.08 => ( ord_less_eq_set_a @ X4 @ Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_93_eq__refl,axiom,
% 4.12/2.08 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( X4 = Y3 )
% 4.12/2.08 => ( ord_le516598614nres_a @ X4 @ Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_94_eq__refl,axiom,
% 4.12/2.08 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 4.12/2.08 ( ( X4 = Y3 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ X4 @ Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_95_eq__refl,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 4.12/2.08 ( ( X4 = Y3 )
% 4.12/2.08 => ( ord_le519537037nres_a @ X4 @ Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_96_antisym,axiom,
% 4.12/2.08 ! [X4: set_a,Y3: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 4.12/2.08 => ( X4 = Y3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_97_antisym,axiom,
% 4.12/2.08 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ Y3 @ X4 )
% 4.12/2.08 => ( X4 = Y3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_98_antisym,axiom,
% 4.12/2.08 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ Y3 @ X4 )
% 4.12/2.08 => ( X4 = Y3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_99_antisym,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 4.12/2.08 => ( X4 = Y3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_100_eq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [X5: set_a,Y5: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 4.12/2.08 & ( ord_less_eq_set_a @ Y5 @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_101_eq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: $o > refine424419629nres_a,Z: $o > refine424419629nres_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [X5: $o > refine424419629nres_a,Y5: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ X5 @ Y5 )
% 4.12/2.08 & ( ord_le516598614nres_a @ Y5 @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_102_eq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: refine787176636t_unit,Z: refine787176636t_unit] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [X5: refine787176636t_unit,Y5: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X5 @ Y5 )
% 4.12/2.08 & ( ord_le1051254044t_unit @ Y5 @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_103_eq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 4.12/2.08 & ( ord_le519537037nres_a @ Y5 @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_104_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_105_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_106_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_107_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_108_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_109_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,F: set_a > refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_110_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_111_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > set_a,C: set_a] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_112_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_113_ord__le__eq__subst,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ( F @ B )
% 4.12/2.08 = C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le516598614nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le516598614nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_114_mem__Collect__eq,axiom,
% 4.12/2.08 ! [A: product_unit,P: product_unit > $o] :
% 4.12/2.08 ( ( member_Product_unit @ A @ ( collect_Product_unit @ P ) )
% 4.12/2.08 = ( P @ A ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_115_mem__Collect__eq,axiom,
% 4.12/2.08 ! [A: a,P: a > $o] :
% 4.12/2.08 ( ( member_a @ A @ ( collect_a @ P ) )
% 4.12/2.08 = ( P @ A ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_116_Collect__mem__eq,axiom,
% 4.12/2.08 ! [A3: set_Product_unit] :
% 4.12/2.08 ( ( collect_Product_unit
% 4.12/2.08 @ ^ [X5: product_unit] : ( member_Product_unit @ X5 @ A3 ) )
% 4.12/2.08 = A3 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_117_Collect__mem__eq,axiom,
% 4.12/2.08 ! [A3: set_a] :
% 4.12/2.08 ( ( collect_a
% 4.12/2.08 @ ^ [X5: a] : ( member_a @ X5 @ A3 ) )
% 4.12/2.08 = A3 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_118_Collect__cong,axiom,
% 4.12/2.08 ! [P: product_unit > $o,Q: product_unit > $o] :
% 4.12/2.08 ( ! [X3: product_unit] :
% 4.12/2.08 ( ( P @ X3 )
% 4.12/2.08 = ( Q @ X3 ) )
% 4.12/2.08 => ( ( collect_Product_unit @ P )
% 4.12/2.08 = ( collect_Product_unit @ Q ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_119_Collect__cong,axiom,
% 4.12/2.08 ! [P: a > $o,Q: a > $o] :
% 4.12/2.08 ( ! [X3: a] :
% 4.12/2.08 ( ( P @ X3 )
% 4.12/2.08 = ( Q @ X3 ) )
% 4.12/2.08 => ( ( collect_a @ P )
% 4.12/2.08 = ( collect_a @ Q ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_120_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_121_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: set_a,F: refine424419629nres_a > set_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_122_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,F: refine424419629nres_a > refine787176636t_unit,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_123_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,F: set_a > refine424419629nres_a,B: set_a,C: set_a] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_124_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_125_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,F: set_a > refine787176636t_unit,B: set_a,C: set_a] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_126_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,F: refine787176636t_unit > refine424419629nres_a,B: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_127_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: set_a,F: refine787176636t_unit > set_a,B: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_128_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_129_ord__eq__le__subst,axiom,
% 4.12/2.08 ! [A: $o > refine424419629nres_a,F: refine424419629nres_a > $o > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( A
% 4.12/2.08 = ( F @ B ) )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le516598614nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le516598614nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_130_order__subst2,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_131_order__subst2,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_132_order__subst2,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_133_order__subst2,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_134_order__subst2,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_135_order__subst2,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,F: set_a > refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ B )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_136_order__subst2,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_137_order__subst2,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > set_a,C: set_a] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_138_order__subst2,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ B )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_139_order__subst2,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ B )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ ( F @ B ) @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le516598614nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le516598614nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_140_order__subst1,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_141_order__subst1,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,F: set_a > refine424419629nres_a,B: set_a,C: set_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_142_order__subst1,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,F: refine787176636t_unit > refine424419629nres_a,B: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_143_order__subst1,axiom,
% 4.12/2.08 ! [A: set_a,F: refine424419629nres_a > set_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_144_order__subst1,axiom,
% 4.12/2.08 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_145_order__subst1,axiom,
% 4.12/2.08 ! [A: set_a,F: refine787176636t_unit > set_a,B: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_146_order__subst1,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,F: refine424419629nres_a > refine787176636t_unit,B: refine424419629nres_a,C: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a,Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_147_order__subst1,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,F: set_a > refine787176636t_unit,B: set_a,C: set_a] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ C )
% 4.12/2.08 => ( ! [X3: set_a,Y6: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_148_order__subst1,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,F: refine787176636t_unit > refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ C )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit,Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_149_order__subst1,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,F: ( $o > refine424419629nres_a ) > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ B @ C )
% 4.12/2.08 => ( ! [X3: $o > refine424419629nres_a,Y6: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ X3 @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y6 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_150_the__RES__inv,axiom,
% 4.12/2.08 ! [M: refine787176636t_unit] :
% 4.12/2.08 ( ( refine579265252t_unit @ M )
% 4.12/2.08 => ( ( refine1777164439t_unit @ ( refine1208325748t_unit @ M ) )
% 4.12/2.08 = M ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_151_the__RES__inv,axiom,
% 4.12/2.08 ! [M: refine424419629nres_a] :
% 4.12/2.08 ( ( refine412683989fail_a @ M )
% 4.12/2.08 => ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ M ) )
% 4.12/2.08 = M ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_152_Greatest__equality,axiom,
% 4.12/2.08 ! [P: set_a > $o,X4: set_a] :
% 4.12/2.08 ( ( P @ X4 )
% 4.12/2.08 => ( ! [Y6: set_a] :
% 4.12/2.08 ( ( P @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ Y6 @ X4 ) )
% 4.12/2.08 => ( ( order_Greatest_set_a @ P )
% 4.12/2.08 = X4 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_153_Greatest__equality,axiom,
% 4.12/2.08 ! [P: ( $o > refine424419629nres_a ) > $o,X4: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( P @ X4 )
% 4.12/2.08 => ( ! [Y6: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( P @ Y6 )
% 4.12/2.08 => ( ord_le516598614nres_a @ Y6 @ X4 ) )
% 4.12/2.08 => ( ( order_245837199nres_a @ P )
% 4.12/2.08 = X4 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_154_Greatest__equality,axiom,
% 4.12/2.08 ! [P: refine787176636t_unit > $o,X4: refine787176636t_unit] :
% 4.12/2.08 ( ( P @ X4 )
% 4.12/2.08 => ( ! [Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( P @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ Y6 @ X4 ) )
% 4.12/2.08 => ( ( order_453013155t_unit @ P )
% 4.12/2.08 = X4 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_155_Greatest__equality,axiom,
% 4.12/2.08 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a] :
% 4.12/2.08 ( ( P @ X4 )
% 4.12/2.08 => ( ! [Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( P @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ Y6 @ X4 ) )
% 4.12/2.08 => ( ( order_1714329108nres_a @ P )
% 4.12/2.08 = X4 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_156_GreatestI2__order,axiom,
% 4.12/2.08 ! [P: set_a > $o,X4: set_a,Q: set_a > $o] :
% 4.12/2.08 ( ( P @ X4 )
% 4.12/2.08 => ( ! [Y6: set_a] :
% 4.12/2.08 ( ( P @ Y6 )
% 4.12/2.08 => ( ord_less_eq_set_a @ Y6 @ X4 ) )
% 4.12/2.08 => ( ! [X3: set_a] :
% 4.12/2.08 ( ( P @ X3 )
% 4.12/2.08 => ( ! [Y7: set_a] :
% 4.12/2.08 ( ( P @ Y7 )
% 4.12/2.08 => ( ord_less_eq_set_a @ Y7 @ X3 ) )
% 4.12/2.08 => ( Q @ X3 ) ) )
% 4.12/2.08 => ( Q @ ( order_Greatest_set_a @ P ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_157_GreatestI2__order,axiom,
% 4.12/2.08 ! [P: ( $o > refine424419629nres_a ) > $o,X4: $o > refine424419629nres_a,Q: ( $o > refine424419629nres_a ) > $o] :
% 4.12/2.08 ( ( P @ X4 )
% 4.12/2.08 => ( ! [Y6: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( P @ Y6 )
% 4.12/2.08 => ( ord_le516598614nres_a @ Y6 @ X4 ) )
% 4.12/2.08 => ( ! [X3: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( P @ X3 )
% 4.12/2.08 => ( ! [Y7: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( P @ Y7 )
% 4.12/2.08 => ( ord_le516598614nres_a @ Y7 @ X3 ) )
% 4.12/2.08 => ( Q @ X3 ) ) )
% 4.12/2.08 => ( Q @ ( order_245837199nres_a @ P ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_158_GreatestI2__order,axiom,
% 4.12/2.08 ! [P: refine787176636t_unit > $o,X4: refine787176636t_unit,Q: refine787176636t_unit > $o] :
% 4.12/2.08 ( ( P @ X4 )
% 4.12/2.08 => ( ! [Y6: refine787176636t_unit] :
% 4.12/2.08 ( ( P @ Y6 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ Y6 @ X4 ) )
% 4.12/2.08 => ( ! [X3: refine787176636t_unit] :
% 4.12/2.08 ( ( P @ X3 )
% 4.12/2.08 => ( ! [Y7: refine787176636t_unit] :
% 4.12/2.08 ( ( P @ Y7 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ Y7 @ X3 ) )
% 4.12/2.08 => ( Q @ X3 ) ) )
% 4.12/2.08 => ( Q @ ( order_453013155t_unit @ P ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_159_GreatestI2__order,axiom,
% 4.12/2.08 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 4.12/2.08 ( ( P @ X4 )
% 4.12/2.08 => ( ! [Y6: refine424419629nres_a] :
% 4.12/2.08 ( ( P @ Y6 )
% 4.12/2.08 => ( ord_le519537037nres_a @ Y6 @ X4 ) )
% 4.12/2.08 => ( ! [X3: refine424419629nres_a] :
% 4.12/2.08 ( ( P @ X3 )
% 4.12/2.08 => ( ! [Y7: refine424419629nres_a] :
% 4.12/2.08 ( ( P @ Y7 )
% 4.12/2.08 => ( ord_le519537037nres_a @ Y7 @ X3 ) )
% 4.12/2.08 => ( Q @ X3 ) ) )
% 4.12/2.08 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_160_le__rel__bool__arg__iff,axiom,
% 4.12/2.08 ( ord_less_eq_o_set_a
% 4.12/2.08 = ( ^ [X6: $o > set_a,Y8: $o > set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 4.12/2.08 & ( ord_less_eq_set_a @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_161_le__rel__bool__arg__iff,axiom,
% 4.12/2.08 ( ord_le1960259811nres_a
% 4.12/2.08 = ( ^ [X6: $o > $o > refine424419629nres_a,Y8: $o > $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 4.12/2.08 & ( ord_le516598614nres_a @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_162_le__rel__bool__arg__iff,axiom,
% 4.12/2.08 ( ord_le1633311077t_unit
% 4.12/2.08 = ( ^ [X6: $o > refine787176636t_unit,Y8: $o > refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 4.12/2.08 & ( ord_le1051254044t_unit @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_163_le__rel__bool__arg__iff,axiom,
% 4.12/2.08 ( ord_le516598614nres_a
% 4.12/2.08 = ( ^ [X6: $o > refine424419629nres_a,Y8: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 4.12/2.08 & ( ord_le519537037nres_a @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_164_ord__eq__le__eq__trans,axiom,
% 4.12/2.08 ! [A: set_a,B: set_a,C: set_a,D: set_a] :
% 4.12/2.08 ( ( A = B )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B @ C )
% 4.12/2.08 => ( ( C = D )
% 4.12/2.08 => ( ord_less_eq_set_a @ A @ D ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_165_ord__eq__le__eq__trans,axiom,
% 4.12/2.08 ! [A: $o > refine424419629nres_a,B: $o > refine424419629nres_a,C: $o > refine424419629nres_a,D: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( A = B )
% 4.12/2.08 => ( ( ord_le516598614nres_a @ B @ C )
% 4.12/2.08 => ( ( C = D )
% 4.12/2.08 => ( ord_le516598614nres_a @ A @ D ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_166_ord__eq__le__eq__trans,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit,B: refine787176636t_unit,C: refine787176636t_unit,D: refine787176636t_unit] :
% 4.12/2.08 ( ( A = B )
% 4.12/2.08 => ( ( ord_le1051254044t_unit @ B @ C )
% 4.12/2.08 => ( ( C = D )
% 4.12/2.08 => ( ord_le1051254044t_unit @ A @ D ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_167_ord__eq__le__eq__trans,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
% 4.12/2.08 ( ( A = B )
% 4.12/2.08 => ( ( ord_le519537037nres_a @ B @ C )
% 4.12/2.08 => ( ( C = D )
% 4.12/2.08 => ( ord_le519537037nres_a @ A @ D ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_168_bind__cong,axiom,
% 4.12/2.08 ! [M: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine424419629nres_a,F3: a > refine424419629nres_a] :
% 4.12/2.08 ( ( M = M3 )
% 4.12/2.08 => ( ! [X3: a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M3 )
% 4.12/2.08 => ( ( F @ X3 )
% 4.12/2.08 = ( F3 @ X3 ) ) )
% 4.12/2.08 => ( ( refine436832838nd_a_a @ M @ F )
% 4.12/2.08 = ( refine436832838nd_a_a @ M3 @ F3 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_169_bind__cong,axiom,
% 4.12/2.08 ! [M: refine787176636t_unit,M3: refine787176636t_unit,F: product_unit > refine787176636t_unit,F3: product_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( M = M3 )
% 4.12/2.08 => ( ! [X3: product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ M3 )
% 4.12/2.08 => ( ( F @ X3 )
% 4.12/2.08 = ( F3 @ X3 ) ) )
% 4.12/2.08 => ( ( refine681446406t_unit @ M @ F )
% 4.12/2.08 = ( refine681446406t_unit @ M3 @ F3 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_170_bind__cong,axiom,
% 4.12/2.08 ! [M: refine787176636t_unit,M3: refine787176636t_unit,F: product_unit > refine424419629nres_a,F3: product_unit > refine424419629nres_a] :
% 4.12/2.08 ( ( M = M3 )
% 4.12/2.08 => ( ! [X3: product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ M3 )
% 4.12/2.08 => ( ( F @ X3 )
% 4.12/2.08 = ( F3 @ X3 ) ) )
% 4.12/2.08 => ( ( refine119808503unit_a @ M @ F )
% 4.12/2.08 = ( refine119808503unit_a @ M3 @ F3 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_171_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a,M5: refine424419629nres_a,F: a > refine787176636t_unit,F3: a > refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ M4 @ M5 )
% 4.12/2.08 => ( ! [X3: a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M4 @ F ) @ ( refine96995669t_unit @ M5 @ F3 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_172_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 4.12/2.08 ! [M4: refine787176636t_unit,M5: refine787176636t_unit,F: product_unit > refine787176636t_unit,F3: product_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ M4 @ M5 )
% 4.12/2.08 => ( ! [X3: product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ M4 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M4 @ F ) @ ( refine681446406t_unit @ M5 @ F3 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_173_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 4.12/2.08 ! [M4: refine787176636t_unit,M5: refine787176636t_unit,F: product_unit > refine424419629nres_a,F3: product_unit > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ M4 @ M5 )
% 4.12/2.08 => ( ! [X3: product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X3 ) @ M4 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( refine119808503unit_a @ M4 @ F ) @ ( refine119808503unit_a @ M5 @ F3 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_174_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a,M5: refine424419629nres_a,F: a > refine424419629nres_a,F3: a > refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ M4 @ M5 )
% 4.12/2.08 => ( ! [X3: a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine436832838nd_a_a @ M5 @ F3 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_175_nofail__simps_I2_J,axiom,
% 4.12/2.08 ! [X: set_Product_unit] : ( refine579265252t_unit @ ( refine1777164439t_unit @ X ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_176_nofail__simps_I2_J,axiom,
% 4.12/2.08 ! [X: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_177_nofail__simps_I3_J,axiom,
% 4.12/2.08 ! [X4: a] : ( refine412683989fail_a @ ( refine2063221604TURN_a @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_178_nofail__simps_I3_J,axiom,
% 4.12/2.08 ! [X4: product_unit] : ( refine579265252t_unit @ ( refine1420258419t_unit @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_179_nres__monad2,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a] :
% 4.12/2.08 ( ( refine436832838nd_a_a @ M4 @ refine2063221604TURN_a )
% 4.12/2.08 = M4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_180_nres__monad2,axiom,
% 4.12/2.08 ! [M4: refine787176636t_unit] :
% 4.12/2.08 ( ( refine681446406t_unit @ M4 @ refine1420258419t_unit )
% 4.12/2.08 = M4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_181_nres__monad1,axiom,
% 4.12/2.08 ! [X4: a,F: a > refine424419629nres_a] :
% 4.12/2.08 ( ( refine436832838nd_a_a @ ( refine2063221604TURN_a @ X4 ) @ F )
% 4.12/2.08 = ( F @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_182_nres__monad1,axiom,
% 4.12/2.08 ! [X4: product_unit,F: product_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( refine681446406t_unit @ ( refine1420258419t_unit @ X4 ) @ F )
% 4.12/2.08 = ( F @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_183_nres__monad1,axiom,
% 4.12/2.08 ! [X4: product_unit,F: product_unit > refine424419629nres_a] :
% 4.12/2.08 ( ( refine119808503unit_a @ ( refine1420258419t_unit @ X4 ) @ F )
% 4.12/2.08 = ( F @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_184_subset__Collect__conv,axiom,
% 4.12/2.08 ! [S: set_Product_unit,P: product_unit > $o] :
% 4.12/2.08 ( ( ord_le1023748749t_unit @ S @ ( collect_Product_unit @ P ) )
% 4.12/2.08 = ( ! [X5: product_unit] :
% 4.12/2.08 ( ( member_Product_unit @ X5 @ S )
% 4.12/2.08 => ( P @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_185_subset__Collect__conv,axiom,
% 4.12/2.08 ! [S: set_a,P: a > $o] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ S @ ( collect_a @ P ) )
% 4.12/2.08 = ( ! [X5: a] :
% 4.12/2.08 ( ( member_a @ X5 @ S )
% 4.12/2.08 => ( P @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_186_nofail__antimono__fun,axiom,
% 4.12/2.08 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 4.12/2.08 ( ( ord_le516598614nres_a @ F @ G )
% 4.12/2.08 => ( ( refine412683989fail_a @ ( G @ X4 ) )
% 4.12/2.08 => ( refine412683989fail_a @ ( F @ X4 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_187_nofail__RES__conv,axiom,
% 4.12/2.08 ( refine579265252t_unit
% 4.12/2.08 = ( ^ [M6: refine787176636t_unit] :
% 4.12/2.08 ? [M7: set_Product_unit] :
% 4.12/2.08 ( M6
% 4.12/2.08 = ( refine1777164439t_unit @ M7 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_188_nofail__RES__conv,axiom,
% 4.12/2.08 ( refine412683989fail_a
% 4.12/2.08 = ( ^ [M6: refine424419629nres_a] :
% 4.12/2.08 ? [M7: set_a] :
% 4.12/2.08 ( M6
% 4.12/2.08 = ( refine1198353288_RES_a @ M7 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_189_pwD1,axiom,
% 4.12/2.08 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ S @ S2 )
% 4.12/2.08 => ( ( refine412683989fail_a @ S2 )
% 4.12/2.08 => ( refine412683989fail_a @ S ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_190_pwD1,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ S @ S2 )
% 4.12/2.08 => ( ( refine579265252t_unit @ S2 )
% 4.12/2.08 => ( refine579265252t_unit @ S ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_191_le__nofailI,axiom,
% 4.12/2.08 ! [M5: refine424419629nres_a,M4: refine424419629nres_a] :
% 4.12/2.08 ( ( ( refine412683989fail_a @ M5 )
% 4.12/2.08 => ( ord_le519537037nres_a @ M4 @ M5 ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ M4 @ M5 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_192_le__nofailI,axiom,
% 4.12/2.08 ! [M5: refine787176636t_unit,M4: refine787176636t_unit] :
% 4.12/2.08 ( ( ( refine579265252t_unit @ M5 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ M4 @ M5 ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ M4 @ M5 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_193_subsetI,axiom,
% 4.12/2.08 ! [A3: set_Product_unit,B3: set_Product_unit] :
% 4.12/2.08 ( ! [X3: product_unit] :
% 4.12/2.08 ( ( member_Product_unit @ X3 @ A3 )
% 4.12/2.08 => ( member_Product_unit @ X3 @ B3 ) )
% 4.12/2.08 => ( ord_le1023748749t_unit @ A3 @ B3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_194_subsetI,axiom,
% 4.12/2.08 ! [A3: set_a,B3: set_a] :
% 4.12/2.08 ( ! [X3: a] :
% 4.12/2.08 ( ( member_a @ X3 @ A3 )
% 4.12/2.08 => ( member_a @ X3 @ B3 ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_195_subset__antisym,axiom,
% 4.12/2.08 ! [A3: set_a,B3: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B3 @ A3 )
% 4.12/2.08 => ( A3 = B3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_196_pw__bind__leI,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit,M4: refine424419629nres_a,F: a > refine787176636t_unit] :
% 4.12/2.08 ( ( ( refine579265252t_unit @ S )
% 4.12/2.08 => ( refine412683989fail_a @ M4 ) )
% 4.12/2.08 => ( ! [X3: a] :
% 4.12/2.08 ( ( refine412683989fail_a @ M4 )
% 4.12/2.08 => ( ( refine1001002027nres_a @ M4 @ X3 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ S ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M4 @ F ) @ S ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_197_pw__bind__leI,axiom,
% 4.12/2.08 ! [S: refine424419629nres_a,M4: refine424419629nres_a,F: a > refine424419629nres_a] :
% 4.12/2.08 ( ( ( refine412683989fail_a @ S )
% 4.12/2.08 => ( refine412683989fail_a @ M4 ) )
% 4.12/2.08 => ( ! [X3: a] :
% 4.12/2.08 ( ( refine412683989fail_a @ M4 )
% 4.12/2.08 => ( ( refine1001002027nres_a @ M4 @ X3 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ S ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ S ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_198_pw__bind__leI,axiom,
% 4.12/2.08 ! [S: refine424419629nres_a,M4: refine787176636t_unit,F: product_unit > refine424419629nres_a] :
% 4.12/2.08 ( ( ( refine412683989fail_a @ S )
% 4.12/2.08 => ( refine579265252t_unit @ M4 ) )
% 4.12/2.08 => ( ! [X3: product_unit] :
% 4.12/2.08 ( ( refine579265252t_unit @ M4 )
% 4.12/2.08 => ( ( refine558004794t_unit @ M4 @ X3 )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X3 ) @ S ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( refine119808503unit_a @ M4 @ F ) @ S ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_199_pw__bind__leI,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit,M4: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( ( refine579265252t_unit @ S )
% 4.12/2.08 => ( refine579265252t_unit @ M4 ) )
% 4.12/2.08 => ( ! [X3: product_unit] :
% 4.12/2.08 ( ( refine579265252t_unit @ M4 )
% 4.12/2.08 => ( ( refine558004794t_unit @ M4 @ X3 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X3 ) @ S ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M4 @ F ) @ S ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_200_pw__bind__le__iff,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a,F: a > refine787176636t_unit,S: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine96995669t_unit @ M4 @ F ) @ S )
% 4.12/2.08 = ( ( ( refine579265252t_unit @ S )
% 4.12/2.08 => ( refine412683989fail_a @ M4 ) )
% 4.12/2.08 & ! [X5: a] :
% 4.12/2.08 ( ( ( refine412683989fail_a @ M4 )
% 4.12/2.08 & ( refine1001002027nres_a @ M4 @ X5 ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X5 ) @ S ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_201_pw__bind__le__iff,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a,F: a > refine424419629nres_a,S: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ S )
% 4.12/2.08 = ( ( ( refine412683989fail_a @ S )
% 4.12/2.08 => ( refine412683989fail_a @ M4 ) )
% 4.12/2.08 & ! [X5: a] :
% 4.12/2.08 ( ( ( refine412683989fail_a @ M4 )
% 4.12/2.08 & ( refine1001002027nres_a @ M4 @ X5 ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X5 ) @ S ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_202_pw__bind__le__iff,axiom,
% 4.12/2.08 ! [M4: refine787176636t_unit,F: product_unit > refine424419629nres_a,S: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine119808503unit_a @ M4 @ F ) @ S )
% 4.12/2.08 = ( ( ( refine412683989fail_a @ S )
% 4.12/2.08 => ( refine579265252t_unit @ M4 ) )
% 4.12/2.08 & ! [X5: product_unit] :
% 4.12/2.08 ( ( ( refine579265252t_unit @ M4 )
% 4.12/2.08 & ( refine558004794t_unit @ M4 @ X5 ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ ( F @ X5 ) @ S ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_203_pw__bind__le__iff,axiom,
% 4.12/2.08 ! [M4: refine787176636t_unit,F: product_unit > refine787176636t_unit,S: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ ( refine681446406t_unit @ M4 @ F ) @ S )
% 4.12/2.08 = ( ( ( refine579265252t_unit @ S )
% 4.12/2.08 => ( refine579265252t_unit @ M4 ) )
% 4.12/2.08 & ! [X5: product_unit] :
% 4.12/2.08 ( ( ( refine579265252t_unit @ M4 )
% 4.12/2.08 & ( refine558004794t_unit @ M4 @ X5 ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ ( F @ X5 ) @ S ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_204_relprop__triggers_I6_J,axiom,
% 4.12/2.08 ! [R: set_a,R2: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ R @ R2 )
% 4.12/2.08 => ( ord_less_eq_set_a @ R @ R2 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_205_in__mono,axiom,
% 4.12/2.08 ! [A3: set_Product_unit,B3: set_Product_unit,X4: product_unit] :
% 4.12/2.08 ( ( ord_le1023748749t_unit @ A3 @ B3 )
% 4.12/2.08 => ( ( member_Product_unit @ X4 @ A3 )
% 4.12/2.08 => ( member_Product_unit @ X4 @ B3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_206_in__mono,axiom,
% 4.12/2.08 ! [A3: set_a,B3: set_a,X4: a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 4.12/2.08 => ( ( member_a @ X4 @ A3 )
% 4.12/2.08 => ( member_a @ X4 @ B3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_207_subsetD,axiom,
% 4.12/2.08 ! [A3: set_Product_unit,B3: set_Product_unit,C: product_unit] :
% 4.12/2.08 ( ( ord_le1023748749t_unit @ A3 @ B3 )
% 4.12/2.08 => ( ( member_Product_unit @ C @ A3 )
% 4.12/2.08 => ( member_Product_unit @ C @ B3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_208_subsetD,axiom,
% 4.12/2.08 ! [A3: set_a,B3: set_a,C: a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 4.12/2.08 => ( ( member_a @ C @ A3 )
% 4.12/2.08 => ( member_a @ C @ B3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_209_inres__simps_I2_J,axiom,
% 4.12/2.08 ! [X: set_Product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ ( refine1777164439t_unit @ X ) )
% 4.12/2.08 = ( ^ [X5: product_unit] : ( member_Product_unit @ X5 @ X ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_210_inres__simps_I2_J,axiom,
% 4.12/2.08 ! [X: set_a] :
% 4.12/2.08 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X ) )
% 4.12/2.08 = ( ^ [X5: a] : ( member_a @ X5 @ X ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_211_inres__simps_I3_J,axiom,
% 4.12/2.08 ! [X4: a] :
% 4.12/2.08 ( ( refine1001002027nres_a @ ( refine2063221604TURN_a @ X4 ) )
% 4.12/2.08 = ( ^ [Y4: a,Z: a] : ( Y4 = Z )
% 4.12/2.08 @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_212_inres__simps_I3_J,axiom,
% 4.12/2.08 ! [X4: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ ( refine1420258419t_unit @ X4 ) )
% 4.12/2.08 = ( ^ [Y4: product_unit,Z: product_unit] : ( Y4 = Z )
% 4.12/2.08 @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_213_pwD2,axiom,
% 4.12/2.08 ! [S: refine424419629nres_a,S2: refine424419629nres_a,X4: a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ S @ S2 )
% 4.12/2.08 => ( ( refine1001002027nres_a @ S @ X4 )
% 4.12/2.08 => ( refine1001002027nres_a @ S2 @ X4 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_214_pwD2,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit,S2: refine787176636t_unit,X4: product_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ S @ S2 )
% 4.12/2.08 => ( ( refine558004794t_unit @ S @ X4 )
% 4.12/2.08 => ( refine558004794t_unit @ S2 @ X4 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_215_pw__eqI,axiom,
% 4.12/2.08 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 4.12/2.08 ( ( ( refine412683989fail_a @ S )
% 4.12/2.08 = ( refine412683989fail_a @ S2 ) )
% 4.12/2.08 => ( ! [X3: a] :
% 4.12/2.08 ( ( refine1001002027nres_a @ S @ X3 )
% 4.12/2.08 = ( refine1001002027nres_a @ S2 @ X3 ) )
% 4.12/2.08 => ( S = S2 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_216_pw__eqI,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 4.12/2.08 ( ( ( refine579265252t_unit @ S )
% 4.12/2.08 = ( refine579265252t_unit @ S2 ) )
% 4.12/2.08 => ( ! [X3: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ S @ X3 )
% 4.12/2.08 = ( refine558004794t_unit @ S2 @ X3 ) )
% 4.12/2.08 => ( S = S2 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_217_pw__eq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 4.12/2.08 ( ( ( refine412683989fail_a @ S3 )
% 4.12/2.08 = ( refine412683989fail_a @ S4 ) )
% 4.12/2.08 & ! [X5: a] :
% 4.12/2.08 ( ( refine1001002027nres_a @ S3 @ X5 )
% 4.12/2.08 = ( refine1001002027nres_a @ S4 @ X5 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_218_pw__eq__iff,axiom,
% 4.12/2.08 ( ( ^ [Y4: refine787176636t_unit,Z: refine787176636t_unit] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [S3: refine787176636t_unit,S4: refine787176636t_unit] :
% 4.12/2.08 ( ( ( refine579265252t_unit @ S3 )
% 4.12/2.08 = ( refine579265252t_unit @ S4 ) )
% 4.12/2.08 & ! [X5: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ S3 @ X5 )
% 4.12/2.08 = ( refine558004794t_unit @ S4 @ X5 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_219_not__nofail__inres,axiom,
% 4.12/2.08 ! [S: refine424419629nres_a,X4: a] :
% 4.12/2.08 ( ~ ( refine412683989fail_a @ S )
% 4.12/2.08 => ( refine1001002027nres_a @ S @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_220_not__nofail__inres,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit,X4: product_unit] :
% 4.12/2.08 ( ~ ( refine579265252t_unit @ S )
% 4.12/2.08 => ( refine558004794t_unit @ S @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_221_pw__le__iff,axiom,
% 4.12/2.08 ( ord_le519537037nres_a
% 4.12/2.08 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 4.12/2.08 ( ( refine412683989fail_a @ S4 )
% 4.12/2.08 => ( ( refine412683989fail_a @ S3 )
% 4.12/2.08 & ! [X5: a] :
% 4.12/2.08 ( ( refine1001002027nres_a @ S3 @ X5 )
% 4.12/2.08 => ( refine1001002027nres_a @ S4 @ X5 ) ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_222_pw__le__iff,axiom,
% 4.12/2.08 ( ord_le1051254044t_unit
% 4.12/2.08 = ( ^ [S3: refine787176636t_unit,S4: refine787176636t_unit] :
% 4.12/2.08 ( ( refine579265252t_unit @ S4 )
% 4.12/2.08 => ( ( refine579265252t_unit @ S3 )
% 4.12/2.08 & ! [X5: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ S3 @ X5 )
% 4.12/2.08 => ( refine558004794t_unit @ S4 @ X5 ) ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_223_pw__leI_H,axiom,
% 4.12/2.08 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 4.12/2.08 ( ( ( refine412683989fail_a @ S2 )
% 4.12/2.08 => ( refine412683989fail_a @ S ) )
% 4.12/2.08 => ( ! [X3: a] :
% 4.12/2.08 ( ( refine412683989fail_a @ S2 )
% 4.12/2.08 => ( ( refine1001002027nres_a @ S @ X3 )
% 4.12/2.08 => ( refine1001002027nres_a @ S2 @ X3 ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ S @ S2 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_224_pw__leI_H,axiom,
% 4.12/2.08 ! [S2: refine787176636t_unit,S: refine787176636t_unit] :
% 4.12/2.08 ( ( ( refine579265252t_unit @ S2 )
% 4.12/2.08 => ( refine579265252t_unit @ S ) )
% 4.12/2.08 => ( ! [X3: product_unit] :
% 4.12/2.08 ( ( refine579265252t_unit @ S2 )
% 4.12/2.08 => ( ( refine558004794t_unit @ S @ X3 )
% 4.12/2.08 => ( refine558004794t_unit @ S2 @ X3 ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ S @ S2 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_225_pw__leI,axiom,
% 4.12/2.08 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 4.12/2.08 ( ( ( refine412683989fail_a @ S2 )
% 4.12/2.08 => ( ( refine412683989fail_a @ S )
% 4.12/2.08 & ! [X3: a] :
% 4.12/2.08 ( ( refine1001002027nres_a @ S @ X3 )
% 4.12/2.08 => ( refine1001002027nres_a @ S2 @ X3 ) ) ) )
% 4.12/2.08 => ( ord_le519537037nres_a @ S @ S2 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_226_pw__leI,axiom,
% 4.12/2.08 ! [S2: refine787176636t_unit,S: refine787176636t_unit] :
% 4.12/2.08 ( ( ( refine579265252t_unit @ S2 )
% 4.12/2.08 => ( ( refine579265252t_unit @ S )
% 4.12/2.08 & ! [X3: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ S @ X3 )
% 4.12/2.08 => ( refine558004794t_unit @ S2 @ X3 ) ) ) )
% 4.12/2.08 => ( ord_le1051254044t_unit @ S @ S2 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_227_pw__bind__nofail,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a,F: a > refine787176636t_unit] :
% 4.12/2.08 ( ( refine579265252t_unit @ ( refine96995669t_unit @ M4 @ F ) )
% 4.12/2.08 = ( ( refine412683989fail_a @ M4 )
% 4.12/2.08 & ! [X5: a] :
% 4.12/2.08 ( ( refine1001002027nres_a @ M4 @ X5 )
% 4.12/2.08 => ( refine579265252t_unit @ ( F @ X5 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_228_pw__bind__nofail,axiom,
% 4.12/2.08 ! [M4: refine787176636t_unit,F: product_unit > refine424419629nres_a] :
% 4.12/2.08 ( ( refine412683989fail_a @ ( refine119808503unit_a @ M4 @ F ) )
% 4.12/2.08 = ( ( refine579265252t_unit @ M4 )
% 4.12/2.08 & ! [X5: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ M4 @ X5 )
% 4.12/2.08 => ( refine412683989fail_a @ ( F @ X5 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_229_pw__bind__nofail,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a,F: a > refine424419629nres_a] :
% 4.12/2.08 ( ( refine412683989fail_a @ ( refine436832838nd_a_a @ M4 @ F ) )
% 4.12/2.08 = ( ( refine412683989fail_a @ M4 )
% 4.12/2.08 & ! [X5: a] :
% 4.12/2.08 ( ( refine1001002027nres_a @ M4 @ X5 )
% 4.12/2.08 => ( refine412683989fail_a @ ( F @ X5 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_230_pw__bind__nofail,axiom,
% 4.12/2.08 ! [M4: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( refine579265252t_unit @ ( refine681446406t_unit @ M4 @ F ) )
% 4.12/2.08 = ( ( refine579265252t_unit @ M4 )
% 4.12/2.08 & ! [X5: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ M4 @ X5 )
% 4.12/2.08 => ( refine579265252t_unit @ ( F @ X5 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_231_inres__def,axiom,
% 4.12/2.08 ( refine1001002027nres_a
% 4.12/2.08 = ( ^ [S3: refine424419629nres_a,X5: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X5 ) @ S3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_232_inres__def,axiom,
% 4.12/2.08 ( refine558004794t_unit
% 4.12/2.08 = ( ^ [S3: refine787176636t_unit,X5: product_unit] : ( ord_le1051254044t_unit @ ( refine1420258419t_unit @ X5 ) @ S3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_233_nf__inres__def,axiom,
% 4.12/2.08 ( refine983493746t_unit
% 4.12/2.08 = ( ^ [M6: refine787176636t_unit,X5: product_unit] :
% 4.12/2.08 ( ( refine579265252t_unit @ M6 )
% 4.12/2.08 & ( refine558004794t_unit @ M6 @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_234_nf__inres__def,axiom,
% 4.12/2.08 ( refine1312857699nres_a
% 4.12/2.08 = ( ^ [M6: refine424419629nres_a,X5: a] :
% 4.12/2.08 ( ( refine412683989fail_a @ M6 )
% 4.12/2.08 & ( refine1001002027nres_a @ M6 @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_235_Collect__mono__iff,axiom,
% 4.12/2.08 ! [P: product_unit > $o,Q: product_unit > $o] :
% 4.12/2.08 ( ( ord_le1023748749t_unit @ ( collect_Product_unit @ P ) @ ( collect_Product_unit @ Q ) )
% 4.12/2.08 = ( ! [X5: product_unit] :
% 4.12/2.08 ( ( P @ X5 )
% 4.12/2.08 => ( Q @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_236_Collect__mono__iff,axiom,
% 4.12/2.08 ! [P: a > $o,Q: a > $o] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 4.12/2.08 = ( ! [X5: a] :
% 4.12/2.08 ( ( P @ X5 )
% 4.12/2.08 => ( Q @ X5 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_237_set__eq__subset,axiom,
% 4.12/2.08 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 4.12/2.08 = ( ^ [A4: set_a,B4: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A4 @ B4 )
% 4.12/2.08 & ( ord_less_eq_set_a @ B4 @ A4 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_238_subset__trans,axiom,
% 4.12/2.08 ! [A3: set_a,B3: set_a,C2: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 4.12/2.08 => ( ord_less_eq_set_a @ A3 @ C2 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_239_Collect__mono,axiom,
% 4.12/2.08 ! [P: product_unit > $o,Q: product_unit > $o] :
% 4.12/2.08 ( ! [X3: product_unit] :
% 4.12/2.08 ( ( P @ X3 )
% 4.12/2.08 => ( Q @ X3 ) )
% 4.12/2.08 => ( ord_le1023748749t_unit @ ( collect_Product_unit @ P ) @ ( collect_Product_unit @ Q ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_240_Collect__mono,axiom,
% 4.12/2.08 ! [P: a > $o,Q: a > $o] :
% 4.12/2.08 ( ! [X3: a] :
% 4.12/2.08 ( ( P @ X3 )
% 4.12/2.08 => ( Q @ X3 ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_241_subset__refl,axiom,
% 4.12/2.08 ! [A3: set_a] : ( ord_less_eq_set_a @ A3 @ A3 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_242_subset__iff,axiom,
% 4.12/2.08 ( ord_le1023748749t_unit
% 4.12/2.08 = ( ^ [A4: set_Product_unit,B4: set_Product_unit] :
% 4.12/2.08 ! [T3: product_unit] :
% 4.12/2.08 ( ( member_Product_unit @ T3 @ A4 )
% 4.12/2.08 => ( member_Product_unit @ T3 @ B4 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_243_subset__iff,axiom,
% 4.12/2.08 ( ord_less_eq_set_a
% 4.12/2.08 = ( ^ [A4: set_a,B4: set_a] :
% 4.12/2.08 ! [T3: a] :
% 4.12/2.08 ( ( member_a @ T3 @ A4 )
% 4.12/2.08 => ( member_a @ T3 @ B4 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_244_equalityD2,axiom,
% 4.12/2.08 ! [A3: set_a,B3: set_a] :
% 4.12/2.08 ( ( A3 = B3 )
% 4.12/2.08 => ( ord_less_eq_set_a @ B3 @ A3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_245_equalityD1,axiom,
% 4.12/2.08 ! [A3: set_a,B3: set_a] :
% 4.12/2.08 ( ( A3 = B3 )
% 4.12/2.08 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_246_subset__eq,axiom,
% 4.12/2.08 ( ord_le1023748749t_unit
% 4.12/2.08 = ( ^ [A4: set_Product_unit,B4: set_Product_unit] :
% 4.12/2.08 ! [X5: product_unit] :
% 4.12/2.08 ( ( member_Product_unit @ X5 @ A4 )
% 4.12/2.08 => ( member_Product_unit @ X5 @ B4 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_247_subset__eq,axiom,
% 4.12/2.08 ( ord_less_eq_set_a
% 4.12/2.08 = ( ^ [A4: set_a,B4: set_a] :
% 4.12/2.08 ! [X5: a] :
% 4.12/2.08 ( ( member_a @ X5 @ A4 )
% 4.12/2.08 => ( member_a @ X5 @ B4 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_248_less__eq__nres_Oelims_I1_J,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 4.12/2.08 ( ( ( ord_le519537037nres_a @ X4 @ Xa )
% 4.12/2.08 = Y3 )
% 4.12/2.08 => ( ( ( Xa = refine464223677AILi_a )
% 4.12/2.08 => ~ Y3 )
% 4.12/2.08 => ( ! [A5: set_a] :
% 4.12/2.08 ( ( X4
% 4.12/2.08 = ( refine1198353288_RES_a @ A5 ) )
% 4.12/2.08 => ! [B5: set_a] :
% 4.12/2.08 ( ( Xa
% 4.12/2.08 = ( refine1198353288_RES_a @ B5 ) )
% 4.12/2.08 => ( Y3
% 4.12/2.08 = ( ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) )
% 4.12/2.08 => ~ ( ( X4 = refine464223677AILi_a )
% 4.12/2.08 => ( ? [Uv: set_a] :
% 4.12/2.08 ( Xa
% 4.12/2.08 = ( refine1198353288_RES_a @ Uv ) )
% 4.12/2.08 => Y3 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_249_less__eq__nres_Oelims_I2_J,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ X4 @ Xa )
% 4.12/2.08 => ( ( Xa != refine464223677AILi_a )
% 4.12/2.08 => ~ ! [A5: set_a] :
% 4.12/2.08 ( ( X4
% 4.12/2.08 = ( refine1198353288_RES_a @ A5 ) )
% 4.12/2.08 => ! [B5: set_a] :
% 4.12/2.08 ( ( Xa
% 4.12/2.08 = ( refine1198353288_RES_a @ B5 ) )
% 4.12/2.08 => ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_250_less__eq__nres_Oelims_I3_J,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 4.12/2.08 ( ~ ( ord_le519537037nres_a @ X4 @ Xa )
% 4.12/2.08 => ( ! [A5: set_a] :
% 4.12/2.08 ( ( X4
% 4.12/2.08 = ( refine1198353288_RES_a @ A5 ) )
% 4.12/2.08 => ! [B5: set_a] :
% 4.12/2.08 ( ( Xa
% 4.12/2.08 = ( refine1198353288_RES_a @ B5 ) )
% 4.12/2.08 => ( ord_less_eq_set_a @ A5 @ B5 ) ) )
% 4.12/2.08 => ~ ( ( X4 = refine464223677AILi_a )
% 4.12/2.08 => ! [Uv: set_a] :
% 4.12/2.08 ( Xa
% 4.12/2.08 != ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_251_nres__order__simps_I22_J,axiom,
% 4.12/2.08 ! [X: set_a,Y3: a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine2063221604TURN_a @ Y3 ) )
% 4.12/2.08 = ( ord_less_eq_set_a @ X @ ( insert_a @ Y3 @ bot_bot_set_a ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_252_less__eq__nres_Osimps_I3_J,axiom,
% 4.12/2.08 ! [Uv2: set_a] :
% 4.12/2.08 ~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv2 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_253_empty__iff,axiom,
% 4.12/2.08 ! [C: a] :
% 4.12/2.08 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_254_all__not__in__conv,axiom,
% 4.12/2.08 ! [A3: set_a] :
% 4.12/2.08 ( ( ! [X5: a] :
% 4.12/2.08 ~ ( member_a @ X5 @ A3 ) )
% 4.12/2.08 = ( A3 = bot_bot_set_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_255_Collect__empty__eq,axiom,
% 4.12/2.08 ! [P: a > $o] :
% 4.12/2.08 ( ( ( collect_a @ P )
% 4.12/2.08 = bot_bot_set_a )
% 4.12/2.08 = ( ! [X5: a] :
% 4.12/2.08 ~ ( P @ X5 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_256_empty__Collect__eq,axiom,
% 4.12/2.08 ! [P: a > $o] :
% 4.12/2.08 ( ( bot_bot_set_a
% 4.12/2.08 = ( collect_a @ P ) )
% 4.12/2.08 = ( ! [X5: a] :
% 4.12/2.08 ~ ( P @ X5 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_257_insertCI,axiom,
% 4.12/2.08 ! [A: a,B3: set_a,B: a] :
% 4.12/2.08 ( ( ~ ( member_a @ A @ B3 )
% 4.12/2.08 => ( A = B ) )
% 4.12/2.08 => ( member_a @ A @ ( insert_a @ B @ B3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_258_insert__iff,axiom,
% 4.12/2.08 ! [A: a,B: a,A3: set_a] :
% 4.12/2.08 ( ( member_a @ A @ ( insert_a @ B @ A3 ) )
% 4.12/2.08 = ( ( A = B )
% 4.12/2.08 | ( member_a @ A @ A3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_259_singletonI,axiom,
% 4.12/2.08 ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_260_insert__subset,axiom,
% 4.12/2.08 ! [X4: a,A3: set_a,B3: set_a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ ( insert_a @ X4 @ A3 ) @ B3 )
% 4.12/2.08 = ( ( member_a @ X4 @ B3 )
% 4.12/2.08 & ( ord_less_eq_set_a @ A3 @ B3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_261_nres__more__simps_I5_J,axiom,
% 4.12/2.08 ! [X4: a,X: set_a] :
% 4.12/2.08 ( ( ( refine2063221604TURN_a @ X4 )
% 4.12/2.08 = ( refine1198353288_RES_a @ X ) )
% 4.12/2.08 = ( ( insert_a @ X4 @ bot_bot_set_a )
% 4.12/2.08 = X ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_262_nres__more__simps_I3_J,axiom,
% 4.12/2.08 ! [X: set_a,X4: a] :
% 4.12/2.08 ( ( ( refine1198353288_RES_a @ X )
% 4.12/2.08 = ( refine2063221604TURN_a @ X4 ) )
% 4.12/2.08 = ( X
% 4.12/2.08 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_263_emptyE,axiom,
% 4.12/2.08 ! [A: a] :
% 4.12/2.08 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_264_insertE,axiom,
% 4.12/2.08 ! [A: a,B: a,A3: set_a] :
% 4.12/2.08 ( ( member_a @ A @ ( insert_a @ B @ A3 ) )
% 4.12/2.08 => ( ( A != B )
% 4.12/2.08 => ( member_a @ A @ A3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_265_equals0D,axiom,
% 4.12/2.08 ! [A3: set_a,A: a] :
% 4.12/2.08 ( ( A3 = bot_bot_set_a )
% 4.12/2.08 => ~ ( member_a @ A @ A3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_266_equals0I,axiom,
% 4.12/2.08 ! [A3: set_a] :
% 4.12/2.08 ( ! [Y6: a] :
% 4.12/2.08 ~ ( member_a @ Y6 @ A3 )
% 4.12/2.08 => ( A3 = bot_bot_set_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_267_insertI1,axiom,
% 4.12/2.08 ! [A: a,B3: set_a] : ( member_a @ A @ ( insert_a @ A @ B3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_268_insertI2,axiom,
% 4.12/2.08 ! [A: a,B3: set_a,B: a] :
% 4.12/2.08 ( ( member_a @ A @ B3 )
% 4.12/2.08 => ( member_a @ A @ ( insert_a @ B @ B3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_269_ex__in__conv,axiom,
% 4.12/2.08 ! [A3: set_a] :
% 4.12/2.08 ( ( ? [X5: a] : ( member_a @ X5 @ A3 ) )
% 4.12/2.08 = ( A3 != bot_bot_set_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_270_Set_Oset__insert,axiom,
% 4.12/2.08 ! [X4: a,A3: set_a] :
% 4.12/2.08 ( ( member_a @ X4 @ A3 )
% 4.12/2.08 => ~ ! [B6: set_a] :
% 4.12/2.08 ( ( A3
% 4.12/2.08 = ( insert_a @ X4 @ B6 ) )
% 4.12/2.08 => ( member_a @ X4 @ B6 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_271_singletonD,axiom,
% 4.12/2.08 ! [B: a,A: a] :
% 4.12/2.08 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 4.12/2.08 => ( B = A ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_272_insert__ident,axiom,
% 4.12/2.08 ! [X4: a,A3: set_a,B3: set_a] :
% 4.12/2.08 ( ~ ( member_a @ X4 @ A3 )
% 4.12/2.08 => ( ~ ( member_a @ X4 @ B3 )
% 4.12/2.08 => ( ( ( insert_a @ X4 @ A3 )
% 4.12/2.08 = ( insert_a @ X4 @ B3 ) )
% 4.12/2.08 = ( A3 = B3 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_273_insert__absorb,axiom,
% 4.12/2.08 ! [A: a,A3: set_a] :
% 4.12/2.08 ( ( member_a @ A @ A3 )
% 4.12/2.08 => ( ( insert_a @ A @ A3 )
% 4.12/2.08 = A3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_274_insert__eq__iff,axiom,
% 4.12/2.08 ! [A: a,A3: set_a,B: a,B3: set_a] :
% 4.12/2.08 ( ~ ( member_a @ A @ A3 )
% 4.12/2.08 => ( ~ ( member_a @ B @ B3 )
% 4.12/2.08 => ( ( ( insert_a @ A @ A3 )
% 4.12/2.08 = ( insert_a @ B @ B3 ) )
% 4.12/2.08 = ( ( ( A = B )
% 4.12/2.08 => ( A3 = B3 ) )
% 4.12/2.08 & ( ( A != B )
% 4.12/2.08 => ? [C3: set_a] :
% 4.12/2.08 ( ( A3
% 4.12/2.08 = ( insert_a @ B @ C3 ) )
% 4.12/2.08 & ~ ( member_a @ B @ C3 )
% 4.12/2.08 & ( B3
% 4.12/2.08 = ( insert_a @ A @ C3 ) )
% 4.12/2.08 & ~ ( member_a @ A @ C3 ) ) ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_275_singleton__iff,axiom,
% 4.12/2.08 ! [B: a,A: a] :
% 4.12/2.08 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 4.12/2.08 = ( B = A ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_276_mk__disjoint__insert,axiom,
% 4.12/2.08 ! [A: a,A3: set_a] :
% 4.12/2.08 ( ( member_a @ A @ A3 )
% 4.12/2.08 => ? [B6: set_a] :
% 4.12/2.08 ( ( A3
% 4.12/2.08 = ( insert_a @ A @ B6 ) )
% 4.12/2.08 & ~ ( member_a @ A @ B6 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_277_set__notEmptyE,axiom,
% 4.12/2.08 ! [S: set_a] :
% 4.12/2.08 ( ( S != bot_bot_set_a )
% 4.12/2.08 => ~ ! [X3: a] :
% 4.12/2.08 ~ ( member_a @ X3 @ S ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_278_memb__imp__not__empty,axiom,
% 4.12/2.08 ! [X4: a,S: set_a] :
% 4.12/2.08 ( ( member_a @ X4 @ S )
% 4.12/2.08 => ( S != bot_bot_set_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_279_bot_Oextremum,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ A ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_280_bot_Oextremum,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_281_bot_Oextremum__unique,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
% 4.12/2.08 = ( A = bot_bo658782032t_unit ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_282_bot_Oextremum__unique,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
% 4.12/2.08 = ( A = bot_bo529555393nres_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_283_bot_Oextremum__uniqueI,axiom,
% 4.12/2.08 ! [A: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ A @ bot_bo658782032t_unit )
% 4.12/2.08 => ( A = bot_bo658782032t_unit ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_284_bot_Oextremum__uniqueI,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
% 4.12/2.08 => ( A = bot_bo529555393nres_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_285_subset__insert,axiom,
% 4.12/2.08 ! [X4: a,A3: set_a,B3: set_a] :
% 4.12/2.08 ( ~ ( member_a @ X4 @ A3 )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ A3 @ ( insert_a @ X4 @ B3 ) )
% 4.12/2.08 = ( ord_less_eq_set_a @ A3 @ B3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_286_RETURN__def,axiom,
% 4.12/2.08 ( refine2063221604TURN_a
% 4.12/2.08 = ( ^ [X5: a] : ( refine1198353288_RES_a @ ( insert_a @ X5 @ bot_bot_set_a ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_287_nres_Odistinct_I1_J,axiom,
% 4.12/2.08 ! [X2: set_a] :
% 4.12/2.08 ( refine464223677AILi_a
% 4.12/2.08 != ( refine1198353288_RES_a @ X2 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_288_nres_Oinduct,axiom,
% 4.12/2.08 ! [P: refine424419629nres_a > $o,Nres: refine424419629nres_a] :
% 4.12/2.08 ( ( P @ refine464223677AILi_a )
% 4.12/2.08 => ( ! [X3: set_a] : ( P @ ( refine1198353288_RES_a @ X3 ) )
% 4.12/2.08 => ( P @ Nres ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_289_nres_Oexhaust,axiom,
% 4.12/2.08 ! [Y3: refine424419629nres_a] :
% 4.12/2.08 ( ( Y3 != refine464223677AILi_a )
% 4.12/2.08 => ~ ! [X22: set_a] :
% 4.12/2.08 ( Y3
% 4.12/2.08 != ( refine1198353288_RES_a @ X22 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_290_sup__nres_Oinduct,axiom,
% 4.12/2.08 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 4.12/2.08 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 4.12/2.08 => ( ! [V2: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V2 ) )
% 4.12/2.08 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 4.12/2.08 => ( P @ A0 @ A1 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_291_less__nres_Oinduct,axiom,
% 4.12/2.08 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 4.12/2.08 ( ! [X_1: refine424419629nres_a] : ( P @ refine464223677AILi_a @ X_1 )
% 4.12/2.08 => ( ! [Uv: set_a] : ( P @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a )
% 4.12/2.08 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 4.12/2.08 => ( P @ A0 @ A1 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_292_less__eq__nres_Oinduct,axiom,
% 4.12/2.08 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 4.12/2.08 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 4.12/2.08 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 4.12/2.08 => ( ! [Uv: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) )
% 4.12/2.08 => ( P @ A0 @ A1 ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_293_less__eq__nres_Osimps_I1_J,axiom,
% 4.12/2.08 ! [Uu2: refine424419629nres_a] : ( ord_le519537037nres_a @ Uu2 @ refine464223677AILi_a ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_294_insert__subsetI,axiom,
% 4.12/2.08 ! [X4: a,A3: set_a,X: set_a] :
% 4.12/2.08 ( ( member_a @ X4 @ A3 )
% 4.12/2.08 => ( ( ord_less_eq_set_a @ X @ A3 )
% 4.12/2.08 => ( ord_less_eq_set_a @ ( insert_a @ X4 @ X ) @ A3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_295_subset__emptyI,axiom,
% 4.12/2.08 ! [A3: set_a] :
% 4.12/2.08 ( ! [X3: a] :
% 4.12/2.08 ~ ( member_a @ X3 @ A3 )
% 4.12/2.08 => ( ord_less_eq_set_a @ A3 @ bot_bot_set_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_296_nres__order__simps_I2_J,axiom,
% 4.12/2.08 ! [M4: refine787176636t_unit] :
% 4.12/2.08 ( ( ord_le1051254044t_unit @ M4 @ bot_bo658782032t_unit )
% 4.12/2.08 = ( M4 = bot_bo658782032t_unit ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_297_nres__order__simps_I2_J,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ M4 @ bot_bo529555393nres_a )
% 4.12/2.08 = ( M4 = bot_bo529555393nres_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_298_nofail__simps_I4_J,axiom,
% 4.12/2.08 refine579265252t_unit @ bot_bo658782032t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(fact_299_inres__simps_I4_J,axiom,
% 4.12/2.08 ( ( refine558004794t_unit @ bot_bo658782032t_unit )
% 4.12/2.08 = ( ^ [Uu3: product_unit] : $false ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_300_bind__SUCCEED,axiom,
% 4.12/2.08 ! [F: product_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( refine681446406t_unit @ bot_bo658782032t_unit @ F )
% 4.12/2.08 = bot_bo658782032t_unit ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_301_nres__more__simps_I2_J,axiom,
% 4.12/2.08 ! [X: set_Product_unit] :
% 4.12/2.08 ( ( ( refine1777164439t_unit @ X )
% 4.12/2.08 = bot_bo658782032t_unit )
% 4.12/2.08 = ( X = bot_bo1087887705t_unit ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_302_nres__more__simps_I2_J,axiom,
% 4.12/2.08 ! [X: set_a] :
% 4.12/2.08 ( ( ( refine1198353288_RES_a @ X )
% 4.12/2.08 = bot_bo529555393nres_a )
% 4.12/2.08 = ( X = bot_bot_set_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_303_nres__more__simps_I1_J,axiom,
% 4.12/2.08 ! [X: set_Product_unit] :
% 4.12/2.08 ( ( bot_bo658782032t_unit
% 4.12/2.08 = ( refine1777164439t_unit @ X ) )
% 4.12/2.08 = ( X = bot_bo1087887705t_unit ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_304_nres__more__simps_I1_J,axiom,
% 4.12/2.08 ! [X: set_a] :
% 4.12/2.08 ( ( bot_bo529555393nres_a
% 4.12/2.08 = ( refine1198353288_RES_a @ X ) )
% 4.12/2.08 = ( X = bot_bot_set_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_305_bot__set__def,axiom,
% 4.12/2.08 ( bot_bot_set_a
% 4.12/2.08 = ( collect_a @ bot_bot_a_o ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_306_nres__order__simps_I1_J,axiom,
% 4.12/2.08 ! [M4: refine787176636t_unit] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ M4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_307_nres__order__simps_I1_J,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ M4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_308_nres__inequalities_I5_J,axiom,
% 4.12/2.08 ! [X4: product_unit] :
% 4.12/2.08 ( bot_bo658782032t_unit
% 4.12/2.08 != ( refine1420258419t_unit @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_309_bot__nres__def,axiom,
% 4.12/2.08 ( bot_bo658782032t_unit
% 4.12/2.08 = ( refine1777164439t_unit @ bot_bo1087887705t_unit ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_310_bot__nres__def,axiom,
% 4.12/2.08 ( bot_bo529555393nres_a
% 4.12/2.08 = ( refine1198353288_RES_a @ bot_bot_set_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_311_SUCCEED__rule,axiom,
% 4.12/2.08 ! [Phi: product_unit > $o] : ( ord_le1051254044t_unit @ bot_bo658782032t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_312_SUCCEED__rule,axiom,
% 4.12/2.08 ! [Phi: a > $o] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_313_is__singletonI_H,axiom,
% 4.12/2.08 ! [A3: set_a] :
% 4.12/2.08 ( ( A3 != bot_bot_set_a )
% 4.12/2.08 => ( ! [X3: a,Y6: a] :
% 4.12/2.08 ( ( member_a @ X3 @ A3 )
% 4.12/2.08 => ( ( member_a @ Y6 @ A3 )
% 4.12/2.08 => ( X3 = Y6 ) ) )
% 4.12/2.08 => ( is_singleton_a @ A3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_314_subset__Compl__singleton,axiom,
% 4.12/2.08 ! [A3: set_a,B: a] :
% 4.12/2.08 ( ( ord_less_eq_set_a @ A3 @ ( uminus_uminus_set_a @ ( insert_a @ B @ bot_bot_set_a ) ) )
% 4.12/2.08 = ( ~ ( member_a @ B @ A3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_315_strictD__simp,axiom,
% 4.12/2.08 ! [F: refine787176636t_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( refine459374679t_unit @ F )
% 4.12/2.08 => ( ( F @ bot_bo658782032t_unit )
% 4.12/2.08 = bot_bo658782032t_unit ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_316_Collect__empty__eq__bot,axiom,
% 4.12/2.08 ! [P: a > $o] :
% 4.12/2.08 ( ( ( collect_a @ P )
% 4.12/2.08 = bot_bot_set_a )
% 4.12/2.08 = ( P = bot_bot_a_o ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_317_ComplI,axiom,
% 4.12/2.08 ! [C: a,A3: set_a] :
% 4.12/2.08 ( ~ ( member_a @ C @ A3 )
% 4.12/2.08 => ( member_a @ C @ ( uminus_uminus_set_a @ A3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_318_Compl__iff,axiom,
% 4.12/2.08 ! [C: a,A3: set_a] :
% 4.12/2.08 ( ( member_a @ C @ ( uminus_uminus_set_a @ A3 ) )
% 4.12/2.08 = ( ~ ( member_a @ C @ A3 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_319_ibind__strict_I1_J,axiom,
% 4.12/2.08 ! [F: product_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( refine681446406t_unit @ bot_bo658782032t_unit @ F )
% 4.12/2.08 = bot_bo658782032t_unit ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_320_ComplD,axiom,
% 4.12/2.08 ! [C: a,A3: set_a] :
% 4.12/2.08 ( ( member_a @ C @ ( uminus_uminus_set_a @ A3 ) )
% 4.12/2.08 => ~ ( member_a @ C @ A3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_321_strictD,axiom,
% 4.12/2.08 ! [F: refine787176636t_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( refine459374679t_unit @ F )
% 4.12/2.08 => ( ( F @ bot_bo658782032t_unit )
% 4.12/2.08 = bot_bo658782032t_unit ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_322_strictI,axiom,
% 4.12/2.08 ! [F: refine787176636t_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( ( F @ bot_bo658782032t_unit )
% 4.12/2.08 = bot_bo658782032t_unit )
% 4.12/2.08 => ( refine459374679t_unit @ F ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_323_strict__def,axiom,
% 4.12/2.08 ( refine459374679t_unit
% 4.12/2.08 = ( ^ [F2: refine787176636t_unit > refine787176636t_unit] :
% 4.12/2.08 ( ( F2 @ bot_bo658782032t_unit )
% 4.12/2.08 = bot_bo658782032t_unit ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_324_bot__empty__eq,axiom,
% 4.12/2.08 ( bot_bot_a_o
% 4.12/2.08 = ( ^ [X5: a] : ( member_a @ X5 @ bot_bot_set_a ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_325_ASSUME__simps_I2_J,axiom,
% 4.12/2.08 ( ( refine23983189ASSUME @ $false )
% 4.12/2.08 = bot_bo658782032t_unit ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_326_pw__flat__le__iff,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 4.12/2.08 ( ( partia1658438072t_unit @ bot_bo658782032t_unit @ S @ S2 )
% 4.12/2.08 = ( ? [X7: product_unit] : ( refine558004794t_unit @ S @ X7 )
% 4.12/2.08 => ( ( ( refine579265252t_unit @ S )
% 4.12/2.08 = ( refine579265252t_unit @ S2 ) )
% 4.12/2.08 & ! [X5: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ S @ X5 )
% 4.12/2.08 = ( refine558004794t_unit @ S2 @ X5 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_327_pw__ASSUME_I2_J,axiom,
% 4.12/2.08 ! [Phi: $o,X4: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ ( refine23983189ASSUME @ Phi ) @ X4 )
% 4.12/2.08 = Phi ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_328_pw__ASSUME_I1_J,axiom,
% 4.12/2.08 ! [Phi: $o] : ( refine579265252t_unit @ ( refine23983189ASSUME @ Phi ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_329_flat__ord__compat_I1_J,axiom,
% 4.12/2.08 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 4.12/2.08 ( ( partia1658438072t_unit @ bot_bo658782032t_unit @ X4 @ Y3 )
% 4.12/2.08 => ( ord_le1051254044t_unit @ X4 @ Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_330_flat__ord__compat_I1_J,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 4.12/2.08 ( ( partia906949161nres_a @ bot_bo529555393nres_a @ X4 @ Y3 )
% 4.12/2.08 => ( ord_le519537037nres_a @ X4 @ Y3 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_331_pw__flat__ge__iff,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit,S2: refine787176636t_unit] :
% 4.12/2.08 ( ( partia1658438072t_unit @ top_to177290092t_unit @ S @ S2 )
% 4.12/2.08 = ( ( refine579265252t_unit @ S )
% 4.12/2.08 => ( ( refine579265252t_unit @ S2 )
% 4.12/2.08 & ! [X5: product_unit] :
% 4.12/2.08 ( ( refine558004794t_unit @ S @ X5 )
% 4.12/2.08 = ( refine558004794t_unit @ S2 @ X5 ) ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_332_nres__order__simps_I4_J,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M4 )
% 4.12/2.08 = ( M4 = top_to231829469nres_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_333_nofail__simps_I1_J,axiom,
% 4.12/2.08 ~ ( refine579265252t_unit @ top_to177290092t_unit ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_334_inres__simps_I1_J,axiom,
% 4.12/2.08 ( ( refine558004794t_unit @ top_to177290092t_unit )
% 4.12/2.08 = ( ^ [Uu3: product_unit] : $true ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_335_flat__ord__compat_I2_J,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 4.12/2.08 ( ( partia906949161nres_a @ top_to231829469nres_a @ X4 @ Y3 )
% 4.12/2.08 => ( ord_le519537037nres_a @ Y3 @ X4 ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_336_top__greatest,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_337_top_Oextremum__unique,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 4.12/2.08 = ( A = top_to231829469nres_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_338_top_Oextremum__uniqueI,axiom,
% 4.12/2.08 ! [A: refine424419629nres_a] :
% 4.12/2.08 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 4.12/2.08 => ( A = top_to231829469nres_a ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_339_meta__le__everything__if__top,axiom,
% 4.12/2.08 ! [M: refine424419629nres_a,X4: refine424419629nres_a] :
% 4.12/2.08 ( ( M = top_to231829469nres_a )
% 4.12/2.08 => ( ord_le519537037nres_a @ X4 @ M ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_340_not__nofail__iff,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit] :
% 4.12/2.08 ( ( ~ ( refine579265252t_unit @ S ) )
% 4.12/2.08 = ( S = top_to177290092t_unit ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_341_nofail__def,axiom,
% 4.12/2.08 ( refine579265252t_unit
% 4.12/2.08 = ( ^ [S3: refine787176636t_unit] : ( S3 != top_to177290092t_unit ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_342_intro__nofail_I2_J,axiom,
% 4.12/2.08 ! [S: refine787176636t_unit] :
% 4.12/2.08 ( ( top_to177290092t_unit != S )
% 4.12/2.08 = ( refine579265252t_unit @ S ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_343_nres__order__simps_I3_J,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a] : ( ord_le519537037nres_a @ M4 @ top_to231829469nres_a ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_344_nres__inequalities_I1_J,axiom,
% 4.12/2.08 ! [X: set_a] :
% 4.12/2.08 ( top_to231829469nres_a
% 4.12/2.08 != ( refine1198353288_RES_a @ X ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_345_nres__cases,axiom,
% 4.12/2.08 ! [M4: refine424419629nres_a] :
% 4.12/2.08 ( ( M4 != top_to231829469nres_a )
% 4.12/2.08 => ~ ! [X8: set_a] :
% 4.12/2.08 ( M4
% 4.12/2.08 != ( refine1198353288_RES_a @ X8 ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_346_nres__inequalities_I4_J,axiom,
% 4.12/2.08 bot_bo658782032t_unit != top_to177290092t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(fact_347_nres__inequalities_I2_J,axiom,
% 4.12/2.08 top_to177290092t_unit != bot_bo658782032t_unit ).
% 4.12/2.08
% 4.12/2.08 thf(fact_348_UNIV__I,axiom,
% 4.12/2.08 ! [X4: a] : ( member_a @ X4 @ top_top_set_a ) ).
% 4.12/2.08
% 4.12/2.08 thf(fact_349_eq__UNIV__iff,axiom,
% 4.12/2.08 ! [S: set_a] :
% 4.12/2.08 ( ( S = top_top_set_a )
% 4.12/2.08 = ( ! [X5: a] : ( member_a @ X5 @ S ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 4.12/2.08 ! [X4: set_a,Y3: set_a] :
% 4.12/2.08 ( ( if_set_a @ $false @ X4 @ Y3 )
% 4.12/2.08 = Y3 ) ).
% 4.12/2.08
% 4.12/2.08 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 4.12/2.08 ! [X4: set_a,Y3: set_a] :
% 4.12/2.08 ( ( if_set_a @ $true @ X4 @ Y3 )
% 4.12/2.08 = X4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 4.12/2.08 ( ( if_Ref1724547303nres_a @ $false @ X4 @ Y3 )
% 4.12/2.08 = Y3 ) ).
% 4.12/2.08
% 4.12/2.08 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 4.12/2.08 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 4.12/2.08 ( ( if_Ref1724547303nres_a @ $true @ X4 @ Y3 )
% 4.12/2.08 = X4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 4.12/2.08 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( if_o_R1705037948nres_a @ $false @ X4 @ Y3 )
% 4.12/2.08 = Y3 ) ).
% 4.12/2.08
% 4.12/2.08 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 4.12/2.08 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 4.12/2.08 ( ( if_o_R1705037948nres_a @ $true @ X4 @ Y3 )
% 4.12/2.08 = X4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 4.12/2.08 ! [P: $o] :
% 4.12/2.08 ( ( P = $true )
% 4.12/2.08 | ( P = $false ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 4.12/2.08 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 4.12/2.08 ( ( if_Ref1369692790t_unit @ $false @ X4 @ Y3 )
% 4.12/2.08 = Y3 ) ).
% 4.12/2.08
% 4.12/2.08 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 4.12/2.08 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 4.12/2.08 ( ( if_Ref1369692790t_unit @ $true @ X4 @ Y3 )
% 4.12/2.08 = X4 ) ).
% 4.12/2.08
% 4.12/2.08 thf(conj_0,hypothesis,
% 4.12/2.08 ( b
% 4.12/2.08 => ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(conj_1,hypothesis,
% 4.12/2.08 ( ~ b
% 4.12/2.08 => ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ).
% 4.12/2.08
% 4.12/2.08 thf(conj_2,conjecture,
% 4.12/2.08 ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ).
% 4.12/2.08 ------------------------
% 4.18/2.13 % (5897)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/2Mi)
% 4.18/2.13 % (5896)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_5795 for (2999ds/27Mi)
% 4.18/2.13 % (5895)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_5795 for (2999ds/4Mi)
% 4.18/2.13 % (5899)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_5795 for (2999ds/275Mi)
% 4.18/2.13 % (5900)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/18Mi)
% 4.18/2.13 % (5894)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/183Mi)
% 4.18/2.13 % (5898)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_5795 for (2999ds/2Mi)
% 4.18/2.13 % (5897)Instruction limit reached!
% 4.18/2.13 % (5897)------------------------------
% 4.18/2.13 % (5897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.13 % (5897)Termination reason: Unknown
% 4.18/2.13 % (5897)Termination phase: shuffling
% 4.18/2.13 % (5898)Instruction limit reached!
% 4.18/2.13 % (5898)------------------------------
% 4.18/2.13 % (5898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.13
% 4.18/2.13 % (5897)Memory used [KB]: 1407
% 4.18/2.13 % (5897)Time elapsed: 0.003 s
% 4.18/2.13 % (5897)Instructions burned: 2 (million)
% 4.18/2.13 % (5897)------------------------------
% 4.18/2.13 % (5897)------------------------------
% 4.18/2.13 % (5898)Termination reason: Unknown
% 4.18/2.13 % (5898)Termination phase: shuffling
% 4.18/2.13
% 4.18/2.13 % (5898)Memory used [KB]: 1407
% 4.18/2.13 % (5898)Time elapsed: 0.003 s
% 4.18/2.13 % (5898)Instructions burned: 2 (million)
% 4.18/2.13 % (5898)------------------------------
% 4.18/2.13 % (5898)------------------------------
% 4.18/2.13 % (5895)Instruction limit reached!
% 4.18/2.13 % (5895)------------------------------
% 4.18/2.13 % (5895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.13 % (5895)Termination reason: Unknown
% 4.18/2.13 % (5895)Termination phase: shuffling
% 4.18/2.13
% 4.18/2.13 % (5895)Memory used [KB]: 1535
% 4.18/2.13 % (5895)Time elapsed: 0.004 s
% 4.18/2.13 % (5895)Instructions burned: 4 (million)
% 4.18/2.13 % (5895)------------------------------
% 4.18/2.13 % (5895)------------------------------
% 4.18/2.14 % (5900)Instruction limit reached!
% 4.18/2.14 % (5900)------------------------------
% 4.18/2.14 % (5900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.14 % (5900)Termination reason: Unknown
% 4.18/2.14 % (5900)Termination phase: shuffling
% 4.18/2.14
% 4.18/2.14 % (5900)Memory used [KB]: 1791
% 4.18/2.14 % (5900)Time elapsed: 0.013 s
% 4.18/2.14 % (5900)Instructions burned: 18 (million)
% 4.18/2.14 % (5900)------------------------------
% 4.18/2.14 % (5900)------------------------------
% 4.18/2.14 % (5896)Instruction limit reached!
% 4.18/2.14 % (5896)------------------------------
% 4.18/2.14 % (5896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.14 % (5896)Termination reason: Unknown
% 4.18/2.14 % (5896)Termination phase: Property scanning
% 4.18/2.14
% 4.18/2.14 % (5896)Memory used [KB]: 1918
% 4.18/2.14 % (5896)Time elapsed: 0.017 s
% 4.18/2.14 % (5896)Instructions burned: 27 (million)
% 4.18/2.14 % (5896)------------------------------
% 4.18/2.14 % (5896)------------------------------
% 4.18/2.15 % (5903)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_5795 for (2999ds/15Mi)
% 4.18/2.15 % (5902)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_5795 for (2999ds/37Mi)
% 4.18/2.15 % (5901)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/3Mi)
% 4.18/2.15 % (5901)Instruction limit reached!
% 4.18/2.15 % (5901)------------------------------
% 4.18/2.15 % (5901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.15 % (5901)Termination reason: Unknown
% 4.18/2.15 % (5901)Termination phase: shuffling
% 4.18/2.15
% 4.18/2.15 % (5901)Memory used [KB]: 1535
% 4.18/2.15 % (5901)Time elapsed: 0.004 s
% 4.18/2.15 % (5901)Instructions burned: 3 (million)
% 4.18/2.15 % (5901)------------------------------
% 4.18/2.15 % (5901)------------------------------
% 4.18/2.16 % (5903)Instruction limit reached!
% 4.18/2.16 % (5903)------------------------------
% 4.18/2.16 % (5903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.16 % (5903)Termination reason: Unknown
% 4.18/2.16 % (5903)Termination phase: shuffling
% 4.18/2.16
% 4.18/2.16 % (5903)Memory used [KB]: 1791
% 4.18/2.16 % (5903)Time elapsed: 0.010 s
% 4.18/2.16 % (5903)Instructions burned: 15 (million)
% 4.18/2.16 % (5903)------------------------------
% 4.18/2.16 % (5903)------------------------------
% 4.18/2.16 % (5904)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_5795 for (2999ds/3Mi)
% 4.18/2.16 % (5904)Instruction limit reached!
% 4.18/2.16 % (5904)------------------------------
% 4.18/2.16 % (5904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.16 % (5904)Termination reason: Unknown
% 4.18/2.16 % (5904)Termination phase: shuffling
% 4.18/2.16
% 4.18/2.16 % (5904)Memory used [KB]: 1535
% 4.18/2.16 % (5904)Time elapsed: 0.005 s
% 4.18/2.16 % (5904)Instructions burned: 4 (million)
% 4.18/2.16 % (5904)------------------------------
% 4.18/2.16 % (5904)------------------------------
% 4.18/2.16 % (5905)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_5795 for (2999ds/1041Mi)
% 4.18/2.17 % (5902)Instruction limit reached!
% 4.18/2.17 % (5902)------------------------------
% 4.18/2.17 % (5902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.17 % (5902)Termination reason: Unknown
% 4.18/2.17 % (5902)Termination phase: shuffling
% 4.18/2.17
% 4.18/2.17 % (5902)Memory used [KB]: 2302
% 4.18/2.17 % (5902)Time elapsed: 0.022 s
% 4.18/2.17 % (5902)Instructions burned: 38 (million)
% 4.18/2.17 % (5902)------------------------------
% 4.18/2.17 % (5902)------------------------------
% 4.18/2.17 % (5906)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/7Mi)
% 4.18/2.18 % (5906)Instruction limit reached!
% 4.18/2.18 % (5906)------------------------------
% 4.18/2.18 % (5906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.18 % (5906)Termination reason: Unknown
% 4.18/2.18 % (5906)Termination phase: shuffling
% 4.18/2.18
% 4.18/2.18 % (5906)Memory used [KB]: 1535
% 4.18/2.18 % (5906)Time elapsed: 0.007 s
% 4.18/2.18 % (5906)Instructions burned: 8 (million)
% 4.18/2.18 % (5906)------------------------------
% 4.18/2.18 % (5906)------------------------------
% 4.18/2.18 % (5907)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/16Mi)
% 4.18/2.18 % (5908)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/3Mi)
% 4.18/2.18 % (5908)Instruction limit reached!
% 4.18/2.18 % (5908)------------------------------
% 4.18/2.18 % (5908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.18 % (5908)Termination reason: Unknown
% 4.18/2.18 % (5908)Termination phase: shuffling
% 4.18/2.18
% 4.18/2.18 % (5908)Memory used [KB]: 1535
% 4.18/2.18 % (5908)Time elapsed: 0.004 s
% 4.18/2.18 % (5908)Instructions burned: 3 (million)
% 4.18/2.18 % (5908)------------------------------
% 4.18/2.18 % (5908)------------------------------
% 4.18/2.19 % (5907)Instruction limit reached!
% 4.18/2.19 % (5907)------------------------------
% 4.18/2.19 % (5907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.19 % (5907)Termination reason: Unknown
% 4.18/2.19 % (5907)Termination phase: shuffling
% 4.18/2.19
% 4.18/2.19 % (5907)Memory used [KB]: 1791
% 4.18/2.19 % (5907)Time elapsed: 0.011 s
% 4.18/2.19 % (5907)Instructions burned: 16 (million)
% 4.18/2.19 % (5907)------------------------------
% 4.18/2.19 % (5907)------------------------------
% 4.18/2.19 % (5909)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/3Mi)
% 4.18/2.19 % (5909)Instruction limit reached!
% 4.18/2.19 % (5909)------------------------------
% 4.18/2.19 % (5909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.19 % (5909)Termination reason: Unknown
% 4.18/2.19 % (5909)Termination phase: shuffling
% 4.18/2.19
% 4.18/2.19 % (5909)Memory used [KB]: 1535
% 4.18/2.19 % (5909)Time elapsed: 0.004 s
% 4.18/2.19 % (5909)Instructions burned: 3 (million)
% 4.18/2.19 % (5909)------------------------------
% 4.18/2.19 % (5909)------------------------------
% 4.18/2.20 % (5910)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/7Mi)
% 4.18/2.20 % (5910)Instruction limit reached!
% 4.18/2.20 % (5910)------------------------------
% 4.18/2.20 % (5910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.20 % (5910)Termination reason: Unknown
% 4.18/2.20 % (5910)Termination phase: shuffling
% 4.18/2.20
% 4.18/2.20 % (5910)Memory used [KB]: 1535
% 4.18/2.20 % (5910)Time elapsed: 0.006 s
% 4.18/2.20 % (5910)Instructions burned: 7 (million)
% 4.18/2.20 % (5910)------------------------------
% 4.18/2.20 % (5910)------------------------------
% 4.18/2.20 % (5911)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/3Mi)
% 4.18/2.21 % (5911)Instruction limit reached!
% 4.18/2.21 % (5911)------------------------------
% 4.18/2.21 % (5911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.21 % (5911)Termination reason: Unknown
% 4.18/2.21 % (5911)Termination phase: shuffling
% 4.18/2.21
% 4.18/2.21 % (5911)Memory used [KB]: 1535
% 4.18/2.21 % (5911)Time elapsed: 0.004 s
% 4.18/2.21 % (5911)Instructions burned: 4 (million)
% 4.18/2.21 % (5911)------------------------------
% 4.18/2.21 % (5911)------------------------------
% 4.18/2.21 % (5912)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5795 for (2999ds/4Mi)
% 4.18/2.21 % (5912)Instruction limit reached!
% 4.18/2.21 % (5912)------------------------------
% 4.18/2.21 % (5912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.21 % (5912)Termination reason: Unknown
% 4.18/2.21 % (5912)Termination phase: shuffling
% 4.18/2.21
% 4.18/2.21 % (5912)Memory used [KB]: 1535
% 4.18/2.21 % (5912)Time elapsed: 0.005 s
% 4.18/2.21 % (5912)Instructions burned: 5 (million)
% 4.18/2.21 % (5912)------------------------------
% 4.18/2.21 % (5912)------------------------------
% 4.18/2.21 % (5913)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/18Mi)
% 4.18/2.22 % (5914)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/710Mi)
% 4.18/2.22 % (5913)Instruction limit reached!
% 4.18/2.22 % (5913)------------------------------
% 4.18/2.22 % (5913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.22 % (5913)Termination reason: Unknown
% 4.18/2.22 % (5913)Termination phase: shuffling
% 4.18/2.22
% 4.18/2.22 % (5913)Memory used [KB]: 1791
% 4.18/2.22 % (5913)Time elapsed: 0.013 s
% 4.18/2.22 % (5913)Instructions burned: 18 (million)
% 4.18/2.22 % (5913)------------------------------
% 4.18/2.22 % (5913)------------------------------
% 4.18/2.22 % (5894)Instruction limit reached!
% 4.18/2.22 % (5894)------------------------------
% 4.18/2.22 % (5894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.22 % (5894)Termination reason: Unknown
% 4.18/2.22 % (5894)Termination phase: Saturation
% 4.18/2.22
% 4.18/2.22 % (5894)Memory used [KB]: 7419
% 4.18/2.22 % (5894)Time elapsed: 0.098 s
% 4.18/2.22 % (5894)Instructions burned: 183 (million)
% 4.18/2.22 % (5894)------------------------------
% 4.18/2.22 % (5894)------------------------------
% 4.18/2.23 % (5915)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/6Mi)
% 4.18/2.23 % (5916)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/902Mi)
% 4.18/2.23 % (5915)Instruction limit reached!
% 4.18/2.23 % (5915)------------------------------
% 4.18/2.23 % (5915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.23 % (5915)Termination reason: Unknown
% 4.18/2.23 % (5915)Termination phase: shuffling
% 4.18/2.23
% 4.18/2.23 % (5915)Memory used [KB]: 1535
% 4.18/2.23 % (5915)Time elapsed: 0.006 s
% 4.18/2.23 % (5915)Instructions burned: 7 (million)
% 4.18/2.23 % (5915)------------------------------
% 4.18/2.23 % (5915)------------------------------
% 4.18/2.24 % (5917)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/21Mi)
% 4.18/2.24 % (5918)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/5Mi)
% 4.18/2.25 % (5918)Instruction limit reached!
% 4.18/2.25 % (5918)------------------------------
% 4.18/2.25 % (5918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.25 % (5918)Termination reason: Unknown
% 4.18/2.25 % (5918)Termination phase: shuffling
% 4.18/2.25
% 4.18/2.25 % (5918)Memory used [KB]: 1535
% 4.18/2.25 % (5918)Time elapsed: 0.005 s
% 4.18/2.25 % (5918)Instructions burned: 6 (million)
% 4.18/2.25 % (5918)------------------------------
% 4.18/2.25 % (5918)------------------------------
% 4.18/2.25 % (5919)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/6Mi)
% 4.18/2.26 % (5917)Instruction limit reached!
% 4.18/2.26 % (5917)------------------------------
% 4.18/2.26 % (5917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.26 % (5917)Termination reason: Unknown
% 4.18/2.26 % (5917)Termination phase: shuffling
% 4.18/2.26
% 4.18/2.26 % (5917)Memory used [KB]: 1918
% 4.18/2.26 % (5917)Time elapsed: 0.014 s
% 4.18/2.26 % (5917)Instructions burned: 22 (million)
% 4.18/2.26 % (5917)------------------------------
% 4.18/2.26 % (5917)------------------------------
% 4.18/2.26 % (5919)Instruction limit reached!
% 4.18/2.26 % (5919)------------------------------
% 4.18/2.26 % (5919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.26 % (5919)Termination reason: Unknown
% 4.18/2.26 % (5919)Termination phase: shuffling
% 4.18/2.26
% 4.18/2.26 % (5919)Memory used [KB]: 1535
% 4.18/2.26 % (5919)Time elapsed: 0.006 s
% 4.18/2.26 % (5919)Instructions burned: 6 (million)
% 4.18/2.26 % (5919)------------------------------
% 4.18/2.26 % (5919)------------------------------
% 4.18/2.27 % (5920)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/377Mi)
% 4.18/2.28 % (5921)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/779Mi)
% 4.18/2.28 % (5922)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_5795 for (2998ds/19Mi)
% 4.18/2.29 % (5914)First to succeed.
% 4.18/2.29 % (5899)Instruction limit reached!
% 4.18/2.29 % (5899)------------------------------
% 4.18/2.29 % (5899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.29 % (5899)Termination reason: Unknown
% 4.18/2.29 % (5899)Termination phase: Saturation
% 4.18/2.29
% 4.18/2.29 % (5899)Memory used [KB]: 7291
% 4.18/2.29 % (5899)Time elapsed: 0.159 s
% 4.18/2.29 % (5899)Instructions burned: 276 (million)
% 4.18/2.29 % (5899)------------------------------
% 4.18/2.29 % (5899)------------------------------
% 4.18/2.29 % (5922)Instruction limit reached!
% 4.18/2.29 % (5922)------------------------------
% 4.18/2.29 % (5922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.29 % (5922)Termination reason: Unknown
% 4.18/2.29 % (5922)Termination phase: shuffling
% 4.18/2.29
% 4.18/2.29 % (5922)Memory used [KB]: 1791
% 4.18/2.29 % (5922)Time elapsed: 0.012 s
% 4.18/2.29 % (5922)Instructions burned: 20 (million)
% 4.18/2.29 % (5922)------------------------------
% 4.18/2.29 % (5922)------------------------------
% 4.18/2.29 % (5914)Refutation found. Thanks to Tanya!
% 4.18/2.29 % SZS status Theorem for DTF2THF_5795
% 4.18/2.29 % SZS output start Proof for DTF2THF_5795
% 4.18/2.29 thf(type_def_5, type, set_a: $tType).
% 4.18/2.29 thf(type_def_7, type, refine424419629nres_a: $tType).
% 4.18/2.29 thf(type_def_8, type, refine787176636t_unit: $tType).
% 4.18/2.29 thf(type_def_9, type, a: $tType).
% 4.18/2.29 thf(type_def_10, type, set_Product_unit: $tType).
% 4.18/2.29 thf(type_def_11, type, product_unit: $tType).
% 4.18/2.29 thf(func_def_0, type, refine787176636t_unit: $tType).
% 4.18/2.29 thf(func_def_1, type, refine424419629nres_a: $tType).
% 4.18/2.29 thf(func_def_2, type, set_Product_unit: $tType).
% 4.18/2.29 thf(func_def_3, type, product_unit: $tType).
% 4.18/2.29 thf(func_def_4, type, set_a: $tType).
% 4.18/2.29 thf(func_def_5, type, a: $tType).
% 4.18/2.29 thf(func_def_6, type, uminus_uminus_set_a: set_a > set_a).
% 4.18/2.29 thf(func_def_7, type, if_o_R1705037948nres_a: $o > ($o > refine424419629nres_a) > ($o > refine424419629nres_a) > $o > refine424419629nres_a).
% 4.18/2.29 thf(func_def_8, type, if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit).
% 4.18/2.29 thf(func_def_9, type, if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a).
% 4.18/2.29 thf(func_def_10, type, if_set_a: $o > set_a > set_a > set_a).
% 4.18/2.29 thf(func_def_11, type, bot_bot_a_o: a > $o).
% 4.18/2.29 thf(func_def_12, type, bot_bo658782032t_unit: refine787176636t_unit).
% 4.18/2.29 thf(func_def_13, type, bot_bo529555393nres_a: refine424419629nres_a).
% 4.18/2.29 thf(func_def_14, type, bot_bo1087887705t_unit: set_Product_unit).
% 4.18/2.29 thf(func_def_15, type, bot_bot_set_a: set_a).
% 4.18/2.29 thf(func_def_16, type, ord_le1960259811nres_a: ($o > $o > refine424419629nres_a) > ($o > $o > refine424419629nres_a) > $o).
% 4.18/2.29 thf(func_def_17, type, ord_le1633311077t_unit: ($o > refine787176636t_unit) > ($o > refine787176636t_unit) > $o).
% 4.18/2.29 thf(func_def_18, type, ord_le516598614nres_a: ($o > refine424419629nres_a) > ($o > refine424419629nres_a) > $o).
% 4.18/2.29 thf(func_def_19, type, ord_less_eq_o_set_a: ($o > set_a) > ($o > set_a) > $o).
% 4.18/2.29 thf(func_def_20, type, ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o).
% 4.18/2.29 thf(func_def_21, type, ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o).
% 4.18/2.29 thf(func_def_22, type, ord_le1023748749t_unit: set_Product_unit > set_Product_unit > $o).
% 4.18/2.29 thf(func_def_23, type, ord_less_eq_set_a: set_a > set_a > $o).
% 4.18/2.29 thf(func_def_24, type, order_245837199nres_a: (($o > refine424419629nres_a) > $o) > $o > refine424419629nres_a).
% 4.18/2.29 thf(func_def_25, type, order_453013155t_unit: (refine787176636t_unit > $o) > refine787176636t_unit).
% 4.18/2.29 thf(func_def_26, type, order_1714329108nres_a: (refine424419629nres_a > $o) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_27, type, order_Greatest_set_a: (set_a > $o) > set_a).
% 4.18/2.29 thf(func_def_28, type, top_to177290092t_unit: refine787176636t_unit).
% 4.18/2.29 thf(func_def_29, type, top_to231829469nres_a: refine424419629nres_a).
% 4.18/2.29 thf(func_def_30, type, top_top_set_a: set_a).
% 4.18/2.29 thf(func_def_31, type, partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o).
% 4.18/2.29 thf(func_def_32, type, partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o).
% 4.18/2.29 thf(func_def_33, type, refine23983189ASSUME: $o > refine787176636t_unit).
% 4.18/2.29 thf(func_def_34, type, refine1420258419t_unit: product_unit > refine787176636t_unit).
% 4.18/2.29 thf(func_def_35, type, refine2063221604TURN_a: a > refine424419629nres_a).
% 4.18/2.29 thf(func_def_36, type, refine681446406t_unit: refine787176636t_unit > (product_unit > refine787176636t_unit) > refine787176636t_unit).
% 4.18/2.29 thf(func_def_37, type, refine119808503unit_a: refine787176636t_unit > (product_unit > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_38, type, refine96995669t_unit: refine424419629nres_a > (a > refine787176636t_unit) > refine787176636t_unit).
% 4.18/2.29 thf(func_def_39, type, refine436832838nd_a_a: refine424419629nres_a > (a > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_40, type, refine558004794t_unit: refine787176636t_unit > product_unit > $o).
% 4.18/2.29 thf(func_def_41, type, refine1001002027nres_a: refine424419629nres_a > a > $o).
% 4.18/2.29 thf(func_def_42, type, refine983493746t_unit: refine787176636t_unit > product_unit > $o).
% 4.18/2.29 thf(func_def_43, type, refine1312857699nres_a: refine424419629nres_a > a > $o).
% 4.18/2.29 thf(func_def_44, type, refine579265252t_unit: refine787176636t_unit > $o).
% 4.18/2.29 thf(func_def_45, type, refine412683989fail_a: refine424419629nres_a > $o).
% 4.18/2.29 thf(func_def_46, type, refine464223677AILi_a: refine424419629nres_a).
% 4.18/2.29 thf(func_def_47, type, refine1777164439t_unit: set_Product_unit > refine787176636t_unit).
% 4.18/2.29 thf(func_def_48, type, refine1198353288_RES_a: set_a > refine424419629nres_a).
% 4.18/2.29 thf(func_def_49, type, refine1208325748t_unit: refine787176636t_unit > set_Product_unit).
% 4.18/2.29 thf(func_def_50, type, refine1822134885_RES_a: refine424419629nres_a > set_a).
% 4.18/2.29 thf(func_def_51, type, refine459374679t_unit: (refine787176636t_unit > refine787176636t_unit) > $o).
% 4.18/2.29 thf(func_def_52, type, collect_Product_unit: (product_unit > $o) > set_Product_unit).
% 4.18/2.29 thf(func_def_53, type, collect_a: (a > $o) > set_a).
% 4.18/2.29 thf(func_def_54, type, insert_a: a > set_a > set_a).
% 4.18/2.29 thf(func_def_55, type, is_singleton_a: set_a > $o).
% 4.18/2.29 thf(func_def_56, type, member_Product_unit: product_unit > set_Product_unit > $o).
% 4.18/2.29 thf(func_def_57, type, member_a: a > set_a > $o).
% 4.18/2.29 thf(func_def_58, type, s1: refine424419629nres_a).
% 4.18/2.29 thf(func_def_59, type, s2: refine424419629nres_a).
% 4.18/2.29 thf(func_def_60, type, phi: a > $o).
% 4.18/2.29 thf(func_def_75, type, sK0: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_76, type, sK1: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_77, type, sK2: (a > $o) > (a > $o) > a).
% 4.18/2.29 thf(func_def_78, type, sK3: (a > $o) > (a > $o) > a).
% 4.18/2.29 thf(func_def_79, type, sK4: (a > $o) > (a > $o) > a).
% 4.18/2.29 thf(func_def_80, type, sK5: set_a > (a > $o) > a).
% 4.18/2.29 thf(func_def_81, type, sK6: set_a > (a > $o) > a).
% 4.18/2.29 thf(func_def_82, type, sK7: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_83, type, sK8: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_84, type, sK9: (a > $o) > a).
% 4.18/2.29 thf(func_def_85, type, sK10: (a > $o) > a).
% 4.18/2.29 thf(func_def_86, type, sK11: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_87, type, sK12: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_88, type, sK13: (a > $o) > (a > $o) > a).
% 4.18/2.29 thf(func_def_89, type, sK14: (a > $o) > (a > $o) > a).
% 4.18/2.29 thf(func_def_90, type, sK15: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_91, type, sK16: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 4.18/2.29 thf(func_def_93, type, ph18: !>[X0: $tType]:(X0)).
% 4.18/2.29 thf(func_def_94, type, sK19: a).
% 4.18/2.29 thf(func_def_95, type, sK20: a).
% 4.18/2.29 thf(func_def_96, type, sK21: a).
% 4.18/2.29 thf(f1446,plain,(
% 4.18/2.29 $false),
% 4.18/2.29 inference(avatar_sat_refutation,[status(thm)],[f1193,f1200,f1381,f1390,f1397,f1445])).
% 4.18/2.29 thf(f1445,plain,(
% 4.18/2.29 spl17_1 | spl17_8 | spl17_11),
% 4.18/2.29 inference(avatar_contradiction_clause,[status(thm)],[f1444])).
% 4.18/2.29 thf(f1444,plain,(
% 4.18/2.29 $false | (spl17_1 | spl17_8 | spl17_11)),
% 4.18/2.29 inference(trivial_inequality_removal,[status(thm)],[f1443])).
% 4.18/2.29 thf(f1443,plain,(
% 4.18/2.29 ($true = $false) | (spl17_1 | spl17_8 | spl17_11)),
% 4.18/2.29 inference(backward_demodulation,[status(thm)],[f1441,f1442])).
% 4.18/2.29 thf(f1442,plain,(
% 4.18/2.29 ((phi @ sK21) = $false) | (spl17_8 | spl17_11)),
% 4.18/2.29 inference(subsumption_resolution,[status(thm)],[f1440,f1292])).
% 4.18/2.29 thf(f1292,plain,(
% 4.18/2.29 (b != $false) | spl17_11),
% 4.18/2.29 inference(avatar_component_clause,[status(thm)],[f1291])).
% 4.18/2.29 thf(f1291,definition,(
% 4.18/2.29 spl17_11 <=> (b = $false)),
% 4.18/2.29 introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition])).
% 4.18/2.29 thf(f1440,plain,(
% 4.18/2.29 ((phi @ sK21) = $false) | (b = $false) | spl17_8),
% 4.18/2.29 inference(binary_proxy_clausification,[status(thm)],[f1438])).
% 4.18/2.29 thf(f1438,plain,(
% 4.18/2.29 (b != (phi @ sK21)) | spl17_8),
% 4.18/2.29 inference(beta_eta_normalization,[status(thm)],[f1437])).
% 4.18/2.29 thf(f1437,plain,(
% 4.18/2.29 ((phi @ sK21) != ((^[Y0 : a]: (b)) @ sK21)) | spl17_8),
% 4.18/2.29 inference(negative_extensionality,[status(thm)],[f1253])).
% 4.18/2.29 thf(f1253,plain,(
% 4.18/2.29 (phi != (^[Y0 : a]: (b))) | spl17_8),
% 4.18/2.29 inference(avatar_component_clause,[status(thm)],[f1251])).
% 4.18/2.29 thf(f1251,definition,(
% 4.18/2.29 spl17_8 <=> (phi = (^[Y0 : a]: (b)))),
% 4.18/2.29 introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition])).
% 4.18/2.29 thf(f1441,plain,(
% 4.18/2.29 ($true = (phi @ sK21)) | (spl17_1 | spl17_8)),
% 4.18/2.29 inference(subsumption_resolution,[status(thm)],[f1439,f1188])).
% 4.18/2.29 thf(f1188,plain,(
% 4.18/2.29 (b != $true) | spl17_1),
% 4.18/2.29 inference(avatar_component_clause,[status(thm)],[f1186])).
% 4.18/2.29 thf(f1186,definition,(
% 4.18/2.29 spl17_1 <=> (b = $true)),
% 4.18/2.29 introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition])).
% 4.18/2.29 thf(f1439,plain,(
% 4.18/2.29 (b = $true) | ($true = (phi @ sK21)) | spl17_8),
% 4.18/2.29 inference(binary_proxy_clausification,[status(thm)],[f1438])).
% 4.18/2.29 thf(f1397,plain,(
% 4.18/2.29 ~spl17_1 | ~spl17_2),
% 4.18/2.29 inference(avatar_contradiction_clause,[status(thm)],[f1396])).
% 4.18/2.29 thf(f1396,plain,(
% 4.18/2.29 $false | (~spl17_1 | ~spl17_2)),
% 4.18/2.29 inference(subsumption_resolution,[status(thm)],[f1395,f1192])).
% 4.18/2.29 thf(f1192,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true) | ~spl17_2),
% 4.18/2.29 inference(avatar_component_clause,[status(thm)],[f1190])).
% 4.18/2.29 thf(f1190,definition,(
% 4.18/2.29 spl17_2 <=> ((ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true)),
% 4.18/2.29 introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition])).
% 4.18/2.29 thf(f1395,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ phi))) != $true) | ~spl17_1),
% 4.18/2.29 inference(forward_demodulation,[status(thm)],[f1394,f1149])).
% 4.18/2.29 thf(f1149,plain,(
% 4.18/2.29 ( ! [X0 : refine424419629nres_a,X1 : refine424419629nres_a] : (((if_Ref1724547303nres_a @ $true @ X1 @ X0) = X1)) )),
% 4.18/2.29 inference(cnf_transformation,[status(thm)],[f456])).
% 4.18/2.29 thf(f456,plain,(
% 4.18/2.29 ! [X0 : refine424419629nres_a,X1 : refine424419629nres_a] : ((if_Ref1724547303nres_a @ $true @ X1 @ X0) = X1)),
% 4.18/2.29 inference(fool_elimination,[status(thm)],[f455])).
% 4.18/2.29 thf(f455,plain,(
% 4.18/2.29 ! [X0 : refine424419629nres_a,X1 : refine424419629nres_a] : (X1 = (if_Ref1724547303nres_a @ $true @ X1 @ X0))),
% 4.18/2.29 inference(rectify,[status(thm)],[f354])).
% 4.18/2.29 thf(f354,axiom,(
% 4.18/2.29 ! [X9 : refine424419629nres_a,X8 : refine424419629nres_a] : (X8 = (if_Ref1724547303nres_a @ $true @ X8 @ X9))),
% 4.18/2.29 file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T)).
% 4.18/2.29 thf(f1394,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ $true @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi))) != $true) | ~spl17_1),
% 4.18/2.29 inference(forward_demodulation,[status(thm)],[f1112,f1187])).
% 4.18/2.29 thf(f1187,plain,(
% 4.18/2.29 (b = $true) | ~spl17_1),
% 4.18/2.29 inference(avatar_component_clause,[status(thm)],[f1186])).
% 4.18/2.29 thf(f1112,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi))) != $true)),
% 4.18/2.29 inference(cnf_transformation,[status(thm)],[f1009])).
% 4.18/2.29 thf(f1009,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi))) != $true)),
% 4.18/2.29 inference(flattening,[status(thm)],[f468])).
% 4.18/2.29 thf(f468,plain,(
% 4.18/2.29 ~((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true)),
% 4.18/2.29 inference(fool_elimination,[status(thm)],[f467])).
% 4.18/2.29 thf(f467,plain,(
% 4.18/2.29 ~(ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi)))),
% 4.18/2.29 inference(rectify,[status(thm)],[f363])).
% 4.18/2.29 thf(f363,negated_conjecture,(
% 4.18/2.29 ~(ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi)))),
% 4.18/2.29 inference(negated_conjecture,[status(cth)],[f362])).
% 4.18/2.29 thf(f362,conjecture,(
% 4.18/2.29 (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi)))),
% 4.18/2.29 file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',conj_2)).
% 4.18/2.29 thf(f1390,plain,(
% 4.18/2.29 ~spl17_3 | ~spl17_11),
% 4.18/2.29 inference(avatar_split_clause,[status(thm)],[f1387,f1291,f1197])).
% 4.18/2.29 thf(f1197,definition,(
% 4.18/2.29 spl17_3 <=> ((ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true)),
% 4.18/2.29 introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition])).
% 4.18/2.29 thf(f1387,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ phi))) != $true) | ~spl17_11),
% 4.18/2.29 inference(forward_demodulation,[status(thm)],[f1385,f1147])).
% 4.18/2.29 thf(f1147,plain,(
% 4.18/2.29 ( ! [X0 : refine424419629nres_a,X1 : refine424419629nres_a] : (((if_Ref1724547303nres_a @ $false @ X1 @ X0) = X0)) )),
% 4.18/2.29 inference(cnf_transformation,[status(thm)],[f625])).
% 4.18/2.29 thf(f625,plain,(
% 4.18/2.29 ! [X0 : refine424419629nres_a,X1 : refine424419629nres_a] : ((if_Ref1724547303nres_a @ $false @ X1 @ X0) = X0)),
% 4.18/2.29 inference(fool_elimination,[status(thm)],[f624])).
% 4.18/2.29 thf(f624,plain,(
% 4.18/2.29 ! [X0 : refine424419629nres_a,X1 : refine424419629nres_a] : ((if_Ref1724547303nres_a @ $false @ X1 @ X0) = X0)),
% 4.18/2.29 inference(rectify,[status(thm)],[f353])).
% 4.18/2.29 thf(f353,axiom,(
% 4.18/2.29 ! [X9 : refine424419629nres_a,X8 : refine424419629nres_a] : ((if_Ref1724547303nres_a @ $false @ X8 @ X9) = X9)),
% 4.18/2.29 file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T)).
% 4.18/2.29 thf(f1385,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ $false @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi))) != $true) | ~spl17_11),
% 4.18/2.29 inference(backward_demodulation,[status(thm)],[f1112,f1293])).
% 4.18/2.29 thf(f1293,plain,(
% 4.18/2.29 (b = $false) | ~spl17_11),
% 4.18/2.29 inference(avatar_component_clause,[status(thm)],[f1291])).
% 4.18/2.29 thf(f1381,plain,(
% 4.18/2.29 spl17_1 | ~spl17_8 | spl17_11),
% 4.18/2.29 inference(avatar_contradiction_clause,[status(thm)],[f1380])).
% 4.18/2.29 thf(f1380,plain,(
% 4.18/2.29 $false | (spl17_1 | ~spl17_8 | spl17_11)),
% 4.18/2.29 inference(trivial_inequality_removal,[status(thm)],[f1379])).
% 4.18/2.29 thf(f1379,plain,(
% 4.18/2.29 ($true = $false) | (spl17_1 | ~spl17_8 | spl17_11)),
% 4.18/2.29 inference(forward_demodulation,[status(thm)],[f1378,f1375])).
% 4.18/2.29 thf(f1375,plain,(
% 4.18/2.29 ( ! [X1 : a] : (((phi @ X1) = $false)) ) | (spl17_1 | ~spl17_8)),
% 4.18/2.29 inference(subsumption_resolution,[status(thm)],[f1373,f1188])).
% 4.18/2.29 thf(f1373,plain,(
% 4.18/2.29 ( ! [X1 : a] : (((phi @ X1) = $false) | (b = $true)) ) | ~spl17_8),
% 4.18/2.29 inference(binary_proxy_clausification,[status(thm)],[f1372])).
% 4.18/2.29 thf(f1372,plain,(
% 4.18/2.29 ( ! [X1 : a] : ((b = (phi @ X1))) ) | ~spl17_8),
% 4.18/2.29 inference(beta_eta_normalization,[status(thm)],[f1367])).
% 4.18/2.29 thf(f1367,plain,(
% 4.18/2.29 ( ! [X1 : a] : ((((^[Y0 : a]: (b)) @ X1) = (phi @ X1))) ) | ~spl17_8),
% 4.18/2.29 inference(argument_congruence,[status(thm)],[f1252])).
% 4.18/2.29 thf(f1252,plain,(
% 4.18/2.29 (phi = (^[Y0 : a]: (b))) | ~spl17_8),
% 4.18/2.29 inference(avatar_component_clause,[status(thm)],[f1251])).
% 4.18/2.29 thf(f1378,plain,(
% 4.18/2.29 ( ! [X1 : a] : (($true = (phi @ X1))) ) | (~spl17_8 | spl17_11)),
% 4.18/2.29 inference(subsumption_resolution,[status(thm)],[f1374,f1292])).
% 4.18/2.29 thf(f1374,plain,(
% 4.18/2.29 ( ! [X1 : a] : ((b = $false) | ($true = (phi @ X1))) ) | ~spl17_8),
% 4.18/2.29 inference(binary_proxy_clausification,[status(thm)],[f1372])).
% 4.18/2.29 thf(f1200,plain,(
% 4.18/2.29 spl17_3 | spl17_1),
% 4.18/2.29 inference(avatar_split_clause,[status(thm)],[f1146,f1186,f1197])).
% 4.18/2.29 thf(f1146,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true) | (b = $true)),
% 4.18/2.29 inference(cnf_transformation,[status(thm)],[f1058])).
% 4.18/2.29 thf(f1058,plain,(
% 4.18/2.29 (b = $true) | ((ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true)),
% 4.18/2.29 inference(ennf_transformation,[status(thm)],[f1010])).
% 4.18/2.29 thf(f1010,plain,(
% 4.18/2.29 (b != $true) => ((ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true)),
% 4.18/2.29 inference(flattening,[status(thm)],[f881])).
% 4.18/2.29 thf(f881,plain,(
% 4.18/2.29 ~(b = $true) => ((ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true)),
% 4.18/2.29 inference(fool_elimination,[status(thm)],[f880])).
% 4.18/2.29 thf(f880,plain,(
% 4.18/2.29 ~b => (ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ phi)))),
% 4.18/2.29 inference(rectify,[status(thm)],[f361])).
% 4.18/2.29 thf(f361,axiom,(
% 4.18/2.29 ~b => (ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ phi)))),
% 4.18/2.29 file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',conj_1)).
% 4.18/2.29 thf(f1193,plain,(
% 4.18/2.29 ~spl17_1 | spl17_2),
% 4.18/2.29 inference(avatar_split_clause,[status(thm)],[f1119,f1190,f1186])).
% 4.18/2.29 thf(f1119,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true) | (b != $true)),
% 4.18/2.29 inference(cnf_transformation,[status(thm)],[f1032])).
% 4.18/2.29 thf(f1032,plain,(
% 4.18/2.29 ((ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true) | (b != $true)),
% 4.18/2.29 inference(ennf_transformation,[status(thm)],[f544])).
% 4.18/2.29 thf(f544,plain,(
% 4.18/2.29 (b = $true) => ((ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ phi))) = $true)),
% 4.18/2.29 inference(fool_elimination,[status(thm)],[f543])).
% 4.18/2.29 thf(f543,plain,(
% 4.18/2.29 b => (ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ phi)))),
% 4.18/2.29 inference(rectify,[status(thm)],[f360])).
% 4.18/2.29 thf(f360,axiom,(
% 4.18/2.29 b => (ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ phi)))),
% 4.18/2.29 file('/export/starexec/sandbox/tmp/tmp.tJPdZ6uyVB/DTF2THF_5795.p',conj_0)).
% 4.18/2.29 % SZS output end Proof for DTF2THF_5795
% 4.18/2.29 % (5914)------------------------------
% 4.18/2.29 % (5914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.18/2.29 % (5914)Termination reason: Refutation
% 4.18/2.29
% 4.18/2.29 % (5914)Memory used [KB]: 6908
% 4.18/2.29 % (5914)Time elapsed: 0.069 s
% 4.18/2.29 % (5914)Instructions burned: 109 (million)
% 4.18/2.29 % (5914)------------------------------
% 4.18/2.29 % (5914)------------------------------
% 4.18/2.29 % (5893)Success in time 0.193 s
%------------------------------------------------------------------------------