%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP162^1 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:03 AM UTC 2026
% Result : Theorem 3.92s 2.47s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 151 ( 42 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 311 ( 7 ~; 7 |; 26 &; 271 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 7 con; 0-4 aty)
% Number of variables : 75 ( 33 ^; 42 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
refine424419629nres_a: $tType ).
thf(type_def_8,type,
set_a: $tType ).
thf(func_def_0,type,
refine424419629nres_a: $tType ).
thf(func_def_1,type,
set_a: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_3,type,
if_a_o: $o > ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_4,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_5,type,
if_set_a: $o > set_a > set_a > set_a ).
thf(func_def_6,type,
inf_inf_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_7,type,
inf_inf_o: $o > $o > $o ).
thf(func_def_8,type,
inf_in262696383nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_9,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(func_def_10,type,
bot_bo529555393nres_a: refine424419629nres_a ).
thf(func_def_11,type,
bot_bot_set_a: set_a ).
thf(func_def_12,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_13,type,
ord_less_eq_o: $o > $o > $o ).
thf(func_def_14,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_15,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_16,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(func_def_17,type,
top_to231829469nres_a: refine424419629nres_a ).
thf(func_def_18,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(func_def_19,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_20,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(func_def_21,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(func_def_22,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(func_def_23,type,
refine464223677AILi_a: refine424419629nres_a ).
thf(func_def_24,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(func_def_25,type,
refine1822134885_RES_a: refine424419629nres_a > set_a ).
thf(func_def_26,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_27,type,
member_a: a > set_a > $o ).
thf(func_def_28,type,
a2: refine424419629nres_a ).
thf(func_def_29,type,
p: a > $o ).
thf(func_def_30,type,
q: a > $o ).
thf(func_def_45,type,
sK0: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_46,type,
sK1: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_47,type,
sK2: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_48,type,
sK3: ( a > $o ) > set_a > ( a > $o ) > a ).
thf(func_def_49,type,
sK4: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_50,type,
sK5: ( a > $o ) > ( a > refine424419629nres_a ) > refine424419629nres_a > a ).
thf(func_def_51,type,
sK6: ( a > $o ) > set_a > a ).
thf(func_def_52,type,
sK7: ( a > $o ) > set_a > ( a > $o ) > a ).
thf(func_def_53,type,
sK8: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_54,type,
sK9: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_55,type,
sK10: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_56,type,
sK11: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_57,type,
sK12: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_58,type,
sK13: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_59,type,
sK14: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_60,type,
sK15: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_61,type,
sK16: ( a > $o ) > refine424419629nres_a > a ).
thf(func_def_63,type,
sK18: ( a > $o ) > set_a > a ).
thf(func_def_64,type,
sK19: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_65,type,
sK20: set_a > ( a > $o ) > a ).
thf(func_def_66,type,
ph21:
!>[X0: $tType] : X0 ).
thf(f1998,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1997]) ).
thf(f1997,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f1093,f1996]) ).
thf(f1996,plain,
( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f1995]) ).
thf(f1995,plain,
( ( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f1973,f1102]) ).
thf(f1102,plain,
( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f882]) ).
thf(f882,plain,
( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f881]) ).
thf(f881,plain,
ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ),
file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_3_assms_I1_J) ).
thf(f1973,plain,
( ( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) )
= $false )
| ( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f1960]) ).
thf(f1960,plain,
( ( $true != $true )
| ( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) )
= $false )
| ( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f1671,f1305]) ).
thf(f1305,plain,
! [X2: refine424419629nres_a,X0: refine424419629nres_a,X1: refine424419629nres_a] :
( ( ( ord_le519537037nres_a @ X1 @ ( inf_in262696383nres_a @ X0 @ X2 ) )
= $true )
| ( $false
= ( ord_le519537037nres_a @ X1 @ X2 ) )
| ( ( ord_le519537037nres_a @ X1 @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1301]) ).
thf(f1301,plain,
! [X2: refine424419629nres_a,X0: refine424419629nres_a,X1: refine424419629nres_a] :
( ( ( ord_le519537037nres_a @ X1 @ ( inf_in262696383nres_a @ X0 @ X2 ) )
= $true )
| ( ( ( ord_le519537037nres_a @ X1 @ X2 )
& ( ord_le519537037nres_a @ X1 @ X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1131]) ).
thf(f1131,plain,
! [X2: refine424419629nres_a,X0: refine424419629nres_a,X1: refine424419629nres_a] :
( ( ord_le519537037nres_a @ X1 @ ( inf_in262696383nres_a @ X0 @ X2 ) )
= ( ( ord_le519537037nres_a @ X1 @ X2 )
& ( ord_le519537037nres_a @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f800]) ).
thf(f800,plain,
! [X0: refine424419629nres_a,X1: refine424419629nres_a,X2: refine424419629nres_a] :
( ( ord_le519537037nres_a @ X1 @ ( inf_in262696383nres_a @ X0 @ X2 ) )
= ( ( ord_le519537037nres_a @ X1 @ X2 )
& ( ord_le519537037nres_a @ X1 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f799]) ).
thf(f799,plain,
! [X0: refine424419629nres_a,X1: refine424419629nres_a,X2: refine424419629nres_a] :
( ( ord_le519537037nres_a @ X1 @ X0 )
& ( ( ord_le519537037nres_a @ X1 @ X2 )
= ( ord_le519537037nres_a @ X1 @ ( inf_in262696383nres_a @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f126]) ).
thf(f126,axiom,
! [X4: refine424419629nres_a,X31: refine424419629nres_a,X32: refine424419629nres_a] :
( ( ord_le519537037nres_a @ X31 @ X4 )
& ( ( ord_le519537037nres_a @ X31 @ X32 )
= ( ord_le519537037nres_a @ X31 @ ( inf_in262696383nres_a @ X4 @ X32 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_125_inf_Obounded__iff) ).
thf(f1671,plain,
( $true
!= ( ord_le519537037nres_a @ a2 @ ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1070,f1639]) ).
thf(f1639,plain,
! [X0: a > $o,X1: a > $o] :
( ( refine1198353288_RES_a
@ ( collect_a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ X1 ) ) @ ( refine1198353288_RES_a @ ( collect_a @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f1253,f1163]) ).
thf(f1163,plain,
! [X0: a > $o,X1: a > $o] :
( ( collect_a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( collect_a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( collect_a @ X0 ) )
& ( member_a @ Y0 @ ( collect_a @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1135]) ).
thf(f1135,plain,
! [X0: a > $o,X1: a > $o] :
( ( collect_a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: set_a,Y1: set_a] :
( collect_a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
& ( member_a @ Y2 @ Y0 ) ) )
@ ( collect_a @ X1 )
@ ( collect_a @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f1051,f1060]) ).
thf(f1060,plain,
( inf_inf_set_a
= ( ^ [Y0: set_a,Y1: set_a] :
( collect_a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
& ( member_a @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f369]) ).
thf(f369,plain,
( inf_inf_set_a
= ( ^ [Y0: set_a,Y1: set_a] :
( collect_a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
& ( member_a @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f368]) ).
thf(f368,plain,
( inf_inf_set_a
= ( ^ [X0: set_a,X1: set_a] :
( collect_a
@ ^ [X2: a] :
( ( member_a @ X2 @ X0 )
& ( member_a @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f269]) ).
thf(f269,axiom,
( inf_inf_set_a
= ( ^ [X47: set_a,X48: set_a] :
( collect_a
@ ^ [X30: a] :
( ( member_a @ X30 @ X47 )
& ( member_a @ X30 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_268_Int__def) ).
thf(f1051,plain,
! [X0: a > $o,X1: a > $o] :
( ( collect_a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( inf_inf_set_a @ ( collect_a @ X1 ) @ ( collect_a @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
thf(f431,plain,
! [X0: a > $o,X1: a > $o] :
( ( collect_a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( inf_inf_set_a @ ( collect_a @ X1 ) @ ( collect_a @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f430]) ).
thf(f430,plain,
! [X0: a > $o,X1: a > $o] :
( ( collect_a
@ ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( inf_inf_set_a @ ( collect_a @ X1 ) @ ( collect_a @ X0 ) ) ),
inference(rectify,[status(thm)],[f273]) ).
thf(f273,axiom,
! [X11: a > $o,X10: a > $o] :
( ( collect_a
@ ^ [X30: a] :
( ( X10 @ X30 )
& ( X11 @ X30 ) ) )
= ( inf_inf_set_a @ ( collect_a @ X10 ) @ ( collect_a @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_272_Collect__conj__eq) ).
thf(f1253,plain,
! [X0: set_a,X1: set_a] :
( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X1 ) @ ( refine1198353288_RES_a @ X0 ) )
= ( refine1198353288_RES_a
@ ( collect_a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X0 )
& ( member_a @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1145]) ).
thf(f1145,plain,
! [X0: set_a,X1: set_a] :
( ( refine1198353288_RES_a
@ ( ^ [Y0: set_a,Y1: set_a] :
( collect_a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
& ( member_a @ Y2 @ Y0 ) ) )
@ X1
@ X0 ) )
= ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X1 ) @ ( refine1198353288_RES_a @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f1101,f1060]) ).
thf(f1101,plain,
! [X0: set_a,X1: set_a] :
( ( refine1198353288_RES_a @ ( inf_inf_set_a @ X1 @ X0 ) )
= ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X1 ) @ ( refine1198353288_RES_a @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f946]) ).
thf(f946,plain,
! [X0: set_a,X1: set_a] :
( ( refine1198353288_RES_a @ ( inf_inf_set_a @ X1 @ X0 ) )
= ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X1 ) @ ( refine1198353288_RES_a @ X0 ) ) ),
inference(rectify,[status(thm)],[f149]) ).
thf(f149,axiom,
! [X4: set_a,X31: set_a] :
( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X31 ) @ ( refine1198353288_RES_a @ X4 ) )
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ X31 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_148_inf__nres_Osimps_I3_J) ).
thf(f1070,plain,
( $true
!= ( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [Y0: a] :
( ( p @ Y0 )
& ( q @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f943]) ).
thf(f943,plain,
( $true
!= ( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [Y0: a] :
( ( p @ Y0 )
& ( q @ Y0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f888]) ).
thf(f888,plain,
( $true
!= ( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [Y0: a] :
( ( p @ Y0 )
& ( q @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f887]) ).
thf(f887,plain,
~ ( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [X0: a] :
( ( q @ X0 )
& ( p @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f358]) ).
thf(f358,negated_conjecture,
~ ( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [X74: a] :
( ( q @ X74 )
& ( p @ X74 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f357]) ).
thf(f357,conjecture,
( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [X74: a] :
( ( q @ X74 )
& ( p @ X74 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',conj_0) ).
thf(f1093,plain,
( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f780]) ).
thf(f780,plain,
( ( ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f779]) ).
thf(f779,plain,
ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ),
file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_2_assms_I2_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP162^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 08:28:03 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 ---- Original DTF file ---
% 0.17/0.43 thf(spec,logic,$$dhol).
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % File : ITP162^1 : TPTP v9.2.1. Released v7.5.0.
% 0.17/0.43 % Domain : Interactive Theorem Proving
% 0.17/0.43 % Problem : Sledgehammer Refine_Basic problem prob_1909__3604894_1
% 0.17/0.43 % Version : Especial.
% 0.17/0.43 % English :
% 0.17/0.43
% 0.17/0.43 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.17/0.43 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.17/0.43 % Source : [Des21]
% 0.17/0.43 % Names : Refine_Basic/prob_1909__3604894_1 [Des21]
% 0.17/0.43
% 0.17/0.43 % Status : Theorem
% 0.17/0.43 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0
% 0.17/0.43 % Syntax : Number of formulae : 388 ( 158 unt; 31 typ; 0 def)
% 0.17/0.43 % Number of atoms : 1039 ( 293 equ; 0 cnn)
% 0.17/0.43 % Maximal formula atoms : 9 ( 2 avg)
% 0.17/0.43 % Number of connectives : 2890 ( 43 ~; 2 |; 36 &;2348 @)
% 0.17/0.43 % ( 0 <=>; 461 =>; 0 <=; 0 <~>)
% 0.17/0.43 % Maximal formula depth : 15 ( 7 avg)
% 0.17/0.43 % Number of types : 4 ( 3 usr)
% 0.17/0.43 % Number of type conns : 430 ( 430 >; 0 *; 0 +; 0 <<)
% 0.17/0.43 % Number of symbols : 31 ( 28 usr; 7 con; 0-4 aty)
% 0.17/0.43 % Number of variables : 1098 ( 126 ^; 970 !; 2 ?;1098 :)
% 0.17/0.43 % SPC : TH0_THM_EQU_NAR
% 0.17/0.43
% 0.17/0.43 % Comments : This file was generated by Sledgehammer 2021-02-23 15:36:21.134
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % Could-be-implicit typings (3)
% 0.17/0.43 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.17/0.43 refine424419629nres_a: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.17/0.43 set_a: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_n_tf__a,type,
% 0.17/0.43 a: $tType ).
% 0.17/0.43
% 0.17/0.43 % Explicit typings (28)
% 0.17/0.43 thf(sy_c_If_001_062_Itf__a_M_Eo_J,type,
% 0.17/0.43 if_a_o: $o > ( a > $o ) > ( a > $o ) > a > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.17/0.43 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 0.17/0.43 if_set_a: $o > set_a > set_a > set_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_Itf__a_M_Eo_J,type,
% 0.17/0.43 inf_inf_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Lattices_Oinf__class_Oinf_001_Eo,type,
% 0.17/0.43 inf_inf_o: $o > $o > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.17/0.43 inf_in262696383nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
% 0.17/0.43 inf_inf_set_a: set_a > set_a > set_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Obot__class_Obot_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.17/0.43 bot_bo529555393nres_a: refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.17/0.43 bot_bot_set_a: set_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J,type,
% 0.17/0.43 ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
% 0.17/0.43 ord_less_eq_o: $o > $o > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.17/0.43 ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.17/0.43 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.17/0.43 order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.17/0.43 top_to231829469nres_a: refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__a,type,
% 0.17/0.43 refine2063221604TURN_a: a > refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001tf__a,type,
% 0.17/0.43 refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__a,type,
% 0.17/0.43 refine1001002027nres_a: refine424419629nres_a > a > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onf__inres_001tf__a,type,
% 0.17/0.43 refine1312857699nres_a: refine424419629nres_a > a > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__a,type,
% 0.17/0.43 refine412683989fail_a: refine424419629nres_a > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_OFAILi_001tf__a,type,
% 0.17/0.43 refine464223677AILi_a: refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__a,type,
% 0.17/0.43 refine1198353288_RES_a: set_a > refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001tf__a,type,
% 0.17/0.43 refine1822134885_RES_a: refine424419629nres_a > set_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.17/0.43 collect_a: ( a > $o ) > set_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_member_001tf__a,type,
% 0.17/0.43 member_a: a > set_a > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_A,type,
% 0.17/0.43 a2: refine424419629nres_a ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_P,type,
% 0.17/0.43 p: a > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_Q,type,
% 0.17/0.43 q: a > $o ).
% 0.17/0.43
% 0.17/0.43 % Relevant facts (349)
% 0.17/0.43 thf(fact_0_nres__more__simps_I4_J,axiom,
% 0.17/0.43 ! [X: set_a,Y: set_a] :
% 0.17/0.43 ( ( ( refine1198353288_RES_a @ X )
% 0.17/0.43 = ( refine1198353288_RES_a @ Y ) )
% 0.17/0.43 = ( X = Y ) ) ).
% 0.17/0.43
% 0.17/0.43 % nres_more_simps(4)
% 0.17/0.43 thf(fact_1_nres_Oinject,axiom,
% 0.17/0.43 ! [X2: set_a,Y2: set_a] :
% 0.17/0.43 ( ( ( refine1198353288_RES_a @ X2 )
% 0.17/0.43 = ( refine1198353288_RES_a @ Y2 ) )
% 0.17/0.43 = ( X2 = Y2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % nres.inject
% 0.17/0.43 thf(fact_2_assms_I2_J,axiom,
% 0.17/0.43 ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) ).
% 0.17/0.43
% 0.17/0.43 % assms(2)
% 0.17/0.43 thf(fact_3_assms_I1_J,axiom,
% 0.17/0.43 ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) ).
% 0.17/0.43
% 0.17/0.43 % assms(1)
% 0.17/0.43 thf(fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062,axiom,
% 0.17/0.43 ord_le519537037nres_a @ a2 @ ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % \<open>A \<le> inf (SPEC P) (SPEC Q)\<close>
% 0.17/0.43 thf(fact_5_if__rule,axiom,
% 0.17/0.43 ! [B: $o,S1: refine424419629nres_a,Phi: a > $o,S2: refine424419629nres_a] :
% 0.17/0.43 ( ( B
% 0.17/0.43 => ( ord_le519537037nres_a @ S1 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.17/0.43 => ( ( ~ B
% 0.17/0.43 => ( ord_le519537037nres_a @ S2 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.17/0.43 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ S1 @ S2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % if_rule
% 0.17/0.43 thf(fact_6_RES__rule,axiom,
% 0.17/0.43 ! [S: set_a,Phi: a > $o] :
% 0.17/0.43 ( ! [X3: a] :
% 0.17/0.43 ( ( member_a @ X3 @ S )
% 0.17/0.43 => ( Phi @ X3 ) )
% 0.17/0.43 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % RES_rule
% 0.17/0.43 thf(fact_7_SPEC__iff,axiom,
% 0.17/0.43 ! [P: refine424419629nres_a,Q: a > $o,R: a > $o] :
% 0.17/0.43 ( ( ord_le519537037nres_a @ P
% 0.17/0.43 @ ( refine1198353288_RES_a
% 0.17/0.43 @ ( collect_a
% 0.17/0.43 @ ^ [S3: a] :
% 0.17/0.43 ( ( Q @ S3 )
% 0.17/0.43 => ( R @ S3 ) ) ) ) )
% 0.17/0.43 => ( ( ord_le519537037nres_a @ P
% 0.17/0.43 @ ( refine1198353288_RES_a
% 0.17/0.43 @ ( collect_a
% 0.17/0.43 @ ^ [S3: a] :
% 0.17/0.43 ( ~ ( Q @ S3 )
% 0.17/0.43 => ~ ( R @ S3 ) ) ) ) )
% 0.17/0.43 => ( ord_le519537037nres_a @ P
% 0.17/0.43 @ ( refine1198353288_RES_a
% 0.17/0.43 @ ( collect_a
% 0.17/0.43 @ ^ [S3: a] :
% 0.17/0.43 ( ( Q @ S3 )
% 0.17/0.43 = ( R @ S3 ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % SPEC_iff
% 0.17/0.43 thf(fact_8_SPEC__rule,axiom,
% 0.17/0.43 ! [Phi: a > $o,Phi2: a > $o] :
% 0.17/0.43 ( ! [X3: a] :
% 0.17/0.43 ( ( Phi @ X3 )
% 0.17/0.43 => ( Phi2 @ X3 ) )
% 0.17/0.43 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % SPEC_rule
% 0.17/0.43 thf(fact_9_SPEC__trans,axiom,
% 0.17/0.43 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Postcond: a > $o] :
% 0.17/0.43 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.17/0.43 => ( ( ord_le519537037nres_a @ Y3 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 0.17/0.43 => ( ord_le519537037nres_a @ X4 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % SPEC_trans
% 0.17/0.43 thf(fact_10_lhs__step__If,axiom,
% 0.17/0.43 ! [B: $o,T: set_a,M: set_a,E: set_a] :
% 0.17/0.43 ( ( B
% 0.17/0.43 => ( ord_less_eq_set_a @ T @ M ) )
% 0.17/0.43 => ( ( ~ B
% 0.17/0.43 => ( ord_less_eq_set_a @ E @ M ) )
% 0.17/0.43 => ( ord_less_eq_set_a @ ( if_set_a @ B @ T @ E ) @ M ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % lhs_step_If
% 0.17/0.43 thf(fact_11_lhs__step__If,axiom,
% 0.17/0.43 ! [B: $o,T: a > $o,M: a > $o,E: a > $o] :
% 0.17/0.43 ( ( B
% 0.17/0.43 => ( ord_less_eq_a_o @ T @ M ) )
% 0.17/0.43 => ( ( ~ B
% 0.17/0.43 => ( ord_less_eq_a_o @ E @ M ) )
% 0.17/0.43 => ( ord_less_eq_a_o @ ( if_a_o @ B @ T @ E ) @ M ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % lhs_step_If
% 0.17/0.43 thf(fact_12_lhs__step__If,axiom,
% 0.17/0.43 ! [B: $o,T: refine424419629nres_a,M: refine424419629nres_a,E: refine424419629nres_a] :
% 0.17/0.43 ( ( B
% 0.17/0.43 => ( ord_le519537037nres_a @ T @ M ) )
% 0.17/0.43 => ( ( ~ B
% 0.17/0.43 => ( ord_le519537037nres_a @ E @ M ) )
% 0.17/0.43 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ M ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % lhs_step_If
% 0.17/0.43 thf(fact_13_use__spec__rule,axiom,
% 0.17/0.43 ! [M: refine424419629nres_a,Psi: a > $o,Phi: a > $o] :
% 0.17/0.43 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ M
% 0.17/0.44 @ ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [S3: a] :
% 0.17/0.44 ( ( Psi @ S3 )
% 0.17/0.44 => ( Phi @ S3 ) ) ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % use_spec_rule
% 0.17/0.44 thf(fact_14_SPEC__cons__rule,axiom,
% 0.17/0.44 ! [M: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.17/0.44 => ( ! [X3: a] :
% 0.17/0.44 ( ( Phi @ X3 )
% 0.17/0.44 => ( Psi @ X3 ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % SPEC_cons_rule
% 0.17/0.44 thf(fact_15_order__mono__setup_Orefl,axiom,
% 0.17/0.44 ! [X4: set_a] : ( ord_less_eq_set_a @ X4 @ X4 ) ).
% 0.17/0.44
% 0.17/0.44 % order_mono_setup.refl
% 0.17/0.44 thf(fact_16_order__mono__setup_Orefl,axiom,
% 0.17/0.44 ! [X4: a > $o] : ( ord_less_eq_a_o @ X4 @ X4 ) ).
% 0.17/0.44
% 0.17/0.44 % order_mono_setup.refl
% 0.17/0.44 thf(fact_17_order__mono__setup_Orefl,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a] : ( ord_le519537037nres_a @ X4 @ X4 ) ).
% 0.17/0.44
% 0.17/0.44 % order_mono_setup.refl
% 0.17/0.44 thf(fact_18_the__RES_Osimps,axiom,
% 0.17/0.44 ! [X: set_a] :
% 0.17/0.44 ( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ X ) )
% 0.17/0.44 = X ) ).
% 0.17/0.44
% 0.17/0.44 % the_RES.simps
% 0.17/0.44 thf(fact_19_nf__inres__RES,axiom,
% 0.17/0.44 ! [X: set_a,X4: a] :
% 0.17/0.44 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X ) @ X4 )
% 0.17/0.44 = ( member_a @ X4 @ X ) ) ).
% 0.17/0.44
% 0.17/0.44 % nf_inres_RES
% 0.17/0.44 thf(fact_20_nf__inres__SPEC,axiom,
% 0.17/0.44 ! [Phi: a > $o,X4: a] :
% 0.17/0.44 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ X4 )
% 0.17/0.44 = ( Phi @ X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % nf_inres_SPEC
% 0.17/0.44 thf(fact_21_le__funD,axiom,
% 0.17/0.44 ! [F: a > $o,G: a > $o,X4: a] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ F @ G )
% 0.17/0.44 => ( ord_less_eq_o @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_funD
% 0.17/0.44 thf(fact_22_le__funE,axiom,
% 0.17/0.44 ! [F: a > $o,G: a > $o,X4: a] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ F @ G )
% 0.17/0.44 => ( ord_less_eq_o @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_funE
% 0.17/0.44 thf(fact_23_le__funI,axiom,
% 0.17/0.44 ! [F: a > $o,G: a > $o] :
% 0.17/0.44 ( ! [X3: a] : ( ord_less_eq_o @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ F @ G ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_funI
% 0.17/0.44 thf(fact_24_Refine__Misc_Oif__mono,axiom,
% 0.17/0.44 ! [B: $o,M1: set_a,M12: set_a,M2: set_a,M22: set_a] :
% 0.17/0.44 ( ( B
% 0.17/0.44 => ( ord_less_eq_set_a @ M1 @ M12 ) )
% 0.17/0.44 => ( ( ~ B
% 0.17/0.44 => ( ord_less_eq_set_a @ M2 @ M22 ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( if_set_a @ B @ M1 @ M2 ) @ ( if_set_a @ B @ M12 @ M22 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Refine_Misc.if_mono
% 0.17/0.44 thf(fact_25_Refine__Misc_Oif__mono,axiom,
% 0.17/0.44 ! [B: $o,M1: a > $o,M12: a > $o,M2: a > $o,M22: a > $o] :
% 0.17/0.44 ( ( B
% 0.17/0.44 => ( ord_less_eq_a_o @ M1 @ M12 ) )
% 0.17/0.44 => ( ( ~ B
% 0.17/0.44 => ( ord_less_eq_a_o @ M2 @ M22 ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( if_a_o @ B @ M1 @ M2 ) @ ( if_a_o @ B @ M12 @ M22 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Refine_Misc.if_mono
% 0.17/0.44 thf(fact_26_Refine__Misc_Oif__mono,axiom,
% 0.17/0.44 ! [B: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M2: refine424419629nres_a,M22: refine424419629nres_a] :
% 0.17/0.44 ( ( B
% 0.17/0.44 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 0.17/0.44 => ( ( ~ B
% 0.17/0.44 => ( ord_le519537037nres_a @ M2 @ M22 ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ M1 @ M2 ) @ ( if_Ref1724547303nres_a @ B @ M12 @ M22 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Refine_Misc.if_mono
% 0.17/0.44 thf(fact_27_le__fun__def,axiom,
% 0.17/0.44 ( ord_less_eq_a_o
% 0.17/0.44 = ( ^ [F2: a > $o,G2: a > $o] :
% 0.17/0.44 ! [X5: a] : ( ord_less_eq_o @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_fun_def
% 0.17/0.44 thf(fact_28_order__subst1,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,F: set_a > refine424419629nres_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst1
% 0.17/0.44 thf(fact_29_order__subst1,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,F: ( a > $o ) > refine424419629nres_a,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst1
% 0.17/0.44 thf(fact_30_order__subst1,axiom,
% 0.17/0.44 ! [A: set_a,F: refine424419629nres_a > set_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst1
% 0.17/0.44 thf(fact_31_order__subst1,axiom,
% 0.17/0.44 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst1
% 0.17/0.44 thf(fact_32_order__subst1,axiom,
% 0.17/0.44 ! [A: set_a,F: ( a > $o ) > set_a,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst1
% 0.17/0.44 thf(fact_33_order__subst1,axiom,
% 0.17/0.44 ! [A: a > $o,F: refine424419629nres_a > a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ ( F @ B ) )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst1
% 0.17/0.44 thf(fact_34_order__subst1,axiom,
% 0.17/0.44 ! [A: a > $o,F: set_a > a > $o,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst1
% 0.17/0.44 thf(fact_35_order__subst1,axiom,
% 0.17/0.44 ! [A: a > $o,F: ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst1
% 0.17/0.44 thf(fact_36_order__subst1,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst1
% 0.17/0.44 thf(fact_37_le__infD2,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infD2
% 0.17/0.44 thf(fact_38_le__infD2,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infD2
% 0.17/0.44 thf(fact_39_le__infD2,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infD2
% 0.17/0.44 thf(fact_40_le__infD1,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infD1
% 0.17/0.44 thf(fact_41_le__infD1,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infD1
% 0.17/0.44 thf(fact_42_le__infD1,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infD1
% 0.17/0.44 thf(fact_43_inf__leI,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ! [X3: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ A )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ X3 @ B )
% 0.17/0.44 => ( ord_less_eq_set_a @ X3 @ C ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_leI
% 0.17/0.44 thf(fact_44_inf__leI,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ! [X3: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ A )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ X3 @ B )
% 0.17/0.44 => ( ord_less_eq_a_o @ X3 @ C ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_leI
% 0.17/0.44 thf(fact_45_inf__leI,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ! [X3: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ A )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ X3 @ B )
% 0.17/0.44 => ( ord_le519537037nres_a @ X3 @ C ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_leI
% 0.17/0.44 thf(fact_46_less__eq__nres_Osimps_I2_J,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 0.17/0.44 = ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_eq_nres.simps(2)
% 0.17/0.44 thf(fact_47_nres__order__simps_I5_J,axiom,
% 0.17/0.44 ! [X: set_a,Y: set_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine1198353288_RES_a @ Y ) )
% 0.17/0.44 = ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.17/0.44
% 0.17/0.44 % nres_order_simps(5)
% 0.17/0.44 thf(fact_48_order__mono__setup_Omono__if,axiom,
% 0.17/0.44 ! [T: set_a,T2: set_a,E: set_a,E2: set_a,B: $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ T @ T2 )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ E @ E2 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( if_set_a @ B @ T @ E ) @ ( if_set_a @ B @ T2 @ E2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_mono_setup.mono_if
% 0.17/0.44 thf(fact_49_order__mono__setup_Omono__if,axiom,
% 0.17/0.44 ! [T: a > $o,T2: a > $o,E: a > $o,E2: a > $o,B: $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ T @ T2 )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ E @ E2 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( if_a_o @ B @ T @ E ) @ ( if_a_o @ B @ T2 @ E2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_mono_setup.mono_if
% 0.17/0.44 thf(fact_50_order__mono__setup_Omono__if,axiom,
% 0.17/0.44 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B: $o] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ T @ T2 )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ E @ E2 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ ( if_Ref1724547303nres_a @ B @ T2 @ E2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_mono_setup.mono_if
% 0.17/0.44 thf(fact_51_dual__order_Oantisym,axiom,
% 0.17/0.44 ! [B: set_a,A: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ B @ A )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.antisym
% 0.17/0.44 thf(fact_52_dual__order_Oantisym,axiom,
% 0.17/0.44 ! [B: a > $o,A: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ B @ A )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.antisym
% 0.17/0.44 thf(fact_53_dual__order_Oantisym,axiom,
% 0.17/0.44 ! [B: refine424419629nres_a,A: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ B @ A )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.antisym
% 0.17/0.44 thf(fact_54_dual__order_Oeq__iff,axiom,
% 0.17/0.44 ( ( ^ [Y5: set_a,Z: set_a] : ( Y5 = Z ) )
% 0.17/0.44 = ( ^ [A2: set_a,B2: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.17/0.44 & ( ord_less_eq_set_a @ A2 @ B2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.eq_iff
% 0.17/0.44 thf(fact_55_dual__order_Oeq__iff,axiom,
% 0.17/0.44 ( ( ^ [Y5: a > $o,Z: a > $o] : ( Y5 = Z ) )
% 0.17/0.44 = ( ^ [A2: a > $o,B2: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ B2 @ A2 )
% 0.17/0.44 & ( ord_less_eq_a_o @ A2 @ B2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.eq_iff
% 0.17/0.44 thf(fact_56_dual__order_Oeq__iff,axiom,
% 0.17/0.44 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 0.17/0.44 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.17/0.44 & ( ord_le519537037nres_a @ A2 @ B2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.eq_iff
% 0.17/0.44 thf(fact_57_dual__order_Otrans,axiom,
% 0.17/0.44 ! [B: set_a,A: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ B @ A )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ C @ B )
% 0.17/0.44 => ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.trans
% 0.17/0.44 thf(fact_58_dual__order_Otrans,axiom,
% 0.17/0.44 ! [B: a > $o,A: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ B @ A )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ C @ B )
% 0.17/0.44 => ( ord_less_eq_a_o @ C @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.trans
% 0.17/0.44 thf(fact_59_dual__order_Otrans,axiom,
% 0.17/0.44 ! [B: refine424419629nres_a,A: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ B @ A )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ C @ B )
% 0.17/0.44 => ( ord_le519537037nres_a @ C @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.trans
% 0.17/0.44 thf(fact_60_dual__order_Orefl,axiom,
% 0.17/0.44 ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.refl
% 0.17/0.44 thf(fact_61_dual__order_Orefl,axiom,
% 0.17/0.44 ! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.refl
% 0.17/0.44 thf(fact_62_dual__order_Orefl,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ) ).
% 0.17/0.44
% 0.17/0.44 % dual_order.refl
% 0.17/0.44 thf(fact_63_order__trans,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ Y3 @ Z2 )
% 0.17/0.44 => ( ord_less_eq_set_a @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_trans
% 0.17/0.44 thf(fact_64_order__trans,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ Y3 @ Z2 )
% 0.17/0.44 => ( ord_less_eq_a_o @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_trans
% 0.17/0.44 thf(fact_65_order__trans,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 0.17/0.44 => ( ord_le519537037nres_a @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_trans
% 0.17/0.44 thf(fact_66_order__class_Oorder_Oantisym,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ A )
% 0.17/0.44 => ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_class.order.antisym
% 0.17/0.44 thf(fact_67_order__class_Oorder_Oantisym,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ A )
% 0.17/0.44 => ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_class.order.antisym
% 0.17/0.44 thf(fact_68_order__class_Oorder_Oantisym,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ A )
% 0.17/0.44 => ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_class.order.antisym
% 0.17/0.44 thf(fact_69_ord__le__eq__trans,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( B = C )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_trans
% 0.17/0.44 thf(fact_70_ord__le__eq__trans,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( B = C )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_trans
% 0.17/0.44 thf(fact_71_ord__le__eq__trans,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( B = C )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_trans
% 0.17/0.44 thf(fact_72_ord__eq__le__trans,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( A = B )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_trans
% 0.17/0.44 thf(fact_73_ord__eq__le__trans,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( A = B )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ C )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_trans
% 0.17/0.44 thf(fact_74_ord__eq__le__trans,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( A = B )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_trans
% 0.17/0.44 thf(fact_75_order__class_Oorder_Oeq__iff,axiom,
% 0.17/0.44 ( ( ^ [Y5: set_a,Z: set_a] : ( Y5 = Z ) )
% 0.17/0.44 = ( ^ [A2: set_a,B2: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.17/0.44 & ( ord_less_eq_set_a @ B2 @ A2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_class.order.eq_iff
% 0.17/0.44 thf(fact_76_order__class_Oorder_Oeq__iff,axiom,
% 0.17/0.44 ( ( ^ [Y5: a > $o,Z: a > $o] : ( Y5 = Z ) )
% 0.17/0.44 = ( ^ [A2: a > $o,B2: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.17/0.44 & ( ord_less_eq_a_o @ B2 @ A2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_class.order.eq_iff
% 0.17/0.44 thf(fact_77_order__class_Oorder_Oeq__iff,axiom,
% 0.17/0.44 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 0.17/0.44 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.17/0.44 & ( ord_le519537037nres_a @ B2 @ A2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_class.order.eq_iff
% 0.17/0.44 thf(fact_78_antisym__conv,axiom,
% 0.17/0.44 ! [Y3: set_a,X4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 0.17/0.44 = ( X4 = Y3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % antisym_conv
% 0.17/0.44 thf(fact_79_antisym__conv,axiom,
% 0.17/0.44 ! [Y3: a > $o,X4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ Y3 @ X4 )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 0.17/0.44 = ( X4 = Y3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % antisym_conv
% 0.17/0.44 thf(fact_80_antisym__conv,axiom,
% 0.17/0.44 ! [Y3: refine424419629nres_a,X4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.17/0.44 = ( X4 = Y3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % antisym_conv
% 0.17/0.44 thf(fact_81_mem__Collect__eq,axiom,
% 0.17/0.44 ! [A: a,P: a > $o] :
% 0.17/0.44 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.17/0.44 = ( P @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % mem_Collect_eq
% 0.17/0.44 thf(fact_82_Collect__mem__eq,axiom,
% 0.17/0.44 ! [A3: set_a] :
% 0.17/0.44 ( ( collect_a
% 0.17/0.44 @ ^ [X5: a] : ( member_a @ X5 @ A3 ) )
% 0.17/0.44 = A3 ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_mem_eq
% 0.17/0.44 thf(fact_83_Collect__cong,axiom,
% 0.17/0.44 ! [P: a > $o,Q: a > $o] :
% 0.17/0.44 ( ! [X3: a] :
% 0.17/0.44 ( ( P @ X3 )
% 0.17/0.44 = ( Q @ X3 ) )
% 0.17/0.44 => ( ( collect_a @ P )
% 0.17/0.44 = ( collect_a @ Q ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_cong
% 0.17/0.44 thf(fact_84_order_Otrans,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order.trans
% 0.17/0.44 thf(fact_85_order_Otrans,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ C )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order.trans
% 0.17/0.44 thf(fact_86_order_Otrans,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order.trans
% 0.17/0.44 thf(fact_87_eq__refl,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] :
% 0.17/0.44 ( ( X4 = Y3 )
% 0.17/0.44 => ( ord_less_eq_set_a @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_refl
% 0.17/0.44 thf(fact_88_eq__refl,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] :
% 0.17/0.44 ( ( X4 = Y3 )
% 0.17/0.44 => ( ord_less_eq_a_o @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_refl
% 0.17/0.44 thf(fact_89_eq__refl,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( X4 = Y3 )
% 0.17/0.44 => ( ord_le519537037nres_a @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_refl
% 0.17/0.44 thf(fact_90_antisym,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 0.17/0.44 => ( X4 = Y3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % antisym
% 0.17/0.44 thf(fact_91_antisym,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ Y3 @ X4 )
% 0.17/0.44 => ( X4 = Y3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % antisym
% 0.17/0.44 thf(fact_92_antisym,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 0.17/0.44 => ( X4 = Y3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % antisym
% 0.17/0.44 thf(fact_93_eq__iff,axiom,
% 0.17/0.44 ( ( ^ [Y5: set_a,Z: set_a] : ( Y5 = Z ) )
% 0.17/0.44 = ( ^ [X5: set_a,Y6: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X5 @ Y6 )
% 0.17/0.44 & ( ord_less_eq_set_a @ Y6 @ X5 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_iff
% 0.17/0.44 thf(fact_94_eq__iff,axiom,
% 0.17/0.44 ( ( ^ [Y5: a > $o,Z: a > $o] : ( Y5 = Z ) )
% 0.17/0.44 = ( ^ [X5: a > $o,Y6: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X5 @ Y6 )
% 0.17/0.44 & ( ord_less_eq_a_o @ Y6 @ X5 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_iff
% 0.17/0.44 thf(fact_95_eq__iff,axiom,
% 0.17/0.44 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 0.17/0.44 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X5 @ Y6 )
% 0.17/0.44 & ( ord_le519537037nres_a @ Y6 @ X5 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % eq_iff
% 0.17/0.44 thf(fact_96_ord__le__eq__subst,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( ( F @ B )
% 0.17/0.44 = C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_subst
% 0.17/0.44 thf(fact_97_ord__le__eq__subst,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( ( F @ B )
% 0.17/0.44 = C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_subst
% 0.17/0.44 thf(fact_98_ord__le__eq__subst,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( ( F @ B )
% 0.17/0.44 = C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_subst
% 0.17/0.44 thf(fact_99_ord__le__eq__subst,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( ( F @ B )
% 0.17/0.44 = C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_subst
% 0.17/0.44 thf(fact_100_ord__le__eq__subst,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,F: set_a > a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( ( F @ B )
% 0.17/0.44 = C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_subst
% 0.17/0.44 thf(fact_101_ord__le__eq__subst,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,F: ( a > $o ) > refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( ( F @ B )
% 0.17/0.44 = C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_subst
% 0.17/0.44 thf(fact_102_ord__le__eq__subst,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( ( F @ B )
% 0.17/0.44 = C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_subst
% 0.17/0.44 thf(fact_103_ord__le__eq__subst,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( ( F @ B )
% 0.17/0.44 = C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_subst
% 0.17/0.44 thf(fact_104_ord__le__eq__subst,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( ( F @ B )
% 0.17/0.44 = C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_le_eq_subst
% 0.17/0.44 thf(fact_105_ord__eq__le__subst,axiom,
% 0.17/0.44 ! [A: set_a,F: refine424419629nres_a > set_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( F @ B ) )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_subst
% 0.17/0.44 thf(fact_106_ord__eq__le__subst,axiom,
% 0.17/0.44 ! [A: a > $o,F: refine424419629nres_a > a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( F @ B ) )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_subst
% 0.17/0.44 thf(fact_107_ord__eq__le__subst,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,F: set_a > refine424419629nres_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_subst
% 0.17/0.44 thf(fact_108_ord__eq__le__subst,axiom,
% 0.17/0.44 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_subst
% 0.17/0.44 thf(fact_109_ord__eq__le__subst,axiom,
% 0.17/0.44 ! [A: a > $o,F: set_a > a > $o,B: set_a,C: set_a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_subst
% 0.17/0.44 thf(fact_110_ord__eq__le__subst,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,F: ( a > $o ) > refine424419629nres_a,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_subst
% 0.17/0.44 thf(fact_111_ord__eq__le__subst,axiom,
% 0.17/0.44 ! [A: set_a,F: ( a > $o ) > set_a,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_subst
% 0.17/0.44 thf(fact_112_ord__eq__le__subst,axiom,
% 0.17/0.44 ! [A: a > $o,F: ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( F @ B ) )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_subst
% 0.17/0.44 thf(fact_113_ord__eq__le__subst,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( F @ B ) )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_subst
% 0.17/0.44 thf(fact_114_order__subst2,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst2
% 0.17/0.44 thf(fact_115_order__subst2,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ ( F @ B ) @ C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst2
% 0.17/0.44 thf(fact_116_order__subst2,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst2
% 0.17/0.44 thf(fact_117_order__subst2,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst2
% 0.17/0.44 thf(fact_118_order__subst2,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,F: set_a > a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ ( F @ B ) @ C )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst2
% 0.17/0.44 thf(fact_119_order__subst2,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,F: ( a > $o ) > refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst2
% 0.17/0.44 thf(fact_120_order__subst2,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst2
% 0.17/0.44 thf(fact_121_order__subst2,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ ( F @ B ) @ C )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst2
% 0.17/0.44 thf(fact_122_order__subst2,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % order_subst2
% 0.17/0.44 thf(fact_123_inf_Obounded__iff,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 0.17/0.44 = ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 & ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.bounded_iff
% 0.17/0.44 thf(fact_124_inf_Obounded__iff,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
% 0.17/0.44 = ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 & ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.bounded_iff
% 0.17/0.44 thf(fact_125_inf_Obounded__iff,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
% 0.17/0.44 = ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 & ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.bounded_iff
% 0.17/0.44 thf(fact_126_le__inf__iff,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) )
% 0.17/0.44 = ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 0.17/0.44 & ( ord_less_eq_set_a @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_inf_iff
% 0.17/0.44 thf(fact_127_le__inf__iff,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) )
% 0.17/0.44 = ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 0.17/0.44 & ( ord_less_eq_a_o @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_inf_iff
% 0.17/0.44 thf(fact_128_le__inf__iff,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) )
% 0.17/0.44 = ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.17/0.44 & ( ord_le519537037nres_a @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_inf_iff
% 0.17/0.44 thf(fact_129_inf__apply,axiom,
% 0.17/0.44 ( inf_inf_a_o
% 0.17/0.44 = ( ^ [F2: a > $o,G2: a > $o,X5: a] : ( inf_inf_o @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_apply
% 0.17/0.44 thf(fact_130_inf_Oidem,axiom,
% 0.17/0.44 ! [A: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ A @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % inf.idem
% 0.17/0.44 thf(fact_131_inf_Oidem,axiom,
% 0.17/0.44 ! [A: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ A @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % inf.idem
% 0.17/0.44 thf(fact_132_inf_Oidem,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ A @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % inf.idem
% 0.17/0.44 thf(fact_133_inf__idem,axiom,
% 0.17/0.44 ! [X4: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ X4 @ X4 )
% 0.17/0.44 = X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_idem
% 0.17/0.44 thf(fact_134_inf__idem,axiom,
% 0.17/0.44 ! [X4: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ X4 @ X4 )
% 0.17/0.44 = X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_idem
% 0.17/0.44 thf(fact_135_inf__idem,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ X4 @ X4 )
% 0.17/0.44 = X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_idem
% 0.17/0.44 thf(fact_136_inf_Oleft__idem,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
% 0.17/0.44 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.left_idem
% 0.17/0.44 thf(fact_137_inf_Oleft__idem,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ A @ B ) )
% 0.17/0.44 = ( inf_inf_a_o @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.left_idem
% 0.17/0.44 thf(fact_138_inf_Oleft__idem,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ A @ B ) )
% 0.17/0.44 = ( inf_in262696383nres_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.left_idem
% 0.17/0.44 thf(fact_139_inf__left__idem,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ X4 @ Y3 ) )
% 0.17/0.44 = ( inf_inf_set_a @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_left_idem
% 0.17/0.44 thf(fact_140_inf__left__idem,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ X4 @ Y3 ) )
% 0.17/0.44 = ( inf_inf_a_o @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_left_idem
% 0.17/0.44 thf(fact_141_inf__left__idem,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ X4 @ Y3 ) )
% 0.17/0.44 = ( inf_in262696383nres_a @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_left_idem
% 0.17/0.44 thf(fact_142_inf_Oright__idem,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
% 0.17/0.44 = ( inf_inf_set_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.right_idem
% 0.17/0.44 thf(fact_143_inf_Oright__idem,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ B )
% 0.17/0.44 = ( inf_inf_a_o @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.right_idem
% 0.17/0.44 thf(fact_144_inf_Oright__idem,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B )
% 0.17/0.44 = ( inf_in262696383nres_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.right_idem
% 0.17/0.44 thf(fact_145_inf__right__idem,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Y3 )
% 0.17/0.44 = ( inf_inf_set_a @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_right_idem
% 0.17/0.44 thf(fact_146_inf__right__idem,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Y3 )
% 0.17/0.44 = ( inf_inf_a_o @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_right_idem
% 0.17/0.44 thf(fact_147_inf__right__idem,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Y3 )
% 0.17/0.44 = ( inf_in262696383nres_a @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_right_idem
% 0.17/0.44 thf(fact_148_inf__nres_Osimps_I3_J,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 0.17/0.44 = ( refine1198353288_RES_a @ ( inf_inf_set_a @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_nres.simps(3)
% 0.17/0.44 thf(fact_149_inf__left__commute,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) )
% 0.17/0.44 = ( inf_inf_set_a @ Y3 @ ( inf_inf_set_a @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_left_commute
% 0.17/0.44 thf(fact_150_inf__left__commute,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) )
% 0.17/0.44 = ( inf_inf_a_o @ Y3 @ ( inf_inf_a_o @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_left_commute
% 0.17/0.44 thf(fact_151_inf__left__commute,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) )
% 0.17/0.44 = ( inf_in262696383nres_a @ Y3 @ ( inf_in262696383nres_a @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_left_commute
% 0.17/0.44 thf(fact_152_inf_Oleft__commute,axiom,
% 0.17/0.44 ! [B: set_a,A: set_a,C: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ B @ ( inf_inf_set_a @ A @ C ) )
% 0.17/0.44 = ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.left_commute
% 0.17/0.44 thf(fact_153_inf_Oleft__commute,axiom,
% 0.17/0.44 ! [B: a > $o,A: a > $o,C: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ B @ ( inf_inf_a_o @ A @ C ) )
% 0.17/0.44 = ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.left_commute
% 0.17/0.44 thf(fact_154_inf_Oleft__commute,axiom,
% 0.17/0.44 ! [B: refine424419629nres_a,A: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ A @ C ) )
% 0.17/0.44 = ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.left_commute
% 0.17/0.44 thf(fact_155_inf__commute,axiom,
% 0.17/0.44 ( inf_inf_set_a
% 0.17/0.44 = ( ^ [X5: set_a,Y6: set_a] : ( inf_inf_set_a @ Y6 @ X5 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_commute
% 0.17/0.44 thf(fact_156_inf__commute,axiom,
% 0.17/0.44 ( inf_inf_a_o
% 0.17/0.44 = ( ^ [X5: a > $o,Y6: a > $o] : ( inf_inf_a_o @ Y6 @ X5 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_commute
% 0.17/0.44 thf(fact_157_inf__commute,axiom,
% 0.17/0.44 ( inf_in262696383nres_a
% 0.17/0.44 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] : ( inf_in262696383nres_a @ Y6 @ X5 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_commute
% 0.17/0.44 thf(fact_158_inf_Ocommute,axiom,
% 0.17/0.44 ( inf_inf_set_a
% 0.17/0.44 = ( ^ [A2: set_a,B2: set_a] : ( inf_inf_set_a @ B2 @ A2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.commute
% 0.17/0.44 thf(fact_159_inf_Ocommute,axiom,
% 0.17/0.44 ( inf_inf_a_o
% 0.17/0.44 = ( ^ [A2: a > $o,B2: a > $o] : ( inf_inf_a_o @ B2 @ A2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.commute
% 0.17/0.44 thf(fact_160_inf_Ocommute,axiom,
% 0.17/0.44 ( inf_in262696383nres_a
% 0.17/0.44 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] : ( inf_in262696383nres_a @ B2 @ A2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.commute
% 0.17/0.44 thf(fact_161_inf__assoc,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Z2 )
% 0.17/0.44 = ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_assoc
% 0.17/0.44 thf(fact_162_inf__assoc,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Z2 )
% 0.17/0.44 = ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_assoc
% 0.17/0.44 thf(fact_163_inf__assoc,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Z2 )
% 0.17/0.44 = ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_assoc
% 0.17/0.44 thf(fact_164_inf_Oassoc,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
% 0.17/0.44 = ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.assoc
% 0.17/0.44 thf(fact_165_inf_Oassoc,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ C )
% 0.17/0.44 = ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.assoc
% 0.17/0.44 thf(fact_166_inf_Oassoc,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C )
% 0.17/0.44 = ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.assoc
% 0.17/0.44 thf(fact_167_boolean__algebra__cancel_Oinf2,axiom,
% 0.17/0.44 ! [B3: set_a,K: set_a,B: set_a,A: set_a] :
% 0.17/0.44 ( ( B3
% 0.17/0.44 = ( inf_inf_set_a @ K @ B ) )
% 0.17/0.44 => ( ( inf_inf_set_a @ A @ B3 )
% 0.17/0.44 = ( inf_inf_set_a @ K @ ( inf_inf_set_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % boolean_algebra_cancel.inf2
% 0.17/0.44 thf(fact_168_boolean__algebra__cancel_Oinf2,axiom,
% 0.17/0.44 ! [B3: a > $o,K: a > $o,B: a > $o,A: a > $o] :
% 0.17/0.44 ( ( B3
% 0.17/0.44 = ( inf_inf_a_o @ K @ B ) )
% 0.17/0.44 => ( ( inf_inf_a_o @ A @ B3 )
% 0.17/0.44 = ( inf_inf_a_o @ K @ ( inf_inf_a_o @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % boolean_algebra_cancel.inf2
% 0.17/0.44 thf(fact_169_boolean__algebra__cancel_Oinf2,axiom,
% 0.17/0.44 ! [B3: refine424419629nres_a,K: refine424419629nres_a,B: refine424419629nres_a,A: refine424419629nres_a] :
% 0.17/0.44 ( ( B3
% 0.17/0.44 = ( inf_in262696383nres_a @ K @ B ) )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ A @ B3 )
% 0.17/0.44 = ( inf_in262696383nres_a @ K @ ( inf_in262696383nres_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % boolean_algebra_cancel.inf2
% 0.17/0.44 thf(fact_170_boolean__algebra__cancel_Oinf1,axiom,
% 0.17/0.44 ! [A3: set_a,K: set_a,A: set_a,B: set_a] :
% 0.17/0.44 ( ( A3
% 0.17/0.44 = ( inf_inf_set_a @ K @ A ) )
% 0.17/0.44 => ( ( inf_inf_set_a @ A3 @ B )
% 0.17/0.44 = ( inf_inf_set_a @ K @ ( inf_inf_set_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % boolean_algebra_cancel.inf1
% 0.17/0.44 thf(fact_171_boolean__algebra__cancel_Oinf1,axiom,
% 0.17/0.44 ! [A3: a > $o,K: a > $o,A: a > $o,B: a > $o] :
% 0.17/0.44 ( ( A3
% 0.17/0.44 = ( inf_inf_a_o @ K @ A ) )
% 0.17/0.44 => ( ( inf_inf_a_o @ A3 @ B )
% 0.17/0.44 = ( inf_inf_a_o @ K @ ( inf_inf_a_o @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % boolean_algebra_cancel.inf1
% 0.17/0.44 thf(fact_172_boolean__algebra__cancel_Oinf1,axiom,
% 0.17/0.44 ! [A3: refine424419629nres_a,K: refine424419629nres_a,A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( A3
% 0.17/0.44 = ( inf_in262696383nres_a @ K @ A ) )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ A3 @ B )
% 0.17/0.44 = ( inf_in262696383nres_a @ K @ ( inf_in262696383nres_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % boolean_algebra_cancel.inf1
% 0.17/0.44 thf(fact_173_inf__fun__def,axiom,
% 0.17/0.44 ( inf_inf_a_o
% 0.17/0.44 = ( ^ [F2: a > $o,G2: a > $o,X5: a] : ( inf_inf_o @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_fun_def
% 0.17/0.44 thf(fact_174_inf__sup__aci_I1_J,axiom,
% 0.17/0.44 ( inf_inf_set_a
% 0.17/0.44 = ( ^ [X5: set_a,Y6: set_a] : ( inf_inf_set_a @ Y6 @ X5 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(1)
% 0.17/0.44 thf(fact_175_inf__sup__aci_I1_J,axiom,
% 0.17/0.44 ( inf_inf_a_o
% 0.17/0.44 = ( ^ [X5: a > $o,Y6: a > $o] : ( inf_inf_a_o @ Y6 @ X5 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(1)
% 0.17/0.44 thf(fact_176_inf__sup__aci_I1_J,axiom,
% 0.17/0.44 ( inf_in262696383nres_a
% 0.17/0.44 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] : ( inf_in262696383nres_a @ Y6 @ X5 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(1)
% 0.17/0.44 thf(fact_177_inf__sup__aci_I2_J,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Z2 )
% 0.17/0.44 = ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(2)
% 0.17/0.44 thf(fact_178_inf__sup__aci_I2_J,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Z2 )
% 0.17/0.44 = ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(2)
% 0.17/0.44 thf(fact_179_inf__sup__aci_I2_J,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Z2 )
% 0.17/0.44 = ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(2)
% 0.17/0.44 thf(fact_180_inf__sup__aci_I3_J,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) )
% 0.17/0.44 = ( inf_inf_set_a @ Y3 @ ( inf_inf_set_a @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(3)
% 0.17/0.44 thf(fact_181_inf__sup__aci_I3_J,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) )
% 0.17/0.44 = ( inf_inf_a_o @ Y3 @ ( inf_inf_a_o @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(3)
% 0.17/0.44 thf(fact_182_inf__sup__aci_I3_J,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) )
% 0.17/0.44 = ( inf_in262696383nres_a @ Y3 @ ( inf_in262696383nres_a @ X4 @ Z2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(3)
% 0.17/0.44 thf(fact_183_inf__sup__aci_I4_J,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ X4 @ Y3 ) )
% 0.17/0.44 = ( inf_inf_set_a @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(4)
% 0.17/0.44 thf(fact_184_inf__sup__aci_I4_J,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ X4 @ Y3 ) )
% 0.17/0.44 = ( inf_inf_a_o @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(4)
% 0.17/0.44 thf(fact_185_inf__sup__aci_I4_J,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ X4 @ Y3 ) )
% 0.17/0.44 = ( inf_in262696383nres_a @ X4 @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_aci(4)
% 0.17/0.44 thf(fact_186_inf__sup__ord_I2_J,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Y3 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_ord(2)
% 0.17/0.44 thf(fact_187_inf__sup__ord_I2_J,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Y3 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_ord(2)
% 0.17/0.44 thf(fact_188_inf__sup__ord_I2_J,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Y3 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_ord(2)
% 0.17/0.44 thf(fact_189_inf__sup__ord_I1_J,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_ord(1)
% 0.17/0.44 thf(fact_190_inf__sup__ord_I1_J,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_ord(1)
% 0.17/0.44 thf(fact_191_inf__sup__ord_I1_J,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_sup_ord(1)
% 0.17/0.44 thf(fact_192_inf__le1,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_le1
% 0.17/0.44 thf(fact_193_inf__le1,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_le1
% 0.17/0.44 thf(fact_194_inf__le1,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_le1
% 0.17/0.44 thf(fact_195_inf__le2,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Y3 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_le2
% 0.17/0.44 thf(fact_196_inf__le2,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Y3 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_le2
% 0.17/0.44 thf(fact_197_inf__le2,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Y3 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_le2
% 0.17/0.44 thf(fact_198_le__infE,axiom,
% 0.17/0.44 ! [X4: set_a,A: set_a,B: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X4 @ ( inf_inf_set_a @ A @ B ) )
% 0.17/0.44 => ~ ( ( ord_less_eq_set_a @ X4 @ A )
% 0.17/0.44 => ~ ( ord_less_eq_set_a @ X4 @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infE
% 0.17/0.44 thf(fact_199_le__infE,axiom,
% 0.17/0.44 ! [X4: a > $o,A: a > $o,B: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X4 @ ( inf_inf_a_o @ A @ B ) )
% 0.17/0.44 => ~ ( ( ord_less_eq_a_o @ X4 @ A )
% 0.17/0.44 => ~ ( ord_less_eq_a_o @ X4 @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infE
% 0.17/0.44 thf(fact_200_le__infE,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X4 @ ( inf_in262696383nres_a @ A @ B ) )
% 0.17/0.44 => ~ ( ( ord_le519537037nres_a @ X4 @ A )
% 0.17/0.44 => ~ ( ord_le519537037nres_a @ X4 @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infE
% 0.17/0.44 thf(fact_201_le__infI,axiom,
% 0.17/0.44 ! [X4: set_a,A: set_a,B: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X4 @ A )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ X4 @ B )
% 0.17/0.44 => ( ord_less_eq_set_a @ X4 @ ( inf_inf_set_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infI
% 0.17/0.44 thf(fact_202_le__infI,axiom,
% 0.17/0.44 ! [X4: a > $o,A: a > $o,B: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X4 @ A )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ X4 @ B )
% 0.17/0.44 => ( ord_less_eq_a_o @ X4 @ ( inf_inf_a_o @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infI
% 0.17/0.44 thf(fact_203_le__infI,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X4 @ A )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ X4 @ B )
% 0.17/0.44 => ( ord_le519537037nres_a @ X4 @ ( inf_in262696383nres_a @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infI
% 0.17/0.44 thf(fact_204_inf__mono,axiom,
% 0.17/0.44 ! [A: set_a,C: set_a,B: set_a,D: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ C )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B @ D )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ ( inf_inf_set_a @ C @ D ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_mono
% 0.17/0.44 thf(fact_205_inf__mono,axiom,
% 0.17/0.44 ! [A: a > $o,C: a > $o,B: a > $o,D: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ C )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ B @ D )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ ( inf_inf_a_o @ C @ D ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_mono
% 0.17/0.44 thf(fact_206_inf__mono,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,C: refine424419629nres_a,B: refine424419629nres_a,D: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ C )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ D )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ ( inf_in262696383nres_a @ C @ D ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_mono
% 0.17/0.44 thf(fact_207_le__infI1,axiom,
% 0.17/0.44 ! [A: set_a,X4: set_a,B: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ X4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infI1
% 0.17/0.44 thf(fact_208_le__infI1,axiom,
% 0.17/0.44 ! [A: a > $o,X4: a > $o,B: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ X4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infI1
% 0.17/0.44 thf(fact_209_le__infI1,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,X4: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ X4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infI1
% 0.17/0.44 thf(fact_210_le__infI2,axiom,
% 0.17/0.44 ! [B: set_a,X4: set_a,A: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ B @ X4 )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infI2
% 0.17/0.44 thf(fact_211_le__infI2,axiom,
% 0.17/0.44 ! [B: a > $o,X4: a > $o,A: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ B @ X4 )
% 0.17/0.44 => ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infI2
% 0.17/0.44 thf(fact_212_le__infI2,axiom,
% 0.17/0.44 ! [B: refine424419629nres_a,X4: refine424419629nres_a,A: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ B @ X4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_infI2
% 0.17/0.44 thf(fact_213_inf_OorderE,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( A
% 0.17/0.44 = ( inf_inf_set_a @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.orderE
% 0.17/0.44 thf(fact_214_inf_OorderE,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( A
% 0.17/0.44 = ( inf_inf_a_o @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.orderE
% 0.17/0.44 thf(fact_215_inf_OorderE,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( A
% 0.17/0.44 = ( inf_in262696383nres_a @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.orderE
% 0.17/0.44 thf(fact_216_inf_OorderI,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( inf_inf_set_a @ A @ B ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.orderI
% 0.17/0.44 thf(fact_217_inf_OorderI,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( inf_inf_a_o @ A @ B ) )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.orderI
% 0.17/0.44 thf(fact_218_inf_OorderI,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( A
% 0.17/0.44 = ( inf_in262696383nres_a @ A @ B ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.orderI
% 0.17/0.44 thf(fact_219_inf__unique,axiom,
% 0.17/0.44 ! [F: set_a > set_a > set_a,X4: set_a,Y3: set_a] :
% 0.17/0.44 ( ! [X3: set_a,Y4: set_a] : ( ord_less_eq_set_a @ ( F @ X3 @ Y4 ) @ X3 )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a] : ( ord_less_eq_set_a @ ( F @ X3 @ Y4 ) @ Y4 )
% 0.17/0.44 => ( ! [X3: set_a,Y4: set_a,Z3: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ X3 @ Z3 )
% 0.17/0.44 => ( ord_less_eq_set_a @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 0.17/0.44 => ( ( inf_inf_set_a @ X4 @ Y3 )
% 0.17/0.44 = ( F @ X4 @ Y3 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_unique
% 0.17/0.44 thf(fact_220_inf__unique,axiom,
% 0.17/0.44 ! [F: ( a > $o ) > ( a > $o ) > a > $o,X4: a > $o,Y3: a > $o] :
% 0.17/0.44 ( ! [X3: a > $o,Y4: a > $o] : ( ord_less_eq_a_o @ ( F @ X3 @ Y4 ) @ X3 )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o] : ( ord_less_eq_a_o @ ( F @ X3 @ Y4 ) @ Y4 )
% 0.17/0.44 => ( ! [X3: a > $o,Y4: a > $o,Z3: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ X3 @ Z3 )
% 0.17/0.44 => ( ord_less_eq_a_o @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 0.17/0.44 => ( ( inf_inf_a_o @ X4 @ Y3 )
% 0.17/0.44 = ( F @ X4 @ Y3 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_unique
% 0.17/0.44 thf(fact_221_inf__unique,axiom,
% 0.17/0.44 ! [F: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a,X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] : ( ord_le519537037nres_a @ ( F @ X3 @ Y4 ) @ X3 )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] : ( ord_le519537037nres_a @ ( F @ X3 @ Y4 ) @ Y4 )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a,Z3: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ X3 @ Z3 )
% 0.17/0.44 => ( ord_le519537037nres_a @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ X4 @ Y3 )
% 0.17/0.44 = ( F @ X4 @ Y3 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_unique
% 0.17/0.44 thf(fact_222_le__iff__inf,axiom,
% 0.17/0.44 ( ord_less_eq_set_a
% 0.17/0.44 = ( ^ [X5: set_a,Y6: set_a] :
% 0.17/0.44 ( ( inf_inf_set_a @ X5 @ Y6 )
% 0.17/0.44 = X5 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_iff_inf
% 0.17/0.44 thf(fact_223_le__iff__inf,axiom,
% 0.17/0.44 ( ord_less_eq_a_o
% 0.17/0.44 = ( ^ [X5: a > $o,Y6: a > $o] :
% 0.17/0.44 ( ( inf_inf_a_o @ X5 @ Y6 )
% 0.17/0.44 = X5 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_iff_inf
% 0.17/0.44 thf(fact_224_le__iff__inf,axiom,
% 0.17/0.44 ( ord_le519537037nres_a
% 0.17/0.44 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ X5 @ Y6 )
% 0.17/0.44 = X5 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_iff_inf
% 0.17/0.44 thf(fact_225_inf_Oabsorb1,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( inf_inf_set_a @ A @ B )
% 0.17/0.44 = A ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.absorb1
% 0.17/0.44 thf(fact_226_inf_Oabsorb1,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( inf_inf_a_o @ A @ B )
% 0.17/0.44 = A ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.absorb1
% 0.17/0.44 thf(fact_227_inf_Oabsorb1,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ A @ B )
% 0.17/0.44 = A ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.absorb1
% 0.17/0.44 thf(fact_228_inf_Oabsorb2,axiom,
% 0.17/0.44 ! [B: set_a,A: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ B @ A )
% 0.17/0.44 => ( ( inf_inf_set_a @ A @ B )
% 0.17/0.44 = B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.absorb2
% 0.17/0.44 thf(fact_229_inf_Oabsorb2,axiom,
% 0.17/0.44 ! [B: a > $o,A: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ B @ A )
% 0.17/0.44 => ( ( inf_inf_a_o @ A @ B )
% 0.17/0.44 = B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.absorb2
% 0.17/0.44 thf(fact_230_inf_Oabsorb2,axiom,
% 0.17/0.44 ! [B: refine424419629nres_a,A: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ B @ A )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ A @ B )
% 0.17/0.44 = B ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.absorb2
% 0.17/0.44 thf(fact_231_inf__absorb1,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 0.17/0.44 => ( ( inf_inf_set_a @ X4 @ Y3 )
% 0.17/0.44 = X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_absorb1
% 0.17/0.44 thf(fact_232_inf__absorb1,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 0.17/0.44 => ( ( inf_inf_a_o @ X4 @ Y3 )
% 0.17/0.44 = X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_absorb1
% 0.17/0.44 thf(fact_233_inf__absorb1,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ X4 @ Y3 )
% 0.17/0.44 = X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_absorb1
% 0.17/0.44 thf(fact_234_inf__absorb2,axiom,
% 0.17/0.44 ! [Y3: set_a,X4: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 0.17/0.44 => ( ( inf_inf_set_a @ X4 @ Y3 )
% 0.17/0.44 = Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_absorb2
% 0.17/0.44 thf(fact_235_inf__absorb2,axiom,
% 0.17/0.44 ! [Y3: a > $o,X4: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ Y3 @ X4 )
% 0.17/0.44 => ( ( inf_inf_a_o @ X4 @ Y3 )
% 0.17/0.44 = Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_absorb2
% 0.17/0.44 thf(fact_236_inf__absorb2,axiom,
% 0.17/0.44 ! [Y3: refine424419629nres_a,X4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ X4 @ Y3 )
% 0.17/0.44 = Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_absorb2
% 0.17/0.44 thf(fact_237_inf_OboundedE,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 0.17/0.44 => ~ ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ~ ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.boundedE
% 0.17/0.44 thf(fact_238_inf_OboundedE,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
% 0.17/0.44 => ~ ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ~ ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.boundedE
% 0.17/0.44 thf(fact_239_inf_OboundedE,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
% 0.17/0.44 => ~ ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ~ ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.boundedE
% 0.17/0.44 thf(fact_240_inf_OboundedI,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a,C: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ A @ C )
% 0.17/0.44 => ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.boundedI
% 0.17/0.44 thf(fact_241_inf_OboundedI,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ A @ B )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ A @ C )
% 0.17/0.44 => ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.boundedI
% 0.17/0.44 thf(fact_242_inf_OboundedI,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ B )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ A @ C )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.boundedI
% 0.17/0.44 thf(fact_243_inf__greatest,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ X4 @ Z2 )
% 0.17/0.44 => ( ord_less_eq_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_greatest
% 0.17/0.44 thf(fact_244_inf__greatest,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 0.17/0.44 => ( ( ord_less_eq_a_o @ X4 @ Z2 )
% 0.17/0.44 => ( ord_less_eq_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_greatest
% 0.17/0.44 thf(fact_245_inf__greatest,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ X4 @ Z2 )
% 0.17/0.44 => ( ord_le519537037nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_greatest
% 0.17/0.44 thf(fact_246_inf_Oorder__iff,axiom,
% 0.17/0.44 ( ord_less_eq_set_a
% 0.17/0.44 = ( ^ [A2: set_a,B2: set_a] :
% 0.17/0.44 ( A2
% 0.17/0.44 = ( inf_inf_set_a @ A2 @ B2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.order_iff
% 0.17/0.44 thf(fact_247_inf_Oorder__iff,axiom,
% 0.17/0.44 ( ord_less_eq_a_o
% 0.17/0.44 = ( ^ [A2: a > $o,B2: a > $o] :
% 0.17/0.44 ( A2
% 0.17/0.44 = ( inf_inf_a_o @ A2 @ B2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.order_iff
% 0.17/0.44 thf(fact_248_inf_Oorder__iff,axiom,
% 0.17/0.44 ( ord_le519537037nres_a
% 0.17/0.44 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.17/0.44 ( A2
% 0.17/0.44 = ( inf_in262696383nres_a @ A2 @ B2 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.order_iff
% 0.17/0.44 thf(fact_249_inf_Ocobounded1,axiom,
% 0.17/0.44 ! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ) ).
% 0.17/0.44
% 0.17/0.44 % inf.cobounded1
% 0.17/0.44 thf(fact_250_inf_Ocobounded1,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ A ) ).
% 0.17/0.44
% 0.17/0.44 % inf.cobounded1
% 0.17/0.44 thf(fact_251_inf_Ocobounded1,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ A ) ).
% 0.17/0.44
% 0.17/0.44 % inf.cobounded1
% 0.17/0.44 thf(fact_252_inf_Ocobounded2,axiom,
% 0.17/0.44 ! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ B ) ).
% 0.17/0.44
% 0.17/0.44 % inf.cobounded2
% 0.17/0.44 thf(fact_253_inf_Ocobounded2,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B ) ).
% 0.17/0.44
% 0.17/0.44 % inf.cobounded2
% 0.17/0.44 thf(fact_254_inf_Oabsorb__iff1,axiom,
% 0.17/0.44 ( ord_le519537037nres_a
% 0.17/0.44 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ A2 @ B2 )
% 0.17/0.44 = A2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.absorb_iff1
% 0.17/0.44 thf(fact_255_inf_Oabsorb__iff2,axiom,
% 0.17/0.44 ( ord_le519537037nres_a
% 0.17/0.44 = ( ^ [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ A2 @ B2 )
% 0.17/0.44 = B2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.absorb_iff2
% 0.17/0.44 thf(fact_256_inf_OcoboundedI1,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,C: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ C )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.coboundedI1
% 0.17/0.44 thf(fact_257_inf_OcoboundedI2,axiom,
% 0.17/0.44 ! [B: refine424419629nres_a,C: refine424419629nres_a,A: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf.coboundedI2
% 0.17/0.44 thf(fact_258_subsetI,axiom,
% 0.17/0.44 ! [A3: set_a,B3: set_a] :
% 0.17/0.44 ( ! [X3: a] :
% 0.17/0.44 ( ( member_a @ X3 @ A3 )
% 0.17/0.44 => ( member_a @ X3 @ B3 ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % subsetI
% 0.17/0.44 thf(fact_259_Collect__subset,axiom,
% 0.17/0.44 ! [A3: set_a,P: a > $o] :
% 0.17/0.44 ( ord_less_eq_set_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ A3 )
% 0.17/0.44 & ( P @ X5 ) ) )
% 0.17/0.44 @ A3 ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_subset
% 0.17/0.44 thf(fact_260_less__eq__set__def,axiom,
% 0.17/0.44 ( ord_less_eq_set_a
% 0.17/0.44 = ( ^ [A4: set_a,B4: set_a] :
% 0.17/0.44 ( ord_less_eq_a_o
% 0.17/0.44 @ ^ [X5: a] : ( member_a @ X5 @ A4 )
% 0.17/0.44 @ ^ [X5: a] : ( member_a @ X5 @ B4 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_eq_set_def
% 0.17/0.44 thf(fact_261_pred__subset__eq,axiom,
% 0.17/0.44 ! [R: set_a,S: set_a] :
% 0.17/0.44 ( ( ord_less_eq_a_o
% 0.17/0.44 @ ^ [X5: a] : ( member_a @ X5 @ R )
% 0.17/0.44 @ ^ [X5: a] : ( member_a @ X5 @ S ) )
% 0.17/0.44 = ( ord_less_eq_set_a @ R @ S ) ) ).
% 0.17/0.44
% 0.17/0.44 % pred_subset_eq
% 0.17/0.44 thf(fact_262_conj__subset__def,axiom,
% 0.17/0.44 ! [A3: set_a,P: a > $o,Q: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A3
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] :
% 0.17/0.44 ( ( P @ X5 )
% 0.17/0.44 & ( Q @ X5 ) ) ) )
% 0.17/0.44 = ( ( ord_less_eq_set_a @ A3 @ ( collect_a @ P ) )
% 0.17/0.44 & ( ord_less_eq_set_a @ A3 @ ( collect_a @ Q ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % conj_subset_def
% 0.17/0.44 thf(fact_263_IntI,axiom,
% 0.17/0.44 ! [C: a,A3: set_a,B3: set_a] :
% 0.17/0.44 ( ( member_a @ C @ A3 )
% 0.17/0.44 => ( ( member_a @ C @ B3 )
% 0.17/0.44 => ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % IntI
% 0.17/0.44 thf(fact_264_Int__iff,axiom,
% 0.17/0.44 ! [C: a,A3: set_a,B3: set_a] :
% 0.17/0.44 ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) )
% 0.17/0.44 = ( ( member_a @ C @ A3 )
% 0.17/0.44 & ( member_a @ C @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_iff
% 0.17/0.44 thf(fact_265_IntE,axiom,
% 0.17/0.44 ! [C: a,A3: set_a,B3: set_a] :
% 0.17/0.44 ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) )
% 0.17/0.44 => ~ ( ( member_a @ C @ A3 )
% 0.17/0.44 => ~ ( member_a @ C @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % IntE
% 0.17/0.44 thf(fact_266_IntD1,axiom,
% 0.17/0.44 ! [C: a,A3: set_a,B3: set_a] :
% 0.17/0.44 ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) )
% 0.17/0.44 => ( member_a @ C @ A3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % IntD1
% 0.17/0.44 thf(fact_267_IntD2,axiom,
% 0.17/0.44 ! [C: a,A3: set_a,B3: set_a] :
% 0.17/0.44 ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) )
% 0.17/0.44 => ( member_a @ C @ B3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % IntD2
% 0.17/0.44 thf(fact_268_Int__def,axiom,
% 0.17/0.44 ( inf_inf_set_a
% 0.17/0.44 = ( ^ [A4: set_a,B4: set_a] :
% 0.17/0.44 ( collect_a
% 0.17/0.44 @ ^ [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ A4 )
% 0.17/0.44 & ( member_a @ X5 @ B4 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_def
% 0.17/0.44 thf(fact_269_Int__Collect,axiom,
% 0.17/0.44 ! [X4: a,A3: set_a,P: a > $o] :
% 0.17/0.44 ( ( member_a @ X4 @ ( inf_inf_set_a @ A3 @ ( collect_a @ P ) ) )
% 0.17/0.44 = ( ( member_a @ X4 @ A3 )
% 0.17/0.44 & ( P @ X4 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_Collect
% 0.17/0.44 thf(fact_270_inf__set__def,axiom,
% 0.17/0.44 ( inf_inf_set_a
% 0.17/0.44 = ( ^ [A4: set_a,B4: set_a] :
% 0.17/0.44 ( collect_a
% 0.17/0.44 @ ( inf_inf_a_o
% 0.17/0.44 @ ^ [X5: a] : ( member_a @ X5 @ A4 )
% 0.17/0.44 @ ^ [X5: a] : ( member_a @ X5 @ B4 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_set_def
% 0.17/0.44 thf(fact_271_inf__Int__eq,axiom,
% 0.17/0.44 ! [R: set_a,S: set_a] :
% 0.17/0.44 ( ( inf_inf_a_o
% 0.17/0.44 @ ^ [X5: a] : ( member_a @ X5 @ R )
% 0.17/0.44 @ ^ [X5: a] : ( member_a @ X5 @ S ) )
% 0.17/0.44 = ( ^ [X5: a] : ( member_a @ X5 @ ( inf_inf_set_a @ R @ S ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_Int_eq
% 0.17/0.44 thf(fact_272_Collect__conj__eq,axiom,
% 0.17/0.44 ! [P: a > $o,Q: a > $o] :
% 0.17/0.44 ( ( collect_a
% 0.17/0.44 @ ^ [X5: a] :
% 0.17/0.44 ( ( P @ X5 )
% 0.17/0.44 & ( Q @ X5 ) ) )
% 0.17/0.44 = ( inf_inf_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_conj_eq
% 0.17/0.44 thf(fact_273_Int__Collect__mono,axiom,
% 0.17/0.44 ! [A3: set_a,B3: set_a,P: a > $o,Q: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.17/0.44 => ( ! [X3: a] :
% 0.17/0.44 ( ( member_a @ X3 @ A3 )
% 0.17/0.44 => ( ( P @ X3 )
% 0.17/0.44 => ( Q @ X3 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A3 @ ( collect_a @ P ) ) @ ( inf_inf_set_a @ B3 @ ( collect_a @ Q ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_Collect_mono
% 0.17/0.44 thf(fact_274_Collect__mono__iff,axiom,
% 0.17/0.44 ! [P: a > $o,Q: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.17/0.44 = ( ! [X5: a] :
% 0.17/0.44 ( ( P @ X5 )
% 0.17/0.44 => ( Q @ X5 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_mono_iff
% 0.17/0.44 thf(fact_275_Collect__mono,axiom,
% 0.17/0.44 ! [P: a > $o,Q: a > $o] :
% 0.17/0.44 ( ! [X3: a] :
% 0.17/0.44 ( ( P @ X3 )
% 0.17/0.44 => ( Q @ X3 ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_mono
% 0.17/0.44 thf(fact_276_subset__iff,axiom,
% 0.17/0.44 ( ord_less_eq_set_a
% 0.17/0.44 = ( ^ [A4: set_a,B4: set_a] :
% 0.17/0.44 ! [T3: a] :
% 0.17/0.44 ( ( member_a @ T3 @ A4 )
% 0.17/0.44 => ( member_a @ T3 @ B4 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % subset_iff
% 0.17/0.44 thf(fact_277_subset__eq,axiom,
% 0.17/0.44 ( ord_less_eq_set_a
% 0.17/0.44 = ( ^ [A4: set_a,B4: set_a] :
% 0.17/0.44 ! [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ A4 )
% 0.17/0.44 => ( member_a @ X5 @ B4 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % subset_eq
% 0.17/0.44 thf(fact_278_subsetD,axiom,
% 0.17/0.44 ! [A3: set_a,B3: set_a,C: a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.17/0.44 => ( ( member_a @ C @ A3 )
% 0.17/0.44 => ( member_a @ C @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % subsetD
% 0.17/0.44 thf(fact_279_in__mono,axiom,
% 0.17/0.44 ! [A3: set_a,B3: set_a,X4: a] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.17/0.44 => ( ( member_a @ X4 @ A3 )
% 0.17/0.44 => ( member_a @ X4 @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % in_mono
% 0.17/0.44 thf(fact_280_subset__Collect__iff,axiom,
% 0.17/0.44 ! [B3: set_a,A3: set_a,P: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ B3
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ A3 )
% 0.17/0.44 & ( P @ X5 ) ) ) )
% 0.17/0.44 = ( ! [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ B3 )
% 0.17/0.44 => ( P @ X5 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % subset_Collect_iff
% 0.17/0.44 thf(fact_281_subset__CollectI,axiom,
% 0.17/0.44 ! [B3: set_a,A3: set_a,Q: a > $o,P: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 0.17/0.44 => ( ! [X3: a] :
% 0.17/0.44 ( ( member_a @ X3 @ B3 )
% 0.17/0.44 => ( ( Q @ X3 )
% 0.17/0.44 => ( P @ X3 ) ) )
% 0.17/0.44 => ( ord_less_eq_set_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ B3 )
% 0.17/0.44 & ( Q @ X5 ) ) )
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ A3 )
% 0.17/0.44 & ( P @ X5 ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % subset_CollectI
% 0.17/0.44 thf(fact_282_Collect__restrict,axiom,
% 0.17/0.44 ! [X: set_a,P: a > $o] :
% 0.17/0.44 ( ord_less_eq_set_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ X )
% 0.17/0.44 & ( P @ X5 ) ) )
% 0.17/0.44 @ X ) ).
% 0.17/0.44
% 0.17/0.44 % Collect_restrict
% 0.17/0.44 thf(fact_283_ord__eq__le__eq__trans,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
% 0.17/0.44 ( ( A = B )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ B @ C )
% 0.17/0.44 => ( ( C = D )
% 0.17/0.44 => ( ord_le519537037nres_a @ A @ D ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % ord_eq_le_eq_trans
% 0.17/0.44 thf(fact_284_subset__Collect__conv,axiom,
% 0.17/0.44 ! [S: set_a,P: a > $o] :
% 0.17/0.44 ( ( ord_less_eq_set_a @ S @ ( collect_a @ P ) )
% 0.17/0.44 = ( ! [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ S )
% 0.17/0.44 => ( P @ X5 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % subset_Collect_conv
% 0.17/0.44 thf(fact_285_prop__restrict,axiom,
% 0.17/0.44 ! [X4: a,Z4: set_a,X: set_a,P: a > $o] :
% 0.17/0.44 ( ( member_a @ X4 @ Z4 )
% 0.17/0.44 => ( ( ord_less_eq_set_a @ Z4
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] :
% 0.17/0.44 ( ( member_a @ X5 @ X )
% 0.17/0.44 & ( P @ X5 ) ) ) )
% 0.17/0.44 => ( P @ X4 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % prop_restrict
% 0.17/0.44 thf(fact_286_inf__nres_Oelims,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( ( inf_in262696383nres_a @ X4 @ Xa )
% 0.17/0.44 = Y3 )
% 0.17/0.44 => ( ( ( Xa = refine464223677AILi_a )
% 0.17/0.44 => ( Y3 != X4 ) )
% 0.17/0.44 => ( ( ( X4 = refine464223677AILi_a )
% 0.17/0.44 => ! [V: set_a] :
% 0.17/0.44 ( ( Xa
% 0.17/0.44 = ( refine1198353288_RES_a @ V ) )
% 0.17/0.44 => ( Y3
% 0.17/0.44 != ( refine1198353288_RES_a @ V ) ) ) )
% 0.17/0.44 => ~ ! [A5: set_a] :
% 0.17/0.44 ( ( X4
% 0.17/0.44 = ( refine1198353288_RES_a @ A5 ) )
% 0.17/0.44 => ! [B5: set_a] :
% 0.17/0.44 ( ( Xa
% 0.17/0.44 = ( refine1198353288_RES_a @ B5 ) )
% 0.17/0.44 => ( Y3
% 0.17/0.44 != ( refine1198353288_RES_a @ ( inf_inf_set_a @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_nres.elims
% 0.17/0.44 thf(fact_287_GreatestI2__order,axiom,
% 0.17/0.44 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 0.17/0.44 ( ( P @ X4 )
% 0.17/0.44 => ( ! [Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( P @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 0.17/0.44 => ( ! [X3: refine424419629nres_a] :
% 0.17/0.44 ( ( P @ X3 )
% 0.17/0.44 => ( ! [Y7: refine424419629nres_a] :
% 0.17/0.44 ( ( P @ Y7 )
% 0.17/0.44 => ( ord_le519537037nres_a @ Y7 @ X3 ) )
% 0.17/0.44 => ( Q @ X3 ) ) )
% 0.17/0.44 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % GreatestI2_order
% 0.17/0.44 thf(fact_288_inf__nres_Osimps_I1_J,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ X4 @ refine464223677AILi_a )
% 0.17/0.44 = X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_nres.simps(1)
% 0.17/0.44 thf(fact_289_nres_Odistinct_I1_J,axiom,
% 0.17/0.44 ! [X2: set_a] :
% 0.17/0.44 ( refine464223677AILi_a
% 0.17/0.44 != ( refine1198353288_RES_a @ X2 ) ) ).
% 0.17/0.44
% 0.17/0.44 % nres.distinct(1)
% 0.17/0.44 thf(fact_290_nres_Oinduct,axiom,
% 0.17/0.44 ! [P: refine424419629nres_a > $o,Nres: refine424419629nres_a] :
% 0.17/0.44 ( ( P @ refine464223677AILi_a )
% 0.17/0.44 => ( ! [X3: set_a] : ( P @ ( refine1198353288_RES_a @ X3 ) )
% 0.17/0.44 => ( P @ Nres ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % nres.induct
% 0.17/0.44 thf(fact_291_nres_Oexhaust,axiom,
% 0.17/0.44 ! [Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( Y3 != refine464223677AILi_a )
% 0.17/0.44 => ~ ! [X22: set_a] :
% 0.17/0.44 ( Y3
% 0.17/0.44 != ( refine1198353288_RES_a @ X22 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % nres.exhaust
% 0.17/0.44 thf(fact_292_sup__nres_Oinduct,axiom,
% 0.17/0.44 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.17/0.44 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.17/0.44 => ( ! [V: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) )
% 0.17/0.44 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.17/0.44 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % sup_nres.induct
% 0.17/0.44 thf(fact_293_less__nres_Oinduct,axiom,
% 0.17/0.44 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.17/0.44 ( ! [X_1: refine424419629nres_a] : ( P @ refine464223677AILi_a @ X_1 )
% 0.17/0.44 => ( ! [Uv: set_a] : ( P @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a )
% 0.17/0.44 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.17/0.44 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_nres.induct
% 0.17/0.44 thf(fact_294_less__eq__nres_Oinduct,axiom,
% 0.17/0.44 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.17/0.44 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.17/0.44 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.17/0.44 => ( ! [Uv: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) )
% 0.17/0.44 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_eq_nres.induct
% 0.17/0.44 thf(fact_295_less__eq__nres_Osimps_I1_J,axiom,
% 0.17/0.44 ! [Uu2: refine424419629nres_a] : ( ord_le519537037nres_a @ Uu2 @ refine464223677AILi_a ) ).
% 0.17/0.44
% 0.17/0.44 % less_eq_nres.simps(1)
% 0.17/0.44 thf(fact_296_less__eq__nres_Osimps_I3_J,axiom,
% 0.17/0.44 ! [Uv2: set_a] :
% 0.17/0.44 ~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv2 ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_eq_nres.simps(3)
% 0.17/0.44 thf(fact_297_inf__nres_Osimps_I2_J,axiom,
% 0.17/0.44 ! [V2: set_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V2 ) )
% 0.17/0.44 = ( refine1198353288_RES_a @ V2 ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_nres.simps(2)
% 0.17/0.44 thf(fact_298_less__eq__nres_Oelims_I1_J,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 0.17/0.44 ( ( ( ord_le519537037nres_a @ X4 @ Xa )
% 0.17/0.44 = Y3 )
% 0.17/0.44 => ( ( ( Xa = refine464223677AILi_a )
% 0.17/0.44 => ~ Y3 )
% 0.17/0.44 => ( ! [A5: set_a] :
% 0.17/0.44 ( ( X4
% 0.17/0.44 = ( refine1198353288_RES_a @ A5 ) )
% 0.17/0.44 => ! [B5: set_a] :
% 0.17/0.44 ( ( Xa
% 0.17/0.44 = ( refine1198353288_RES_a @ B5 ) )
% 0.17/0.44 => ( Y3
% 0.17/0.44 = ( ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) )
% 0.17/0.44 => ~ ( ( X4 = refine464223677AILi_a )
% 0.17/0.44 => ( ? [Uv: set_a] :
% 0.17/0.44 ( Xa
% 0.17/0.44 = ( refine1198353288_RES_a @ Uv ) )
% 0.17/0.44 => Y3 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_eq_nres.elims(1)
% 0.17/0.44 thf(fact_299_less__eq__nres_Oelims_I2_J,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ X4 @ Xa )
% 0.17/0.44 => ( ( Xa != refine464223677AILi_a )
% 0.17/0.44 => ~ ! [A5: set_a] :
% 0.17/0.44 ( ( X4
% 0.17/0.44 = ( refine1198353288_RES_a @ A5 ) )
% 0.17/0.44 => ! [B5: set_a] :
% 0.17/0.44 ( ( Xa
% 0.17/0.44 = ( refine1198353288_RES_a @ B5 ) )
% 0.17/0.44 => ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_eq_nres.elims(2)
% 0.17/0.44 thf(fact_300_less__eq__nres_Oelims_I3_J,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.17/0.44 ( ~ ( ord_le519537037nres_a @ X4 @ Xa )
% 0.17/0.44 => ( ! [A5: set_a] :
% 0.17/0.44 ( ( X4
% 0.17/0.44 = ( refine1198353288_RES_a @ A5 ) )
% 0.17/0.44 => ! [B5: set_a] :
% 0.17/0.44 ( ( Xa
% 0.17/0.44 = ( refine1198353288_RES_a @ B5 ) )
% 0.17/0.44 => ( ord_less_eq_set_a @ A5 @ B5 ) ) )
% 0.17/0.44 => ~ ( ( X4 = refine464223677AILi_a )
% 0.17/0.44 => ! [Uv: set_a] :
% 0.17/0.44 ( Xa
% 0.17/0.44 != ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % less_eq_nres.elims(3)
% 0.17/0.44 thf(fact_301_Greatest__equality,axiom,
% 0.17/0.44 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a] :
% 0.17/0.44 ( ( P @ X4 )
% 0.17/0.44 => ( ! [Y4: refine424419629nres_a] :
% 0.17/0.44 ( ( P @ Y4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 0.17/0.44 => ( ( order_1714329108nres_a @ P )
% 0.17/0.44 = X4 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Greatest_equality
% 0.17/0.44 thf(fact_302_the__RES__inv,axiom,
% 0.17/0.44 ! [M: refine424419629nres_a] :
% 0.17/0.44 ( ( refine412683989fail_a @ M )
% 0.17/0.44 => ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ M ) )
% 0.17/0.44 = M ) ) ).
% 0.17/0.44
% 0.17/0.44 % the_RES_inv
% 0.17/0.44 thf(fact_303_inf__RETURN__SPEC_I1_J,axiom,
% 0.17/0.44 ! [X4: a,Phi: a > $o] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.17/0.44 = ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [Y6: a] :
% 0.17/0.44 ( ( Y6 = X4 )
% 0.17/0.44 & ( Phi @ X4 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_RETURN_SPEC(1)
% 0.17/0.44 thf(fact_304_nofail__simps_I2_J,axiom,
% 0.17/0.44 ! [X: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X ) ) ).
% 0.17/0.44
% 0.17/0.44 % nofail_simps(2)
% 0.17/0.44 thf(fact_305_nres__order__simps_I20_J,axiom,
% 0.17/0.44 ! [X4: a,Y3: a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine2063221604TURN_a @ Y3 ) )
% 0.17/0.44 = ( X4 = Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % nres_order_simps(20)
% 0.17/0.44 thf(fact_306_nres__order__simps_I21_J,axiom,
% 0.17/0.44 ! [X4: a,Y: set_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ Y ) )
% 0.17/0.44 = ( member_a @ X4 @ Y ) ) ).
% 0.17/0.44
% 0.17/0.44 % nres_order_simps(21)
% 0.17/0.44 thf(fact_307_inf__RETURN__SPEC_I2_J,axiom,
% 0.17/0.44 ! [Phi: a > $o,X4: a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine2063221604TURN_a @ X4 ) )
% 0.17/0.44 = ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [Y6: a] :
% 0.17/0.44 ( ( Y6 = X4 )
% 0.17/0.44 & ( Phi @ X4 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_RETURN_SPEC(2)
% 0.17/0.44 thf(fact_308_pwD1,axiom,
% 0.17/0.44 ! [S: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ S @ S4 )
% 0.17/0.44 => ( ( refine412683989fail_a @ S4 )
% 0.17/0.44 => ( refine412683989fail_a @ S ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % pwD1
% 0.17/0.44 thf(fact_309_le__nofailI,axiom,
% 0.17/0.44 ! [M3: refine424419629nres_a,M4: refine424419629nres_a] :
% 0.17/0.44 ( ( ( refine412683989fail_a @ M3 )
% 0.17/0.44 => ( ord_le519537037nres_a @ M4 @ M3 ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ M4 @ M3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_nofailI
% 0.17/0.44 thf(fact_310_nofail__RES__conv,axiom,
% 0.17/0.44 ( refine412683989fail_a
% 0.17/0.44 = ( ^ [M5: refine424419629nres_a] :
% 0.17/0.44 ? [M6: set_a] :
% 0.17/0.44 ( M5
% 0.17/0.44 = ( refine1198353288_RES_a @ M6 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % nofail_RES_conv
% 0.17/0.44 thf(fact_311_SPEC__eq__is__RETURN_I1_J,axiom,
% 0.17/0.44 ! [X4: a] :
% 0.17/0.44 ( ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 0.17/0.44 @ X4 ) ) )
% 0.17/0.44 = ( refine2063221604TURN_a @ X4 ) ) ).
% 0.17/0.44
% 0.17/0.44 % SPEC_eq_is_RETURN(1)
% 0.17/0.44 thf(fact_312_RETURN__SPEC__conv,axiom,
% 0.17/0.44 ( refine2063221604TURN_a
% 0.17/0.44 = ( ^ [R2: a] :
% 0.17/0.44 ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] : ( X5 = R2 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % RETURN_SPEC_conv
% 0.17/0.44 thf(fact_313_SPEC__eq__is__RETURN_I2_J,axiom,
% 0.17/0.44 ! [Y3: a] :
% 0.17/0.44 ( ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] : ( X5 = Y3 ) ) )
% 0.17/0.44 = ( refine2063221604TURN_a @ Y3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % SPEC_eq_is_RETURN(2)
% 0.17/0.44 thf(fact_314_pw__inf__nofail,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( refine412683989fail_a @ ( inf_in262696383nres_a @ A @ B ) )
% 0.17/0.44 = ( ( refine412683989fail_a @ A )
% 0.17/0.44 | ( refine412683989fail_a @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % pw_inf_nofail
% 0.17/0.44 thf(fact_315_le__RES__nofailI,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,X4: set_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ X4 ) )
% 0.17/0.44 => ( refine412683989fail_a @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_RES_nofailI
% 0.17/0.44 thf(fact_316_RETURN__rule,axiom,
% 0.17/0.44 ! [Phi: a > $o,X4: a] :
% 0.17/0.44 ( ( Phi @ X4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % RETURN_rule
% 0.17/0.44 thf(fact_317_lhs__step__RES,axiom,
% 0.17/0.44 ! [X: set_a,M: refine424419629nres_a] :
% 0.17/0.44 ( ! [X3: a] :
% 0.17/0.44 ( ( member_a @ X3 @ X )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ M ) ) ).
% 0.17/0.44
% 0.17/0.44 % lhs_step_RES
% 0.17/0.44 thf(fact_318_RETURN__to__SPEC__rule,axiom,
% 0.17/0.44 ! [M: refine424419629nres_a,V2: a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ M
% 0.17/0.44 @ ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 0.17/0.44 @ V2 ) ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ M @ ( refine2063221604TURN_a @ V2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % RETURN_to_SPEC_rule
% 0.17/0.44 thf(fact_319_lhs__step__SPEC,axiom,
% 0.17/0.44 ! [Phi: a > $o,M: refine424419629nres_a] :
% 0.17/0.44 ( ! [X3: a] :
% 0.17/0.44 ( ( Phi @ X3 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ M ) ) ).
% 0.17/0.44
% 0.17/0.44 % lhs_step_SPEC
% 0.17/0.44 thf(fact_320_inf__RETURN__RES_I2_J,axiom,
% 0.17/0.44 ! [X4: a,X: set_a] :
% 0.17/0.44 ( ( ( member_a @ X4 @ X )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine2063221604TURN_a @ X4 ) )
% 0.17/0.44 = ( refine2063221604TURN_a @ X4 ) ) )
% 0.17/0.44 & ( ~ ( member_a @ X4 @ X )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine2063221604TURN_a @ X4 ) )
% 0.17/0.44 = bot_bo529555393nres_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_RETURN_RES(2)
% 0.17/0.44 thf(fact_321_inf__RETURN__RES_I1_J,axiom,
% 0.17/0.44 ! [X4: a,X: set_a] :
% 0.17/0.44 ( ( ( member_a @ X4 @ X )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ X ) )
% 0.17/0.44 = ( refine2063221604TURN_a @ X4 ) ) )
% 0.17/0.44 & ( ~ ( member_a @ X4 @ X )
% 0.17/0.44 => ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ X ) )
% 0.17/0.44 = bot_bo529555393nres_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_RETURN_RES(1)
% 0.17/0.44 thf(fact_322_inf__bot__right,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ X4 @ bot_bo529555393nres_a )
% 0.17/0.44 = bot_bo529555393nres_a ) ).
% 0.17/0.44
% 0.17/0.44 % inf_bot_right
% 0.17/0.44 thf(fact_323_inf__bot__left,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ bot_bo529555393nres_a @ X4 )
% 0.17/0.44 = bot_bo529555393nres_a ) ).
% 0.17/0.44
% 0.17/0.44 % inf_bot_left
% 0.17/0.44 thf(fact_324_nres__order__simps_I2_J,axiom,
% 0.17/0.44 ! [M4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ M4 @ bot_bo529555393nres_a )
% 0.17/0.44 = ( M4 = bot_bo529555393nres_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % nres_order_simps(2)
% 0.17/0.44 thf(fact_325_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.17/0.44 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine424419629nres_a,F3: a > refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ M4 @ M3 )
% 0.17/0.44 => ( ! [X3: a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine436832838nd_a_a @ M3 @ F3 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.17/0.44 thf(fact_326_le__SPEC__bindI,axiom,
% 0.17/0.44 ! [Phi: a > $o,X4: a,M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.17/0.44 ( ( Phi @ X4 )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ M @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ F ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % le_SPEC_bindI
% 0.17/0.44 thf(fact_327_RES__bind__choose,axiom,
% 0.17/0.44 ! [X4: a,X: set_a,M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.17/0.44 ( ( member_a @ X4 @ X )
% 0.17/0.44 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ M @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % RES_bind_choose
% 0.17/0.44 thf(fact_328_SUCCEED__rule,axiom,
% 0.17/0.44 ! [Phi: a > $o] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % SUCCEED_rule
% 0.17/0.44 thf(fact_329_bot_Oextremum__uniqueI,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
% 0.17/0.44 => ( A = bot_bo529555393nres_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % bot.extremum_uniqueI
% 0.17/0.44 thf(fact_330_bot_Oextremum__unique,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
% 0.17/0.44 = ( A = bot_bo529555393nres_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % bot.extremum_unique
% 0.17/0.44 thf(fact_331_bot_Oextremum,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ) ).
% 0.17/0.44
% 0.17/0.44 % bot.extremum
% 0.17/0.44 thf(fact_332_nres__order__simps_I1_J,axiom,
% 0.17/0.44 ! [M4: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ M4 ) ).
% 0.17/0.44
% 0.17/0.44 % nres_order_simps(1)
% 0.17/0.44 thf(fact_333_bind__rule__complete,axiom,
% 0.17/0.44 ! [M4: refine424419629nres_a,F: a > refine424419629nres_a,Phi: a > $o] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.17/0.44 = ( ord_le519537037nres_a @ M4
% 0.17/0.44 @ ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] : ( ord_le519537037nres_a @ ( F @ X5 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % bind_rule_complete
% 0.17/0.44 thf(fact_334_specify__left,axiom,
% 0.17/0.44 ! [M: refine424419629nres_a,Phi: a > $o,F: a > refine424419629nres_a,M4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.17/0.44 => ( ! [X3: a] :
% 0.17/0.44 ( ( Phi @ X3 )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ M4 ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ M4 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % specify_left
% 0.17/0.44 thf(fact_335_bind__rule,axiom,
% 0.17/0.44 ! [M4: refine424419629nres_a,F: a > refine424419629nres_a,Phi: a > $o] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ M4
% 0.17/0.44 @ ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] : ( ord_le519537037nres_a @ ( F @ X5 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % bind_rule
% 0.17/0.44 thf(fact_336_bind__le__nofailI,axiom,
% 0.17/0.44 ! [M: refine424419629nres_a,F: a > refine424419629nres_a,M7: refine424419629nres_a] :
% 0.17/0.44 ( ( refine412683989fail_a @ M )
% 0.17/0.44 => ( ! [X3: a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( F @ X3 ) @ M7 ) )
% 0.17/0.44 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ M7 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % bind_le_nofailI
% 0.17/0.44 thf(fact_337_bind__le__shift,axiom,
% 0.17/0.44 ! [M: refine424419629nres_a,F: a > refine424419629nres_a,M7: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ M7 )
% 0.17/0.44 = ( ord_le519537037nres_a @ M
% 0.17/0.44 @ ( if_Ref1724547303nres_a @ ( refine412683989fail_a @ M7 )
% 0.17/0.44 @ ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [X5: a] : ( ord_le519537037nres_a @ ( F @ X5 ) @ M7 ) ) )
% 0.17/0.44 @ top_to231829469nres_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % bind_le_shift
% 0.17/0.44 thf(fact_338_inf__top__left,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ top_to231829469nres_a @ X4 )
% 0.17/0.44 = X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_top_left
% 0.17/0.44 thf(fact_339_inf__top__right,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ X4 @ top_to231829469nres_a )
% 0.17/0.44 = X4 ) ).
% 0.17/0.44
% 0.17/0.44 % inf_top_right
% 0.17/0.44 thf(fact_340_inf__eq__top__iff,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( ( inf_in262696383nres_a @ X4 @ Y3 )
% 0.17/0.44 = top_to231829469nres_a )
% 0.17/0.44 = ( ( X4 = top_to231829469nres_a )
% 0.17/0.44 & ( Y3 = top_to231829469nres_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_eq_top_iff
% 0.17/0.44 thf(fact_341_top__eq__inf__iff,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( top_to231829469nres_a
% 0.17/0.44 = ( inf_in262696383nres_a @ X4 @ Y3 ) )
% 0.17/0.44 = ( ( X4 = top_to231829469nres_a )
% 0.17/0.44 & ( Y3 = top_to231829469nres_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % top_eq_inf_iff
% 0.17/0.44 thf(fact_342_inf__top_Oeq__neutr__iff,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( ( inf_in262696383nres_a @ A @ B )
% 0.17/0.44 = top_to231829469nres_a )
% 0.17/0.44 = ( ( A = top_to231829469nres_a )
% 0.17/0.44 & ( B = top_to231829469nres_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_top.eq_neutr_iff
% 0.17/0.44 thf(fact_343_inf__top_Oleft__neutral,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ top_to231829469nres_a @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % inf_top.left_neutral
% 0.17/0.44 thf(fact_344_inf__top_Oneutr__eq__iff,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.17/0.44 ( ( top_to231829469nres_a
% 0.17/0.44 = ( inf_in262696383nres_a @ A @ B ) )
% 0.17/0.44 = ( ( A = top_to231829469nres_a )
% 0.17/0.44 & ( B = top_to231829469nres_a ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inf_top.neutr_eq_iff
% 0.17/0.44 thf(fact_345_inf__top_Oright__neutral,axiom,
% 0.17/0.44 ! [A: refine424419629nres_a] :
% 0.17/0.44 ( ( inf_in262696383nres_a @ A @ top_to231829469nres_a )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % inf_top.right_neutral
% 0.17/0.44 thf(fact_346_inres__simps_I2_J,axiom,
% 0.17/0.44 ! [X: set_a] :
% 0.17/0.44 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X ) )
% 0.17/0.44 = ( ^ [X5: a] : ( member_a @ X5 @ X ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % inres_simps(2)
% 0.17/0.44 thf(fact_347_nres__order__simps_I4_J,axiom,
% 0.17/0.44 ! [M4: refine424419629nres_a] :
% 0.17/0.44 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M4 )
% 0.17/0.44 = ( M4 = top_to231829469nres_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % nres_order_simps(4)
% 0.17/0.44 thf(fact_348_nres__more__simps_I1_J,axiom,
% 0.17/0.44 ! [X: set_a] :
% 0.17/0.44 ( ( bot_bo529555393nres_a
% 0.17/0.44 = ( refine1198353288_RES_a @ X ) )
% 0.17/0.44 = ( X = bot_bot_set_a ) ) ).
% 0.17/0.44
% 0.17/0.44 % nres_more_simps(1)
% 0.17/0.44
% 0.17/0.44 % Helper facts (7)
% 0.17/0.44 thf(help_If_2_1_If_001_062_Itf__a_M_Eo_J_T,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] :
% 0.17/0.44 ( ( if_a_o @ $false @ X4 @ Y3 )
% 0.17/0.44 = Y3 ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_1_1_If_001_062_Itf__a_M_Eo_J_T,axiom,
% 0.17/0.44 ! [X4: a > $o,Y3: a > $o] :
% 0.17/0.44 ( ( if_a_o @ $true @ X4 @ Y3 )
% 0.17/0.44 = X4 ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] :
% 0.17/0.44 ( ( if_set_a @ $false @ X4 @ Y3 )
% 0.17/0.44 = Y3 ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.17/0.44 ! [X4: set_a,Y3: set_a] :
% 0.17/0.44 ( ( if_set_a @ $true @ X4 @ Y3 )
% 0.17/0.44 = X4 ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.17/0.44 ! [P: $o] :
% 0.17/0.44 ( ( P = $true )
% 0.17/0.44 | ( P = $false ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( if_Ref1724547303nres_a @ $false @ X4 @ Y3 )
% 0.17/0.44 = Y3 ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.17/0.44 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.17/0.44 ( ( if_Ref1724547303nres_a @ $true @ X4 @ Y3 )
% 0.17/0.44 = X4 ) ).
% 0.17/0.44
% 0.17/0.44 % Conjectures (1)
% 0.17/0.44 thf(conj_0,conjecture,
% 0.17/0.44 ( ord_le519537037nres_a @ a2
% 0.17/0.44 @ ( refine1198353288_RES_a
% 0.17/0.44 @ ( collect_a
% 0.17/0.44 @ ^ [V3: a] :
% 0.17/0.44 ( ( p @ V3 )
% 0.17/0.44 & ( q @ V3 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 3.71/1.97 ---- Embedded in THF ---
% 3.71/1.98 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.71/1.98 %%% Generated on Tue Feb 24 08:28:04 EST 2026
% 3.71/1.98 %%% using '$$dhol' embedding, version 1.3.0.
% 3.71/1.98 %%% Logic specification used:
% 3.71/1.98 %%% thf(spec, logic, $$dhol).
% 3.71/1.98
% 3.71/1.98 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2DTF25888.p
% See solution above
% 3.71/1.98 ------------------------
% 3.91/2.03 ---- Cleaned THF ---
% 3.91/2.03 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.91/2.03 refine424419629nres_a: $tType ).
% 3.91/2.03
% 3.91/2.03 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 3.91/2.03 set_a: $tType ).
% 3.91/2.03
% 3.91/2.03 thf(ty_n_tf__a,type,
% 3.91/2.03 a: $tType ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_If_001_062_Itf__a_M_Eo_J,type,
% 3.91/2.03 if_a_o: $o > ( a > $o ) > ( a > $o ) > a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.91/2.03 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 3.91/2.03 if_set_a: $o > set_a > set_a > set_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_Itf__a_M_Eo_J,type,
% 3.91/2.03 inf_inf_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Lattices_Oinf__class_Oinf_001_Eo,type,
% 3.91/2.03 inf_inf_o: $o > $o > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.91/2.03 inf_in262696383nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
% 3.91/2.03 inf_inf_set_a: set_a > set_a > set_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Orderings_Obot__class_Obot_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.91/2.03 bot_bo529555393nres_a: refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 3.91/2.03 bot_bot_set_a: set_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J,type,
% 3.91/2.03 ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
% 3.91/2.03 ord_less_eq_o: $o > $o > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.91/2.03 ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 3.91/2.03 ord_less_eq_set_a: set_a > set_a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.91/2.03 order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.91/2.03 top_to231829469nres_a: refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__a,type,
% 3.91/2.03 refine2063221604TURN_a: a > refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Obind_001tf__a_001tf__a,type,
% 3.91/2.03 refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__a,type,
% 3.91/2.03 refine1001002027nres_a: refine424419629nres_a > a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onf__inres_001tf__a,type,
% 3.91/2.03 refine1312857699nres_a: refine424419629nres_a > a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__a,type,
% 3.91/2.03 refine412683989fail_a: refine424419629nres_a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_OFAILi_001tf__a,type,
% 3.91/2.03 refine464223677AILi_a: refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__a,type,
% 3.91/2.03 refine1198353288_RES_a: set_a > refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001tf__a,type,
% 3.91/2.03 refine1822134885_RES_a: refine424419629nres_a > set_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_Set_OCollect_001tf__a,type,
% 3.91/2.03 collect_a: ( a > $o ) > set_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_c_member_001tf__a,type,
% 3.91/2.03 member_a: a > set_a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_v_A,type,
% 3.91/2.03 a2: refine424419629nres_a ).
% 3.91/2.03
% 3.91/2.03 thf(sy_v_P,type,
% 3.91/2.03 p: a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(sy_v_Q,type,
% 3.91/2.03 q: a > $o ).
% 3.91/2.03
% 3.91/2.03 thf(fact_0_nres__more__simps_I4_J,axiom,
% 3.91/2.03 ! [X: set_a,Y: set_a] :
% 3.91/2.03 ( ( ( refine1198353288_RES_a @ X )
% 3.91/2.03 = ( refine1198353288_RES_a @ Y ) )
% 3.91/2.03 = ( X = Y ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_1_nres_Oinject,axiom,
% 3.91/2.03 ! [X2: set_a,Y2: set_a] :
% 3.91/2.03 ( ( ( refine1198353288_RES_a @ X2 )
% 3.91/2.03 = ( refine1198353288_RES_a @ Y2 ) )
% 3.91/2.03 = ( X2 = Y2 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_2_assms_I2_J,axiom,
% 3.91/2.03 ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_3_assms_I1_J,axiom,
% 3.91/2.03 ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062,axiom,
% 3.91/2.03 ord_le519537037nres_a @ a2 @ ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_5_if__rule,axiom,
% 3.91/2.03 ! [B: $o,S1: refine424419629nres_a,Phi: a > $o,S2: refine424419629nres_a] :
% 3.91/2.03 ( ( B
% 3.91/2.03 => ( ord_le519537037nres_a @ S1 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 3.91/2.03 => ( ( ~ B
% 3.91/2.03 => ( ord_le519537037nres_a @ S2 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ S1 @ S2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_6_RES__rule,axiom,
% 3.91/2.03 ! [S: set_a,Phi: a > $o] :
% 3.91/2.03 ( ! [X3: a] :
% 3.91/2.03 ( ( member_a @ X3 @ S )
% 3.91/2.03 => ( Phi @ X3 ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_7_SPEC__iff,axiom,
% 3.91/2.03 ! [P: refine424419629nres_a,Q: a > $o,R: a > $o] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ P
% 3.91/2.03 @ ( refine1198353288_RES_a
% 3.91/2.03 @ ( collect_a
% 3.91/2.03 @ ^ [S3: a] :
% 3.91/2.03 ( ( Q @ S3 )
% 3.91/2.03 => ( R @ S3 ) ) ) ) )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ P
% 3.91/2.03 @ ( refine1198353288_RES_a
% 3.91/2.03 @ ( collect_a
% 3.91/2.03 @ ^ [S3: a] :
% 3.91/2.03 ( ~ ( Q @ S3 )
% 3.91/2.03 => ~ ( R @ S3 ) ) ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ P
% 3.91/2.03 @ ( refine1198353288_RES_a
% 3.91/2.03 @ ( collect_a
% 3.91/2.03 @ ^ [S3: a] :
% 3.91/2.03 ( ( Q @ S3 )
% 3.91/2.03 = ( R @ S3 ) ) ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_8_SPEC__rule,axiom,
% 3.91/2.03 ! [Phi: a > $o,Phi2: a > $o] :
% 3.91/2.03 ( ! [X3: a] :
% 3.91/2.03 ( ( Phi @ X3 )
% 3.91/2.03 => ( Phi2 @ X3 ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_9_SPEC__trans,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Postcond: a > $o] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ Y3 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ X4 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_10_lhs__step__If,axiom,
% 3.91/2.03 ! [B: $o,T: set_a,M: set_a,E: set_a] :
% 3.91/2.03 ( ( B
% 3.91/2.03 => ( ord_less_eq_set_a @ T @ M ) )
% 3.91/2.03 => ( ( ~ B
% 3.91/2.03 => ( ord_less_eq_set_a @ E @ M ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( if_set_a @ B @ T @ E ) @ M ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_11_lhs__step__If,axiom,
% 3.91/2.03 ! [B: $o,T: a > $o,M: a > $o,E: a > $o] :
% 3.91/2.03 ( ( B
% 3.91/2.03 => ( ord_less_eq_a_o @ T @ M ) )
% 3.91/2.03 => ( ( ~ B
% 3.91/2.03 => ( ord_less_eq_a_o @ E @ M ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( if_a_o @ B @ T @ E ) @ M ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_12_lhs__step__If,axiom,
% 3.91/2.03 ! [B: $o,T: refine424419629nres_a,M: refine424419629nres_a,E: refine424419629nres_a] :
% 3.91/2.03 ( ( B
% 3.91/2.03 => ( ord_le519537037nres_a @ T @ M ) )
% 3.91/2.03 => ( ( ~ B
% 3.91/2.03 => ( ord_le519537037nres_a @ E @ M ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ M ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_13_use__spec__rule,axiom,
% 3.91/2.03 ! [M: refine424419629nres_a,Psi: a > $o,Phi: a > $o] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ M
% 3.91/2.03 @ ( refine1198353288_RES_a
% 3.91/2.03 @ ( collect_a
% 3.91/2.03 @ ^ [S3: a] :
% 3.91/2.03 ( ( Psi @ S3 )
% 3.91/2.03 => ( Phi @ S3 ) ) ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_14_SPEC__cons__rule,axiom,
% 3.91/2.03 ! [M: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 3.91/2.03 => ( ! [X3: a] :
% 3.91/2.03 ( ( Phi @ X3 )
% 3.91/2.03 => ( Psi @ X3 ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_15_order__mono__setup_Orefl,axiom,
% 3.91/2.03 ! [X4: set_a] : ( ord_less_eq_set_a @ X4 @ X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_16_order__mono__setup_Orefl,axiom,
% 3.91/2.03 ! [X4: a > $o] : ( ord_less_eq_a_o @ X4 @ X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_17_order__mono__setup_Orefl,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a] : ( ord_le519537037nres_a @ X4 @ X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_18_the__RES_Osimps,axiom,
% 3.91/2.03 ! [X: set_a] :
% 3.91/2.03 ( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ X ) )
% 3.91/2.03 = X ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_19_nf__inres__RES,axiom,
% 3.91/2.03 ! [X: set_a,X4: a] :
% 3.91/2.03 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X ) @ X4 )
% 3.91/2.03 = ( member_a @ X4 @ X ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_20_nf__inres__SPEC,axiom,
% 3.91/2.03 ! [Phi: a > $o,X4: a] :
% 3.91/2.03 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ X4 )
% 3.91/2.03 = ( Phi @ X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_21_le__funD,axiom,
% 3.91/2.03 ! [F: a > $o,G: a > $o,X4: a] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ F @ G )
% 3.91/2.03 => ( ord_less_eq_o @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_22_le__funE,axiom,
% 3.91/2.03 ! [F: a > $o,G: a > $o,X4: a] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ F @ G )
% 3.91/2.03 => ( ord_less_eq_o @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_23_le__funI,axiom,
% 3.91/2.03 ! [F: a > $o,G: a > $o] :
% 3.91/2.03 ( ! [X3: a] : ( ord_less_eq_o @ ( F @ X3 ) @ ( G @ X3 ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ F @ G ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_24_Refine__Misc_Oif__mono,axiom,
% 3.91/2.03 ! [B: $o,M1: set_a,M12: set_a,M2: set_a,M22: set_a] :
% 3.91/2.03 ( ( B
% 3.91/2.03 => ( ord_less_eq_set_a @ M1 @ M12 ) )
% 3.91/2.03 => ( ( ~ B
% 3.91/2.03 => ( ord_less_eq_set_a @ M2 @ M22 ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( if_set_a @ B @ M1 @ M2 ) @ ( if_set_a @ B @ M12 @ M22 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_25_Refine__Misc_Oif__mono,axiom,
% 3.91/2.03 ! [B: $o,M1: a > $o,M12: a > $o,M2: a > $o,M22: a > $o] :
% 3.91/2.03 ( ( B
% 3.91/2.03 => ( ord_less_eq_a_o @ M1 @ M12 ) )
% 3.91/2.03 => ( ( ~ B
% 3.91/2.03 => ( ord_less_eq_a_o @ M2 @ M22 ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( if_a_o @ B @ M1 @ M2 ) @ ( if_a_o @ B @ M12 @ M22 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_26_Refine__Misc_Oif__mono,axiom,
% 3.91/2.03 ! [B: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M2: refine424419629nres_a,M22: refine424419629nres_a] :
% 3.91/2.03 ( ( B
% 3.91/2.03 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 3.91/2.03 => ( ( ~ B
% 3.91/2.03 => ( ord_le519537037nres_a @ M2 @ M22 ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ M1 @ M2 ) @ ( if_Ref1724547303nres_a @ B @ M12 @ M22 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_27_le__fun__def,axiom,
% 3.91/2.03 ( ord_less_eq_a_o
% 3.91/2.03 = ( ^ [F2: a > $o,G2: a > $o] :
% 3.91/2.03 ! [X5: a] : ( ord_less_eq_o @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_28_order__subst1,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,F: set_a > refine424419629nres_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_29_order__subst1,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,F: ( a > $o ) > refine424419629nres_a,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_30_order__subst1,axiom,
% 3.91/2.03 ! [A: set_a,F: refine424419629nres_a > set_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_31_order__subst1,axiom,
% 3.91/2.03 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_32_order__subst1,axiom,
% 3.91/2.03 ! [A: set_a,F: ( a > $o ) > set_a,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_33_order__subst1,axiom,
% 3.91/2.03 ! [A: a > $o,F: refine424419629nres_a > a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ ( F @ B ) )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_34_order__subst1,axiom,
% 3.91/2.03 ! [A: a > $o,F: set_a > a > $o,B: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_35_order__subst1,axiom,
% 3.91/2.03 ! [A: a > $o,F: ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_36_order__subst1,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_37_le__infD2,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ C ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_38_le__infD2,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ C ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_39_le__infD2,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ C ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_40_le__infD1,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_41_le__infD1,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_42_le__infD1,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_43_inf__leI,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ! [X3: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ A )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ X3 @ B )
% 3.91/2.03 => ( ord_less_eq_set_a @ X3 @ C ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ C ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_44_inf__leI,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ! [X3: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ A )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ X3 @ B )
% 3.91/2.03 => ( ord_less_eq_a_o @ X3 @ C ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ C ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_45_inf__leI,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ! [X3: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ A )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ X3 @ B )
% 3.91/2.03 => ( ord_le519537037nres_a @ X3 @ C ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_46_less__eq__nres_Osimps_I2_J,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 3.91/2.03 = ( ord_less_eq_set_a @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_47_nres__order__simps_I5_J,axiom,
% 3.91/2.03 ! [X: set_a,Y: set_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine1198353288_RES_a @ Y ) )
% 3.91/2.03 = ( ord_less_eq_set_a @ X @ Y ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_48_order__mono__setup_Omono__if,axiom,
% 3.91/2.03 ! [T: set_a,T2: set_a,E: set_a,E2: set_a,B: $o] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ T @ T2 )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ E @ E2 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( if_set_a @ B @ T @ E ) @ ( if_set_a @ B @ T2 @ E2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_49_order__mono__setup_Omono__if,axiom,
% 3.91/2.03 ! [T: a > $o,T2: a > $o,E: a > $o,E2: a > $o,B: $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ T @ T2 )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ E @ E2 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( if_a_o @ B @ T @ E ) @ ( if_a_o @ B @ T2 @ E2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_50_order__mono__setup_Omono__if,axiom,
% 3.91/2.03 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B: $o] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ T @ T2 )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ E @ E2 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ ( if_Ref1724547303nres_a @ B @ T2 @ E2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_51_dual__order_Oantisym,axiom,
% 3.91/2.03 ! [B: set_a,A: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ B @ A )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( A = B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_52_dual__order_Oantisym,axiom,
% 3.91/2.03 ! [B: a > $o,A: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ B @ A )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( A = B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_53_dual__order_Oantisym,axiom,
% 3.91/2.03 ! [B: refine424419629nres_a,A: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ B @ A )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( A = B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_54_dual__order_Oeq__iff,axiom,
% 3.91/2.03 ( ( ^ [Y5: set_a,Z: set_a] : ( Y5 = Z ) )
% 3.91/2.03 = ( ^ [A2: set_a,B2: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 3.91/2.03 & ( ord_less_eq_set_a @ A2 @ B2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_55_dual__order_Oeq__iff,axiom,
% 3.91/2.03 ( ( ^ [Y5: a > $o,Z: a > $o] : ( Y5 = Z ) )
% 3.91/2.03 = ( ^ [A2: a > $o,B2: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ B2 @ A2 )
% 3.91/2.03 & ( ord_less_eq_a_o @ A2 @ B2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_56_dual__order_Oeq__iff,axiom,
% 3.91/2.03 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 3.91/2.03 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 3.91/2.03 & ( ord_le519537037nres_a @ A2 @ B2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_57_dual__order_Otrans,axiom,
% 3.91/2.03 ! [B: set_a,A: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ B @ A )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ C @ B )
% 3.91/2.03 => ( ord_less_eq_set_a @ C @ A ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_58_dual__order_Otrans,axiom,
% 3.91/2.03 ! [B: a > $o,A: a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ B @ A )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ C @ B )
% 3.91/2.03 => ( ord_less_eq_a_o @ C @ A ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_59_dual__order_Otrans,axiom,
% 3.91/2.03 ! [B: refine424419629nres_a,A: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ B @ A )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ C @ B )
% 3.91/2.03 => ( ord_le519537037nres_a @ C @ A ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_60_dual__order_Orefl,axiom,
% 3.91/2.03 ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_61_dual__order_Orefl,axiom,
% 3.91/2.03 ! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_62_dual__order_Orefl,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_63_order__trans,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ Y3 @ Z2 )
% 3.91/2.03 => ( ord_less_eq_set_a @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_64_order__trans,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ Y3 @ Z2 )
% 3.91/2.03 => ( ord_less_eq_a_o @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_65_order__trans,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 3.91/2.03 => ( ord_le519537037nres_a @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_66_order__class_Oorder_Oantisym,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ A )
% 3.91/2.03 => ( A = B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_67_order__class_Oorder_Oantisym,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ A )
% 3.91/2.03 => ( A = B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_68_order__class_Oorder_Oantisym,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ A )
% 3.91/2.03 => ( A = B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_69_ord__le__eq__trans,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( B = C )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_70_ord__le__eq__trans,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( B = C )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_71_ord__le__eq__trans,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( B = C )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_72_ord__eq__le__trans,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( A = B )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ C )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_73_ord__eq__le__trans,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( A = B )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ C )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_74_ord__eq__le__trans,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( A = B )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_75_order__class_Oorder_Oeq__iff,axiom,
% 3.91/2.03 ( ( ^ [Y5: set_a,Z: set_a] : ( Y5 = Z ) )
% 3.91/2.03 = ( ^ [A2: set_a,B2: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.91/2.03 & ( ord_less_eq_set_a @ B2 @ A2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_76_order__class_Oorder_Oeq__iff,axiom,
% 3.91/2.03 ( ( ^ [Y5: a > $o,Z: a > $o] : ( Y5 = Z ) )
% 3.91/2.03 = ( ^ [A2: a > $o,B2: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 3.91/2.03 & ( ord_less_eq_a_o @ B2 @ A2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_77_order__class_Oorder_Oeq__iff,axiom,
% 3.91/2.03 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 3.91/2.03 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.91/2.03 & ( ord_le519537037nres_a @ B2 @ A2 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_78_antisym__conv,axiom,
% 3.91/2.03 ! [Y3: set_a,X4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 3.91/2.03 = ( X4 = Y3 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_79_antisym__conv,axiom,
% 3.91/2.03 ! [Y3: a > $o,X4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ Y3 @ X4 )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 3.91/2.03 = ( X4 = Y3 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_80_antisym__conv,axiom,
% 3.91/2.03 ! [Y3: refine424419629nres_a,X4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.91/2.03 = ( X4 = Y3 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_81_mem__Collect__eq,axiom,
% 3.91/2.03 ! [A: a,P: a > $o] :
% 3.91/2.03 ( ( member_a @ A @ ( collect_a @ P ) )
% 3.91/2.03 = ( P @ A ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_82_Collect__mem__eq,axiom,
% 3.91/2.03 ! [A3: set_a] :
% 3.91/2.03 ( ( collect_a
% 3.91/2.03 @ ^ [X5: a] : ( member_a @ X5 @ A3 ) )
% 3.91/2.03 = A3 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_83_Collect__cong,axiom,
% 3.91/2.03 ! [P: a > $o,Q: a > $o] :
% 3.91/2.03 ( ! [X3: a] :
% 3.91/2.03 ( ( P @ X3 )
% 3.91/2.03 = ( Q @ X3 ) )
% 3.91/2.03 => ( ( collect_a @ P )
% 3.91/2.03 = ( collect_a @ Q ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_84_order_Otrans,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ C )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_85_order_Otrans,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ C )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_86_order_Otrans,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_87_eq__refl,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] :
% 3.91/2.03 ( ( X4 = Y3 )
% 3.91/2.03 => ( ord_less_eq_set_a @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_88_eq__refl,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] :
% 3.91/2.03 ( ( X4 = Y3 )
% 3.91/2.03 => ( ord_less_eq_a_o @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_89_eq__refl,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.03 ( ( X4 = Y3 )
% 3.91/2.03 => ( ord_le519537037nres_a @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_90_antisym,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 3.91/2.03 => ( X4 = Y3 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_91_antisym,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ Y3 @ X4 )
% 3.91/2.03 => ( X4 = Y3 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_92_antisym,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 3.91/2.03 => ( X4 = Y3 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_93_eq__iff,axiom,
% 3.91/2.03 ( ( ^ [Y5: set_a,Z: set_a] : ( Y5 = Z ) )
% 3.91/2.03 = ( ^ [X5: set_a,Y6: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X5 @ Y6 )
% 3.91/2.03 & ( ord_less_eq_set_a @ Y6 @ X5 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_94_eq__iff,axiom,
% 3.91/2.03 ( ( ^ [Y5: a > $o,Z: a > $o] : ( Y5 = Z ) )
% 3.91/2.03 = ( ^ [X5: a > $o,Y6: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X5 @ Y6 )
% 3.91/2.03 & ( ord_less_eq_a_o @ Y6 @ X5 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_95_eq__iff,axiom,
% 3.91/2.03 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 3.91/2.03 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X5 @ Y6 )
% 3.91/2.03 & ( ord_le519537037nres_a @ Y6 @ X5 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_96_ord__le__eq__subst,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( ( F @ B )
% 3.91/2.03 = C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_97_ord__le__eq__subst,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( ( F @ B )
% 3.91/2.03 = C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_98_ord__le__eq__subst,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( ( F @ B )
% 3.91/2.03 = C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_99_ord__le__eq__subst,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( ( F @ B )
% 3.91/2.03 = C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_100_ord__le__eq__subst,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,F: set_a > a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( ( F @ B )
% 3.91/2.03 = C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_101_ord__le__eq__subst,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,F: ( a > $o ) > refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( ( F @ B )
% 3.91/2.03 = C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_102_ord__le__eq__subst,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( ( F @ B )
% 3.91/2.03 = C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_103_ord__le__eq__subst,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( ( F @ B )
% 3.91/2.03 = C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_104_ord__le__eq__subst,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( ( F @ B )
% 3.91/2.03 = C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_105_ord__eq__le__subst,axiom,
% 3.91/2.03 ! [A: set_a,F: refine424419629nres_a > set_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( F @ B ) )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_106_ord__eq__le__subst,axiom,
% 3.91/2.03 ! [A: a > $o,F: refine424419629nres_a > a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( F @ B ) )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_107_ord__eq__le__subst,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,F: set_a > refine424419629nres_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_108_ord__eq__le__subst,axiom,
% 3.91/2.03 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_109_ord__eq__le__subst,axiom,
% 3.91/2.03 ! [A: a > $o,F: set_a > a > $o,B: set_a,C: set_a] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_110_ord__eq__le__subst,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,F: ( a > $o ) > refine424419629nres_a,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_111_ord__eq__le__subst,axiom,
% 3.91/2.03 ! [A: set_a,F: ( a > $o ) > set_a,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_112_ord__eq__le__subst,axiom,
% 3.91/2.03 ! [A: a > $o,F: ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( F @ B ) )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_113_ord__eq__le__subst,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( F @ B ) )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_114_order__subst2,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_115_order__subst2,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ ( F @ B ) @ C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_116_order__subst2,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_117_order__subst2,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_118_order__subst2,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,F: set_a > a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ ( F @ B ) @ C )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_119_order__subst2,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,F: ( a > $o ) > refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_120_order__subst2,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_121_order__subst2,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ ( F @ B ) @ C )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_122_order__subst2,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_123_inf_Obounded__iff,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 3.91/2.03 = ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 & ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_124_inf_Obounded__iff,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
% 3.91/2.03 = ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 & ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_125_inf_Obounded__iff,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
% 3.91/2.03 = ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 & ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_126_le__inf__iff,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) )
% 3.91/2.03 = ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 3.91/2.03 & ( ord_less_eq_set_a @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_127_le__inf__iff,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) )
% 3.91/2.03 = ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 3.91/2.03 & ( ord_less_eq_a_o @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_128_le__inf__iff,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) )
% 3.91/2.03 = ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.91/2.03 & ( ord_le519537037nres_a @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_129_inf__apply,axiom,
% 3.91/2.03 ( inf_inf_a_o
% 3.91/2.03 = ( ^ [F2: a > $o,G2: a > $o,X5: a] : ( inf_inf_o @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_130_inf_Oidem,axiom,
% 3.91/2.03 ! [A: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ A @ A )
% 3.91/2.03 = A ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_131_inf_Oidem,axiom,
% 3.91/2.03 ! [A: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ A @ A )
% 3.91/2.03 = A ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_132_inf_Oidem,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ A @ A )
% 3.91/2.03 = A ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_133_inf__idem,axiom,
% 3.91/2.03 ! [X4: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ X4 @ X4 )
% 3.91/2.03 = X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_134_inf__idem,axiom,
% 3.91/2.03 ! [X4: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ X4 @ X4 )
% 3.91/2.03 = X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_135_inf__idem,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ X4 @ X4 )
% 3.91/2.03 = X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_136_inf_Oleft__idem,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
% 3.91/2.03 = ( inf_inf_set_a @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_137_inf_Oleft__idem,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ A @ B ) )
% 3.91/2.03 = ( inf_inf_a_o @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_138_inf_Oleft__idem,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ A @ B ) )
% 3.91/2.03 = ( inf_in262696383nres_a @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_139_inf__left__idem,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ X4 @ Y3 ) )
% 3.91/2.03 = ( inf_inf_set_a @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_140_inf__left__idem,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ X4 @ Y3 ) )
% 3.91/2.03 = ( inf_inf_a_o @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_141_inf__left__idem,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ X4 @ Y3 ) )
% 3.91/2.03 = ( inf_in262696383nres_a @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_142_inf_Oright__idem,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
% 3.91/2.03 = ( inf_inf_set_a @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_143_inf_Oright__idem,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ B )
% 3.91/2.03 = ( inf_inf_a_o @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_144_inf_Oright__idem,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B )
% 3.91/2.03 = ( inf_in262696383nres_a @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_145_inf__right__idem,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Y3 )
% 3.91/2.03 = ( inf_inf_set_a @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_146_inf__right__idem,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Y3 )
% 3.91/2.03 = ( inf_inf_a_o @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_147_inf__right__idem,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Y3 )
% 3.91/2.03 = ( inf_in262696383nres_a @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_148_inf__nres_Osimps_I3_J,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 3.91/2.03 = ( refine1198353288_RES_a @ ( inf_inf_set_a @ A @ B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_149_inf__left__commute,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) )
% 3.91/2.03 = ( inf_inf_set_a @ Y3 @ ( inf_inf_set_a @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_150_inf__left__commute,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) )
% 3.91/2.03 = ( inf_inf_a_o @ Y3 @ ( inf_inf_a_o @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_151_inf__left__commute,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) )
% 3.91/2.03 = ( inf_in262696383nres_a @ Y3 @ ( inf_in262696383nres_a @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_152_inf_Oleft__commute,axiom,
% 3.91/2.03 ! [B: set_a,A: set_a,C: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ B @ ( inf_inf_set_a @ A @ C ) )
% 3.91/2.03 = ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_153_inf_Oleft__commute,axiom,
% 3.91/2.03 ! [B: a > $o,A: a > $o,C: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ B @ ( inf_inf_a_o @ A @ C ) )
% 3.91/2.03 = ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_154_inf_Oleft__commute,axiom,
% 3.91/2.03 ! [B: refine424419629nres_a,A: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ A @ C ) )
% 3.91/2.03 = ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_155_inf__commute,axiom,
% 3.91/2.03 ( inf_inf_set_a
% 3.91/2.03 = ( ^ [X5: set_a,Y6: set_a] : ( inf_inf_set_a @ Y6 @ X5 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_156_inf__commute,axiom,
% 3.91/2.03 ( inf_inf_a_o
% 3.91/2.03 = ( ^ [X5: a > $o,Y6: a > $o] : ( inf_inf_a_o @ Y6 @ X5 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_157_inf__commute,axiom,
% 3.91/2.03 ( inf_in262696383nres_a
% 3.91/2.03 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] : ( inf_in262696383nres_a @ Y6 @ X5 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_158_inf_Ocommute,axiom,
% 3.91/2.03 ( inf_inf_set_a
% 3.91/2.03 = ( ^ [A2: set_a,B2: set_a] : ( inf_inf_set_a @ B2 @ A2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_159_inf_Ocommute,axiom,
% 3.91/2.03 ( inf_inf_a_o
% 3.91/2.03 = ( ^ [A2: a > $o,B2: a > $o] : ( inf_inf_a_o @ B2 @ A2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_160_inf_Ocommute,axiom,
% 3.91/2.03 ( inf_in262696383nres_a
% 3.91/2.03 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] : ( inf_in262696383nres_a @ B2 @ A2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_161_inf__assoc,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Z2 )
% 3.91/2.03 = ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_162_inf__assoc,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Z2 )
% 3.91/2.03 = ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_163_inf__assoc,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Z2 )
% 3.91/2.03 = ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_164_inf_Oassoc,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
% 3.91/2.03 = ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_165_inf_Oassoc,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ C )
% 3.91/2.03 = ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_166_inf_Oassoc,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C )
% 3.91/2.03 = ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_167_boolean__algebra__cancel_Oinf2,axiom,
% 3.91/2.03 ! [B3: set_a,K: set_a,B: set_a,A: set_a] :
% 3.91/2.03 ( ( B3
% 3.91/2.03 = ( inf_inf_set_a @ K @ B ) )
% 3.91/2.03 => ( ( inf_inf_set_a @ A @ B3 )
% 3.91/2.03 = ( inf_inf_set_a @ K @ ( inf_inf_set_a @ A @ B ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_168_boolean__algebra__cancel_Oinf2,axiom,
% 3.91/2.03 ! [B3: a > $o,K: a > $o,B: a > $o,A: a > $o] :
% 3.91/2.03 ( ( B3
% 3.91/2.03 = ( inf_inf_a_o @ K @ B ) )
% 3.91/2.03 => ( ( inf_inf_a_o @ A @ B3 )
% 3.91/2.03 = ( inf_inf_a_o @ K @ ( inf_inf_a_o @ A @ B ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_169_boolean__algebra__cancel_Oinf2,axiom,
% 3.91/2.03 ! [B3: refine424419629nres_a,K: refine424419629nres_a,B: refine424419629nres_a,A: refine424419629nres_a] :
% 3.91/2.03 ( ( B3
% 3.91/2.03 = ( inf_in262696383nres_a @ K @ B ) )
% 3.91/2.03 => ( ( inf_in262696383nres_a @ A @ B3 )
% 3.91/2.03 = ( inf_in262696383nres_a @ K @ ( inf_in262696383nres_a @ A @ B ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_170_boolean__algebra__cancel_Oinf1,axiom,
% 3.91/2.03 ! [A3: set_a,K: set_a,A: set_a,B: set_a] :
% 3.91/2.03 ( ( A3
% 3.91/2.03 = ( inf_inf_set_a @ K @ A ) )
% 3.91/2.03 => ( ( inf_inf_set_a @ A3 @ B )
% 3.91/2.03 = ( inf_inf_set_a @ K @ ( inf_inf_set_a @ A @ B ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_171_boolean__algebra__cancel_Oinf1,axiom,
% 3.91/2.03 ! [A3: a > $o,K: a > $o,A: a > $o,B: a > $o] :
% 3.91/2.03 ( ( A3
% 3.91/2.03 = ( inf_inf_a_o @ K @ A ) )
% 3.91/2.03 => ( ( inf_inf_a_o @ A3 @ B )
% 3.91/2.03 = ( inf_inf_a_o @ K @ ( inf_inf_a_o @ A @ B ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_172_boolean__algebra__cancel_Oinf1,axiom,
% 3.91/2.03 ! [A3: refine424419629nres_a,K: refine424419629nres_a,A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( A3
% 3.91/2.03 = ( inf_in262696383nres_a @ K @ A ) )
% 3.91/2.03 => ( ( inf_in262696383nres_a @ A3 @ B )
% 3.91/2.03 = ( inf_in262696383nres_a @ K @ ( inf_in262696383nres_a @ A @ B ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_173_inf__fun__def,axiom,
% 3.91/2.03 ( inf_inf_a_o
% 3.91/2.03 = ( ^ [F2: a > $o,G2: a > $o,X5: a] : ( inf_inf_o @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_174_inf__sup__aci_I1_J,axiom,
% 3.91/2.03 ( inf_inf_set_a
% 3.91/2.03 = ( ^ [X5: set_a,Y6: set_a] : ( inf_inf_set_a @ Y6 @ X5 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_175_inf__sup__aci_I1_J,axiom,
% 3.91/2.03 ( inf_inf_a_o
% 3.91/2.03 = ( ^ [X5: a > $o,Y6: a > $o] : ( inf_inf_a_o @ Y6 @ X5 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_176_inf__sup__aci_I1_J,axiom,
% 3.91/2.03 ( inf_in262696383nres_a
% 3.91/2.03 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] : ( inf_in262696383nres_a @ Y6 @ X5 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_177_inf__sup__aci_I2_J,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Z2 )
% 3.91/2.03 = ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_178_inf__sup__aci_I2_J,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Z2 )
% 3.91/2.03 = ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_179_inf__sup__aci_I2_J,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Z2 )
% 3.91/2.03 = ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_180_inf__sup__aci_I3_J,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) )
% 3.91/2.03 = ( inf_inf_set_a @ Y3 @ ( inf_inf_set_a @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_181_inf__sup__aci_I3_J,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) )
% 3.91/2.03 = ( inf_inf_a_o @ Y3 @ ( inf_inf_a_o @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_182_inf__sup__aci_I3_J,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) )
% 3.91/2.03 = ( inf_in262696383nres_a @ Y3 @ ( inf_in262696383nres_a @ X4 @ Z2 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_183_inf__sup__aci_I4_J,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ X4 @ ( inf_inf_set_a @ X4 @ Y3 ) )
% 3.91/2.03 = ( inf_inf_set_a @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_184_inf__sup__aci_I4_J,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ X4 @ ( inf_inf_a_o @ X4 @ Y3 ) )
% 3.91/2.03 = ( inf_inf_a_o @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_185_inf__sup__aci_I4_J,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ X4 @ ( inf_in262696383nres_a @ X4 @ Y3 ) )
% 3.91/2.03 = ( inf_in262696383nres_a @ X4 @ Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_186_inf__sup__ord_I2_J,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Y3 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_187_inf__sup__ord_I2_J,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Y3 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_188_inf__sup__ord_I2_J,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Y3 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_189_inf__sup__ord_I1_J,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_190_inf__sup__ord_I1_J,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_191_inf__sup__ord_I1_J,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_192_inf__le1,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_193_inf__le1,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_194_inf__le1,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ X4 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_195_inf__le2,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ X4 @ Y3 ) @ Y3 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_196_inf__le2,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ X4 @ Y3 ) @ Y3 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_197_inf__le2,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ X4 @ Y3 ) @ Y3 ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_198_le__infE,axiom,
% 3.91/2.03 ! [X4: set_a,A: set_a,B: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X4 @ ( inf_inf_set_a @ A @ B ) )
% 3.91/2.03 => ~ ( ( ord_less_eq_set_a @ X4 @ A )
% 3.91/2.03 => ~ ( ord_less_eq_set_a @ X4 @ B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_199_le__infE,axiom,
% 3.91/2.03 ! [X4: a > $o,A: a > $o,B: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X4 @ ( inf_inf_a_o @ A @ B ) )
% 3.91/2.03 => ~ ( ( ord_less_eq_a_o @ X4 @ A )
% 3.91/2.03 => ~ ( ord_less_eq_a_o @ X4 @ B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_200_le__infE,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X4 @ ( inf_in262696383nres_a @ A @ B ) )
% 3.91/2.03 => ~ ( ( ord_le519537037nres_a @ X4 @ A )
% 3.91/2.03 => ~ ( ord_le519537037nres_a @ X4 @ B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_201_le__infI,axiom,
% 3.91/2.03 ! [X4: set_a,A: set_a,B: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X4 @ A )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ X4 @ B )
% 3.91/2.03 => ( ord_less_eq_set_a @ X4 @ ( inf_inf_set_a @ A @ B ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_202_le__infI,axiom,
% 3.91/2.03 ! [X4: a > $o,A: a > $o,B: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X4 @ A )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ X4 @ B )
% 3.91/2.03 => ( ord_less_eq_a_o @ X4 @ ( inf_inf_a_o @ A @ B ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_203_le__infI,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X4 @ A )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ X4 @ B )
% 3.91/2.03 => ( ord_le519537037nres_a @ X4 @ ( inf_in262696383nres_a @ A @ B ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_204_inf__mono,axiom,
% 3.91/2.03 ! [A: set_a,C: set_a,B: set_a,D: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ C )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ B @ D )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ ( inf_inf_set_a @ C @ D ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_205_inf__mono,axiom,
% 3.91/2.03 ! [A: a > $o,C: a > $o,B: a > $o,D: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ C )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ B @ D )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ ( inf_inf_a_o @ C @ D ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_206_inf__mono,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,C: refine424419629nres_a,B: refine424419629nres_a,D: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ C )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ B @ D )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ ( inf_in262696383nres_a @ C @ D ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_207_le__infI1,axiom,
% 3.91/2.03 ! [A: set_a,X4: set_a,B: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ X4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_208_le__infI1,axiom,
% 3.91/2.03 ! [A: a > $o,X4: a > $o,B: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ X4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_209_le__infI1,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,X4: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ X4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_210_le__infI2,axiom,
% 3.91/2.03 ! [B: set_a,X4: set_a,A: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ B @ X4 )
% 3.91/2.03 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_211_le__infI2,axiom,
% 3.91/2.03 ! [B: a > $o,X4: a > $o,A: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ B @ X4 )
% 3.91/2.03 => ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_212_le__infI2,axiom,
% 3.91/2.03 ! [B: refine424419629nres_a,X4: refine424419629nres_a,A: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ B @ X4 )
% 3.91/2.03 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_213_inf_OorderE,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( A
% 3.91/2.03 = ( inf_inf_set_a @ A @ B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_214_inf_OorderE,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( A
% 3.91/2.03 = ( inf_inf_a_o @ A @ B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_215_inf_OorderE,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( A
% 3.91/2.03 = ( inf_in262696383nres_a @ A @ B ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_216_inf_OorderI,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( inf_inf_set_a @ A @ B ) )
% 3.91/2.03 => ( ord_less_eq_set_a @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_217_inf_OorderI,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( inf_inf_a_o @ A @ B ) )
% 3.91/2.03 => ( ord_less_eq_a_o @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_218_inf_OorderI,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( A
% 3.91/2.03 = ( inf_in262696383nres_a @ A @ B ) )
% 3.91/2.03 => ( ord_le519537037nres_a @ A @ B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_219_inf__unique,axiom,
% 3.91/2.03 ! [F: set_a > set_a > set_a,X4: set_a,Y3: set_a] :
% 3.91/2.03 ( ! [X3: set_a,Y4: set_a] : ( ord_less_eq_set_a @ ( F @ X3 @ Y4 ) @ X3 )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a] : ( ord_less_eq_set_a @ ( F @ X3 @ Y4 ) @ Y4 )
% 3.91/2.03 => ( ! [X3: set_a,Y4: set_a,Z3: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X3 @ Y4 )
% 3.91/2.03 => ( ( ord_less_eq_set_a @ X3 @ Z3 )
% 3.91/2.03 => ( ord_less_eq_set_a @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 3.91/2.03 => ( ( inf_inf_set_a @ X4 @ Y3 )
% 3.91/2.03 = ( F @ X4 @ Y3 ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_220_inf__unique,axiom,
% 3.91/2.03 ! [F: ( a > $o ) > ( a > $o ) > a > $o,X4: a > $o,Y3: a > $o] :
% 3.91/2.03 ( ! [X3: a > $o,Y4: a > $o] : ( ord_less_eq_a_o @ ( F @ X3 @ Y4 ) @ X3 )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o] : ( ord_less_eq_a_o @ ( F @ X3 @ Y4 ) @ Y4 )
% 3.91/2.03 => ( ! [X3: a > $o,Y4: a > $o,Z3: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X3 @ Y4 )
% 3.91/2.03 => ( ( ord_less_eq_a_o @ X3 @ Z3 )
% 3.91/2.03 => ( ord_less_eq_a_o @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 3.91/2.03 => ( ( inf_inf_a_o @ X4 @ Y3 )
% 3.91/2.03 = ( F @ X4 @ Y3 ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_221_inf__unique,axiom,
% 3.91/2.03 ! [F: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a,X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.03 ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] : ( ord_le519537037nres_a @ ( F @ X3 @ Y4 ) @ X3 )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] : ( ord_le519537037nres_a @ ( F @ X3 @ Y4 ) @ Y4 )
% 3.91/2.03 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a,Z3: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.91/2.03 => ( ( ord_le519537037nres_a @ X3 @ Z3 )
% 3.91/2.03 => ( ord_le519537037nres_a @ X3 @ ( F @ Y4 @ Z3 ) ) ) )
% 3.91/2.03 => ( ( inf_in262696383nres_a @ X4 @ Y3 )
% 3.91/2.03 = ( F @ X4 @ Y3 ) ) ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_222_le__iff__inf,axiom,
% 3.91/2.03 ( ord_less_eq_set_a
% 3.91/2.03 = ( ^ [X5: set_a,Y6: set_a] :
% 3.91/2.03 ( ( inf_inf_set_a @ X5 @ Y6 )
% 3.91/2.03 = X5 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_223_le__iff__inf,axiom,
% 3.91/2.03 ( ord_less_eq_a_o
% 3.91/2.03 = ( ^ [X5: a > $o,Y6: a > $o] :
% 3.91/2.03 ( ( inf_inf_a_o @ X5 @ Y6 )
% 3.91/2.03 = X5 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_224_le__iff__inf,axiom,
% 3.91/2.03 ( ord_le519537037nres_a
% 3.91/2.03 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] :
% 3.91/2.03 ( ( inf_in262696383nres_a @ X5 @ Y6 )
% 3.91/2.03 = X5 ) ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_225_inf_Oabsorb1,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.03 => ( ( inf_inf_set_a @ A @ B )
% 3.91/2.03 = A ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_226_inf_Oabsorb1,axiom,
% 3.91/2.03 ! [A: a > $o,B: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.03 => ( ( inf_inf_a_o @ A @ B )
% 3.91/2.03 = A ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_227_inf_Oabsorb1,axiom,
% 3.91/2.03 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.03 => ( ( inf_in262696383nres_a @ A @ B )
% 3.91/2.03 = A ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_228_inf_Oabsorb2,axiom,
% 3.91/2.03 ! [B: set_a,A: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ B @ A )
% 3.91/2.03 => ( ( inf_inf_set_a @ A @ B )
% 3.91/2.03 = B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_229_inf_Oabsorb2,axiom,
% 3.91/2.03 ! [B: a > $o,A: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ B @ A )
% 3.91/2.03 => ( ( inf_inf_a_o @ A @ B )
% 3.91/2.03 = B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_230_inf_Oabsorb2,axiom,
% 3.91/2.03 ! [B: refine424419629nres_a,A: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ B @ A )
% 3.91/2.03 => ( ( inf_in262696383nres_a @ A @ B )
% 3.91/2.03 = B ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_231_inf__absorb1,axiom,
% 3.91/2.03 ! [X4: set_a,Y3: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 3.91/2.03 => ( ( inf_inf_set_a @ X4 @ Y3 )
% 3.91/2.03 = X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_232_inf__absorb1,axiom,
% 3.91/2.03 ! [X4: a > $o,Y3: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 3.91/2.03 => ( ( inf_inf_a_o @ X4 @ Y3 )
% 3.91/2.03 = X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_233_inf__absorb1,axiom,
% 3.91/2.03 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.91/2.03 => ( ( inf_in262696383nres_a @ X4 @ Y3 )
% 3.91/2.03 = X4 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_234_inf__absorb2,axiom,
% 3.91/2.03 ! [Y3: set_a,X4: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ Y3 @ X4 )
% 3.91/2.03 => ( ( inf_inf_set_a @ X4 @ Y3 )
% 3.91/2.03 = Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_235_inf__absorb2,axiom,
% 3.91/2.03 ! [Y3: a > $o,X4: a > $o] :
% 3.91/2.03 ( ( ord_less_eq_a_o @ Y3 @ X4 )
% 3.91/2.03 => ( ( inf_inf_a_o @ X4 @ Y3 )
% 3.91/2.03 = Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_236_inf__absorb2,axiom,
% 3.91/2.03 ! [Y3: refine424419629nres_a,X4: refine424419629nres_a] :
% 3.91/2.03 ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 3.91/2.03 => ( ( inf_in262696383nres_a @ X4 @ Y3 )
% 3.91/2.03 = Y3 ) ) ).
% 3.91/2.03
% 3.91/2.03 thf(fact_237_inf_OboundedE,axiom,
% 3.91/2.03 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.03 ( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
% 3.91/2.04 => ~ ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.04 => ~ ( ord_less_eq_set_a @ A @ C ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_238_inf_OboundedE,axiom,
% 3.91/2.04 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.04 ( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
% 3.91/2.04 => ~ ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.04 => ~ ( ord_less_eq_a_o @ A @ C ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_239_inf_OboundedE,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
% 3.91/2.04 => ~ ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.04 => ~ ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_240_inf_OboundedI,axiom,
% 3.91/2.04 ! [A: set_a,B: set_a,C: set_a] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ A @ B )
% 3.91/2.04 => ( ( ord_less_eq_set_a @ A @ C )
% 3.91/2.04 => ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_241_inf_OboundedI,axiom,
% 3.91/2.04 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.91/2.04 ( ( ord_less_eq_a_o @ A @ B )
% 3.91/2.04 => ( ( ord_less_eq_a_o @ A @ C )
% 3.91/2.04 => ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_242_inf_OboundedI,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ A @ B )
% 3.91/2.04 => ( ( ord_le519537037nres_a @ A @ C )
% 3.91/2.04 => ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_243_inf__greatest,axiom,
% 3.91/2.04 ! [X4: set_a,Y3: set_a,Z2: set_a] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ X4 @ Y3 )
% 3.91/2.04 => ( ( ord_less_eq_set_a @ X4 @ Z2 )
% 3.91/2.04 => ( ord_less_eq_set_a @ X4 @ ( inf_inf_set_a @ Y3 @ Z2 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_244_inf__greatest,axiom,
% 3.91/2.04 ! [X4: a > $o,Y3: a > $o,Z2: a > $o] :
% 3.91/2.04 ( ( ord_less_eq_a_o @ X4 @ Y3 )
% 3.91/2.04 => ( ( ord_less_eq_a_o @ X4 @ Z2 )
% 3.91/2.04 => ( ord_less_eq_a_o @ X4 @ ( inf_inf_a_o @ Y3 @ Z2 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_245_inf__greatest,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.91/2.04 => ( ( ord_le519537037nres_a @ X4 @ Z2 )
% 3.91/2.04 => ( ord_le519537037nres_a @ X4 @ ( inf_in262696383nres_a @ Y3 @ Z2 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_246_inf_Oorder__iff,axiom,
% 3.91/2.04 ( ord_less_eq_set_a
% 3.91/2.04 = ( ^ [A2: set_a,B2: set_a] :
% 3.91/2.04 ( A2
% 3.91/2.04 = ( inf_inf_set_a @ A2 @ B2 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_247_inf_Oorder__iff,axiom,
% 3.91/2.04 ( ord_less_eq_a_o
% 3.91/2.04 = ( ^ [A2: a > $o,B2: a > $o] :
% 3.91/2.04 ( A2
% 3.91/2.04 = ( inf_inf_a_o @ A2 @ B2 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_248_inf_Oorder__iff,axiom,
% 3.91/2.04 ( ord_le519537037nres_a
% 3.91/2.04 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.91/2.04 ( A2
% 3.91/2.04 = ( inf_in262696383nres_a @ A2 @ B2 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_249_inf_Ocobounded1,axiom,
% 3.91/2.04 ! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_250_inf_Ocobounded1,axiom,
% 3.91/2.04 ! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ A ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_251_inf_Ocobounded1,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ A ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_252_inf_Ocobounded2,axiom,
% 3.91/2.04 ! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ B ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_253_inf_Ocobounded2,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_254_inf_Oabsorb__iff1,axiom,
% 3.91/2.04 ( ord_le519537037nres_a
% 3.91/2.04 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ A2 @ B2 )
% 3.91/2.04 = A2 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_255_inf_Oabsorb__iff2,axiom,
% 3.91/2.04 ( ord_le519537037nres_a
% 3.91/2.04 = ( ^ [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ A2 @ B2 )
% 3.91/2.04 = B2 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_256_inf_OcoboundedI1,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,C: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ A @ C )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_257_inf_OcoboundedI2,axiom,
% 3.91/2.04 ! [B: refine424419629nres_a,C: refine424419629nres_a,A: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_258_subsetI,axiom,
% 3.91/2.04 ! [A3: set_a,B3: set_a] :
% 3.91/2.04 ( ! [X3: a] :
% 3.91/2.04 ( ( member_a @ X3 @ A3 )
% 3.91/2.04 => ( member_a @ X3 @ B3 ) )
% 3.91/2.04 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_259_Collect__subset,axiom,
% 3.91/2.04 ! [A3: set_a,P: a > $o] :
% 3.91/2.04 ( ord_less_eq_set_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ A3 )
% 3.91/2.04 & ( P @ X5 ) ) )
% 3.91/2.04 @ A3 ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_260_less__eq__set__def,axiom,
% 3.91/2.04 ( ord_less_eq_set_a
% 3.91/2.04 = ( ^ [A4: set_a,B4: set_a] :
% 3.91/2.04 ( ord_less_eq_a_o
% 3.91/2.04 @ ^ [X5: a] : ( member_a @ X5 @ A4 )
% 3.91/2.04 @ ^ [X5: a] : ( member_a @ X5 @ B4 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_261_pred__subset__eq,axiom,
% 3.91/2.04 ! [R: set_a,S: set_a] :
% 3.91/2.04 ( ( ord_less_eq_a_o
% 3.91/2.04 @ ^ [X5: a] : ( member_a @ X5 @ R )
% 3.91/2.04 @ ^ [X5: a] : ( member_a @ X5 @ S ) )
% 3.91/2.04 = ( ord_less_eq_set_a @ R @ S ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_262_conj__subset__def,axiom,
% 3.91/2.04 ! [A3: set_a,P: a > $o,Q: a > $o] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ A3
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] :
% 3.91/2.04 ( ( P @ X5 )
% 3.91/2.04 & ( Q @ X5 ) ) ) )
% 3.91/2.04 = ( ( ord_less_eq_set_a @ A3 @ ( collect_a @ P ) )
% 3.91/2.04 & ( ord_less_eq_set_a @ A3 @ ( collect_a @ Q ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_263_IntI,axiom,
% 3.91/2.04 ! [C: a,A3: set_a,B3: set_a] :
% 3.91/2.04 ( ( member_a @ C @ A3 )
% 3.91/2.04 => ( ( member_a @ C @ B3 )
% 3.91/2.04 => ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_264_Int__iff,axiom,
% 3.91/2.04 ! [C: a,A3: set_a,B3: set_a] :
% 3.91/2.04 ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) )
% 3.91/2.04 = ( ( member_a @ C @ A3 )
% 3.91/2.04 & ( member_a @ C @ B3 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_265_IntE,axiom,
% 3.91/2.04 ! [C: a,A3: set_a,B3: set_a] :
% 3.91/2.04 ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) )
% 3.91/2.04 => ~ ( ( member_a @ C @ A3 )
% 3.91/2.04 => ~ ( member_a @ C @ B3 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_266_IntD1,axiom,
% 3.91/2.04 ! [C: a,A3: set_a,B3: set_a] :
% 3.91/2.04 ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) )
% 3.91/2.04 => ( member_a @ C @ A3 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_267_IntD2,axiom,
% 3.91/2.04 ! [C: a,A3: set_a,B3: set_a] :
% 3.91/2.04 ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B3 ) )
% 3.91/2.04 => ( member_a @ C @ B3 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_268_Int__def,axiom,
% 3.91/2.04 ( inf_inf_set_a
% 3.91/2.04 = ( ^ [A4: set_a,B4: set_a] :
% 3.91/2.04 ( collect_a
% 3.91/2.04 @ ^ [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ A4 )
% 3.91/2.04 & ( member_a @ X5 @ B4 ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_269_Int__Collect,axiom,
% 3.91/2.04 ! [X4: a,A3: set_a,P: a > $o] :
% 3.91/2.04 ( ( member_a @ X4 @ ( inf_inf_set_a @ A3 @ ( collect_a @ P ) ) )
% 3.91/2.04 = ( ( member_a @ X4 @ A3 )
% 3.91/2.04 & ( P @ X4 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_270_inf__set__def,axiom,
% 3.91/2.04 ( inf_inf_set_a
% 3.91/2.04 = ( ^ [A4: set_a,B4: set_a] :
% 3.91/2.04 ( collect_a
% 3.91/2.04 @ ( inf_inf_a_o
% 3.91/2.04 @ ^ [X5: a] : ( member_a @ X5 @ A4 )
% 3.91/2.04 @ ^ [X5: a] : ( member_a @ X5 @ B4 ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_271_inf__Int__eq,axiom,
% 3.91/2.04 ! [R: set_a,S: set_a] :
% 3.91/2.04 ( ( inf_inf_a_o
% 3.91/2.04 @ ^ [X5: a] : ( member_a @ X5 @ R )
% 3.91/2.04 @ ^ [X5: a] : ( member_a @ X5 @ S ) )
% 3.91/2.04 = ( ^ [X5: a] : ( member_a @ X5 @ ( inf_inf_set_a @ R @ S ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_272_Collect__conj__eq,axiom,
% 3.91/2.04 ! [P: a > $o,Q: a > $o] :
% 3.91/2.04 ( ( collect_a
% 3.91/2.04 @ ^ [X5: a] :
% 3.91/2.04 ( ( P @ X5 )
% 3.91/2.04 & ( Q @ X5 ) ) )
% 3.91/2.04 = ( inf_inf_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_273_Int__Collect__mono,axiom,
% 3.91/2.04 ! [A3: set_a,B3: set_a,P: a > $o,Q: a > $o] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 3.91/2.04 => ( ! [X3: a] :
% 3.91/2.04 ( ( member_a @ X3 @ A3 )
% 3.91/2.04 => ( ( P @ X3 )
% 3.91/2.04 => ( Q @ X3 ) ) )
% 3.91/2.04 => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A3 @ ( collect_a @ P ) ) @ ( inf_inf_set_a @ B3 @ ( collect_a @ Q ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_274_Collect__mono__iff,axiom,
% 3.91/2.04 ! [P: a > $o,Q: a > $o] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 3.91/2.04 = ( ! [X5: a] :
% 3.91/2.04 ( ( P @ X5 )
% 3.91/2.04 => ( Q @ X5 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_275_Collect__mono,axiom,
% 3.91/2.04 ! [P: a > $o,Q: a > $o] :
% 3.91/2.04 ( ! [X3: a] :
% 3.91/2.04 ( ( P @ X3 )
% 3.91/2.04 => ( Q @ X3 ) )
% 3.91/2.04 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_276_subset__iff,axiom,
% 3.91/2.04 ( ord_less_eq_set_a
% 3.91/2.04 = ( ^ [A4: set_a,B4: set_a] :
% 3.91/2.04 ! [T3: a] :
% 3.91/2.04 ( ( member_a @ T3 @ A4 )
% 3.91/2.04 => ( member_a @ T3 @ B4 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_277_subset__eq,axiom,
% 3.91/2.04 ( ord_less_eq_set_a
% 3.91/2.04 = ( ^ [A4: set_a,B4: set_a] :
% 3.91/2.04 ! [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ A4 )
% 3.91/2.04 => ( member_a @ X5 @ B4 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_278_subsetD,axiom,
% 3.91/2.04 ! [A3: set_a,B3: set_a,C: a] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 3.91/2.04 => ( ( member_a @ C @ A3 )
% 3.91/2.04 => ( member_a @ C @ B3 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_279_in__mono,axiom,
% 3.91/2.04 ! [A3: set_a,B3: set_a,X4: a] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 3.91/2.04 => ( ( member_a @ X4 @ A3 )
% 3.91/2.04 => ( member_a @ X4 @ B3 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_280_subset__Collect__iff,axiom,
% 3.91/2.04 ! [B3: set_a,A3: set_a,P: a > $o] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 3.91/2.04 => ( ( ord_less_eq_set_a @ B3
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ A3 )
% 3.91/2.04 & ( P @ X5 ) ) ) )
% 3.91/2.04 = ( ! [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ B3 )
% 3.91/2.04 => ( P @ X5 ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_281_subset__CollectI,axiom,
% 3.91/2.04 ! [B3: set_a,A3: set_a,Q: a > $o,P: a > $o] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 3.91/2.04 => ( ! [X3: a] :
% 3.91/2.04 ( ( member_a @ X3 @ B3 )
% 3.91/2.04 => ( ( Q @ X3 )
% 3.91/2.04 => ( P @ X3 ) ) )
% 3.91/2.04 => ( ord_less_eq_set_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ B3 )
% 3.91/2.04 & ( Q @ X5 ) ) )
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ A3 )
% 3.91/2.04 & ( P @ X5 ) ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_282_Collect__restrict,axiom,
% 3.91/2.04 ! [X: set_a,P: a > $o] :
% 3.91/2.04 ( ord_less_eq_set_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ X )
% 3.91/2.04 & ( P @ X5 ) ) )
% 3.91/2.04 @ X ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_283_ord__eq__le__eq__trans,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
% 3.91/2.04 ( ( A = B )
% 3.91/2.04 => ( ( ord_le519537037nres_a @ B @ C )
% 3.91/2.04 => ( ( C = D )
% 3.91/2.04 => ( ord_le519537037nres_a @ A @ D ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_284_subset__Collect__conv,axiom,
% 3.91/2.04 ! [S: set_a,P: a > $o] :
% 3.91/2.04 ( ( ord_less_eq_set_a @ S @ ( collect_a @ P ) )
% 3.91/2.04 = ( ! [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ S )
% 3.91/2.04 => ( P @ X5 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_285_prop__restrict,axiom,
% 3.91/2.04 ! [X4: a,Z4: set_a,X: set_a,P: a > $o] :
% 3.91/2.04 ( ( member_a @ X4 @ Z4 )
% 3.91/2.04 => ( ( ord_less_eq_set_a @ Z4
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] :
% 3.91/2.04 ( ( member_a @ X5 @ X )
% 3.91/2.04 & ( P @ X5 ) ) ) )
% 3.91/2.04 => ( P @ X4 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_286_inf__nres_Oelims,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.04 ( ( ( inf_in262696383nres_a @ X4 @ Xa )
% 3.91/2.04 = Y3 )
% 3.91/2.04 => ( ( ( Xa = refine464223677AILi_a )
% 3.91/2.04 => ( Y3 != X4 ) )
% 3.91/2.04 => ( ( ( X4 = refine464223677AILi_a )
% 3.91/2.04 => ! [V: set_a] :
% 3.91/2.04 ( ( Xa
% 3.91/2.04 = ( refine1198353288_RES_a @ V ) )
% 3.91/2.04 => ( Y3
% 3.91/2.04 != ( refine1198353288_RES_a @ V ) ) ) )
% 3.91/2.04 => ~ ! [A5: set_a] :
% 3.91/2.04 ( ( X4
% 3.91/2.04 = ( refine1198353288_RES_a @ A5 ) )
% 3.91/2.04 => ! [B5: set_a] :
% 3.91/2.04 ( ( Xa
% 3.91/2.04 = ( refine1198353288_RES_a @ B5 ) )
% 3.91/2.04 => ( Y3
% 3.91/2.04 != ( refine1198353288_RES_a @ ( inf_inf_set_a @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_287_GreatestI2__order,axiom,
% 3.91/2.04 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 3.91/2.04 ( ( P @ X4 )
% 3.91/2.04 => ( ! [Y4: refine424419629nres_a] :
% 3.91/2.04 ( ( P @ Y4 )
% 3.91/2.04 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 3.91/2.04 => ( ! [X3: refine424419629nres_a] :
% 3.91/2.04 ( ( P @ X3 )
% 3.91/2.04 => ( ! [Y7: refine424419629nres_a] :
% 3.91/2.04 ( ( P @ Y7 )
% 3.91/2.04 => ( ord_le519537037nres_a @ Y7 @ X3 ) )
% 3.91/2.04 => ( Q @ X3 ) ) )
% 3.91/2.04 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_288_inf__nres_Osimps_I1_J,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ X4 @ refine464223677AILi_a )
% 3.91/2.04 = X4 ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_289_nres_Odistinct_I1_J,axiom,
% 3.91/2.04 ! [X2: set_a] :
% 3.91/2.04 ( refine464223677AILi_a
% 3.91/2.04 != ( refine1198353288_RES_a @ X2 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_290_nres_Oinduct,axiom,
% 3.91/2.04 ! [P: refine424419629nres_a > $o,Nres: refine424419629nres_a] :
% 3.91/2.04 ( ( P @ refine464223677AILi_a )
% 3.91/2.04 => ( ! [X3: set_a] : ( P @ ( refine1198353288_RES_a @ X3 ) )
% 3.91/2.04 => ( P @ Nres ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_291_nres_Oexhaust,axiom,
% 3.91/2.04 ! [Y3: refine424419629nres_a] :
% 3.91/2.04 ( ( Y3 != refine464223677AILi_a )
% 3.91/2.04 => ~ ! [X22: set_a] :
% 3.91/2.04 ( Y3
% 3.91/2.04 != ( refine1198353288_RES_a @ X22 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_292_sup__nres_Oinduct,axiom,
% 3.91/2.04 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 3.91/2.04 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 3.91/2.04 => ( ! [V: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) )
% 3.91/2.04 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 3.91/2.04 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_293_less__nres_Oinduct,axiom,
% 3.91/2.04 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 3.91/2.04 ( ! [X_1: refine424419629nres_a] : ( P @ refine464223677AILi_a @ X_1 )
% 3.91/2.04 => ( ! [Uv: set_a] : ( P @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a )
% 3.91/2.04 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 3.91/2.04 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_294_less__eq__nres_Oinduct,axiom,
% 3.91/2.04 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 3.91/2.04 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 3.91/2.04 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 3.91/2.04 => ( ! [Uv: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) )
% 3.91/2.04 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_295_less__eq__nres_Osimps_I1_J,axiom,
% 3.91/2.04 ! [Uu2: refine424419629nres_a] : ( ord_le519537037nres_a @ Uu2 @ refine464223677AILi_a ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_296_less__eq__nres_Osimps_I3_J,axiom,
% 3.91/2.04 ! [Uv2: set_a] :
% 3.91/2.04 ~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv2 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_297_inf__nres_Osimps_I2_J,axiom,
% 3.91/2.04 ! [V2: set_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V2 ) )
% 3.91/2.04 = ( refine1198353288_RES_a @ V2 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_298_less__eq__nres_Oelims_I1_J,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 3.91/2.04 ( ( ( ord_le519537037nres_a @ X4 @ Xa )
% 3.91/2.04 = Y3 )
% 3.91/2.04 => ( ( ( Xa = refine464223677AILi_a )
% 3.91/2.04 => ~ Y3 )
% 3.91/2.04 => ( ! [A5: set_a] :
% 3.91/2.04 ( ( X4
% 3.91/2.04 = ( refine1198353288_RES_a @ A5 ) )
% 3.91/2.04 => ! [B5: set_a] :
% 3.91/2.04 ( ( Xa
% 3.91/2.04 = ( refine1198353288_RES_a @ B5 ) )
% 3.91/2.04 => ( Y3
% 3.91/2.04 = ( ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) )
% 3.91/2.04 => ~ ( ( X4 = refine464223677AILi_a )
% 3.91/2.04 => ( ? [Uv: set_a] :
% 3.91/2.04 ( Xa
% 3.91/2.04 = ( refine1198353288_RES_a @ Uv ) )
% 3.91/2.04 => Y3 ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_299_less__eq__nres_Oelims_I2_J,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ X4 @ Xa )
% 3.91/2.04 => ( ( Xa != refine464223677AILi_a )
% 3.91/2.04 => ~ ! [A5: set_a] :
% 3.91/2.04 ( ( X4
% 3.91/2.04 = ( refine1198353288_RES_a @ A5 ) )
% 3.91/2.04 => ! [B5: set_a] :
% 3.91/2.04 ( ( Xa
% 3.91/2.04 = ( refine1198353288_RES_a @ B5 ) )
% 3.91/2.04 => ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_300_less__eq__nres_Oelims_I3_J,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.91/2.04 ( ~ ( ord_le519537037nres_a @ X4 @ Xa )
% 3.91/2.04 => ( ! [A5: set_a] :
% 3.91/2.04 ( ( X4
% 3.91/2.04 = ( refine1198353288_RES_a @ A5 ) )
% 3.91/2.04 => ! [B5: set_a] :
% 3.91/2.04 ( ( Xa
% 3.91/2.04 = ( refine1198353288_RES_a @ B5 ) )
% 3.91/2.04 => ( ord_less_eq_set_a @ A5 @ B5 ) ) )
% 3.91/2.04 => ~ ( ( X4 = refine464223677AILi_a )
% 3.91/2.04 => ! [Uv: set_a] :
% 3.91/2.04 ( Xa
% 3.91/2.04 != ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_301_Greatest__equality,axiom,
% 3.91/2.04 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a] :
% 3.91/2.04 ( ( P @ X4 )
% 3.91/2.04 => ( ! [Y4: refine424419629nres_a] :
% 3.91/2.04 ( ( P @ Y4 )
% 3.91/2.04 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 3.91/2.04 => ( ( order_1714329108nres_a @ P )
% 3.91/2.04 = X4 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_302_the__RES__inv,axiom,
% 3.91/2.04 ! [M: refine424419629nres_a] :
% 3.91/2.04 ( ( refine412683989fail_a @ M )
% 3.91/2.04 => ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ M ) )
% 3.91/2.04 = M ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_303_inf__RETURN__SPEC_I1_J,axiom,
% 3.91/2.04 ! [X4: a,Phi: a > $o] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 3.91/2.04 = ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [Y6: a] :
% 3.91/2.04 ( ( Y6 = X4 )
% 3.91/2.04 & ( Phi @ X4 ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_304_nofail__simps_I2_J,axiom,
% 3.91/2.04 ! [X: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_305_nres__order__simps_I20_J,axiom,
% 3.91/2.04 ! [X4: a,Y3: a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine2063221604TURN_a @ Y3 ) )
% 3.91/2.04 = ( X4 = Y3 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_306_nres__order__simps_I21_J,axiom,
% 3.91/2.04 ! [X4: a,Y: set_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ Y ) )
% 3.91/2.04 = ( member_a @ X4 @ Y ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_307_inf__RETURN__SPEC_I2_J,axiom,
% 3.91/2.04 ! [Phi: a > $o,X4: a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine2063221604TURN_a @ X4 ) )
% 3.91/2.04 = ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [Y6: a] :
% 3.91/2.04 ( ( Y6 = X4 )
% 3.91/2.04 & ( Phi @ X4 ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_308_pwD1,axiom,
% 3.91/2.04 ! [S: refine424419629nres_a,S4: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ S @ S4 )
% 3.91/2.04 => ( ( refine412683989fail_a @ S4 )
% 3.91/2.04 => ( refine412683989fail_a @ S ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_309_le__nofailI,axiom,
% 3.91/2.04 ! [M3: refine424419629nres_a,M4: refine424419629nres_a] :
% 3.91/2.04 ( ( ( refine412683989fail_a @ M3 )
% 3.91/2.04 => ( ord_le519537037nres_a @ M4 @ M3 ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ M4 @ M3 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_310_nofail__RES__conv,axiom,
% 3.91/2.04 ( refine412683989fail_a
% 3.91/2.04 = ( ^ [M5: refine424419629nres_a] :
% 3.91/2.04 ? [M6: set_a] :
% 3.91/2.04 ( M5
% 3.91/2.04 = ( refine1198353288_RES_a @ M6 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_311_SPEC__eq__is__RETURN_I1_J,axiom,
% 3.91/2.04 ! [X4: a] :
% 3.91/2.04 ( ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 3.91/2.04 @ X4 ) ) )
% 3.91/2.04 = ( refine2063221604TURN_a @ X4 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_312_RETURN__SPEC__conv,axiom,
% 3.91/2.04 ( refine2063221604TURN_a
% 3.91/2.04 = ( ^ [R2: a] :
% 3.91/2.04 ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] : ( X5 = R2 ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_313_SPEC__eq__is__RETURN_I2_J,axiom,
% 3.91/2.04 ! [Y3: a] :
% 3.91/2.04 ( ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] : ( X5 = Y3 ) ) )
% 3.91/2.04 = ( refine2063221604TURN_a @ Y3 ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_314_pw__inf__nofail,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.04 ( ( refine412683989fail_a @ ( inf_in262696383nres_a @ A @ B ) )
% 3.91/2.04 = ( ( refine412683989fail_a @ A )
% 3.91/2.04 | ( refine412683989fail_a @ B ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_315_le__RES__nofailI,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,X4: set_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ X4 ) )
% 3.91/2.04 => ( refine412683989fail_a @ A ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_316_RETURN__rule,axiom,
% 3.91/2.04 ! [Phi: a > $o,X4: a] :
% 3.91/2.04 ( ( Phi @ X4 )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_317_lhs__step__RES,axiom,
% 3.91/2.04 ! [X: set_a,M: refine424419629nres_a] :
% 3.91/2.04 ( ! [X3: a] :
% 3.91/2.04 ( ( member_a @ X3 @ X )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ M ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_318_RETURN__to__SPEC__rule,axiom,
% 3.91/2.04 ! [M: refine424419629nres_a,V2: a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ M
% 3.91/2.04 @ ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 3.91/2.04 @ V2 ) ) ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ M @ ( refine2063221604TURN_a @ V2 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_319_lhs__step__SPEC,axiom,
% 3.91/2.04 ! [Phi: a > $o,M: refine424419629nres_a] :
% 3.91/2.04 ( ! [X3: a] :
% 3.91/2.04 ( ( Phi @ X3 )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ M ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_320_inf__RETURN__RES_I2_J,axiom,
% 3.91/2.04 ! [X4: a,X: set_a] :
% 3.91/2.04 ( ( ( member_a @ X4 @ X )
% 3.91/2.04 => ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine2063221604TURN_a @ X4 ) )
% 3.91/2.04 = ( refine2063221604TURN_a @ X4 ) ) )
% 3.91/2.04 & ( ~ ( member_a @ X4 @ X )
% 3.91/2.04 => ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine2063221604TURN_a @ X4 ) )
% 3.91/2.04 = bot_bo529555393nres_a ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_321_inf__RETURN__RES_I1_J,axiom,
% 3.91/2.04 ! [X4: a,X: set_a] :
% 3.91/2.04 ( ( ( member_a @ X4 @ X )
% 3.91/2.04 => ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ X ) )
% 3.91/2.04 = ( refine2063221604TURN_a @ X4 ) ) )
% 3.91/2.04 & ( ~ ( member_a @ X4 @ X )
% 3.91/2.04 => ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ X ) )
% 3.91/2.04 = bot_bo529555393nres_a ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_322_inf__bot__right,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ X4 @ bot_bo529555393nres_a )
% 3.91/2.04 = bot_bo529555393nres_a ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_323_inf__bot__left,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ bot_bo529555393nres_a @ X4 )
% 3.91/2.04 = bot_bo529555393nres_a ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_324_nres__order__simps_I2_J,axiom,
% 3.91/2.04 ! [M4: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ M4 @ bot_bo529555393nres_a )
% 3.91/2.04 = ( M4 = bot_bo529555393nres_a ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_325_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 3.91/2.04 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine424419629nres_a,F3: a > refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ M4 @ M3 )
% 3.91/2.04 => ( ! [X3: a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F3 @ X3 ) ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine436832838nd_a_a @ M3 @ F3 ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_326_le__SPEC__bindI,axiom,
% 3.91/2.04 ! [Phi: a > $o,X4: a,M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 3.91/2.04 ( ( Phi @ X4 )
% 3.91/2.04 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ M @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ F ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_327_RES__bind__choose,axiom,
% 3.91/2.04 ! [X4: a,X: set_a,M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 3.91/2.04 ( ( member_a @ X4 @ X )
% 3.91/2.04 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ M @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_328_SUCCEED__rule,axiom,
% 3.91/2.04 ! [Phi: a > $o] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_329_bot_Oextremum__uniqueI,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
% 3.91/2.04 => ( A = bot_bo529555393nres_a ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_330_bot_Oextremum__unique,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
% 3.91/2.04 = ( A = bot_bo529555393nres_a ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_331_bot_Oextremum,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_332_nres__order__simps_I1_J,axiom,
% 3.91/2.04 ! [M4: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ M4 ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_333_bind__rule__complete,axiom,
% 3.91/2.04 ! [M4: refine424419629nres_a,F: a > refine424419629nres_a,Phi: a > $o] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 3.91/2.04 = ( ord_le519537037nres_a @ M4
% 3.91/2.04 @ ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] : ( ord_le519537037nres_a @ ( F @ X5 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_334_specify__left,axiom,
% 3.91/2.04 ! [M: refine424419629nres_a,Phi: a > $o,F: a > refine424419629nres_a,M4: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 3.91/2.04 => ( ! [X3: a] :
% 3.91/2.04 ( ( Phi @ X3 )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( F @ X3 ) @ M4 ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ M4 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_335_bind__rule,axiom,
% 3.91/2.04 ! [M4: refine424419629nres_a,F: a > refine424419629nres_a,Phi: a > $o] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ M4
% 3.91/2.04 @ ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] : ( ord_le519537037nres_a @ ( F @ X5 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_336_bind__le__nofailI,axiom,
% 3.91/2.04 ! [M: refine424419629nres_a,F: a > refine424419629nres_a,M7: refine424419629nres_a] :
% 3.91/2.04 ( ( refine412683989fail_a @ M )
% 3.91/2.04 => ( ! [X3: a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( F @ X3 ) @ M7 ) )
% 3.91/2.04 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ M7 ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_337_bind__le__shift,axiom,
% 3.91/2.04 ! [M: refine424419629nres_a,F: a > refine424419629nres_a,M7: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ M7 )
% 3.91/2.04 = ( ord_le519537037nres_a @ M
% 3.91/2.04 @ ( if_Ref1724547303nres_a @ ( refine412683989fail_a @ M7 )
% 3.91/2.04 @ ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [X5: a] : ( ord_le519537037nres_a @ ( F @ X5 ) @ M7 ) ) )
% 3.91/2.04 @ top_to231829469nres_a ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_338_inf__top__left,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ top_to231829469nres_a @ X4 )
% 3.91/2.04 = X4 ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_339_inf__top__right,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ X4 @ top_to231829469nres_a )
% 3.91/2.04 = X4 ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_340_inf__eq__top__iff,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.04 ( ( ( inf_in262696383nres_a @ X4 @ Y3 )
% 3.91/2.04 = top_to231829469nres_a )
% 3.91/2.04 = ( ( X4 = top_to231829469nres_a )
% 3.91/2.04 & ( Y3 = top_to231829469nres_a ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_341_top__eq__inf__iff,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.04 ( ( top_to231829469nres_a
% 3.91/2.04 = ( inf_in262696383nres_a @ X4 @ Y3 ) )
% 3.91/2.04 = ( ( X4 = top_to231829469nres_a )
% 3.91/2.04 & ( Y3 = top_to231829469nres_a ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_342_inf__top_Oeq__neutr__iff,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.04 ( ( ( inf_in262696383nres_a @ A @ B )
% 3.91/2.04 = top_to231829469nres_a )
% 3.91/2.04 = ( ( A = top_to231829469nres_a )
% 3.91/2.04 & ( B = top_to231829469nres_a ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_343_inf__top_Oleft__neutral,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ top_to231829469nres_a @ A )
% 3.91/2.04 = A ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_344_inf__top_Oneutr__eq__iff,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.91/2.04 ( ( top_to231829469nres_a
% 3.91/2.04 = ( inf_in262696383nres_a @ A @ B ) )
% 3.91/2.04 = ( ( A = top_to231829469nres_a )
% 3.91/2.04 & ( B = top_to231829469nres_a ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_345_inf__top_Oright__neutral,axiom,
% 3.91/2.04 ! [A: refine424419629nres_a] :
% 3.91/2.04 ( ( inf_in262696383nres_a @ A @ top_to231829469nres_a )
% 3.91/2.04 = A ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_346_inres__simps_I2_J,axiom,
% 3.91/2.04 ! [X: set_a] :
% 3.91/2.04 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X ) )
% 3.91/2.04 = ( ^ [X5: a] : ( member_a @ X5 @ X ) ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_347_nres__order__simps_I4_J,axiom,
% 3.91/2.04 ! [M4: refine424419629nres_a] :
% 3.91/2.04 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M4 )
% 3.91/2.04 = ( M4 = top_to231829469nres_a ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(fact_348_nres__more__simps_I1_J,axiom,
% 3.91/2.04 ! [X: set_a] :
% 3.91/2.04 ( ( bot_bo529555393nres_a
% 3.91/2.04 = ( refine1198353288_RES_a @ X ) )
% 3.91/2.04 = ( X = bot_bot_set_a ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(help_If_2_1_If_001_062_Itf__a_M_Eo_J_T,axiom,
% 3.91/2.04 ! [X4: a > $o,Y3: a > $o] :
% 3.91/2.04 ( ( if_a_o @ $false @ X4 @ Y3 )
% 3.91/2.04 = Y3 ) ).
% 3.91/2.04
% 3.91/2.04 thf(help_If_1_1_If_001_062_Itf__a_M_Eo_J_T,axiom,
% 3.91/2.04 ! [X4: a > $o,Y3: a > $o] :
% 3.91/2.04 ( ( if_a_o @ $true @ X4 @ Y3 )
% 3.91/2.04 = X4 ) ).
% 3.91/2.04
% 3.91/2.04 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 3.91/2.04 ! [X4: set_a,Y3: set_a] :
% 3.91/2.04 ( ( if_set_a @ $false @ X4 @ Y3 )
% 3.91/2.04 = Y3 ) ).
% 3.91/2.04
% 3.91/2.04 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 3.91/2.04 ! [X4: set_a,Y3: set_a] :
% 3.91/2.04 ( ( if_set_a @ $true @ X4 @ Y3 )
% 3.91/2.04 = X4 ) ).
% 3.91/2.04
% 3.91/2.04 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 3.91/2.04 ! [P: $o] :
% 3.91/2.04 ( ( P = $true )
% 3.91/2.04 | ( P = $false ) ) ).
% 3.91/2.04
% 3.91/2.04 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.04 ( ( if_Ref1724547303nres_a @ $false @ X4 @ Y3 )
% 3.91/2.04 = Y3 ) ).
% 3.91/2.04
% 3.91/2.04 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 3.91/2.04 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.91/2.04 ( ( if_Ref1724547303nres_a @ $true @ X4 @ Y3 )
% 3.91/2.04 = X4 ) ).
% 3.91/2.04
% 3.91/2.04 thf(conj_0,conjecture,
% 3.91/2.04 ( ord_le519537037nres_a @ a2
% 3.91/2.04 @ ( refine1198353288_RES_a
% 3.91/2.04 @ ( collect_a
% 3.91/2.04 @ ^ [V3: a] :
% 3.91/2.04 ( ( p @ V3 )
% 3.91/2.04 & ( q @ V3 ) ) ) ) ) ).
% 3.91/2.04 ------------------------
% 3.91/2.08 % (25991)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_25888 for (2999ds/2Mi)
% 3.91/2.08 % (25987)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/183Mi)
% 3.91/2.08 % (25992)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_25888 for (2999ds/275Mi)
% 3.91/2.08 % (25989)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_25888 for (2999ds/27Mi)
% 3.91/2.08 % (25990)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/2Mi)
% 3.91/2.08 % (25993)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/18Mi)
% 3.91/2.08 % (25988)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_25888 for (2999ds/4Mi)
% 3.91/2.08 % (25990)Instruction limit reached!
% 3.91/2.08 % (25990)------------------------------
% 3.91/2.08 % (25990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.08 % (25990)Termination reason: Unknown
% 3.91/2.08 % (25990)Termination phase: shuffling
% 3.91/2.08
% 3.91/2.08 % (25990)Memory used [KB]: 1407
% 3.91/2.08 % (25990)Time elapsed: 0.004 s
% 3.91/2.08 % (25990)Instructions burned: 2 (million)
% 3.91/2.08 % (25990)------------------------------
% 3.91/2.08 % (25990)------------------------------
% 3.91/2.08 % (25991)Instruction limit reached!
% 3.91/2.08 % (25991)------------------------------
% 3.91/2.08 % (25991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.08 % (25991)Termination reason: Unknown
% 3.91/2.08 % (25991)Termination phase: shuffling
% 3.91/2.08
% 3.91/2.08 % (25991)Memory used [KB]: 1407
% 3.91/2.08 % (25991)Time elapsed: 0.004 s
% 3.91/2.08 % (25991)Instructions burned: 3 (million)
% 3.91/2.08 % (25991)------------------------------
% 3.91/2.08 % (25991)------------------------------
% 3.91/2.08 % (25988)Instruction limit reached!
% 3.91/2.08 % (25988)------------------------------
% 3.91/2.08 % (25988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.08 % (25988)Termination reason: Unknown
% 3.91/2.08 % (25988)Termination phase: shuffling
% 3.91/2.08
% 3.91/2.08 % (25988)Memory used [KB]: 1535
% 3.91/2.08 % (25988)Time elapsed: 0.004 s
% 3.91/2.08 % (25988)Instructions burned: 4 (million)
% 3.91/2.08 % (25988)------------------------------
% 3.91/2.08 % (25988)------------------------------
% 3.91/2.09 % (25993)Instruction limit reached!
% 3.91/2.09 % (25993)------------------------------
% 3.91/2.09 % (25993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.09 % (25993)Termination reason: Unknown
% 3.91/2.09 % (25993)Termination phase: shuffling
% 3.91/2.09
% 3.91/2.09 % (25993)Memory used [KB]: 1663
% 3.91/2.09 % (25993)Time elapsed: 0.012 s
% 3.91/2.09 % (25993)Instructions burned: 18 (million)
% 3.91/2.09 % (25993)------------------------------
% 3.91/2.09 % (25993)------------------------------
% 3.91/2.10 % (25989)Instruction limit reached!
% 3.91/2.10 % (25989)------------------------------
% 3.91/2.10 % (25989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.10 % (25989)Termination reason: Unknown
% 3.91/2.10 % (25989)Termination phase: Property scanning
% 3.91/2.10
% 3.91/2.10 % (25989)Memory used [KB]: 1918
% 3.91/2.10 % (25989)Time elapsed: 0.017 s
% 3.91/2.10 % (25989)Instructions burned: 28 (million)
% 3.91/2.10 % (25989)------------------------------
% 3.91/2.10 % (25989)------------------------------
% 3.91/2.10 % (25996)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_25888 for (2999ds/15Mi)
% 3.91/2.10 % (25995)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_25888 for (2999ds/37Mi)
% 3.91/2.10 % (25994)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/3Mi)
% 3.91/2.10 % (25994)Instruction limit reached!
% 3.91/2.10 % (25994)------------------------------
% 3.91/2.10 % (25994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.10 % (25994)Termination reason: Unknown
% 3.91/2.10 % (25994)Termination phase: shuffling
% 3.91/2.10
% 3.91/2.10 % (25994)Memory used [KB]: 1407
% 3.91/2.10 % (25994)Time elapsed: 0.004 s
% 3.91/2.10 % (25994)Instructions burned: 4 (million)
% 3.91/2.10 % (25994)------------------------------
% 3.91/2.10 % (25994)------------------------------
% 3.91/2.11 % (25996)Instruction limit reached!
% 3.91/2.11 % (25996)------------------------------
% 3.91/2.11 % (25996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.11 % (25996)Termination reason: Unknown
% 3.91/2.11 % (25996)Termination phase: shuffling
% 3.91/2.11
% 3.91/2.11 % (25997)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_25888 for (2999ds/3Mi)
% 3.91/2.11 % (25996)Memory used [KB]: 1663
% 3.91/2.11 % (25996)Time elapsed: 0.011 s
% 3.91/2.11 % (25996)Instructions burned: 16 (million)
% 3.91/2.11 % (25996)------------------------------
% 3.91/2.11 % (25996)------------------------------
% 3.91/2.11 % (25997)Instruction limit reached!
% 3.91/2.11 % (25997)------------------------------
% 3.91/2.11 % (25997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.11 % (25997)Termination reason: Unknown
% 3.91/2.11 % (25997)Termination phase: shuffling
% 3.91/2.11
% 3.91/2.11 % (25997)Memory used [KB]: 1407
% 3.91/2.11 % (25997)Time elapsed: 0.004 s
% 3.91/2.11 % (25997)Instructions burned: 3 (million)
% 3.91/2.11 % (25997)------------------------------
% 3.91/2.11 % (25997)------------------------------
% 3.91/2.12 % (25998)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_25888 for (2999ds/1041Mi)
% 3.91/2.12 % (25995)Instruction limit reached!
% 3.91/2.12 % (25995)------------------------------
% 3.91/2.12 % (25995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.12 % (25995)Termination reason: Unknown
% 3.91/2.12 % (25995)Termination phase: shuffling
% 3.91/2.12
% 3.91/2.12 % (25995)Memory used [KB]: 2174
% 3.91/2.12 % (25995)Time elapsed: 0.021 s
% 3.91/2.12 % (25995)Instructions burned: 37 (million)
% 3.91/2.12 % (25995)------------------------------
% 3.91/2.12 % (25995)------------------------------
% 3.91/2.12 % (25999)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/7Mi)
% 3.91/2.13 % (25999)Instruction limit reached!
% 3.91/2.13 % (25999)------------------------------
% 3.91/2.13 % (25999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.91/2.13 % (25999)Termination reason: Unknown
% 3.91/2.13 % (25999)Termination phase: shuffling
% 3.91/2.13
% 3.91/2.13 % (25999)Memory used [KB]: 1535
% 3.91/2.13 % (25999)Time elapsed: 0.006 s
% 3.91/2.13 % (25999)Instructions burned: 7 (million)
% 3.91/2.13 % (25999)------------------------------
% 3.91/2.13 % (25999)------------------------------
% 3.92/2.13 % (26000)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/16Mi)
% 3.92/2.13 % (26001)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_25888 for (2999ds/3Mi)
% 3.92/2.13 % (26001)Instruction limit reached!
% 3.92/2.13 % (26001)------------------------------
% 3.92/2.13 % (26001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.13 % (26001)Termination reason: Unknown
% 3.92/2.13 % (26001)Termination phase: shuffling
% 3.92/2.13
% 3.92/2.13 % (26001)Memory used [KB]: 1535
% 3.92/2.13 % (26001)Time elapsed: 0.004 s
% 3.92/2.13 % (26001)Instructions burned: 4 (million)
% 3.92/2.13 % (26001)------------------------------
% 3.92/2.13 % (26001)------------------------------
% 3.92/2.14 % (26000)Instruction limit reached!
% 3.92/2.14 % (26000)------------------------------
% 3.92/2.14 % (26000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.14 % (26000)Termination reason: Unknown
% 3.92/2.14 % (26000)Termination phase: shuffling
% 3.92/2.14
% 3.92/2.14 % (26000)Memory used [KB]: 1663
% 3.92/2.14 % (26000)Time elapsed: 0.011 s
% 3.92/2.14 % (26000)Instructions burned: 16 (million)
% 3.92/2.14 % (26000)------------------------------
% 3.92/2.14 % (26000)------------------------------
% 3.92/2.14 % (26002)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_25888 for (2999ds/3Mi)
% 3.92/2.14 % (26002)Instruction limit reached!
% 3.92/2.14 % (26002)------------------------------
% 3.92/2.14 % (26002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.14 % (26002)Termination reason: Unknown
% 3.92/2.14 % (26002)Termination phase: shuffling
% 3.92/2.14
% 3.92/2.14 % (26002)Memory used [KB]: 1535
% 3.92/2.14 % (26002)Time elapsed: 0.005 s
% 3.92/2.14 % (26002)Instructions burned: 4 (million)
% 3.92/2.14 % (26002)------------------------------
% 3.92/2.14 % (26002)------------------------------
% 3.92/2.15 % (26003)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/7Mi)
% 3.92/2.15 % (26003)Instruction limit reached!
% 3.92/2.15 % (26003)------------------------------
% 3.92/2.15 % (26003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.15 % (26003)Termination reason: Unknown
% 3.92/2.15 % (26003)Termination phase: shuffling
% 3.92/2.15
% 3.92/2.15 % (26003)Memory used [KB]: 1535
% 3.92/2.15 % (26003)Time elapsed: 0.006 s
% 3.92/2.15 % (26003)Instructions burned: 8 (million)
% 3.92/2.15 % (26003)------------------------------
% 3.92/2.15 % (26003)------------------------------
% 3.92/2.15 % (26004)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/3Mi)
% 3.92/2.15 % (26004)Instruction limit reached!
% 3.92/2.15 % (26004)------------------------------
% 3.92/2.15 % (26004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.15 % (26004)Termination reason: Unknown
% 3.92/2.15 % (26004)Termination phase: shuffling
% 3.92/2.15
% 3.92/2.15 % (26004)Memory used [KB]: 1407
% 3.92/2.15 % (26004)Time elapsed: 0.004 s
% 3.92/2.15 % (26004)Instructions burned: 4 (million)
% 3.92/2.15 % (26004)------------------------------
% 3.92/2.15 % (26004)------------------------------
% 3.92/2.16 % (26005)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/4Mi)
% 3.92/2.16 % (26005)Instruction limit reached!
% 3.92/2.16 % (26005)------------------------------
% 3.92/2.16 % (26005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.16 % (26005)Termination reason: Unknown
% 3.92/2.16 % (26005)Termination phase: shuffling
% 3.92/2.16
% 3.92/2.16 % (26005)Memory used [KB]: 1535
% 3.92/2.16 % (26005)Time elapsed: 0.005 s
% 3.92/2.16 % (26005)Instructions burned: 4 (million)
% 3.92/2.16 % (26005)------------------------------
% 3.92/2.16 % (26005)------------------------------
% 3.92/2.16 % (26006)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25888 for (2999ds/18Mi)
% 3.92/2.17 % (26007)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25888 for (2998ds/710Mi)
% 3.92/2.17 % (26006)Instruction limit reached!
% 3.92/2.17 % (26006)------------------------------
% 3.92/2.17 % (26006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.17 % (26006)Termination reason: Unknown
% 3.92/2.17 % (26006)Termination phase: shuffling
% 3.92/2.17
% 3.92/2.17 % (26006)Memory used [KB]: 1791
% 3.92/2.17 % (26006)Time elapsed: 0.012 s
% 3.92/2.17 % (26006)Instructions burned: 18 (million)
% 3.92/2.17 % (26006)------------------------------
% 3.92/2.17 % (26006)------------------------------
% 3.92/2.17 % (26008)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25888 for (2998ds/6Mi)
% 3.92/2.18 % (26008)Instruction limit reached!
% 3.92/2.18 % (26008)------------------------------
% 3.92/2.18 % (26008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.18 % (26008)Termination reason: Unknown
% 3.92/2.18 % (26008)Termination phase: shuffling
% 3.92/2.18
% 3.92/2.18 % (26008)Memory used [KB]: 1535
% 3.92/2.18 % (26008)Time elapsed: 0.005 s
% 3.92/2.18 % (26008)Instructions burned: 6 (million)
% 3.92/2.18 % (26008)------------------------------
% 3.92/2.18 % (26008)------------------------------
% 3.92/2.18 % (25987)Instruction limit reached!
% 3.92/2.18 % (25987)------------------------------
% 3.92/2.18 % (25987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.18 % (25987)Termination reason: Unknown
% 3.92/2.18 % (25987)Termination phase: Saturation
% 3.92/2.18
% 3.92/2.18 % (25987)Memory used [KB]: 7291
% 3.92/2.18 % (25987)Time elapsed: 0.099 s
% 3.92/2.18 % (25987)Instructions burned: 183 (million)
% 3.92/2.18 % (25987)------------------------------
% 3.92/2.18 % (25987)------------------------------
% 3.92/2.18 % (26009)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_25888 for (2998ds/902Mi)
% 3.92/2.19 % (26010)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_25888 for (2998ds/21Mi)
% 3.92/2.20 % (26011)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25888 for (2998ds/5Mi)
% 3.92/2.20 % (26012)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_25888 for (2998ds/6Mi)
% 3.92/2.20 % (26011)Instruction limit reached!
% 3.92/2.20 % (26011)------------------------------
% 3.92/2.20 % (26011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.20 % (26011)Termination reason: Unknown
% 3.92/2.20 % (26011)Termination phase: shuffling
% 3.92/2.20
% 3.92/2.20 % (26011)Memory used [KB]: 1535
% 3.92/2.20 % (26011)Time elapsed: 0.005 s
% 3.92/2.20 % (26011)Instructions burned: 5 (million)
% 3.92/2.20 % (26011)------------------------------
% 3.92/2.20 % (26011)------------------------------
% 3.92/2.20 % (26012)Instruction limit reached!
% 3.92/2.20 % (26012)------------------------------
% 3.92/2.20 % (26012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.20 % (26012)Termination reason: Unknown
% 3.92/2.20 % (26012)Termination phase: shuffling
% 3.92/2.20
% 3.92/2.20 % (26012)Memory used [KB]: 1535
% 3.92/2.20 % (26012)Time elapsed: 0.006 s
% 3.92/2.20 % (26012)Instructions burned: 7 (million)
% 3.92/2.20 % (26012)------------------------------
% 3.92/2.20 % (26012)------------------------------
% 3.92/2.20 % (26010)Instruction limit reached!
% 3.92/2.20 % (26010)------------------------------
% 3.92/2.20 % (26010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.20 % (26010)Termination reason: Unknown
% 3.92/2.20 % (26010)Termination phase: shuffling
% 3.92/2.20
% 3.92/2.20 % (26010)Memory used [KB]: 1791
% 3.92/2.20 % (26010)Time elapsed: 0.014 s
% 3.92/2.20 % (26010)Instructions burned: 21 (million)
% 3.92/2.20 % (26010)------------------------------
% 3.92/2.20 % (26010)------------------------------
% 3.92/2.22 % (26014)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_25888 for (2998ds/779Mi)
% 3.92/2.22 % (26013)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_25888 for (2998ds/377Mi)
% 3.92/2.23 % (26015)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_25888 for (2998ds/19Mi)
% 3.92/2.23 % (25992)Instruction limit reached!
% 3.92/2.23 % (25992)------------------------------
% 3.92/2.23 % (25992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.23 % (25992)Termination reason: Unknown
% 3.92/2.23 % (25992)Termination phase: Saturation
% 3.92/2.23
% 3.92/2.23 % (25992)Memory used [KB]: 7675
% 3.92/2.23 % (25992)Time elapsed: 0.154 s
% 3.92/2.23 % (25992)Instructions burned: 276 (million)
% 3.92/2.23 % (25992)------------------------------
% 3.92/2.23 % (25992)------------------------------
% 3.92/2.24 % (26015)Instruction limit reached!
% 3.92/2.24 % (26015)------------------------------
% 3.92/2.24 % (26015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.24 % (26015)Termination reason: Unknown
% 3.92/2.24 % (26015)Termination phase: shuffling
% 3.92/2.24
% 3.92/2.24 % (26015)Memory used [KB]: 1791
% 3.92/2.24 % (26015)Time elapsed: 0.013 s
% 3.92/2.24 % (26015)Instructions burned: 20 (million)
% 3.92/2.24 % (26015)------------------------------
% 3.92/2.24 % (26015)------------------------------
% 3.92/2.25 % (26016)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_25888 for (2998ds/879Mi)
% 3.92/2.26 % (26017)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_25888 for (2998ds/17Mi)
% 3.92/2.27 % (26017)Instruction limit reached!
% 3.92/2.27 % (26017)------------------------------
% 3.92/2.27 % (26017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.27 % (26017)Termination reason: Unknown
% 3.92/2.27 % (26017)Termination phase: shuffling
% 3.92/2.27
% 3.92/2.27 % (26017)Memory used [KB]: 1663
% 3.92/2.27 % (26017)Time elapsed: 0.012 s
% 3.92/2.27 % (26017)Instructions burned: 17 (million)
% 3.92/2.27 % (26017)------------------------------
% 3.92/2.27 % (26017)------------------------------
% 3.92/2.29 % (26018)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25888 for (2997ds/3Mi)
% 3.92/2.29 % (26018)Instruction limit reached!
% 3.92/2.29 % (26018)------------------------------
% 3.92/2.29 % (26018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.29 % (26018)Termination reason: Unknown
% 3.92/2.29 % (26018)Termination phase: shuffling
% 3.92/2.29
% 3.92/2.29 % (26018)Memory used [KB]: 1535
% 3.92/2.29 % (26018)Time elapsed: 0.005 s
% 3.92/2.29 % (26018)Instructions burned: 4 (million)
% 3.92/2.29 % (26018)------------------------------
% 3.92/2.29 % (26018)------------------------------
% 3.92/2.31 % (26019)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_25888 for (2997ds/30Mi)
% 3.92/2.33 % (26019)Instruction limit reached!
% 3.92/2.33 % (26019)------------------------------
% 3.92/2.33 % (26019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.33 % (26019)Termination reason: Unknown
% 3.92/2.33 % (26019)Termination phase: shuffling
% 3.92/2.33
% 3.92/2.33 % (26019)Memory used [KB]: 1918
% 3.92/2.33 % (26019)Time elapsed: 0.019 s
% 3.92/2.33 % (26019)Instructions burned: 30 (million)
% 3.92/2.33 % (26019)------------------------------
% 3.92/2.33 % (26019)------------------------------
% 3.92/2.35 % (26020)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_25888 for (2997ds/127Mi)
% 3.92/2.42 % (26020)Instruction limit reached!
% 3.92/2.42 % (26020)------------------------------
% 3.92/2.42 % (26020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.42 % (26020)Termination reason: Unknown
% 3.92/2.42 % (26020)Termination phase: Property scanning
% 3.92/2.42
% 3.92/2.42 % (26020)Memory used [KB]: 2686
% 3.92/2.42 % (26020)Time elapsed: 0.072 s
% 3.92/2.42 % (26020)Instructions burned: 127 (million)
% 3.92/2.42 % (26020)------------------------------
% 3.92/2.42 % (26020)------------------------------
% 3.92/2.42 % (26013)Instruction limit reached!
% 3.92/2.42 % (26013)------------------------------
% 3.92/2.42 % (26013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.42 % (26013)Termination reason: Unknown
% 3.92/2.42 % (26013)Termination phase: Saturation
% 3.92/2.42
% 3.92/2.42 % (26013)Memory used [KB]: 8315
% 3.92/2.42 % (26013)Time elapsed: 0.207 s
% 3.92/2.42 % (26013)Instructions burned: 378 (million)
% 3.92/2.42 % (26013)------------------------------
% 3.92/2.42 % (26013)------------------------------
% 3.92/2.44 % (26022)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_25888 for (2996ds/3Mi)
% 3.92/2.44 % (26021)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_25888 for (2996ds/100Mi)
% 3.92/2.45 % (26022)Instruction limit reached!
% 3.92/2.45 % (26022)------------------------------
% 3.92/2.45 % (26022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.45 % (26022)Termination reason: Unknown
% 3.92/2.45 % (26022)Termination phase: shuffling
% 3.92/2.45
% 3.92/2.45 % (26022)Memory used [KB]: 1535
% 3.92/2.45 % (26022)Time elapsed: 0.004 s
% 3.92/2.45 % (26022)Instructions burned: 4 (million)
% 3.92/2.45 % (26022)------------------------------
% 3.92/2.45 % (26022)------------------------------
% 3.92/2.47 % (26016)First to succeed.
% 3.92/2.47 % (26023)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_25888 for (2995ds/20Mi)
% 3.92/2.47 % (26016)Refutation found. Thanks to Tanya!
% 3.92/2.47 % SZS status Theorem for DTF2THF_25888
% 3.92/2.47 % SZS output start Proof for DTF2THF_25888
% 3.92/2.47 thf(type_def_5, type, a: $tType).
% 3.92/2.47 thf(type_def_7, type, refine424419629nres_a: $tType).
% 3.92/2.47 thf(type_def_8, type, set_a: $tType).
% 3.92/2.47 thf(func_def_0, type, refine424419629nres_a: $tType).
% 3.92/2.47 thf(func_def_1, type, set_a: $tType).
% 3.92/2.47 thf(func_def_2, type, a: $tType).
% 3.92/2.47 thf(func_def_3, type, if_a_o: $o > (a > $o) > (a > $o) > a > $o).
% 3.92/2.47 thf(func_def_4, type, if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a).
% 3.92/2.47 thf(func_def_5, type, if_set_a: $o > set_a > set_a > set_a).
% 3.92/2.47 thf(func_def_6, type, inf_inf_a_o: (a > $o) > (a > $o) > a > $o).
% 3.92/2.47 thf(func_def_7, type, inf_inf_o: $o > $o > $o).
% 3.92/2.47 thf(func_def_8, type, inf_in262696383nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a).
% 3.92/2.47 thf(func_def_9, type, inf_inf_set_a: set_a > set_a > set_a).
% 3.92/2.47 thf(func_def_10, type, bot_bo529555393nres_a: refine424419629nres_a).
% 3.92/2.47 thf(func_def_11, type, bot_bot_set_a: set_a).
% 3.92/2.47 thf(func_def_12, type, ord_less_eq_a_o: (a > $o) > (a > $o) > $o).
% 3.92/2.47 thf(func_def_13, type, ord_less_eq_o: $o > $o > $o).
% 3.92/2.47 thf(func_def_14, type, ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o).
% 3.92/2.47 thf(func_def_15, type, ord_less_eq_set_a: set_a > set_a > $o).
% 3.92/2.47 thf(func_def_16, type, order_1714329108nres_a: (refine424419629nres_a > $o) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_17, type, top_to231829469nres_a: refine424419629nres_a).
% 3.92/2.47 thf(func_def_18, type, refine2063221604TURN_a: a > refine424419629nres_a).
% 3.92/2.47 thf(func_def_19, type, refine436832838nd_a_a: refine424419629nres_a > (a > refine424419629nres_a) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_20, type, refine1001002027nres_a: refine424419629nres_a > a > $o).
% 3.92/2.47 thf(func_def_21, type, refine1312857699nres_a: refine424419629nres_a > a > $o).
% 3.92/2.47 thf(func_def_22, type, refine412683989fail_a: refine424419629nres_a > $o).
% 3.92/2.47 thf(func_def_23, type, refine464223677AILi_a: refine424419629nres_a).
% 3.92/2.47 thf(func_def_24, type, refine1198353288_RES_a: set_a > refine424419629nres_a).
% 3.92/2.47 thf(func_def_25, type, refine1822134885_RES_a: refine424419629nres_a > set_a).
% 3.92/2.47 thf(func_def_26, type, collect_a: (a > $o) > set_a).
% 3.92/2.47 thf(func_def_27, type, member_a: a > set_a > $o).
% 3.92/2.47 thf(func_def_28, type, a2: refine424419629nres_a).
% 3.92/2.47 thf(func_def_29, type, p: a > $o).
% 3.92/2.47 thf(func_def_30, type, q: a > $o).
% 3.92/2.47 thf(func_def_45, type, sK0: (a > $o) > (a > $o) > a).
% 3.92/2.47 thf(func_def_46, type, sK1: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_47, type, sK2: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_48, type, sK3: (a > $o) > set_a > (a > $o) > a).
% 3.92/2.47 thf(func_def_49, type, sK4: (a > $o) > (a > $o) > a).
% 3.92/2.47 thf(func_def_50, type, sK5: (a > $o) > (a > refine424419629nres_a) > refine424419629nres_a > a).
% 3.92/2.47 thf(func_def_51, type, sK6: (a > $o) > set_a > a).
% 3.92/2.47 thf(func_def_52, type, sK7: (a > $o) > set_a > (a > $o) > a).
% 3.92/2.47 thf(func_def_53, type, sK8: (a > $o) > (a > $o) > a).
% 3.92/2.47 thf(func_def_54, type, sK9: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_55, type, sK10: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_56, type, sK11: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_57, type, sK12: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_58, type, sK13: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_59, type, sK14: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.92/2.47 thf(func_def_60, type, sK15: (a > $o) > (a > $o) > a).
% 3.92/2.47 thf(func_def_61, type, sK16: (a > $o) > refine424419629nres_a > a).
% 3.92/2.47 thf(func_def_63, type, sK18: (a > $o) > set_a > a).
% 3.92/2.47 thf(func_def_64, type, sK19: (a > $o) > (a > $o) > a).
% 3.92/2.47 thf(func_def_65, type, sK20: set_a > (a > $o) > a).
% 3.92/2.47 thf(func_def_66, type, ph21: !>[X0: $tType]:(X0)).
% 3.92/2.47 thf(f1998,plain,(
% 3.92/2.47 $false),
% 3.92/2.47 inference(trivial_inequality_removal,[status(thm)],[f1997])).
% 3.92/2.47 thf(f1997,plain,(
% 3.92/2.47 ($false = $true)),
% 3.92/2.47 inference(backward_demodulation,[status(thm)],[f1093,f1996])).
% 3.92/2.47 thf(f1996,plain,(
% 3.92/2.47 ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ q))) = $false)),
% 3.92/2.47 inference(trivial_inequality_removal,[status(thm)],[f1995])).
% 3.92/2.47 thf(f1995,plain,(
% 3.92/2.47 ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ q))) = $false) | ($false = $true)),
% 3.92/2.47 inference(forward_demodulation,[status(thm)],[f1973,f1102])).
% 3.92/2.47 thf(f1102,plain,(
% 3.92/2.47 ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ p))) = $true)),
% 3.92/2.47 inference(cnf_transformation,[status(thm)],[f882])).
% 3.92/2.47 thf(f882,plain,(
% 3.92/2.47 ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ p))) = $true)),
% 3.92/2.47 inference(fool_elimination,[status(thm)],[f881])).
% 3.92/2.47 thf(f881,plain,(
% 3.92/2.47 (ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ p)))),
% 3.92/2.47 inference(rectify,[status(thm)],[f4])).
% 3.92/2.47 thf(f4,axiom,(
% 3.92/2.47 (ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ p)))),
% 3.92/2.47 file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_3_assms_I1_J)).
% 3.92/2.47 thf(f1973,plain,(
% 3.92/2.47 ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ p))) = $false) | ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ q))) = $false)),
% 3.92/2.47 inference(trivial_inequality_removal,[status(thm)],[f1960])).
% 3.92/2.47 thf(f1960,plain,(
% 3.92/2.47 ($true != $true) | ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ p))) = $false) | ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ q))) = $false)),
% 3.92/2.47 inference(superposition,[status(thm)],[f1671,f1305])).
% 3.92/2.47 thf(f1305,plain,(
% 3.92/2.47 ( ! [X2 : refine424419629nres_a,X0 : refine424419629nres_a,X1 : refine424419629nres_a] : (((ord_le519537037nres_a @ X1 @ (inf_in262696383nres_a @ X0 @ X2)) = $true) | ($false = (ord_le519537037nres_a @ X1 @ X2)) | ((ord_le519537037nres_a @ X1 @ X0) = $false)) )),
% 3.92/2.47 inference(binary_proxy_clausification,[status(thm)],[f1301])).
% 3.92/2.47 thf(f1301,plain,(
% 3.92/2.47 ( ! [X2 : refine424419629nres_a,X0 : refine424419629nres_a,X1 : refine424419629nres_a] : (((ord_le519537037nres_a @ X1 @ (inf_in262696383nres_a @ X0 @ X2)) = $true) | (((ord_le519537037nres_a @ X1 @ X2) & (ord_le519537037nres_a @ X1 @ X0)) = $false)) )),
% 3.92/2.47 inference(binary_proxy_clausification,[status(thm)],[f1131])).
% 3.92/2.47 thf(f1131,plain,(
% 3.92/2.47 ( ! [X2 : refine424419629nres_a,X0 : refine424419629nres_a,X1 : refine424419629nres_a] : (((ord_le519537037nres_a @ X1 @ (inf_in262696383nres_a @ X0 @ X2)) = ((ord_le519537037nres_a @ X1 @ X2) & (ord_le519537037nres_a @ X1 @ X0)))) )),
% 3.92/2.47 inference(cnf_transformation,[status(thm)],[f800])).
% 3.92/2.47 thf(f800,plain,(
% 3.92/2.47 ! [X0 : refine424419629nres_a,X1 : refine424419629nres_a,X2 : refine424419629nres_a] : ((ord_le519537037nres_a @ X1 @ (inf_in262696383nres_a @ X0 @ X2)) = ((ord_le519537037nres_a @ X1 @ X2) & (ord_le519537037nres_a @ X1 @ X0)))),
% 3.92/2.47 inference(fool_elimination,[status(thm)],[f799])).
% 3.92/2.47 thf(f799,plain,(
% 3.92/2.47 ! [X0 : refine424419629nres_a,X1 : refine424419629nres_a,X2 : refine424419629nres_a] : ((ord_le519537037nres_a @ X1 @ X0) & (ord_le519537037nres_a @ X1 @ X2) = (ord_le519537037nres_a @ X1 @ (inf_in262696383nres_a @ X0 @ X2)))),
% 3.92/2.47 inference(rectify,[status(thm)],[f126])).
% 3.92/2.47 thf(f126,axiom,(
% 3.92/2.47 ! [X4 : refine424419629nres_a,X31 : refine424419629nres_a,X32 : refine424419629nres_a] : ((ord_le519537037nres_a @ X31 @ X4) & (ord_le519537037nres_a @ X31 @ X32) = (ord_le519537037nres_a @ X31 @ (inf_in262696383nres_a @ X4 @ X32)))),
% 3.92/2.47 file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_125_inf_Obounded__iff)).
% 3.92/2.47 thf(f1671,plain,(
% 3.92/2.47 ($true != (ord_le519537037nres_a @ a2 @ (inf_in262696383nres_a @ (refine1198353288_RES_a @ (collect_a @ q)) @ (refine1198353288_RES_a @ (collect_a @ p)))))),
% 3.92/2.47 inference(backward_demodulation,[status(thm)],[f1070,f1639])).
% 3.92/2.47 thf(f1639,plain,(
% 3.92/2.47 ( ! [X0 : a > $o,X1 : a > $o] : (((refine1198353288_RES_a @ (collect_a @ (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))))) = (inf_in262696383nres_a @ (refine1198353288_RES_a @ (collect_a @ X1)) @ (refine1198353288_RES_a @ (collect_a @ X0))))) )),
% 3.92/2.47 inference(superposition,[status(thm)],[f1253,f1163])).
% 3.92/2.47 thf(f1163,plain,(
% 3.92/2.47 ( ! [X0 : a > $o,X1 : a > $o] : (((collect_a @ (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) = (collect_a @ (^[Y0 : a]: ((member_a @ Y0 @ (collect_a @ X0)) & (member_a @ Y0 @ (collect_a @ X1))))))) )),
% 3.92/2.47 inference(beta_eta_normalization,[status(thm)],[f1135])).
% 3.92/2.47 thf(f1135,plain,(
% 3.92/2.47 ( ! [X0 : a > $o,X1 : a > $o] : (((collect_a @ (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) = ((^[Y0 : set_a]: ((^[Y1 : set_a]: (collect_a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) & (member_a @ Y2 @ Y0))))))) @ (collect_a @ X1) @ (collect_a @ X0)))) )),
% 3.92/2.47 inference(definition_unfolding,[status(thm)],[f1051,f1060])).
% 3.92/2.47 thf(f1060,plain,(
% 3.92/2.47 (inf_inf_set_a = (^[Y0 : set_a]: ((^[Y1 : set_a]: (collect_a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) & (member_a @ Y2 @ Y0))))))))),
% 3.92/2.47 inference(cnf_transformation,[status(thm)],[f369])).
% 3.92/2.47 thf(f369,plain,(
% 3.92/2.47 (inf_inf_set_a = (^[Y0 : set_a]: ((^[Y1 : set_a]: (collect_a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) & (member_a @ Y2 @ Y0))))))))),
% 3.92/2.47 inference(fool_elimination,[status(thm)],[f368])).
% 3.92/2.47 thf(f368,plain,(
% 3.92/2.47 (inf_inf_set_a = (^[X0 : set_a, X1 : set_a] : (collect_a @ (^[X2 : a] : ((member_a @ X2 @ X0) & (member_a @ X2 @ X1))))))),
% 3.92/2.47 inference(rectify,[status(thm)],[f269])).
% 3.92/2.47 thf(f269,axiom,(
% 3.92/2.47 (inf_inf_set_a = (^[X47 : set_a, X48 : set_a] : (collect_a @ (^[X30 : a] : ((member_a @ X30 @ X47) & (member_a @ X30 @ X48))))))),
% 3.92/2.47 file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_268_Int__def)).
% 3.92/2.47 thf(f1051,plain,(
% 3.92/2.47 ( ! [X0 : a > $o,X1 : a > $o] : (((collect_a @ (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) = (inf_inf_set_a @ (collect_a @ X1) @ (collect_a @ X0)))) )),
% 3.92/2.47 inference(cnf_transformation,[status(thm)],[f431])).
% 3.92/2.47 thf(f431,plain,(
% 3.92/2.47 ! [X0 : a > $o,X1 : a > $o] : ((collect_a @ (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) = (inf_inf_set_a @ (collect_a @ X1) @ (collect_a @ X0)))),
% 3.92/2.47 inference(fool_elimination,[status(thm)],[f430])).
% 3.92/2.47 thf(f430,plain,(
% 3.92/2.47 ! [X0 : a > $o,X1 : a > $o] : ((collect_a @ (^[X2 : a] : ((X1 @ X2) & (X0 @ X2)))) = (inf_inf_set_a @ (collect_a @ X1) @ (collect_a @ X0)))),
% 3.92/2.47 inference(rectify,[status(thm)],[f273])).
% 3.92/2.47 thf(f273,axiom,(
% 3.92/2.47 ! [X11 : a > $o,X10 : a > $o] : ((collect_a @ (^[X30 : a] : ((X10 @ X30) & (X11 @ X30)))) = (inf_inf_set_a @ (collect_a @ X10) @ (collect_a @ X11)))),
% 3.92/2.47 file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_272_Collect__conj__eq)).
% 3.92/2.47 thf(f1253,plain,(
% 3.92/2.47 ( ! [X0 : set_a,X1 : set_a] : (((inf_in262696383nres_a @ (refine1198353288_RES_a @ X1) @ (refine1198353288_RES_a @ X0)) = (refine1198353288_RES_a @ (collect_a @ (^[Y0 : a]: ((member_a @ Y0 @ X0) & (member_a @ Y0 @ X1))))))) )),
% 3.92/2.47 inference(beta_eta_normalization,[status(thm)],[f1145])).
% 3.92/2.47 thf(f1145,plain,(
% 3.92/2.47 ( ! [X0 : set_a,X1 : set_a] : (((refine1198353288_RES_a @ ((^[Y0 : set_a]: ((^[Y1 : set_a]: (collect_a @ (^[Y2 : a]: ((member_a @ Y2 @ Y1) & (member_a @ Y2 @ Y0))))))) @ X1 @ X0)) = (inf_in262696383nres_a @ (refine1198353288_RES_a @ X1) @ (refine1198353288_RES_a @ X0)))) )),
% 3.92/2.47 inference(definition_unfolding,[status(thm)],[f1101,f1060])).
% 3.92/2.47 thf(f1101,plain,(
% 3.92/2.47 ( ! [X0 : set_a,X1 : set_a] : (((refine1198353288_RES_a @ (inf_inf_set_a @ X1 @ X0)) = (inf_in262696383nres_a @ (refine1198353288_RES_a @ X1) @ (refine1198353288_RES_a @ X0)))) )),
% 3.92/2.47 inference(cnf_transformation,[status(thm)],[f946])).
% 3.92/2.47 thf(f946,plain,(
% 3.92/2.47 ! [X0 : set_a,X1 : set_a] : ((refine1198353288_RES_a @ (inf_inf_set_a @ X1 @ X0)) = (inf_in262696383nres_a @ (refine1198353288_RES_a @ X1) @ (refine1198353288_RES_a @ X0)))),
% 3.92/2.47 inference(rectify,[status(thm)],[f149])).
% 3.92/2.47 thf(f149,axiom,(
% 3.92/2.47 ! [X4 : set_a,X31 : set_a] : ((inf_in262696383nres_a @ (refine1198353288_RES_a @ X31) @ (refine1198353288_RES_a @ X4)) = (refine1198353288_RES_a @ (inf_inf_set_a @ X31 @ X4)))),
% 3.92/2.47 file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_148_inf__nres_Osimps_I3_J)).
% 3.92/2.47 thf(f1070,plain,(
% 3.92/2.47 ($true != (ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0)))))))),
% 3.92/2.47 inference(cnf_transformation,[status(thm)],[f943])).
% 3.92/2.47 thf(f943,plain,(
% 3.92/2.47 ($true != (ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0)))))))),
% 3.92/2.47 inference(flattening,[status(thm)],[f888])).
% 3.92/2.47 thf(f888,plain,(
% 3.92/2.47 ~($true = (ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0)))))))),
% 3.92/2.47 inference(fool_elimination,[status(thm)],[f887])).
% 3.92/2.47 thf(f887,plain,(
% 3.92/2.47 ~(ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ (^[X0 : a] : ((q @ X0) & (p @ X0))))))),
% 3.92/2.47 inference(rectify,[status(thm)],[f358])).
% 3.92/2.47 thf(f358,negated_conjecture,(
% 3.92/2.47 ~(ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ (^[X74 : a] : ((q @ X74) & (p @ X74))))))),
% 3.92/2.47 inference(negated_conjecture,[status(cth)],[f357])).
% 3.92/2.47 thf(f357,conjecture,(
% 3.92/2.47 (ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ (^[X74 : a] : ((q @ X74) & (p @ X74))))))),
% 3.92/2.47 file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',conj_0)).
% 3.92/2.47 thf(f1093,plain,(
% 3.92/2.47 ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ q))) = $true)),
% 3.92/2.47 inference(cnf_transformation,[status(thm)],[f780])).
% 3.92/2.47 thf(f780,plain,(
% 3.92/2.47 ((ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ q))) = $true)),
% 3.92/2.47 inference(fool_elimination,[status(thm)],[f779])).
% 3.92/2.47 thf(f779,plain,(
% 3.92/2.47 (ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ q)))),
% 3.92/2.47 inference(rectify,[status(thm)],[f3])).
% 3.92/2.47 thf(f3,axiom,(
% 3.92/2.47 (ord_le519537037nres_a @ a2 @ (refine1198353288_RES_a @ (collect_a @ q)))),
% 3.92/2.47 file('/export/starexec/sandbox/tmp/tmp.Jaa1RgOkTc/DTF2THF_25888.p',fact_2_assms_I2_J)).
% 3.92/2.47 % SZS output end Proof for DTF2THF_25888
% 3.92/2.47 % (26016)------------------------------
% 3.92/2.47 % (26016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.92/2.47 % (26016)Termination reason: Refutation
% 3.92/2.47
% 3.92/2.47 % (26016)Memory used [KB]: 7547
% 3.92/2.47 % (26016)Time elapsed: 0.217 s
% 3.92/2.47 % (26016)Instructions burned: 363 (million)
% 3.92/2.47 % (26016)------------------------------
% 3.92/2.47 % (26016)------------------------------
% 3.92/2.47 % (25986)Success in time 0.427 s
%------------------------------------------------------------------------------